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Modelling of transient liquid phase bondingY Zhou W F Gale and T H North

Modelling of transient liquid phase (TLP) bondingis reviewed The outputs produced duringanalytical and numerical modelling are discussedin detail and compared with actual experimentalresults produced when joining simple binary alloysystems The effects of increased diffusivity atbase material grain boundaries of grain boundarymotion and of grain boundary grooving onisothermal solidification during TLP bonding aredescribed There is a critical need for detailedresearch in which modelling output is closelyrelated to direct microstructural observationsduring bonding of complex alloy systems

IMR280

copy 1995 The Institute of Materials and ASM InternationalDr Zhou is Research and Development EngineerFuel Materials Branch AECL Research Chalk RiverLaboratories Chalk River ON Canada Dr Gale is AssistantProfessor Materials Research and Education CenterAuburn University Auburn AL USA Dr North isWICNSERC Professor Department of Metallurgy andMaterials Science University of Toronto Toronto ONCanada

IntroductionDiffusion controlled growth or dissolution of anunstable phase is important in a wide range ofmetallurgical situationsl such as

(i) in solid-gas (vapour) systems when an inter-mediate aluminide phase grows duringaluminisation of nickel base alloy materials

(ii) in solid-solid systems when a second phasegrows and subsequently dissolves duringsolution heat treatmentf or when an inter-mediate layer grows in a thermal barriercoating

(iii) in solid-liquid systems when the liquid phasegrows andor shrinks during liquid phase sin-tering 7 or during transient liquid phase (TLP)bonding

During TLP bonding a thin layer of liquid forms atthe joint interface wets the contacting substrates andthen solidifies isothermallyP- Liquid film formationduring TLP bonding depends on the formation of alow melting point eutectic or peritectic at the jointinterface An interlayer (filler metal) is clamped be-tween the contacting metal surfaces and the entireassembly is heated to the bonding temperature Atthe bonding temperature the interlayer forms a liquideither directly or by reaction with the base metalThe resulting liquid film resolidifies isothermally whenthe joint is held at the bonding temperatureFollowing isothermal solidification the joint ishomogenised either at the bonding temperature or atsome lower temperature All stages of TLP bonding(interlayer and base metal melting isothermal solidi-fication and joint homogenisation) depend on solute

diffusion from the joint centreline region into the basematerial

In certain situations liquid formation can occurwithout the introduction of an interlayer at the bond-line For example solute diffusion during heatingpromotes formation of a low melting point eutecticin Zircaloy 2-AISI 304 stainless steel jointsHowever in this case the liquid film width increasescontinuously at the bonding temperature Since thisis quite a different situation from that assumed duringTLP bonding (where the liquid width increases to amaximum value before isothermal solidification) thisjoining process is generally termed eutectic bondingAs would be expected the success of eutectic bondingdepends on being able to produce a uniform temper-ature distribution across the whole joint and oncareful control of bonding temperature and holdingtime

Transient liquid phase bonding has been employedin a range of applications since it produces jointsthat have microstructural and hence mechanical prop-erties similar to those of the base material Transientliquid phase bonding has the following advantages

1 Joint formation depends on an isothermalrelatively low temperature bonding mechanism

2 No interface remains after the TLP bondingoperation

3 Since the joining technique depends on capillaryfilling the joint preparation before TLP bonding isrelatively simple Also using the wide gap TLP bond-ing technique permits repair of defects up to 100 urnwide1112

4 In contrast to diffusion bondingPr the joiningprocess is highly tolerant to the presence of a fayingsurface oxide layer For this reason and because ofthe absence of thermal stresses TLP bonding is idealwhen joining intermetallic base materials whichhave stable oxide surface films are highly sensi-tive to microstructural changes and have poor lowtemperature ductilityPt

5 The bonding process is ideal when joining basematerials which are inherently susceptible to hotcracking or post-weld heat treatment crackingproblems

6 The bonding process is ideally suited for thefabrication of large and complex shaped components

Transient liquid phase bonding has been used whenjoining nickel base and iron base superalloy mater-ials91220-40when joining titanium alloys41-44 whenjoining stainless steel when joining aluminiumwhen joining aluminium base and titanium base metalmatrix compositesFlt during dissimilar joining ofcopper to austenitic stainless steel55 and when joiningmicrocircuitry componentst- Non-metals have alsobeen joined using TLP bonding for example siliconnitride has been bonded at 1550degC using an oxynitrideglass In this case the key requirement is that theglass composition must be selected so that thermalexpansion mismatch is minimised

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182 Zhou et ale Modelling of transient liquid phase bonding

Rationale for reviewAlthough TLP bonding has been widely applied theunderlying basis for its use rests on empirical testing~uch published research on final joint quality empha-sises the results of engineering assessments ie evalu-ations of high temperature tensile strength creeprupture strength thermal shock resistance corrosionresistance fatigue properties and so on Considerablework is still required to provide a quantitative predic-tion of the optimum bonding conditions (interlayercomposition bonding temperature holding time)during TLP bonding However much research hasbeen carried out on modelling of diffusion controlledgrowth or dissolution of an unstable phase (as isencountered during TLP bonding) using analyticaland finite element modelling techniques In additiona number of microstructural investigations (of varyingdetail) of TLP bonding have been completedFtWith this in mind the present review describes thestatus of research in process modelling of TLP bond-ing The advantages and disadvantages of analyticaland numerical modelling are discussed based on acomparison of calculated output with the experi-mental results produced when examining simplebinary alloy systems Finally the extent to whichmodelling output and microstructural observationscan be correlated in complex alloy joints is reviewedSince much research has been published on TLPbonding of nickel base superalloys the results pro-duced in this particular area are reviewed as anexample of the application of modelling when joiningcomplex alloy systems The future needs in TLPbonding research are associated with the developmentof a much clearer relationship between modellingoutput and direct microstructural observations

Basis of processStages in TLP bondingDuvall et al examined TLP bonding of Ni-Cr -Cobase superalloy material using Ni-B filler metal andsuggested that the TLP bonding process comprisedthree different stages namely base metal dissolutionisothermal solidification of the liquid phase and jointhomogenisation However Tuah- Poku et al8 investi-gated TLP bonding of silver using pure copper fillermetal and suggested that filler metal melting andwidening of the liquid zone at the bonding temper-ature were separate stages There is consequentlysome dispute concerning the detailed characteristicsof the base metal dissolution stage

MacDonald and Eagar65 pointed out that a furtherstage should be included in TLP bonding in order toaccount for solute diffusion during the heating cycleto the bonding temperature This assertion was basedon an analysis of the experimental results publishedby Niemann and Garret when they joined AI-Bcomposite base material using thin copper foils Whenthe heating rate between room temperature and theeutectic temperature is very slow insufficient liquidforms at the resulting bonding temperature (owing todiffusion of copper from the copper filler metal intothe base material during the heating stage) and verypoor joint mechanical properties are produced It isworth emphasising that the heating rate between the

International Materials Reviews 1995 Vol 40 No5

t L1Qu1dQ)

L] TB~roLQ)cE TNQ)

t-- P

A B

Composition

1 Hypothetical binary phase diagram witheutectic point

eutectic temperature and the bonding temperaturealso has an important effect on the process kineticswhich occur during TLP bonding Solute diffusion inthe temperature range from the filler metal meltingpoint TM to the bonding temperature TB may allowsolidification to occur before the selected bondingtemperature is reached This particular situation wasmodelled by Nakagawa et al66 during TLP bondingof Nickel 200 base metal using Ni-19 at-P fillermetal Solidification occurred when the heating ratebetween TM and TB was very slow ( 1 K s- 1) andwhen a thin (5 urn] filler metal was used In additionthe likelihood of solidification at temperaturesbetween TM and TB increased markedly when the fillermetal contained a high diffusivity melting pointdepressant such as boron It is worth noting that theheating rate from the eutectic temperature to thebonding temperature can be very slow unless induc-tive heating is employed during TLP bonding Forexample Zhou67 obtained a heating rate of 2middot5 K S-l

between the eutectic temperature (850degC) and thebonding temperature (1150degC) when joining 10 mmlong x 10 mm dia cylindrical Nickel 200 test sam-ples using Ni-19 at-P filler metal in a verticalradiation furnace

Based on the above commentary the differentstages during TLP bonding require further classifi-cation With this in mind an overall classification ofthe different stages in TLP bonding is presentedbelow It is convenient to describe this classificationof TLP bonding using the binary eutectic equilibriumphase diagram and the time-temperature relationshipshown in Figs 1 and 2 It is worth noting that thisclassification equally applies when a eutectic alloyfiller metal is employed (see Figs 1 and 3a) and whena single element filler metal is used during TLPbonding (see Figs 1 and 3b)

Stage IThis is the heating stage where the component isheated from room temperature to the filler metal

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I llmiddot1 IImiddot2 In IV(1)L

TB(Q c

dL --L(1)C eE(1) TNt-

Tfme (Log scale)

2 Schematic showing different stages duringheating cycle of TLP bonding where TB isbonding temperature and TM is melting pointof filler metal

melting temperature (from point 0 to point a inFig 2) During heating interdiffusion occurs betweenthe filler metal and base material so that the soluteconcentration CaS at the base materialfiller metalinterface changes with temperature following thesolvus line in the binary phase diagram (see Fig 1)Niemann and Garret pointed out that the heatingstage is particularly important when the filler metalis very thin (since all the filler metal can be consumedduring heating to the bonding temperature) In thisconnection Li et al54 examined TLP bonding ofalumina bearing metal matrix composite materialusing thin copper foils and found that the minimuminterlayer thickness for satisfactory joint formationincreased from 0middot6 to 2 urn when the heating ratedecreased from 5 to 1 K s - 1

Stage IIThis is the dissolution stage (from point a to point band then to point c in Fig 2) when the base metaldissolves into the liquid and hence the width of theliquid zone increases This stage can be subdividedas follows

Stage 11-1In this stage the temperature increases from themelting point to the bonding temperature (frompoint a to point b in Fig 2) and the solute concen-trations CLa and CaL and CLP and CPL at the solidliquid interfaces are changing with temperature fol-lowing the solidus and liquidus lines in the binaryphase diagram

Stage 11-2This is when isothermal dissolution occurs at thebonding temperature (from point b to point c inFig 2) When a single element interlayer B is used inthe binary eutectic alloy system three metallurgicalphases (a 3and liquid) are present at the beginningof the dissolution stage Stages 11-1 and II-2a (seeFig3b) proceed and the 3-phase disappears duringstage II-2b At the end of stage II the liquid zone hasreached its maximum width

Zhou et al Modelling of transient liquid phase bonding 183

L~ ~

___ i---S-peclm-en-----oi=======II___rrt=o bull

___0c_as__ s_tageI ffi_c_as __IIIIII I

~=~ ~L[l ~La n-2b~ ~agen~ ~I I

Wmax I Wmax I~ middot4

~age~max axStageIV

I

CF

n-in-za

a b

3 Schematic showing concentration profilesduring TLP bonding using a eutectic filler metaland b single element filler metal

Again it is worth noting that isothermal dissolutionof the base metal might not occur at the bondingtemperature if the heating rate between TM and TB isvery slow and a thin eutectic composition filler metalcontaining a high diffusivity melting point depressantis used

Stage IIIThis is the isothermal solidification stage where theliquid zone solidifies as a result of solute diffusioninto the base metal at the bonding temperature (frompoint c to point d in Fig 2) The solute concentra-tions at the solidliquid interface CLa and CaL areunchanged during this stage and the width of theliquid zone decreases continuously until the jointcompletely solidifies The solute distribution in theliquid is uniform during almost all of the isothermalsolidifica tion stage6668

The isothermal solidification stage is generallyconsidered to be the most important since the com-pletion time required for the entire TLP bondingprocess is largely determined by the time required forcompletion of isothermal solidification (see forexample Refs 869) This readily explains why muchresearch has been carried out on this particular aspectof the bonding process

Stage IVThis is the homogenisation stage where solid statesolute redistribution occurs (from point d to point e

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184 Zhou et al Modelling of transient liquid phase bonding

in Fig 2) The homogenisation temperature need notbe that used during stages II and III and this oper-ation is generally terminated when the maximumsolute concentration at the joint centreline reachessome preselected value

The two crucial factors in the TLP bonding processare that the completed joint has a chemical compos-ition located in the single phase region of the binaryequilibrium phase diagram (Fig 1) and the joiningprocess approaches this end point through solutediffusion Figure 3 confirms that use of a singleelement filler metal will markedly increase the maxi-mum liquid width and hence the time required forjoint completion during TLP bonding (comparedwith the situation when an equivalent thickness eutec-tic composition filler metal is employed) However itis important to emphasise that TLP bonding is acontinuous process and Figs 1-3 are only presentedas a basis for understanding the physical phenomenathat occur during the joining operation

Process modellingMuch modelling research to date has involved theuse of analytical methods812217071 However theanalytical approach treats the joining process as anumber of discrete steps and this is not what actuallyoccurs during TLP bonding For example the com-pletion time required for solute homogenisation willdepend on the solute distribution immediately follow-ing completion of the isothermal solidification stageIn addition the analytical calculations for each stageof the joining process depend on the error functionsolution and parabolic law assumptions and thesemay be considered only as approximate solutions Incontrast numerical modelling has the key advantagethat it can treat base metal dissolution isothermalsolidification and solute homogenisation as inter-dependent sequential processes Furthermore numer-ical modelling can be readily applied to two- or three-dimensional joining situations or when the fabricatedcomponents have complicated shapes

Local equilibrium at the migrating interface isgenerally assumed when modelling two phasediffusion controlled problems However this is anapproximation since local equilibrium is generallynot attained at the solidliquid interface Also it isgenerally assumed that the formation of the liquidphase assures complete wetting of the base metaland production of a sound joint and this may notnecessarily be the case during TLP bonding

Basic solutions for diffusion equationsAnalytical modelling of TLP bonding depends onclassical solutions for Ficks diffusion equationsFor the sake of brevity the present discussion will belimited to two cases only

The first case occurs when the surface of a semi-infinite specimen with an initial solute concentrationCM is maintained at composition Co for all t gt 0values ie

C(yO)=CM bullbull

C(O t) = Co

(1)

(2)

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where t is time and y the distance from the surfaceand the solute concentration in the specimen is

C(y t) = Co + (CM - Co) erf( 4~)12) (3)

where D is the solute diffusion coefficient The rateat which the diffusing species enters the specimen isgiven by the relation

( OC) D(CM - Co)D - 12 bull bull bull bull bull bull (4)oy y=O (nDt)

The total amount M of diffusing substance whichhas entered the medium at time t is found byintegrating the above equation with respect to t

Mt=2(Co-CM)(~tr2 (5)

The second case is when the initial thickness (2h) ofthe source of the diffusing species (Co) is of the orderof the diffusion distance (Dt)12 ie

C(y 0) = CoC(y 0) = CM

h~y~Oygth

(6)

(7)

where eM is the initial concentration of diffusant inthe specimen The solute concentration is given bythe relation

1C(y t) = CM + 2 (Co - CM)

x erf[(D~)~2] - err[(D~)~2] (8)

Analytical solutions for TLP bondingAs pointed out above analytical solutions have beenderived for each individual stage in TLP bonding Itis tacitly assumed that the output of any stage doesnot affect the operating conditions that apply insubsequent stages of the TLP bonding process

Heating stageEquation (5) was used by Niemann and Garret tocalculate the loss of the copper from an electroplatedcopper layer during the heating cycle from roomtemperature to the bonding temperature (when join-ing AI-B composite material) They developed therelation

xp = 1middot1284Pa(Cas - CM)(Dst)12 bullbullbullbull (9)

where x is the thickness of copper coating lost throughdiffusion Pc the density of copper Ds the diffusioncoefficient of copper in aluminium t time CaS thesolubility of copper in aluminium Pa the density ofthe alloy and CM the initial copper concentration inthe aluminium substrate Niemann and Garretassumed constant CaS and D values in their calcu-lations However both the diffusion coefficient andsolid solubility limit increase with temperature Withthis in mind MacDonald and Eagar65 suggested thisproblem could be overcome through the use of theeffective diffusion coefficient proposed by ShewrnonIt is worth pointing out that this diffusion problemis easily solved using numerical techniquesi

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T=1423K K=22~unls

T=1388K K=03~ms500

400

300

c~ 200S0 100is

200 400 600 1000800

Holding time S

4 Relation between the dissolution parameterP and holding time at various holdingtemperatures (during TLP bonding of nickelbase superalloy material MBF-007 using andMBF-80 filler metal) (after Ref 31)

Dissolution stageNo analytical solution is available for stage 11-1 ofTLP bonding (base metal dissolution during theheating cycle from the eutectic temperature to thebonding temperature) since the solute concentrationsCLa and CaL at the interface vary with temperatureIn this connection only limited work has been carriedout to determine the process kinetics during stage 11-2of the TLP bonding process (base metal dissolutionat the bonding temperature)

Nakao et al examined isothermal dissolutionduring TLP bonding (stage 11-2 in Fig2) andbased on the Nernst-Brunner theory (see Ref 66)developed a dissolution parameter P

[~(~+Ph)JP = Kt = h In h( ) (10)P ~-~

where ~ is the width of base metal dissolved attime t ~ the equilibrium (saturated) dissolutionwidth p the ratio of the densities of the liquid andsolid phases h half of the initial liquid width andK a constant During TLP bonding of nickel basesuperalloy base material using Ni-155 wt-Cr fillermetal this dissolution parameter was related linearlyto holding time (see Fig 4) Nakao et al31 thereforeconcluded that the Nernst-Brunner theory could beused to explain dissolution during TLP bondingHowever Nakagawa et al66 pointed out that the keyassumptions of a thin boundary layer and a largebulk liquid region in the Nernst-Brunner theory didnot apply during TLP bonding and solute diffusioninto the base metal was neglected in the calculationsmade by Nakao et al It is worth noting that thewidth of the liquid layer was held constant duringthe TLP bonding experiments carried out by Nakaoet al When however silver base metal was TLPbonded using copper filler metal the liquid widthformed at the bonding temperature was not heldconstant and a non-linear relation was observedbetween the dissolution parameter and holdingtime8bull66

Lesoult 70 applied a square root law solution toestimate the time required for interlayer melting whena pure metal interlayer was used in a binary eutecticalloy system However MacDonald and Eagar65 havepointed out that Lesoults assumption that the final

Zhou et a Modelling of transient liquid phase bonding 185

width of the liquid zone equals the interlayer width(when melting of the interlayer is completed) is doubt-ful since base metal dissolution occurs when theinterlayer melts In this connection Liu et al76 devel-oped a model that accounts for base metal meltingduring liquid formation They used a general errorfunction solution to describe the solute distributionin the liquid zone when modelling stage 11-2a (thedissolution stage when three metallurgical phasesexist) and assumed that there was no solute diffusioninto the base metal These assumptions are question-able The error function solution is really only appli-cable for infinite or semi-infinite media and the liquidzone is very thin in comparison with the solutediffusion rate in the liquid during TLP bondingFurthermore solute diffusion into the base metal canaffect the process kinetics during stage II of TLPbonding

In summary analytical methods are difficult toapply during modelling of the dissolution stage duringTLP bonding It is shown in the section Comparisonof numerical and analytical output below thatnumerical methods are more eflfective when solvingthis particular problemIsothermal solidificationSolute distribution in the liquid can be considereduniform during the isothermal solidification stage ofTLP bonding6667and therefore solute diffusion inthe liquid can be ignored In addition the base metalcan be assumed to be semi-infinite because solutediffusion in the solid is relatively slow The isothermalsolidification stage during TLP bonding can beanalytically modelled as a single phase diffusioncontrolled moving interface problem (see Fig 5)

Lynch et al77 first linked interface movement withthe mass balance at the liquidsolid interface butfailed to provide an analytical solution for thisproblem Tuah-Poku et al8 proposed a method forestimating the completion time required to the iso-thermal solidification stage of TLP bonding In theirtreatment the problem was simplified to a half semi-infinite base metal with a surface on which the soluteconcentration was maintained at CaL Consequentlyan error function solution can be employed todescribe the solute distribution in the base metal

C(y t) = CaL + CaL err[(4~)12J (11)

where CaL is the solute concentration in solid atthe interface The total solute amount M that hasentered the base metal at time t can be calculatedfrom the relation

(Dst)12

Mt = 2CaL ---- bull (12)

If the amount of solute diffused into the base metalduring the heating and dissolution stages is ignoredthe total amount of solute diffused into the base metalequals the original solute content of the filler metal ie

(Dst)12

CF ~ = 4CaL ---- bullbull (13)

where CF is the solute content in the filler metal and

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186 Zhou et al Modelling of transient liquid phase bonding

C

oo t=o-t

IIIIII

CM

CLa

Cal

o y(t) Wmax2

Centre l1ne ofJo1nt

5 Concentration profile along specimen lengthduring isothermal solidification stage

VJiO the initial width of the filler metal The completiontime for isothermal solidification can therefore becalculated using the relation

n (CFWO)2ts=- - (14)16Ds CcxL

Similar treatments of this problem have been reportedby Ikawa et al22 Nakao et al31 and Onzawa et al49

A more rigorous treatment of the problem waspresented by Lesoult His derivation is almost ident-ical with that described by Danckwerts when hederived a general solution for unsteady state linearheat conduction or diffusion A general error functionsolution is assumed in the solid phase

Cs(y t) = Ai + A2 erfL (Dt) 12] (15)

where A1 and A2 are constants determined by thespecific boundary conditions When y ~ 00

Cs(oo t) = A1 + A2 = CM bull bull bull bull bull bull bull (16)

and at the moving interface

Cs(yen t) = Ai + A2 err[ 2(D~)12] = CaL (17)

Since equation (17) has to be satisfied for all valuesof t Y must be proportional to t12 ie

Y = K( 4Dst)12 (18)

where K is a constant The mass balance at the

International Materials Reviews 1995 Vol 40 No5

interface produces the relation

(CLcx - CcxL) dYd(t) = Ds(iJC~(Y t))t Y y=Y(t)

Solving equations (15) and (19) leads to

K(1 + erf K)n12 CcxL - CM

exp(-K2) CLa-CcxL

(19)

(20)

y

Similar solutions were derived by Sakamoto et al79and Ramirez and Liu80 It is worth noting that in thederivations of Lesoult and Liu et al76 the termexp( - K2) is higher than the fraction indicated inequation (20) Also Le Blanc and Mevrel used anidentical derivation procedure to obtain a formulationwhich accounts for boron consumption as a result ofboride formation during TLP bonding of nickel basesuperalloy base material

The completion time for isothermal solidificationduring TLP bonding can be calculated using therelation

W~axt ----s - 16K2Ds

(21)

where Wmax is the maximum liquid width calculatedusing the mass balance method

Derivation of equation (14) depends on the assump-tion that the solute distribution is given by equa-tion (11) and this is only exact for a stationaryinterface Since the liquidsolid interface migratesduring TLP bonding it is important to determine theconditions when this assumption can be appliedSolving equations (15)-(17) we obtain

CM - CaL CM - CaLCS(Y t) = CM- 1- erf(K) + 1- erf(K)

X err[ 2 (Dt)12 ] (22)

K is the factor related to the solute distribution inequation (20) and therefore when K ~ 0 anderf(K) ~ 1 equation (22) becomes

Cs(Y t) = CL + (CM- Cd erf[ 2(Dt)12 ] (23)

This is identical to equations (3) and (11) It followsthat the solute distribution in the solid can becalculated using equation (11) when K is very small

Homogenisation stageEquation (8) was used by Ikawa et al22 to model thesolute distribution during homogenisation of TLPbonded nickel base superalloy material In their for-mulation h was half the maximum liquid width atthe end of the base metal dissolution period and Coequalled CLa The solute concentration attained itsmaximum value at the centreline of the specimen(x = 0) when

Cmax = C(O t) = CM + (Co - CM)

x err[ 4 (Dt)12 ] (24)

When examining the aluminium redistribution during

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Zhou et al Modelling of transient liquid phase bonding 187

90 ------------------

bull80 bullbullcP-

o bull0 70)(

c0bullbullbullc5

60

50 -J--------r-------r-------r---o 100 200

Holding time ks

bull experimental test resultscalculated results

6 Calculated and experimentally measuredaluminium concentrations at the joint centrelineduring homogenisation of TLP bonded nickelbase superalloy material using MBF-80filler metal at 1453K (after Ref 12) c isconcentration of aluminium at time t Cb isaluminium concentration in base metal

homogenisation of nickel base superalloy materialNakao et al31 observed close agreement between theresults calculated using equation (24) and the experi-mental values (for much of the homogenisationperiod) However there was a distinct differencebetween the analytical calculations and the experi-mental values during the early stages of the homo-genisation treatment (see Fig 6) Nakao et al12

suggested that this difference was due to a criticalassumption in the analytical results (that the alumin-ium concentration in the joint centreline was uniformat the beginning of the homogenisation period)

Zhou67 also used equation (24) to model the homo-genisation stage during TLP bonding In that studyh was half the filler metal thickness (~2) and Cothe initial solute concentration in the filler metal CFbull

This particular approach has the advantage that themaximum liquid width need not be calculated usingequation (24)

Numerical simulation of TLP bondingNakagawa et al66 modelled dissolution behaviourduring TLP bonding of Nickel 200 base metal usingNi-P and Ni-Cr-P filler metals This research con-firmed the critical effect that both the filler metalthickness and the heating rate between the filler metalmelting temperature and the bonding temperaturehad on the base metal dissolution process An explicitfinite difference method was employed to calculatesolute diffusion in liquid and solid phases and astepwise mechanical mass balance method wasused to determine solidliquid interface movementHowever the approach of Nakagawa et al hadinherent problems since the exact location of thesolidliquid interface could be determined using thestepwise mass balance technique and extremely long

20

15

10

05 0 Experimental- Calculated

o~ 0 - 3 10 - 2 10 - 1 1 00 10 1

2Dtl

300 7 Comparison of calculated and experimentalresults during TLP bonding of single crystalnickel (after Ref 67)

calculation times were required when the whole TLPbonding process was modelled

These problems were overcome by developing afully implicit finite difference model that simulatedthe TLP bonding process in a continuous mannerFigure 7 compares the calculated and experimentaltest results during TLP bonding of single crystalnickel The results are in excellent agreement and ashort computation time is required This numericalmodel output can be used to

(i) predict the completion times required fordissolution isothermal solidification andhomogenisation

(ii) predict the solute concentration distributionboth in the solid phase and in the liquid phasethroughout TLP bonding (see Figs 8-10)these results cannot be calculated usinganalytical methods

(iii) select the optimum filler metal (chemistrythickness) and bonding temperature which willensure that the TLP bonding operation iscompleted in a reasonable time frame

(iv) examine diffusion controlled two phasemoving interface problems other than TLPbonding for example the fully implicit finitedifference model has been applied to the solu-tion treatment of thin multilayer a and f3 brassdiffusion couples81-83

Figure 11 shows the influence of changes in the equi-librium solute content in solid at the bonding tem-perature CaL on the completion times required forbase metal dissolution isothermal solidification andhomogenisation CaL can be varied by altering thesolute content in the filler metal or by changing thebonding temperature Increasing the CaL valuedecreases the time required for completion of iso-thermal solidification and also the time required forhomogenisation Thus the time required for com-pletion of the entire TLP bonding process (dissolu-tion isothermal solidification and homogenisation)will not be affected by an increase in the CaL value

It has been suggested that selection of the optimumbonding temperature during TLP bonding dependson the interplay of increasing solute diffusivity anddecreasing equilibrium solute concentration in the

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25 ----------------- 20cac Uquid Solid0 bullbull 15e bullbullbull bullc bullbullbullbullBc 10 ------ --~---I0 I() I

oS II

5 i 0165I

(5 Time=O s 336 s() I

I

---00 10 20 30 40 50

Distance from liquid centreline JU11

8 Change in solute concentration profile duringbase metal dissolution stage (after Ref 68)

solid However this idea is based wholly on aconsideration of the isothermal solidification stageduring TLP bonding the critical homogenisationstage during TLP bonding is not taken into accountSince variation of the equilibrium solute concen-tration in the solid has no influence on the timerequired for completion of the whole TLP bondingoperation the highest possible bonding temperatureshould be selected during joining This will increasethe rate of solute diffusion into the base metal Inpractice the maximum bonding temperatures will belimited by the need for compatibility with the heattreatment requirements of the base materialComparison of numerical and analytical outputIn the analytical approach it -is assumed that move-ment of the solidliquid interface Y during isothermalsolidification obeys a parabolic law

Y = 2f3(t12) = 2K(Dst)12 (25)

where the constant f3 defines the rate of interfacemovement During numerical calculations f3 isevaluated using the relation

f3 = ~ = (t)12 dY (26)2 d(t12) dt

The f3 parameter is a particularly useful means of

15 I-

10 bullbullbullbull-- bullbullbullbull---r--7-----I I Liquid e Solidimiddot

1900 5 Tlme=3365

i --- _--_1

5 -3200 s

10 4020 30

Distance from liquid centreline JU11

9 Change in solute concentration profile duringisothermal solidification stage (after Ref 68)

International Materials Reviews 1995 Vol 40 No5

fI 10 Time=7000 scac0ca bullbullbullbullbullbullbullbulla-C 9200 S bullbullbullbullbullbullB 05c0()

oS(5()

000 200 400 600 800

Distance from joint centreline JU11

10 Change in solute concentration profile duringhomogenisation stage (after Ref 68)

comparing the output of analytical and numericalcalculations Figure 12 shows the variation of thef3 parameter during base metal dissolution and sub-sequent isothermal solidification for a hypotheticalTLP bonding situation The value of f3decreasesprogressively and approaches zero when base metaldissolution is almost completed In fact f3 decreasesto a value of -0185 urn S-12 and this is identicalto the analytical solution (equation (20)) Thus theisothermal solidification stage during TLP bondingcan be readily estimated using an analytical solutionfor example Fig 13 shows the results when nickelbase material is TLP bonded using Ni-B filler metalIn direct contrast base metal dissolution depends ona non-parabolic relation and no single value of f3 cancharacterise solidliquid interface movement

The remarkable difference between the output ofnumerical and analytical solutions during base metaldissolution and isothermal solidification occurs be-cause the analytical calculations assume that solutediffusion occurs wholly in solid state and that liquidphase is not formed during the joining operation

o Dissolution ~Ifla Homogenisation

105 -----------------

Solidificationbull Total

en 103cDEi= 102

101

100

50200

Cal al

11 Effect of solidus composition at bondingtemperature CaL on completion times requiredfor dissolution isothermal solidification andhomogenisation (after Ref 68)

100

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10

8

0 6~1 4rS

2

0

-210- 1 10deg0- 2

Numerical

Analytical

Eo+~~ Isothermal solidification

Bonding time s

12 Comparison between numerical and analyticalcalculated p values where the constant pdefines the rate of interface movement (afterRef 67)

Figure 14 compares the results of analytical andnumerical calculations of the homogenisation stageduring TLP bonding Numerical and analyticalresults are in close agreement during part of thehomogenisation stage although differences are appar-ent early and late in the processing cycle The devi-ation between the numerical and analytical resultslate in the homogenisation stage (in Fig 14) resultsfrom the semi-infinite test specimen assumption inthe analytical calculations

It can be concluded therefore that simple analyti-cal solutions can be used to estimate the completiontimes for isothermal solidification and for estimatingthe solute concentration at the joint centreline Itshould be noted that the error function required inthe analytical solution must be found by solvingequation (20) numerically Also direct parameterinput into a numerical program can permit readyprediction of the completion times for dissolutionisothermal solidification or homogenisation (for anychosen bonding temperature and filler metal-basemetal combination)

Modelling of real systemsMuch research to date on modelling of TLP bond-ing has involved two aspects The first aspect is

e 30=1-c~ 20i~u 10Q)

w

00

Bonding temperature K

bull 1393bull 1433

bull 1473

40Holding time S

13 Relation between holding time at differentbonding temperatures and eutectic widthduring TLP bonding of nickel base materialusing Ni-B filler metal (after Ref 31)

20 60 80

Zhou et al Modelling of transient liquid phase bonding 189

Isothermalsolidification I Homogenisation

gtltDissolution-1lt

AnaJytimiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot bullNumerical bull

Bonding time s

14 Calculated changes in solute concentration atspecimen centreline during TLP bonding(after Ref 68)

one-dimensional modelling only However whenTuah-Poku et al8 compared their analyticallycalculated and experimental completion times forisothermal solidification during TLP bonding of silverusing copper filler metal they observed a markeddifference in these results They suggested that thisdifference might be due to liquid penetration at grainboundaries in the base metal (this increased the solidiliquid interfacial area for solute diffusion) This effecthas been confirmed in research by Kokawa et al85

and Saida et al86 (Fig 15) With this in mind onedimensional modelling results are really only usefulwhen single crystal or very coarse grained polycrystalsubstrates are joined using TLP bonding

The second aspect is the solution of a two phasemoving interface problem in a simple binary alloysystem eg pure nickel base material bonded using aNi-P interlayer The implicit assumptions are thatlocal equilibrium exists at the migrating interfaceduring TLP bonding and that formation of an inter-mediate phase does not occur during isothermalsolidification However this is an approximation sincelocal equilibrium is generally not attained at the solidiliquid interface Furthermore direct experimentalevidence has been presented by Gale and Wallach64

E 301

- ~C1) 0gt-

20 -~uC1)-sC1)

~ 10 -0

s-C~

0 0

A Single-crystal+ Coarse grain (d=34mm)

o Fine grain high purity (d=33JUTl)

A 0 Fine grain low purity (d=40JUTl)+o

o A+o

J J

300 400200

Holdingtime ~s

15 TLP bonding of nickel base metals withdifferent grain sizes d is mean grain sizebefore TLP bonding (after Refs 85 86)

100

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190 Zhou et at Modelling of transient liquid phase bonding

L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

International Materials Reviews 1995 Vol 40 No5

L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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30

~ 20

5

~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

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55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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182 Zhou et ale Modelling of transient liquid phase bonding

Rationale for reviewAlthough TLP bonding has been widely applied theunderlying basis for its use rests on empirical testing~uch published research on final joint quality empha-sises the results of engineering assessments ie evalu-ations of high temperature tensile strength creeprupture strength thermal shock resistance corrosionresistance fatigue properties and so on Considerablework is still required to provide a quantitative predic-tion of the optimum bonding conditions (interlayercomposition bonding temperature holding time)during TLP bonding However much research hasbeen carried out on modelling of diffusion controlledgrowth or dissolution of an unstable phase (as isencountered during TLP bonding) using analyticaland finite element modelling techniques In additiona number of microstructural investigations (of varyingdetail) of TLP bonding have been completedFtWith this in mind the present review describes thestatus of research in process modelling of TLP bond-ing The advantages and disadvantages of analyticaland numerical modelling are discussed based on acomparison of calculated output with the experi-mental results produced when examining simplebinary alloy systems Finally the extent to whichmodelling output and microstructural observationscan be correlated in complex alloy joints is reviewedSince much research has been published on TLPbonding of nickel base superalloys the results pro-duced in this particular area are reviewed as anexample of the application of modelling when joiningcomplex alloy systems The future needs in TLPbonding research are associated with the developmentof a much clearer relationship between modellingoutput and direct microstructural observations

Basis of processStages in TLP bondingDuvall et al examined TLP bonding of Ni-Cr -Cobase superalloy material using Ni-B filler metal andsuggested that the TLP bonding process comprisedthree different stages namely base metal dissolutionisothermal solidification of the liquid phase and jointhomogenisation However Tuah- Poku et al8 investi-gated TLP bonding of silver using pure copper fillermetal and suggested that filler metal melting andwidening of the liquid zone at the bonding temper-ature were separate stages There is consequentlysome dispute concerning the detailed characteristicsof the base metal dissolution stage

MacDonald and Eagar65 pointed out that a furtherstage should be included in TLP bonding in order toaccount for solute diffusion during the heating cycleto the bonding temperature This assertion was basedon an analysis of the experimental results publishedby Niemann and Garret when they joined AI-Bcomposite base material using thin copper foils Whenthe heating rate between room temperature and theeutectic temperature is very slow insufficient liquidforms at the resulting bonding temperature (owing todiffusion of copper from the copper filler metal intothe base material during the heating stage) and verypoor joint mechanical properties are produced It isworth emphasising that the heating rate between the

International Materials Reviews 1995 Vol 40 No5

t L1Qu1dQ)

L] TB~roLQ)cE TNQ)

t-- P

A B

Composition

1 Hypothetical binary phase diagram witheutectic point

eutectic temperature and the bonding temperaturealso has an important effect on the process kineticswhich occur during TLP bonding Solute diffusion inthe temperature range from the filler metal meltingpoint TM to the bonding temperature TB may allowsolidification to occur before the selected bondingtemperature is reached This particular situation wasmodelled by Nakagawa et al66 during TLP bondingof Nickel 200 base metal using Ni-19 at-P fillermetal Solidification occurred when the heating ratebetween TM and TB was very slow ( 1 K s- 1) andwhen a thin (5 urn] filler metal was used In additionthe likelihood of solidification at temperaturesbetween TM and TB increased markedly when the fillermetal contained a high diffusivity melting pointdepressant such as boron It is worth noting that theheating rate from the eutectic temperature to thebonding temperature can be very slow unless induc-tive heating is employed during TLP bonding Forexample Zhou67 obtained a heating rate of 2middot5 K S-l

between the eutectic temperature (850degC) and thebonding temperature (1150degC) when joining 10 mmlong x 10 mm dia cylindrical Nickel 200 test sam-ples using Ni-19 at-P filler metal in a verticalradiation furnace

Based on the above commentary the differentstages during TLP bonding require further classifi-cation With this in mind an overall classification ofthe different stages in TLP bonding is presentedbelow It is convenient to describe this classificationof TLP bonding using the binary eutectic equilibriumphase diagram and the time-temperature relationshipshown in Figs 1 and 2 It is worth noting that thisclassification equally applies when a eutectic alloyfiller metal is employed (see Figs 1 and 3a) and whena single element filler metal is used during TLPbonding (see Figs 1 and 3b)

Stage IThis is the heating stage where the component isheated from room temperature to the filler metal

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I llmiddot1 IImiddot2 In IV(1)L

TB(Q c

dL --L(1)C eE(1) TNt-

Tfme (Log scale)

2 Schematic showing different stages duringheating cycle of TLP bonding where TB isbonding temperature and TM is melting pointof filler metal

melting temperature (from point 0 to point a inFig 2) During heating interdiffusion occurs betweenthe filler metal and base material so that the soluteconcentration CaS at the base materialfiller metalinterface changes with temperature following thesolvus line in the binary phase diagram (see Fig 1)Niemann and Garret pointed out that the heatingstage is particularly important when the filler metalis very thin (since all the filler metal can be consumedduring heating to the bonding temperature) In thisconnection Li et al54 examined TLP bonding ofalumina bearing metal matrix composite materialusing thin copper foils and found that the minimuminterlayer thickness for satisfactory joint formationincreased from 0middot6 to 2 urn when the heating ratedecreased from 5 to 1 K s - 1

Stage IIThis is the dissolution stage (from point a to point band then to point c in Fig 2) when the base metaldissolves into the liquid and hence the width of theliquid zone increases This stage can be subdividedas follows

Stage 11-1In this stage the temperature increases from themelting point to the bonding temperature (frompoint a to point b in Fig 2) and the solute concen-trations CLa and CaL and CLP and CPL at the solidliquid interfaces are changing with temperature fol-lowing the solidus and liquidus lines in the binaryphase diagram

Stage 11-2This is when isothermal dissolution occurs at thebonding temperature (from point b to point c inFig 2) When a single element interlayer B is used inthe binary eutectic alloy system three metallurgicalphases (a 3and liquid) are present at the beginningof the dissolution stage Stages 11-1 and II-2a (seeFig3b) proceed and the 3-phase disappears duringstage II-2b At the end of stage II the liquid zone hasreached its maximum width

Zhou et al Modelling of transient liquid phase bonding 183

L~ ~

___ i---S-peclm-en-----oi=======II___rrt=o bull

___0c_as__ s_tageI ffi_c_as __IIIIII I

~=~ ~L[l ~La n-2b~ ~agen~ ~I I

Wmax I Wmax I~ middot4

~age~max axStageIV

I

CF

n-in-za

a b

3 Schematic showing concentration profilesduring TLP bonding using a eutectic filler metaland b single element filler metal

Again it is worth noting that isothermal dissolutionof the base metal might not occur at the bondingtemperature if the heating rate between TM and TB isvery slow and a thin eutectic composition filler metalcontaining a high diffusivity melting point depressantis used

Stage IIIThis is the isothermal solidification stage where theliquid zone solidifies as a result of solute diffusioninto the base metal at the bonding temperature (frompoint c to point d in Fig 2) The solute concentra-tions at the solidliquid interface CLa and CaL areunchanged during this stage and the width of theliquid zone decreases continuously until the jointcompletely solidifies The solute distribution in theliquid is uniform during almost all of the isothermalsolidifica tion stage6668

The isothermal solidification stage is generallyconsidered to be the most important since the com-pletion time required for the entire TLP bondingprocess is largely determined by the time required forcompletion of isothermal solidification (see forexample Refs 869) This readily explains why muchresearch has been carried out on this particular aspectof the bonding process

Stage IVThis is the homogenisation stage where solid statesolute redistribution occurs (from point d to point e

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184 Zhou et al Modelling of transient liquid phase bonding

in Fig 2) The homogenisation temperature need notbe that used during stages II and III and this oper-ation is generally terminated when the maximumsolute concentration at the joint centreline reachessome preselected value

The two crucial factors in the TLP bonding processare that the completed joint has a chemical compos-ition located in the single phase region of the binaryequilibrium phase diagram (Fig 1) and the joiningprocess approaches this end point through solutediffusion Figure 3 confirms that use of a singleelement filler metal will markedly increase the maxi-mum liquid width and hence the time required forjoint completion during TLP bonding (comparedwith the situation when an equivalent thickness eutec-tic composition filler metal is employed) However itis important to emphasise that TLP bonding is acontinuous process and Figs 1-3 are only presentedas a basis for understanding the physical phenomenathat occur during the joining operation

Process modellingMuch modelling research to date has involved theuse of analytical methods812217071 However theanalytical approach treats the joining process as anumber of discrete steps and this is not what actuallyoccurs during TLP bonding For example the com-pletion time required for solute homogenisation willdepend on the solute distribution immediately follow-ing completion of the isothermal solidification stageIn addition the analytical calculations for each stageof the joining process depend on the error functionsolution and parabolic law assumptions and thesemay be considered only as approximate solutions Incontrast numerical modelling has the key advantagethat it can treat base metal dissolution isothermalsolidification and solute homogenisation as inter-dependent sequential processes Furthermore numer-ical modelling can be readily applied to two- or three-dimensional joining situations or when the fabricatedcomponents have complicated shapes

Local equilibrium at the migrating interface isgenerally assumed when modelling two phasediffusion controlled problems However this is anapproximation since local equilibrium is generallynot attained at the solidliquid interface Also it isgenerally assumed that the formation of the liquidphase assures complete wetting of the base metaland production of a sound joint and this may notnecessarily be the case during TLP bonding

Basic solutions for diffusion equationsAnalytical modelling of TLP bonding depends onclassical solutions for Ficks diffusion equationsFor the sake of brevity the present discussion will belimited to two cases only

The first case occurs when the surface of a semi-infinite specimen with an initial solute concentrationCM is maintained at composition Co for all t gt 0values ie

C(yO)=CM bullbull

C(O t) = Co

(1)

(2)

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where t is time and y the distance from the surfaceand the solute concentration in the specimen is

C(y t) = Co + (CM - Co) erf( 4~)12) (3)

where D is the solute diffusion coefficient The rateat which the diffusing species enters the specimen isgiven by the relation

( OC) D(CM - Co)D - 12 bull bull bull bull bull bull (4)oy y=O (nDt)

The total amount M of diffusing substance whichhas entered the medium at time t is found byintegrating the above equation with respect to t

Mt=2(Co-CM)(~tr2 (5)

The second case is when the initial thickness (2h) ofthe source of the diffusing species (Co) is of the orderof the diffusion distance (Dt)12 ie

C(y 0) = CoC(y 0) = CM

h~y~Oygth

(6)

(7)

where eM is the initial concentration of diffusant inthe specimen The solute concentration is given bythe relation

1C(y t) = CM + 2 (Co - CM)

x erf[(D~)~2] - err[(D~)~2] (8)

Analytical solutions for TLP bondingAs pointed out above analytical solutions have beenderived for each individual stage in TLP bonding Itis tacitly assumed that the output of any stage doesnot affect the operating conditions that apply insubsequent stages of the TLP bonding process

Heating stageEquation (5) was used by Niemann and Garret tocalculate the loss of the copper from an electroplatedcopper layer during the heating cycle from roomtemperature to the bonding temperature (when join-ing AI-B composite material) They developed therelation

xp = 1middot1284Pa(Cas - CM)(Dst)12 bullbullbullbull (9)

where x is the thickness of copper coating lost throughdiffusion Pc the density of copper Ds the diffusioncoefficient of copper in aluminium t time CaS thesolubility of copper in aluminium Pa the density ofthe alloy and CM the initial copper concentration inthe aluminium substrate Niemann and Garretassumed constant CaS and D values in their calcu-lations However both the diffusion coefficient andsolid solubility limit increase with temperature Withthis in mind MacDonald and Eagar65 suggested thisproblem could be overcome through the use of theeffective diffusion coefficient proposed by ShewrnonIt is worth pointing out that this diffusion problemis easily solved using numerical techniquesi

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T=1423K K=22~unls

T=1388K K=03~ms500

400

300

c~ 200S0 100is

200 400 600 1000800

Holding time S

4 Relation between the dissolution parameterP and holding time at various holdingtemperatures (during TLP bonding of nickelbase superalloy material MBF-007 using andMBF-80 filler metal) (after Ref 31)

Dissolution stageNo analytical solution is available for stage 11-1 ofTLP bonding (base metal dissolution during theheating cycle from the eutectic temperature to thebonding temperature) since the solute concentrationsCLa and CaL at the interface vary with temperatureIn this connection only limited work has been carriedout to determine the process kinetics during stage 11-2of the TLP bonding process (base metal dissolutionat the bonding temperature)

Nakao et al examined isothermal dissolutionduring TLP bonding (stage 11-2 in Fig2) andbased on the Nernst-Brunner theory (see Ref 66)developed a dissolution parameter P

[~(~+Ph)JP = Kt = h In h( ) (10)P ~-~

where ~ is the width of base metal dissolved attime t ~ the equilibrium (saturated) dissolutionwidth p the ratio of the densities of the liquid andsolid phases h half of the initial liquid width andK a constant During TLP bonding of nickel basesuperalloy base material using Ni-155 wt-Cr fillermetal this dissolution parameter was related linearlyto holding time (see Fig 4) Nakao et al31 thereforeconcluded that the Nernst-Brunner theory could beused to explain dissolution during TLP bondingHowever Nakagawa et al66 pointed out that the keyassumptions of a thin boundary layer and a largebulk liquid region in the Nernst-Brunner theory didnot apply during TLP bonding and solute diffusioninto the base metal was neglected in the calculationsmade by Nakao et al It is worth noting that thewidth of the liquid layer was held constant duringthe TLP bonding experiments carried out by Nakaoet al When however silver base metal was TLPbonded using copper filler metal the liquid widthformed at the bonding temperature was not heldconstant and a non-linear relation was observedbetween the dissolution parameter and holdingtime8bull66

Lesoult 70 applied a square root law solution toestimate the time required for interlayer melting whena pure metal interlayer was used in a binary eutecticalloy system However MacDonald and Eagar65 havepointed out that Lesoults assumption that the final

Zhou et a Modelling of transient liquid phase bonding 185

width of the liquid zone equals the interlayer width(when melting of the interlayer is completed) is doubt-ful since base metal dissolution occurs when theinterlayer melts In this connection Liu et al76 devel-oped a model that accounts for base metal meltingduring liquid formation They used a general errorfunction solution to describe the solute distributionin the liquid zone when modelling stage 11-2a (thedissolution stage when three metallurgical phasesexist) and assumed that there was no solute diffusioninto the base metal These assumptions are question-able The error function solution is really only appli-cable for infinite or semi-infinite media and the liquidzone is very thin in comparison with the solutediffusion rate in the liquid during TLP bondingFurthermore solute diffusion into the base metal canaffect the process kinetics during stage II of TLPbonding

In summary analytical methods are difficult toapply during modelling of the dissolution stage duringTLP bonding It is shown in the section Comparisonof numerical and analytical output below thatnumerical methods are more eflfective when solvingthis particular problemIsothermal solidificationSolute distribution in the liquid can be considereduniform during the isothermal solidification stage ofTLP bonding6667and therefore solute diffusion inthe liquid can be ignored In addition the base metalcan be assumed to be semi-infinite because solutediffusion in the solid is relatively slow The isothermalsolidification stage during TLP bonding can beanalytically modelled as a single phase diffusioncontrolled moving interface problem (see Fig 5)

Lynch et al77 first linked interface movement withthe mass balance at the liquidsolid interface butfailed to provide an analytical solution for thisproblem Tuah-Poku et al8 proposed a method forestimating the completion time required to the iso-thermal solidification stage of TLP bonding In theirtreatment the problem was simplified to a half semi-infinite base metal with a surface on which the soluteconcentration was maintained at CaL Consequentlyan error function solution can be employed todescribe the solute distribution in the base metal

C(y t) = CaL + CaL err[(4~)12J (11)

where CaL is the solute concentration in solid atthe interface The total solute amount M that hasentered the base metal at time t can be calculatedfrom the relation

(Dst)12

Mt = 2CaL ---- bull (12)

If the amount of solute diffused into the base metalduring the heating and dissolution stages is ignoredthe total amount of solute diffused into the base metalequals the original solute content of the filler metal ie

(Dst)12

CF ~ = 4CaL ---- bullbull (13)

where CF is the solute content in the filler metal and

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186 Zhou et al Modelling of transient liquid phase bonding

C

oo t=o-t

IIIIII

CM

CLa

Cal

o y(t) Wmax2

Centre l1ne ofJo1nt

5 Concentration profile along specimen lengthduring isothermal solidification stage

VJiO the initial width of the filler metal The completiontime for isothermal solidification can therefore becalculated using the relation

n (CFWO)2ts=- - (14)16Ds CcxL

Similar treatments of this problem have been reportedby Ikawa et al22 Nakao et al31 and Onzawa et al49

A more rigorous treatment of the problem waspresented by Lesoult His derivation is almost ident-ical with that described by Danckwerts when hederived a general solution for unsteady state linearheat conduction or diffusion A general error functionsolution is assumed in the solid phase

Cs(y t) = Ai + A2 erfL (Dt) 12] (15)

where A1 and A2 are constants determined by thespecific boundary conditions When y ~ 00

Cs(oo t) = A1 + A2 = CM bull bull bull bull bull bull bull (16)

and at the moving interface

Cs(yen t) = Ai + A2 err[ 2(D~)12] = CaL (17)

Since equation (17) has to be satisfied for all valuesof t Y must be proportional to t12 ie

Y = K( 4Dst)12 (18)

where K is a constant The mass balance at the

International Materials Reviews 1995 Vol 40 No5

interface produces the relation

(CLcx - CcxL) dYd(t) = Ds(iJC~(Y t))t Y y=Y(t)

Solving equations (15) and (19) leads to

K(1 + erf K)n12 CcxL - CM

exp(-K2) CLa-CcxL

(19)

(20)

y

Similar solutions were derived by Sakamoto et al79and Ramirez and Liu80 It is worth noting that in thederivations of Lesoult and Liu et al76 the termexp( - K2) is higher than the fraction indicated inequation (20) Also Le Blanc and Mevrel used anidentical derivation procedure to obtain a formulationwhich accounts for boron consumption as a result ofboride formation during TLP bonding of nickel basesuperalloy base material

The completion time for isothermal solidificationduring TLP bonding can be calculated using therelation

W~axt ----s - 16K2Ds

(21)

where Wmax is the maximum liquid width calculatedusing the mass balance method

Derivation of equation (14) depends on the assump-tion that the solute distribution is given by equa-tion (11) and this is only exact for a stationaryinterface Since the liquidsolid interface migratesduring TLP bonding it is important to determine theconditions when this assumption can be appliedSolving equations (15)-(17) we obtain

CM - CaL CM - CaLCS(Y t) = CM- 1- erf(K) + 1- erf(K)

X err[ 2 (Dt)12 ] (22)

K is the factor related to the solute distribution inequation (20) and therefore when K ~ 0 anderf(K) ~ 1 equation (22) becomes

Cs(Y t) = CL + (CM- Cd erf[ 2(Dt)12 ] (23)

This is identical to equations (3) and (11) It followsthat the solute distribution in the solid can becalculated using equation (11) when K is very small

Homogenisation stageEquation (8) was used by Ikawa et al22 to model thesolute distribution during homogenisation of TLPbonded nickel base superalloy material In their for-mulation h was half the maximum liquid width atthe end of the base metal dissolution period and Coequalled CLa The solute concentration attained itsmaximum value at the centreline of the specimen(x = 0) when

Cmax = C(O t) = CM + (Co - CM)

x err[ 4 (Dt)12 ] (24)

When examining the aluminium redistribution during

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Zhou et al Modelling of transient liquid phase bonding 187

90 ------------------

bull80 bullbullcP-

o bull0 70)(

c0bullbullbullc5

60

50 -J--------r-------r-------r---o 100 200

Holding time ks

bull experimental test resultscalculated results

6 Calculated and experimentally measuredaluminium concentrations at the joint centrelineduring homogenisation of TLP bonded nickelbase superalloy material using MBF-80filler metal at 1453K (after Ref 12) c isconcentration of aluminium at time t Cb isaluminium concentration in base metal

homogenisation of nickel base superalloy materialNakao et al31 observed close agreement between theresults calculated using equation (24) and the experi-mental values (for much of the homogenisationperiod) However there was a distinct differencebetween the analytical calculations and the experi-mental values during the early stages of the homo-genisation treatment (see Fig 6) Nakao et al12

suggested that this difference was due to a criticalassumption in the analytical results (that the alumin-ium concentration in the joint centreline was uniformat the beginning of the homogenisation period)

Zhou67 also used equation (24) to model the homo-genisation stage during TLP bonding In that studyh was half the filler metal thickness (~2) and Cothe initial solute concentration in the filler metal CFbull

This particular approach has the advantage that themaximum liquid width need not be calculated usingequation (24)

Numerical simulation of TLP bondingNakagawa et al66 modelled dissolution behaviourduring TLP bonding of Nickel 200 base metal usingNi-P and Ni-Cr-P filler metals This research con-firmed the critical effect that both the filler metalthickness and the heating rate between the filler metalmelting temperature and the bonding temperaturehad on the base metal dissolution process An explicitfinite difference method was employed to calculatesolute diffusion in liquid and solid phases and astepwise mechanical mass balance method wasused to determine solidliquid interface movementHowever the approach of Nakagawa et al hadinherent problems since the exact location of thesolidliquid interface could be determined using thestepwise mass balance technique and extremely long

20

15

10

05 0 Experimental- Calculated

o~ 0 - 3 10 - 2 10 - 1 1 00 10 1

2Dtl

300 7 Comparison of calculated and experimentalresults during TLP bonding of single crystalnickel (after Ref 67)

calculation times were required when the whole TLPbonding process was modelled

These problems were overcome by developing afully implicit finite difference model that simulatedthe TLP bonding process in a continuous mannerFigure 7 compares the calculated and experimentaltest results during TLP bonding of single crystalnickel The results are in excellent agreement and ashort computation time is required This numericalmodel output can be used to

(i) predict the completion times required fordissolution isothermal solidification andhomogenisation

(ii) predict the solute concentration distributionboth in the solid phase and in the liquid phasethroughout TLP bonding (see Figs 8-10)these results cannot be calculated usinganalytical methods

(iii) select the optimum filler metal (chemistrythickness) and bonding temperature which willensure that the TLP bonding operation iscompleted in a reasonable time frame

(iv) examine diffusion controlled two phasemoving interface problems other than TLPbonding for example the fully implicit finitedifference model has been applied to the solu-tion treatment of thin multilayer a and f3 brassdiffusion couples81-83

Figure 11 shows the influence of changes in the equi-librium solute content in solid at the bonding tem-perature CaL on the completion times required forbase metal dissolution isothermal solidification andhomogenisation CaL can be varied by altering thesolute content in the filler metal or by changing thebonding temperature Increasing the CaL valuedecreases the time required for completion of iso-thermal solidification and also the time required forhomogenisation Thus the time required for com-pletion of the entire TLP bonding process (dissolu-tion isothermal solidification and homogenisation)will not be affected by an increase in the CaL value

It has been suggested that selection of the optimumbonding temperature during TLP bonding dependson the interplay of increasing solute diffusivity anddecreasing equilibrium solute concentration in the

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25 ----------------- 20cac Uquid Solid0 bullbull 15e bullbullbull bullc bullbullbullbullBc 10 ------ --~---I0 I() I

oS II

5 i 0165I

(5 Time=O s 336 s() I

I

---00 10 20 30 40 50

Distance from liquid centreline JU11

8 Change in solute concentration profile duringbase metal dissolution stage (after Ref 68)

solid However this idea is based wholly on aconsideration of the isothermal solidification stageduring TLP bonding the critical homogenisationstage during TLP bonding is not taken into accountSince variation of the equilibrium solute concen-tration in the solid has no influence on the timerequired for completion of the whole TLP bondingoperation the highest possible bonding temperatureshould be selected during joining This will increasethe rate of solute diffusion into the base metal Inpractice the maximum bonding temperatures will belimited by the need for compatibility with the heattreatment requirements of the base materialComparison of numerical and analytical outputIn the analytical approach it -is assumed that move-ment of the solidliquid interface Y during isothermalsolidification obeys a parabolic law

Y = 2f3(t12) = 2K(Dst)12 (25)

where the constant f3 defines the rate of interfacemovement During numerical calculations f3 isevaluated using the relation

f3 = ~ = (t)12 dY (26)2 d(t12) dt

The f3 parameter is a particularly useful means of

15 I-

10 bullbullbullbull-- bullbullbullbull---r--7-----I I Liquid e Solidimiddot

1900 5 Tlme=3365

i --- _--_1

5 -3200 s

10 4020 30

Distance from liquid centreline JU11

9 Change in solute concentration profile duringisothermal solidification stage (after Ref 68)

International Materials Reviews 1995 Vol 40 No5

fI 10 Time=7000 scac0ca bullbullbullbullbullbullbullbulla-C 9200 S bullbullbullbullbullbullB 05c0()

oS(5()

000 200 400 600 800

Distance from joint centreline JU11

10 Change in solute concentration profile duringhomogenisation stage (after Ref 68)

comparing the output of analytical and numericalcalculations Figure 12 shows the variation of thef3 parameter during base metal dissolution and sub-sequent isothermal solidification for a hypotheticalTLP bonding situation The value of f3decreasesprogressively and approaches zero when base metaldissolution is almost completed In fact f3 decreasesto a value of -0185 urn S-12 and this is identicalto the analytical solution (equation (20)) Thus theisothermal solidification stage during TLP bondingcan be readily estimated using an analytical solutionfor example Fig 13 shows the results when nickelbase material is TLP bonded using Ni-B filler metalIn direct contrast base metal dissolution depends ona non-parabolic relation and no single value of f3 cancharacterise solidliquid interface movement

The remarkable difference between the output ofnumerical and analytical solutions during base metaldissolution and isothermal solidification occurs be-cause the analytical calculations assume that solutediffusion occurs wholly in solid state and that liquidphase is not formed during the joining operation

o Dissolution ~Ifla Homogenisation

105 -----------------

Solidificationbull Total

en 103cDEi= 102

101

100

50200

Cal al

11 Effect of solidus composition at bondingtemperature CaL on completion times requiredfor dissolution isothermal solidification andhomogenisation (after Ref 68)

100

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10

8

0 6~1 4rS

2

0

-210- 1 10deg0- 2

Numerical

Analytical

Eo+~~ Isothermal solidification

Bonding time s

12 Comparison between numerical and analyticalcalculated p values where the constant pdefines the rate of interface movement (afterRef 67)

Figure 14 compares the results of analytical andnumerical calculations of the homogenisation stageduring TLP bonding Numerical and analyticalresults are in close agreement during part of thehomogenisation stage although differences are appar-ent early and late in the processing cycle The devi-ation between the numerical and analytical resultslate in the homogenisation stage (in Fig 14) resultsfrom the semi-infinite test specimen assumption inthe analytical calculations

It can be concluded therefore that simple analyti-cal solutions can be used to estimate the completiontimes for isothermal solidification and for estimatingthe solute concentration at the joint centreline Itshould be noted that the error function required inthe analytical solution must be found by solvingequation (20) numerically Also direct parameterinput into a numerical program can permit readyprediction of the completion times for dissolutionisothermal solidification or homogenisation (for anychosen bonding temperature and filler metal-basemetal combination)

Modelling of real systemsMuch research to date on modelling of TLP bond-ing has involved two aspects The first aspect is

e 30=1-c~ 20i~u 10Q)

w

00

Bonding temperature K

bull 1393bull 1433

bull 1473

40Holding time S

13 Relation between holding time at differentbonding temperatures and eutectic widthduring TLP bonding of nickel base materialusing Ni-B filler metal (after Ref 31)

20 60 80

Zhou et al Modelling of transient liquid phase bonding 189

Isothermalsolidification I Homogenisation

gtltDissolution-1lt

AnaJytimiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot bullNumerical bull

Bonding time s

14 Calculated changes in solute concentration atspecimen centreline during TLP bonding(after Ref 68)

one-dimensional modelling only However whenTuah-Poku et al8 compared their analyticallycalculated and experimental completion times forisothermal solidification during TLP bonding of silverusing copper filler metal they observed a markeddifference in these results They suggested that thisdifference might be due to liquid penetration at grainboundaries in the base metal (this increased the solidiliquid interfacial area for solute diffusion) This effecthas been confirmed in research by Kokawa et al85

and Saida et al86 (Fig 15) With this in mind onedimensional modelling results are really only usefulwhen single crystal or very coarse grained polycrystalsubstrates are joined using TLP bonding

The second aspect is the solution of a two phasemoving interface problem in a simple binary alloysystem eg pure nickel base material bonded using aNi-P interlayer The implicit assumptions are thatlocal equilibrium exists at the migrating interfaceduring TLP bonding and that formation of an inter-mediate phase does not occur during isothermalsolidification However this is an approximation sincelocal equilibrium is generally not attained at the solidiliquid interface Furthermore direct experimentalevidence has been presented by Gale and Wallach64

E 301

- ~C1) 0gt-

20 -~uC1)-sC1)

~ 10 -0

s-C~

0 0

A Single-crystal+ Coarse grain (d=34mm)

o Fine grain high purity (d=33JUTl)

A 0 Fine grain low purity (d=40JUTl)+o

o A+o

J J

300 400200

Holdingtime ~s

15 TLP bonding of nickel base metals withdifferent grain sizes d is mean grain sizebefore TLP bonding (after Refs 85 86)

100

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190 Zhou et at Modelling of transient liquid phase bonding

L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

International Materials Reviews 1995 Vol 40 No5

L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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30

~ 20

5

~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

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73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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I llmiddot1 IImiddot2 In IV(1)L

TB(Q c

dL --L(1)C eE(1) TNt-

Tfme (Log scale)

2 Schematic showing different stages duringheating cycle of TLP bonding where TB isbonding temperature and TM is melting pointof filler metal

melting temperature (from point 0 to point a inFig 2) During heating interdiffusion occurs betweenthe filler metal and base material so that the soluteconcentration CaS at the base materialfiller metalinterface changes with temperature following thesolvus line in the binary phase diagram (see Fig 1)Niemann and Garret pointed out that the heatingstage is particularly important when the filler metalis very thin (since all the filler metal can be consumedduring heating to the bonding temperature) In thisconnection Li et al54 examined TLP bonding ofalumina bearing metal matrix composite materialusing thin copper foils and found that the minimuminterlayer thickness for satisfactory joint formationincreased from 0middot6 to 2 urn when the heating ratedecreased from 5 to 1 K s - 1

Stage IIThis is the dissolution stage (from point a to point band then to point c in Fig 2) when the base metaldissolves into the liquid and hence the width of theliquid zone increases This stage can be subdividedas follows

Stage 11-1In this stage the temperature increases from themelting point to the bonding temperature (frompoint a to point b in Fig 2) and the solute concen-trations CLa and CaL and CLP and CPL at the solidliquid interfaces are changing with temperature fol-lowing the solidus and liquidus lines in the binaryphase diagram

Stage 11-2This is when isothermal dissolution occurs at thebonding temperature (from point b to point c inFig 2) When a single element interlayer B is used inthe binary eutectic alloy system three metallurgicalphases (a 3and liquid) are present at the beginningof the dissolution stage Stages 11-1 and II-2a (seeFig3b) proceed and the 3-phase disappears duringstage II-2b At the end of stage II the liquid zone hasreached its maximum width

Zhou et al Modelling of transient liquid phase bonding 183

L~ ~

___ i---S-peclm-en-----oi=======II___rrt=o bull

___0c_as__ s_tageI ffi_c_as __IIIIII I

~=~ ~L[l ~La n-2b~ ~agen~ ~I I

Wmax I Wmax I~ middot4

~age~max axStageIV

I

CF

n-in-za

a b

3 Schematic showing concentration profilesduring TLP bonding using a eutectic filler metaland b single element filler metal

Again it is worth noting that isothermal dissolutionof the base metal might not occur at the bondingtemperature if the heating rate between TM and TB isvery slow and a thin eutectic composition filler metalcontaining a high diffusivity melting point depressantis used

Stage IIIThis is the isothermal solidification stage where theliquid zone solidifies as a result of solute diffusioninto the base metal at the bonding temperature (frompoint c to point d in Fig 2) The solute concentra-tions at the solidliquid interface CLa and CaL areunchanged during this stage and the width of theliquid zone decreases continuously until the jointcompletely solidifies The solute distribution in theliquid is uniform during almost all of the isothermalsolidifica tion stage6668

The isothermal solidification stage is generallyconsidered to be the most important since the com-pletion time required for the entire TLP bondingprocess is largely determined by the time required forcompletion of isothermal solidification (see forexample Refs 869) This readily explains why muchresearch has been carried out on this particular aspectof the bonding process

Stage IVThis is the homogenisation stage where solid statesolute redistribution occurs (from point d to point e

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184 Zhou et al Modelling of transient liquid phase bonding

in Fig 2) The homogenisation temperature need notbe that used during stages II and III and this oper-ation is generally terminated when the maximumsolute concentration at the joint centreline reachessome preselected value

The two crucial factors in the TLP bonding processare that the completed joint has a chemical compos-ition located in the single phase region of the binaryequilibrium phase diagram (Fig 1) and the joiningprocess approaches this end point through solutediffusion Figure 3 confirms that use of a singleelement filler metal will markedly increase the maxi-mum liquid width and hence the time required forjoint completion during TLP bonding (comparedwith the situation when an equivalent thickness eutec-tic composition filler metal is employed) However itis important to emphasise that TLP bonding is acontinuous process and Figs 1-3 are only presentedas a basis for understanding the physical phenomenathat occur during the joining operation

Process modellingMuch modelling research to date has involved theuse of analytical methods812217071 However theanalytical approach treats the joining process as anumber of discrete steps and this is not what actuallyoccurs during TLP bonding For example the com-pletion time required for solute homogenisation willdepend on the solute distribution immediately follow-ing completion of the isothermal solidification stageIn addition the analytical calculations for each stageof the joining process depend on the error functionsolution and parabolic law assumptions and thesemay be considered only as approximate solutions Incontrast numerical modelling has the key advantagethat it can treat base metal dissolution isothermalsolidification and solute homogenisation as inter-dependent sequential processes Furthermore numer-ical modelling can be readily applied to two- or three-dimensional joining situations or when the fabricatedcomponents have complicated shapes

Local equilibrium at the migrating interface isgenerally assumed when modelling two phasediffusion controlled problems However this is anapproximation since local equilibrium is generallynot attained at the solidliquid interface Also it isgenerally assumed that the formation of the liquidphase assures complete wetting of the base metaland production of a sound joint and this may notnecessarily be the case during TLP bonding

Basic solutions for diffusion equationsAnalytical modelling of TLP bonding depends onclassical solutions for Ficks diffusion equationsFor the sake of brevity the present discussion will belimited to two cases only

The first case occurs when the surface of a semi-infinite specimen with an initial solute concentrationCM is maintained at composition Co for all t gt 0values ie

C(yO)=CM bullbull

C(O t) = Co

(1)

(2)

International Materials Reviews 1995 Vol 40 No5

where t is time and y the distance from the surfaceand the solute concentration in the specimen is

C(y t) = Co + (CM - Co) erf( 4~)12) (3)

where D is the solute diffusion coefficient The rateat which the diffusing species enters the specimen isgiven by the relation

( OC) D(CM - Co)D - 12 bull bull bull bull bull bull (4)oy y=O (nDt)

The total amount M of diffusing substance whichhas entered the medium at time t is found byintegrating the above equation with respect to t

Mt=2(Co-CM)(~tr2 (5)

The second case is when the initial thickness (2h) ofthe source of the diffusing species (Co) is of the orderof the diffusion distance (Dt)12 ie

C(y 0) = CoC(y 0) = CM

h~y~Oygth

(6)

(7)

where eM is the initial concentration of diffusant inthe specimen The solute concentration is given bythe relation

1C(y t) = CM + 2 (Co - CM)

x erf[(D~)~2] - err[(D~)~2] (8)

Analytical solutions for TLP bondingAs pointed out above analytical solutions have beenderived for each individual stage in TLP bonding Itis tacitly assumed that the output of any stage doesnot affect the operating conditions that apply insubsequent stages of the TLP bonding process

Heating stageEquation (5) was used by Niemann and Garret tocalculate the loss of the copper from an electroplatedcopper layer during the heating cycle from roomtemperature to the bonding temperature (when join-ing AI-B composite material) They developed therelation

xp = 1middot1284Pa(Cas - CM)(Dst)12 bullbullbullbull (9)

where x is the thickness of copper coating lost throughdiffusion Pc the density of copper Ds the diffusioncoefficient of copper in aluminium t time CaS thesolubility of copper in aluminium Pa the density ofthe alloy and CM the initial copper concentration inthe aluminium substrate Niemann and Garretassumed constant CaS and D values in their calcu-lations However both the diffusion coefficient andsolid solubility limit increase with temperature Withthis in mind MacDonald and Eagar65 suggested thisproblem could be overcome through the use of theeffective diffusion coefficient proposed by ShewrnonIt is worth pointing out that this diffusion problemis easily solved using numerical techniquesi

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T=1423K K=22~unls

T=1388K K=03~ms500

400

300

c~ 200S0 100is

200 400 600 1000800

Holding time S

4 Relation between the dissolution parameterP and holding time at various holdingtemperatures (during TLP bonding of nickelbase superalloy material MBF-007 using andMBF-80 filler metal) (after Ref 31)

Dissolution stageNo analytical solution is available for stage 11-1 ofTLP bonding (base metal dissolution during theheating cycle from the eutectic temperature to thebonding temperature) since the solute concentrationsCLa and CaL at the interface vary with temperatureIn this connection only limited work has been carriedout to determine the process kinetics during stage 11-2of the TLP bonding process (base metal dissolutionat the bonding temperature)

Nakao et al examined isothermal dissolutionduring TLP bonding (stage 11-2 in Fig2) andbased on the Nernst-Brunner theory (see Ref 66)developed a dissolution parameter P

[~(~+Ph)JP = Kt = h In h( ) (10)P ~-~

where ~ is the width of base metal dissolved attime t ~ the equilibrium (saturated) dissolutionwidth p the ratio of the densities of the liquid andsolid phases h half of the initial liquid width andK a constant During TLP bonding of nickel basesuperalloy base material using Ni-155 wt-Cr fillermetal this dissolution parameter was related linearlyto holding time (see Fig 4) Nakao et al31 thereforeconcluded that the Nernst-Brunner theory could beused to explain dissolution during TLP bondingHowever Nakagawa et al66 pointed out that the keyassumptions of a thin boundary layer and a largebulk liquid region in the Nernst-Brunner theory didnot apply during TLP bonding and solute diffusioninto the base metal was neglected in the calculationsmade by Nakao et al It is worth noting that thewidth of the liquid layer was held constant duringthe TLP bonding experiments carried out by Nakaoet al When however silver base metal was TLPbonded using copper filler metal the liquid widthformed at the bonding temperature was not heldconstant and a non-linear relation was observedbetween the dissolution parameter and holdingtime8bull66

Lesoult 70 applied a square root law solution toestimate the time required for interlayer melting whena pure metal interlayer was used in a binary eutecticalloy system However MacDonald and Eagar65 havepointed out that Lesoults assumption that the final

Zhou et a Modelling of transient liquid phase bonding 185

width of the liquid zone equals the interlayer width(when melting of the interlayer is completed) is doubt-ful since base metal dissolution occurs when theinterlayer melts In this connection Liu et al76 devel-oped a model that accounts for base metal meltingduring liquid formation They used a general errorfunction solution to describe the solute distributionin the liquid zone when modelling stage 11-2a (thedissolution stage when three metallurgical phasesexist) and assumed that there was no solute diffusioninto the base metal These assumptions are question-able The error function solution is really only appli-cable for infinite or semi-infinite media and the liquidzone is very thin in comparison with the solutediffusion rate in the liquid during TLP bondingFurthermore solute diffusion into the base metal canaffect the process kinetics during stage II of TLPbonding

In summary analytical methods are difficult toapply during modelling of the dissolution stage duringTLP bonding It is shown in the section Comparisonof numerical and analytical output below thatnumerical methods are more eflfective when solvingthis particular problemIsothermal solidificationSolute distribution in the liquid can be considereduniform during the isothermal solidification stage ofTLP bonding6667and therefore solute diffusion inthe liquid can be ignored In addition the base metalcan be assumed to be semi-infinite because solutediffusion in the solid is relatively slow The isothermalsolidification stage during TLP bonding can beanalytically modelled as a single phase diffusioncontrolled moving interface problem (see Fig 5)

Lynch et al77 first linked interface movement withthe mass balance at the liquidsolid interface butfailed to provide an analytical solution for thisproblem Tuah-Poku et al8 proposed a method forestimating the completion time required to the iso-thermal solidification stage of TLP bonding In theirtreatment the problem was simplified to a half semi-infinite base metal with a surface on which the soluteconcentration was maintained at CaL Consequentlyan error function solution can be employed todescribe the solute distribution in the base metal

C(y t) = CaL + CaL err[(4~)12J (11)

where CaL is the solute concentration in solid atthe interface The total solute amount M that hasentered the base metal at time t can be calculatedfrom the relation

(Dst)12

Mt = 2CaL ---- bull (12)

If the amount of solute diffused into the base metalduring the heating and dissolution stages is ignoredthe total amount of solute diffused into the base metalequals the original solute content of the filler metal ie

(Dst)12

CF ~ = 4CaL ---- bullbull (13)

where CF is the solute content in the filler metal and

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186 Zhou et al Modelling of transient liquid phase bonding

C

oo t=o-t

IIIIII

CM

CLa

Cal

o y(t) Wmax2

Centre l1ne ofJo1nt

5 Concentration profile along specimen lengthduring isothermal solidification stage

VJiO the initial width of the filler metal The completiontime for isothermal solidification can therefore becalculated using the relation

n (CFWO)2ts=- - (14)16Ds CcxL

Similar treatments of this problem have been reportedby Ikawa et al22 Nakao et al31 and Onzawa et al49

A more rigorous treatment of the problem waspresented by Lesoult His derivation is almost ident-ical with that described by Danckwerts when hederived a general solution for unsteady state linearheat conduction or diffusion A general error functionsolution is assumed in the solid phase

Cs(y t) = Ai + A2 erfL (Dt) 12] (15)

where A1 and A2 are constants determined by thespecific boundary conditions When y ~ 00

Cs(oo t) = A1 + A2 = CM bull bull bull bull bull bull bull (16)

and at the moving interface

Cs(yen t) = Ai + A2 err[ 2(D~)12] = CaL (17)

Since equation (17) has to be satisfied for all valuesof t Y must be proportional to t12 ie

Y = K( 4Dst)12 (18)

where K is a constant The mass balance at the

International Materials Reviews 1995 Vol 40 No5

interface produces the relation

(CLcx - CcxL) dYd(t) = Ds(iJC~(Y t))t Y y=Y(t)

Solving equations (15) and (19) leads to

K(1 + erf K)n12 CcxL - CM

exp(-K2) CLa-CcxL

(19)

(20)

y

Similar solutions were derived by Sakamoto et al79and Ramirez and Liu80 It is worth noting that in thederivations of Lesoult and Liu et al76 the termexp( - K2) is higher than the fraction indicated inequation (20) Also Le Blanc and Mevrel used anidentical derivation procedure to obtain a formulationwhich accounts for boron consumption as a result ofboride formation during TLP bonding of nickel basesuperalloy base material

The completion time for isothermal solidificationduring TLP bonding can be calculated using therelation

W~axt ----s - 16K2Ds

(21)

where Wmax is the maximum liquid width calculatedusing the mass balance method

Derivation of equation (14) depends on the assump-tion that the solute distribution is given by equa-tion (11) and this is only exact for a stationaryinterface Since the liquidsolid interface migratesduring TLP bonding it is important to determine theconditions when this assumption can be appliedSolving equations (15)-(17) we obtain

CM - CaL CM - CaLCS(Y t) = CM- 1- erf(K) + 1- erf(K)

X err[ 2 (Dt)12 ] (22)

K is the factor related to the solute distribution inequation (20) and therefore when K ~ 0 anderf(K) ~ 1 equation (22) becomes

Cs(Y t) = CL + (CM- Cd erf[ 2(Dt)12 ] (23)

This is identical to equations (3) and (11) It followsthat the solute distribution in the solid can becalculated using equation (11) when K is very small

Homogenisation stageEquation (8) was used by Ikawa et al22 to model thesolute distribution during homogenisation of TLPbonded nickel base superalloy material In their for-mulation h was half the maximum liquid width atthe end of the base metal dissolution period and Coequalled CLa The solute concentration attained itsmaximum value at the centreline of the specimen(x = 0) when

Cmax = C(O t) = CM + (Co - CM)

x err[ 4 (Dt)12 ] (24)

When examining the aluminium redistribution during

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Zhou et al Modelling of transient liquid phase bonding 187

90 ------------------

bull80 bullbullcP-

o bull0 70)(

c0bullbullbullc5

60

50 -J--------r-------r-------r---o 100 200

Holding time ks

bull experimental test resultscalculated results

6 Calculated and experimentally measuredaluminium concentrations at the joint centrelineduring homogenisation of TLP bonded nickelbase superalloy material using MBF-80filler metal at 1453K (after Ref 12) c isconcentration of aluminium at time t Cb isaluminium concentration in base metal

homogenisation of nickel base superalloy materialNakao et al31 observed close agreement between theresults calculated using equation (24) and the experi-mental values (for much of the homogenisationperiod) However there was a distinct differencebetween the analytical calculations and the experi-mental values during the early stages of the homo-genisation treatment (see Fig 6) Nakao et al12

suggested that this difference was due to a criticalassumption in the analytical results (that the alumin-ium concentration in the joint centreline was uniformat the beginning of the homogenisation period)

Zhou67 also used equation (24) to model the homo-genisation stage during TLP bonding In that studyh was half the filler metal thickness (~2) and Cothe initial solute concentration in the filler metal CFbull

This particular approach has the advantage that themaximum liquid width need not be calculated usingequation (24)

Numerical simulation of TLP bondingNakagawa et al66 modelled dissolution behaviourduring TLP bonding of Nickel 200 base metal usingNi-P and Ni-Cr-P filler metals This research con-firmed the critical effect that both the filler metalthickness and the heating rate between the filler metalmelting temperature and the bonding temperaturehad on the base metal dissolution process An explicitfinite difference method was employed to calculatesolute diffusion in liquid and solid phases and astepwise mechanical mass balance method wasused to determine solidliquid interface movementHowever the approach of Nakagawa et al hadinherent problems since the exact location of thesolidliquid interface could be determined using thestepwise mass balance technique and extremely long

20

15

10

05 0 Experimental- Calculated

o~ 0 - 3 10 - 2 10 - 1 1 00 10 1

2Dtl

300 7 Comparison of calculated and experimentalresults during TLP bonding of single crystalnickel (after Ref 67)

calculation times were required when the whole TLPbonding process was modelled

These problems were overcome by developing afully implicit finite difference model that simulatedthe TLP bonding process in a continuous mannerFigure 7 compares the calculated and experimentaltest results during TLP bonding of single crystalnickel The results are in excellent agreement and ashort computation time is required This numericalmodel output can be used to

(i) predict the completion times required fordissolution isothermal solidification andhomogenisation

(ii) predict the solute concentration distributionboth in the solid phase and in the liquid phasethroughout TLP bonding (see Figs 8-10)these results cannot be calculated usinganalytical methods

(iii) select the optimum filler metal (chemistrythickness) and bonding temperature which willensure that the TLP bonding operation iscompleted in a reasonable time frame

(iv) examine diffusion controlled two phasemoving interface problems other than TLPbonding for example the fully implicit finitedifference model has been applied to the solu-tion treatment of thin multilayer a and f3 brassdiffusion couples81-83

Figure 11 shows the influence of changes in the equi-librium solute content in solid at the bonding tem-perature CaL on the completion times required forbase metal dissolution isothermal solidification andhomogenisation CaL can be varied by altering thesolute content in the filler metal or by changing thebonding temperature Increasing the CaL valuedecreases the time required for completion of iso-thermal solidification and also the time required forhomogenisation Thus the time required for com-pletion of the entire TLP bonding process (dissolu-tion isothermal solidification and homogenisation)will not be affected by an increase in the CaL value

It has been suggested that selection of the optimumbonding temperature during TLP bonding dependson the interplay of increasing solute diffusivity anddecreasing equilibrium solute concentration in the

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25 ----------------- 20cac Uquid Solid0 bullbull 15e bullbullbull bullc bullbullbullbullBc 10 ------ --~---I0 I() I

oS II

5 i 0165I

(5 Time=O s 336 s() I

I

---00 10 20 30 40 50

Distance from liquid centreline JU11

8 Change in solute concentration profile duringbase metal dissolution stage (after Ref 68)

solid However this idea is based wholly on aconsideration of the isothermal solidification stageduring TLP bonding the critical homogenisationstage during TLP bonding is not taken into accountSince variation of the equilibrium solute concen-tration in the solid has no influence on the timerequired for completion of the whole TLP bondingoperation the highest possible bonding temperatureshould be selected during joining This will increasethe rate of solute diffusion into the base metal Inpractice the maximum bonding temperatures will belimited by the need for compatibility with the heattreatment requirements of the base materialComparison of numerical and analytical outputIn the analytical approach it -is assumed that move-ment of the solidliquid interface Y during isothermalsolidification obeys a parabolic law

Y = 2f3(t12) = 2K(Dst)12 (25)

where the constant f3 defines the rate of interfacemovement During numerical calculations f3 isevaluated using the relation

f3 = ~ = (t)12 dY (26)2 d(t12) dt

The f3 parameter is a particularly useful means of

15 I-

10 bullbullbullbull-- bullbullbullbull---r--7-----I I Liquid e Solidimiddot

1900 5 Tlme=3365

i --- _--_1

5 -3200 s

10 4020 30

Distance from liquid centreline JU11

9 Change in solute concentration profile duringisothermal solidification stage (after Ref 68)

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fI 10 Time=7000 scac0ca bullbullbullbullbullbullbullbulla-C 9200 S bullbullbullbullbullbullB 05c0()

oS(5()

000 200 400 600 800

Distance from joint centreline JU11

10 Change in solute concentration profile duringhomogenisation stage (after Ref 68)

comparing the output of analytical and numericalcalculations Figure 12 shows the variation of thef3 parameter during base metal dissolution and sub-sequent isothermal solidification for a hypotheticalTLP bonding situation The value of f3decreasesprogressively and approaches zero when base metaldissolution is almost completed In fact f3 decreasesto a value of -0185 urn S-12 and this is identicalto the analytical solution (equation (20)) Thus theisothermal solidification stage during TLP bondingcan be readily estimated using an analytical solutionfor example Fig 13 shows the results when nickelbase material is TLP bonded using Ni-B filler metalIn direct contrast base metal dissolution depends ona non-parabolic relation and no single value of f3 cancharacterise solidliquid interface movement

The remarkable difference between the output ofnumerical and analytical solutions during base metaldissolution and isothermal solidification occurs be-cause the analytical calculations assume that solutediffusion occurs wholly in solid state and that liquidphase is not formed during the joining operation

o Dissolution ~Ifla Homogenisation

105 -----------------

Solidificationbull Total

en 103cDEi= 102

101

100

50200

Cal al

11 Effect of solidus composition at bondingtemperature CaL on completion times requiredfor dissolution isothermal solidification andhomogenisation (after Ref 68)

100

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10

8

0 6~1 4rS

2

0

-210- 1 10deg0- 2

Numerical

Analytical

Eo+~~ Isothermal solidification

Bonding time s

12 Comparison between numerical and analyticalcalculated p values where the constant pdefines the rate of interface movement (afterRef 67)

Figure 14 compares the results of analytical andnumerical calculations of the homogenisation stageduring TLP bonding Numerical and analyticalresults are in close agreement during part of thehomogenisation stage although differences are appar-ent early and late in the processing cycle The devi-ation between the numerical and analytical resultslate in the homogenisation stage (in Fig 14) resultsfrom the semi-infinite test specimen assumption inthe analytical calculations

It can be concluded therefore that simple analyti-cal solutions can be used to estimate the completiontimes for isothermal solidification and for estimatingthe solute concentration at the joint centreline Itshould be noted that the error function required inthe analytical solution must be found by solvingequation (20) numerically Also direct parameterinput into a numerical program can permit readyprediction of the completion times for dissolutionisothermal solidification or homogenisation (for anychosen bonding temperature and filler metal-basemetal combination)

Modelling of real systemsMuch research to date on modelling of TLP bond-ing has involved two aspects The first aspect is

e 30=1-c~ 20i~u 10Q)

w

00

Bonding temperature K

bull 1393bull 1433

bull 1473

40Holding time S

13 Relation between holding time at differentbonding temperatures and eutectic widthduring TLP bonding of nickel base materialusing Ni-B filler metal (after Ref 31)

20 60 80

Zhou et al Modelling of transient liquid phase bonding 189

Isothermalsolidification I Homogenisation

gtltDissolution-1lt

AnaJytimiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot bullNumerical bull

Bonding time s

14 Calculated changes in solute concentration atspecimen centreline during TLP bonding(after Ref 68)

one-dimensional modelling only However whenTuah-Poku et al8 compared their analyticallycalculated and experimental completion times forisothermal solidification during TLP bonding of silverusing copper filler metal they observed a markeddifference in these results They suggested that thisdifference might be due to liquid penetration at grainboundaries in the base metal (this increased the solidiliquid interfacial area for solute diffusion) This effecthas been confirmed in research by Kokawa et al85

and Saida et al86 (Fig 15) With this in mind onedimensional modelling results are really only usefulwhen single crystal or very coarse grained polycrystalsubstrates are joined using TLP bonding

The second aspect is the solution of a two phasemoving interface problem in a simple binary alloysystem eg pure nickel base material bonded using aNi-P interlayer The implicit assumptions are thatlocal equilibrium exists at the migrating interfaceduring TLP bonding and that formation of an inter-mediate phase does not occur during isothermalsolidification However this is an approximation sincelocal equilibrium is generally not attained at the solidiliquid interface Furthermore direct experimentalevidence has been presented by Gale and Wallach64

E 301

- ~C1) 0gt-

20 -~uC1)-sC1)

~ 10 -0

s-C~

0 0

A Single-crystal+ Coarse grain (d=34mm)

o Fine grain high purity (d=33JUTl)

A 0 Fine grain low purity (d=40JUTl)+o

o A+o

J J

300 400200

Holdingtime ~s

15 TLP bonding of nickel base metals withdifferent grain sizes d is mean grain sizebefore TLP bonding (after Refs 85 86)

100

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190 Zhou et at Modelling of transient liquid phase bonding

L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

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L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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30

~ 20

5

~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

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4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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184 Zhou et al Modelling of transient liquid phase bonding

in Fig 2) The homogenisation temperature need notbe that used during stages II and III and this oper-ation is generally terminated when the maximumsolute concentration at the joint centreline reachessome preselected value

The two crucial factors in the TLP bonding processare that the completed joint has a chemical compos-ition located in the single phase region of the binaryequilibrium phase diagram (Fig 1) and the joiningprocess approaches this end point through solutediffusion Figure 3 confirms that use of a singleelement filler metal will markedly increase the maxi-mum liquid width and hence the time required forjoint completion during TLP bonding (comparedwith the situation when an equivalent thickness eutec-tic composition filler metal is employed) However itis important to emphasise that TLP bonding is acontinuous process and Figs 1-3 are only presentedas a basis for understanding the physical phenomenathat occur during the joining operation

Process modellingMuch modelling research to date has involved theuse of analytical methods812217071 However theanalytical approach treats the joining process as anumber of discrete steps and this is not what actuallyoccurs during TLP bonding For example the com-pletion time required for solute homogenisation willdepend on the solute distribution immediately follow-ing completion of the isothermal solidification stageIn addition the analytical calculations for each stageof the joining process depend on the error functionsolution and parabolic law assumptions and thesemay be considered only as approximate solutions Incontrast numerical modelling has the key advantagethat it can treat base metal dissolution isothermalsolidification and solute homogenisation as inter-dependent sequential processes Furthermore numer-ical modelling can be readily applied to two- or three-dimensional joining situations or when the fabricatedcomponents have complicated shapes

Local equilibrium at the migrating interface isgenerally assumed when modelling two phasediffusion controlled problems However this is anapproximation since local equilibrium is generallynot attained at the solidliquid interface Also it isgenerally assumed that the formation of the liquidphase assures complete wetting of the base metaland production of a sound joint and this may notnecessarily be the case during TLP bonding

Basic solutions for diffusion equationsAnalytical modelling of TLP bonding depends onclassical solutions for Ficks diffusion equationsFor the sake of brevity the present discussion will belimited to two cases only

The first case occurs when the surface of a semi-infinite specimen with an initial solute concentrationCM is maintained at composition Co for all t gt 0values ie

C(yO)=CM bullbull

C(O t) = Co

(1)

(2)

International Materials Reviews 1995 Vol 40 No5

where t is time and y the distance from the surfaceand the solute concentration in the specimen is

C(y t) = Co + (CM - Co) erf( 4~)12) (3)

where D is the solute diffusion coefficient The rateat which the diffusing species enters the specimen isgiven by the relation

( OC) D(CM - Co)D - 12 bull bull bull bull bull bull (4)oy y=O (nDt)

The total amount M of diffusing substance whichhas entered the medium at time t is found byintegrating the above equation with respect to t

Mt=2(Co-CM)(~tr2 (5)

The second case is when the initial thickness (2h) ofthe source of the diffusing species (Co) is of the orderof the diffusion distance (Dt)12 ie

C(y 0) = CoC(y 0) = CM

h~y~Oygth

(6)

(7)

where eM is the initial concentration of diffusant inthe specimen The solute concentration is given bythe relation

1C(y t) = CM + 2 (Co - CM)

x erf[(D~)~2] - err[(D~)~2] (8)

Analytical solutions for TLP bondingAs pointed out above analytical solutions have beenderived for each individual stage in TLP bonding Itis tacitly assumed that the output of any stage doesnot affect the operating conditions that apply insubsequent stages of the TLP bonding process

Heating stageEquation (5) was used by Niemann and Garret tocalculate the loss of the copper from an electroplatedcopper layer during the heating cycle from roomtemperature to the bonding temperature (when join-ing AI-B composite material) They developed therelation

xp = 1middot1284Pa(Cas - CM)(Dst)12 bullbullbullbull (9)

where x is the thickness of copper coating lost throughdiffusion Pc the density of copper Ds the diffusioncoefficient of copper in aluminium t time CaS thesolubility of copper in aluminium Pa the density ofthe alloy and CM the initial copper concentration inthe aluminium substrate Niemann and Garretassumed constant CaS and D values in their calcu-lations However both the diffusion coefficient andsolid solubility limit increase with temperature Withthis in mind MacDonald and Eagar65 suggested thisproblem could be overcome through the use of theeffective diffusion coefficient proposed by ShewrnonIt is worth pointing out that this diffusion problemis easily solved using numerical techniquesi

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T=1423K K=22~unls

T=1388K K=03~ms500

400

300

c~ 200S0 100is

200 400 600 1000800

Holding time S

4 Relation between the dissolution parameterP and holding time at various holdingtemperatures (during TLP bonding of nickelbase superalloy material MBF-007 using andMBF-80 filler metal) (after Ref 31)

Dissolution stageNo analytical solution is available for stage 11-1 ofTLP bonding (base metal dissolution during theheating cycle from the eutectic temperature to thebonding temperature) since the solute concentrationsCLa and CaL at the interface vary with temperatureIn this connection only limited work has been carriedout to determine the process kinetics during stage 11-2of the TLP bonding process (base metal dissolutionat the bonding temperature)

Nakao et al examined isothermal dissolutionduring TLP bonding (stage 11-2 in Fig2) andbased on the Nernst-Brunner theory (see Ref 66)developed a dissolution parameter P

[~(~+Ph)JP = Kt = h In h( ) (10)P ~-~

where ~ is the width of base metal dissolved attime t ~ the equilibrium (saturated) dissolutionwidth p the ratio of the densities of the liquid andsolid phases h half of the initial liquid width andK a constant During TLP bonding of nickel basesuperalloy base material using Ni-155 wt-Cr fillermetal this dissolution parameter was related linearlyto holding time (see Fig 4) Nakao et al31 thereforeconcluded that the Nernst-Brunner theory could beused to explain dissolution during TLP bondingHowever Nakagawa et al66 pointed out that the keyassumptions of a thin boundary layer and a largebulk liquid region in the Nernst-Brunner theory didnot apply during TLP bonding and solute diffusioninto the base metal was neglected in the calculationsmade by Nakao et al It is worth noting that thewidth of the liquid layer was held constant duringthe TLP bonding experiments carried out by Nakaoet al When however silver base metal was TLPbonded using copper filler metal the liquid widthformed at the bonding temperature was not heldconstant and a non-linear relation was observedbetween the dissolution parameter and holdingtime8bull66

Lesoult 70 applied a square root law solution toestimate the time required for interlayer melting whena pure metal interlayer was used in a binary eutecticalloy system However MacDonald and Eagar65 havepointed out that Lesoults assumption that the final

Zhou et a Modelling of transient liquid phase bonding 185

width of the liquid zone equals the interlayer width(when melting of the interlayer is completed) is doubt-ful since base metal dissolution occurs when theinterlayer melts In this connection Liu et al76 devel-oped a model that accounts for base metal meltingduring liquid formation They used a general errorfunction solution to describe the solute distributionin the liquid zone when modelling stage 11-2a (thedissolution stage when three metallurgical phasesexist) and assumed that there was no solute diffusioninto the base metal These assumptions are question-able The error function solution is really only appli-cable for infinite or semi-infinite media and the liquidzone is very thin in comparison with the solutediffusion rate in the liquid during TLP bondingFurthermore solute diffusion into the base metal canaffect the process kinetics during stage II of TLPbonding

In summary analytical methods are difficult toapply during modelling of the dissolution stage duringTLP bonding It is shown in the section Comparisonof numerical and analytical output below thatnumerical methods are more eflfective when solvingthis particular problemIsothermal solidificationSolute distribution in the liquid can be considereduniform during the isothermal solidification stage ofTLP bonding6667and therefore solute diffusion inthe liquid can be ignored In addition the base metalcan be assumed to be semi-infinite because solutediffusion in the solid is relatively slow The isothermalsolidification stage during TLP bonding can beanalytically modelled as a single phase diffusioncontrolled moving interface problem (see Fig 5)

Lynch et al77 first linked interface movement withthe mass balance at the liquidsolid interface butfailed to provide an analytical solution for thisproblem Tuah-Poku et al8 proposed a method forestimating the completion time required to the iso-thermal solidification stage of TLP bonding In theirtreatment the problem was simplified to a half semi-infinite base metal with a surface on which the soluteconcentration was maintained at CaL Consequentlyan error function solution can be employed todescribe the solute distribution in the base metal

C(y t) = CaL + CaL err[(4~)12J (11)

where CaL is the solute concentration in solid atthe interface The total solute amount M that hasentered the base metal at time t can be calculatedfrom the relation

(Dst)12

Mt = 2CaL ---- bull (12)

If the amount of solute diffused into the base metalduring the heating and dissolution stages is ignoredthe total amount of solute diffused into the base metalequals the original solute content of the filler metal ie

(Dst)12

CF ~ = 4CaL ---- bullbull (13)

where CF is the solute content in the filler metal and

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186 Zhou et al Modelling of transient liquid phase bonding

C

oo t=o-t

IIIIII

CM

CLa

Cal

o y(t) Wmax2

Centre l1ne ofJo1nt

5 Concentration profile along specimen lengthduring isothermal solidification stage

VJiO the initial width of the filler metal The completiontime for isothermal solidification can therefore becalculated using the relation

n (CFWO)2ts=- - (14)16Ds CcxL

Similar treatments of this problem have been reportedby Ikawa et al22 Nakao et al31 and Onzawa et al49

A more rigorous treatment of the problem waspresented by Lesoult His derivation is almost ident-ical with that described by Danckwerts when hederived a general solution for unsteady state linearheat conduction or diffusion A general error functionsolution is assumed in the solid phase

Cs(y t) = Ai + A2 erfL (Dt) 12] (15)

where A1 and A2 are constants determined by thespecific boundary conditions When y ~ 00

Cs(oo t) = A1 + A2 = CM bull bull bull bull bull bull bull (16)

and at the moving interface

Cs(yen t) = Ai + A2 err[ 2(D~)12] = CaL (17)

Since equation (17) has to be satisfied for all valuesof t Y must be proportional to t12 ie

Y = K( 4Dst)12 (18)

where K is a constant The mass balance at the

International Materials Reviews 1995 Vol 40 No5

interface produces the relation

(CLcx - CcxL) dYd(t) = Ds(iJC~(Y t))t Y y=Y(t)

Solving equations (15) and (19) leads to

K(1 + erf K)n12 CcxL - CM

exp(-K2) CLa-CcxL

(19)

(20)

y

Similar solutions were derived by Sakamoto et al79and Ramirez and Liu80 It is worth noting that in thederivations of Lesoult and Liu et al76 the termexp( - K2) is higher than the fraction indicated inequation (20) Also Le Blanc and Mevrel used anidentical derivation procedure to obtain a formulationwhich accounts for boron consumption as a result ofboride formation during TLP bonding of nickel basesuperalloy base material

The completion time for isothermal solidificationduring TLP bonding can be calculated using therelation

W~axt ----s - 16K2Ds

(21)

where Wmax is the maximum liquid width calculatedusing the mass balance method

Derivation of equation (14) depends on the assump-tion that the solute distribution is given by equa-tion (11) and this is only exact for a stationaryinterface Since the liquidsolid interface migratesduring TLP bonding it is important to determine theconditions when this assumption can be appliedSolving equations (15)-(17) we obtain

CM - CaL CM - CaLCS(Y t) = CM- 1- erf(K) + 1- erf(K)

X err[ 2 (Dt)12 ] (22)

K is the factor related to the solute distribution inequation (20) and therefore when K ~ 0 anderf(K) ~ 1 equation (22) becomes

Cs(Y t) = CL + (CM- Cd erf[ 2(Dt)12 ] (23)

This is identical to equations (3) and (11) It followsthat the solute distribution in the solid can becalculated using equation (11) when K is very small

Homogenisation stageEquation (8) was used by Ikawa et al22 to model thesolute distribution during homogenisation of TLPbonded nickel base superalloy material In their for-mulation h was half the maximum liquid width atthe end of the base metal dissolution period and Coequalled CLa The solute concentration attained itsmaximum value at the centreline of the specimen(x = 0) when

Cmax = C(O t) = CM + (Co - CM)

x err[ 4 (Dt)12 ] (24)

When examining the aluminium redistribution during

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Zhou et al Modelling of transient liquid phase bonding 187

90 ------------------

bull80 bullbullcP-

o bull0 70)(

c0bullbullbullc5

60

50 -J--------r-------r-------r---o 100 200

Holding time ks

bull experimental test resultscalculated results

6 Calculated and experimentally measuredaluminium concentrations at the joint centrelineduring homogenisation of TLP bonded nickelbase superalloy material using MBF-80filler metal at 1453K (after Ref 12) c isconcentration of aluminium at time t Cb isaluminium concentration in base metal

homogenisation of nickel base superalloy materialNakao et al31 observed close agreement between theresults calculated using equation (24) and the experi-mental values (for much of the homogenisationperiod) However there was a distinct differencebetween the analytical calculations and the experi-mental values during the early stages of the homo-genisation treatment (see Fig 6) Nakao et al12

suggested that this difference was due to a criticalassumption in the analytical results (that the alumin-ium concentration in the joint centreline was uniformat the beginning of the homogenisation period)

Zhou67 also used equation (24) to model the homo-genisation stage during TLP bonding In that studyh was half the filler metal thickness (~2) and Cothe initial solute concentration in the filler metal CFbull

This particular approach has the advantage that themaximum liquid width need not be calculated usingequation (24)

Numerical simulation of TLP bondingNakagawa et al66 modelled dissolution behaviourduring TLP bonding of Nickel 200 base metal usingNi-P and Ni-Cr-P filler metals This research con-firmed the critical effect that both the filler metalthickness and the heating rate between the filler metalmelting temperature and the bonding temperaturehad on the base metal dissolution process An explicitfinite difference method was employed to calculatesolute diffusion in liquid and solid phases and astepwise mechanical mass balance method wasused to determine solidliquid interface movementHowever the approach of Nakagawa et al hadinherent problems since the exact location of thesolidliquid interface could be determined using thestepwise mass balance technique and extremely long

20

15

10

05 0 Experimental- Calculated

o~ 0 - 3 10 - 2 10 - 1 1 00 10 1

2Dtl

300 7 Comparison of calculated and experimentalresults during TLP bonding of single crystalnickel (after Ref 67)

calculation times were required when the whole TLPbonding process was modelled

These problems were overcome by developing afully implicit finite difference model that simulatedthe TLP bonding process in a continuous mannerFigure 7 compares the calculated and experimentaltest results during TLP bonding of single crystalnickel The results are in excellent agreement and ashort computation time is required This numericalmodel output can be used to

(i) predict the completion times required fordissolution isothermal solidification andhomogenisation

(ii) predict the solute concentration distributionboth in the solid phase and in the liquid phasethroughout TLP bonding (see Figs 8-10)these results cannot be calculated usinganalytical methods

(iii) select the optimum filler metal (chemistrythickness) and bonding temperature which willensure that the TLP bonding operation iscompleted in a reasonable time frame

(iv) examine diffusion controlled two phasemoving interface problems other than TLPbonding for example the fully implicit finitedifference model has been applied to the solu-tion treatment of thin multilayer a and f3 brassdiffusion couples81-83

Figure 11 shows the influence of changes in the equi-librium solute content in solid at the bonding tem-perature CaL on the completion times required forbase metal dissolution isothermal solidification andhomogenisation CaL can be varied by altering thesolute content in the filler metal or by changing thebonding temperature Increasing the CaL valuedecreases the time required for completion of iso-thermal solidification and also the time required forhomogenisation Thus the time required for com-pletion of the entire TLP bonding process (dissolu-tion isothermal solidification and homogenisation)will not be affected by an increase in the CaL value

It has been suggested that selection of the optimumbonding temperature during TLP bonding dependson the interplay of increasing solute diffusivity anddecreasing equilibrium solute concentration in the

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188 Zhou et al Modelling of transient liquid phase bonding

25 ----------------- 20cac Uquid Solid0 bullbull 15e bullbullbull bullc bullbullbullbullBc 10 ------ --~---I0 I() I

oS II

5 i 0165I

(5 Time=O s 336 s() I

I

---00 10 20 30 40 50

Distance from liquid centreline JU11

8 Change in solute concentration profile duringbase metal dissolution stage (after Ref 68)

solid However this idea is based wholly on aconsideration of the isothermal solidification stageduring TLP bonding the critical homogenisationstage during TLP bonding is not taken into accountSince variation of the equilibrium solute concen-tration in the solid has no influence on the timerequired for completion of the whole TLP bondingoperation the highest possible bonding temperatureshould be selected during joining This will increasethe rate of solute diffusion into the base metal Inpractice the maximum bonding temperatures will belimited by the need for compatibility with the heattreatment requirements of the base materialComparison of numerical and analytical outputIn the analytical approach it -is assumed that move-ment of the solidliquid interface Y during isothermalsolidification obeys a parabolic law

Y = 2f3(t12) = 2K(Dst)12 (25)

where the constant f3 defines the rate of interfacemovement During numerical calculations f3 isevaluated using the relation

f3 = ~ = (t)12 dY (26)2 d(t12) dt

The f3 parameter is a particularly useful means of

15 I-

10 bullbullbullbull-- bullbullbullbull---r--7-----I I Liquid e Solidimiddot

1900 5 Tlme=3365

i --- _--_1

5 -3200 s

10 4020 30

Distance from liquid centreline JU11

9 Change in solute concentration profile duringisothermal solidification stage (after Ref 68)

International Materials Reviews 1995 Vol 40 No5

fI 10 Time=7000 scac0ca bullbullbullbullbullbullbullbulla-C 9200 S bullbullbullbullbullbullB 05c0()

oS(5()

000 200 400 600 800

Distance from joint centreline JU11

10 Change in solute concentration profile duringhomogenisation stage (after Ref 68)

comparing the output of analytical and numericalcalculations Figure 12 shows the variation of thef3 parameter during base metal dissolution and sub-sequent isothermal solidification for a hypotheticalTLP bonding situation The value of f3decreasesprogressively and approaches zero when base metaldissolution is almost completed In fact f3 decreasesto a value of -0185 urn S-12 and this is identicalto the analytical solution (equation (20)) Thus theisothermal solidification stage during TLP bondingcan be readily estimated using an analytical solutionfor example Fig 13 shows the results when nickelbase material is TLP bonded using Ni-B filler metalIn direct contrast base metal dissolution depends ona non-parabolic relation and no single value of f3 cancharacterise solidliquid interface movement

The remarkable difference between the output ofnumerical and analytical solutions during base metaldissolution and isothermal solidification occurs be-cause the analytical calculations assume that solutediffusion occurs wholly in solid state and that liquidphase is not formed during the joining operation

o Dissolution ~Ifla Homogenisation

105 -----------------

Solidificationbull Total

en 103cDEi= 102

101

100

50200

Cal al

11 Effect of solidus composition at bondingtemperature CaL on completion times requiredfor dissolution isothermal solidification andhomogenisation (after Ref 68)

100

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10

8

0 6~1 4rS

2

0

-210- 1 10deg0- 2

Numerical

Analytical

Eo+~~ Isothermal solidification

Bonding time s

12 Comparison between numerical and analyticalcalculated p values where the constant pdefines the rate of interface movement (afterRef 67)

Figure 14 compares the results of analytical andnumerical calculations of the homogenisation stageduring TLP bonding Numerical and analyticalresults are in close agreement during part of thehomogenisation stage although differences are appar-ent early and late in the processing cycle The devi-ation between the numerical and analytical resultslate in the homogenisation stage (in Fig 14) resultsfrom the semi-infinite test specimen assumption inthe analytical calculations

It can be concluded therefore that simple analyti-cal solutions can be used to estimate the completiontimes for isothermal solidification and for estimatingthe solute concentration at the joint centreline Itshould be noted that the error function required inthe analytical solution must be found by solvingequation (20) numerically Also direct parameterinput into a numerical program can permit readyprediction of the completion times for dissolutionisothermal solidification or homogenisation (for anychosen bonding temperature and filler metal-basemetal combination)

Modelling of real systemsMuch research to date on modelling of TLP bond-ing has involved two aspects The first aspect is

e 30=1-c~ 20i~u 10Q)

w

00

Bonding temperature K

bull 1393bull 1433

bull 1473

40Holding time S

13 Relation between holding time at differentbonding temperatures and eutectic widthduring TLP bonding of nickel base materialusing Ni-B filler metal (after Ref 31)

20 60 80

Zhou et al Modelling of transient liquid phase bonding 189

Isothermalsolidification I Homogenisation

gtltDissolution-1lt

AnaJytimiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot bullNumerical bull

Bonding time s

14 Calculated changes in solute concentration atspecimen centreline during TLP bonding(after Ref 68)

one-dimensional modelling only However whenTuah-Poku et al8 compared their analyticallycalculated and experimental completion times forisothermal solidification during TLP bonding of silverusing copper filler metal they observed a markeddifference in these results They suggested that thisdifference might be due to liquid penetration at grainboundaries in the base metal (this increased the solidiliquid interfacial area for solute diffusion) This effecthas been confirmed in research by Kokawa et al85

and Saida et al86 (Fig 15) With this in mind onedimensional modelling results are really only usefulwhen single crystal or very coarse grained polycrystalsubstrates are joined using TLP bonding

The second aspect is the solution of a two phasemoving interface problem in a simple binary alloysystem eg pure nickel base material bonded using aNi-P interlayer The implicit assumptions are thatlocal equilibrium exists at the migrating interfaceduring TLP bonding and that formation of an inter-mediate phase does not occur during isothermalsolidification However this is an approximation sincelocal equilibrium is generally not attained at the solidiliquid interface Furthermore direct experimentalevidence has been presented by Gale and Wallach64

E 301

- ~C1) 0gt-

20 -~uC1)-sC1)

~ 10 -0

s-C~

0 0

A Single-crystal+ Coarse grain (d=34mm)

o Fine grain high purity (d=33JUTl)

A 0 Fine grain low purity (d=40JUTl)+o

o A+o

J J

300 400200

Holdingtime ~s

15 TLP bonding of nickel base metals withdifferent grain sizes d is mean grain sizebefore TLP bonding (after Refs 85 86)

100

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190 Zhou et at Modelling of transient liquid phase bonding

L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

International Materials Reviews 1995 Vol 40 No5

L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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30

~ 20

5

~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

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4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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T=1423K K=22~unls

T=1388K K=03~ms500

400

300

c~ 200S0 100is

200 400 600 1000800

Holding time S

4 Relation between the dissolution parameterP and holding time at various holdingtemperatures (during TLP bonding of nickelbase superalloy material MBF-007 using andMBF-80 filler metal) (after Ref 31)

Dissolution stageNo analytical solution is available for stage 11-1 ofTLP bonding (base metal dissolution during theheating cycle from the eutectic temperature to thebonding temperature) since the solute concentrationsCLa and CaL at the interface vary with temperatureIn this connection only limited work has been carriedout to determine the process kinetics during stage 11-2of the TLP bonding process (base metal dissolutionat the bonding temperature)

Nakao et al examined isothermal dissolutionduring TLP bonding (stage 11-2 in Fig2) andbased on the Nernst-Brunner theory (see Ref 66)developed a dissolution parameter P

[~(~+Ph)JP = Kt = h In h( ) (10)P ~-~

where ~ is the width of base metal dissolved attime t ~ the equilibrium (saturated) dissolutionwidth p the ratio of the densities of the liquid andsolid phases h half of the initial liquid width andK a constant During TLP bonding of nickel basesuperalloy base material using Ni-155 wt-Cr fillermetal this dissolution parameter was related linearlyto holding time (see Fig 4) Nakao et al31 thereforeconcluded that the Nernst-Brunner theory could beused to explain dissolution during TLP bondingHowever Nakagawa et al66 pointed out that the keyassumptions of a thin boundary layer and a largebulk liquid region in the Nernst-Brunner theory didnot apply during TLP bonding and solute diffusioninto the base metal was neglected in the calculationsmade by Nakao et al It is worth noting that thewidth of the liquid layer was held constant duringthe TLP bonding experiments carried out by Nakaoet al When however silver base metal was TLPbonded using copper filler metal the liquid widthformed at the bonding temperature was not heldconstant and a non-linear relation was observedbetween the dissolution parameter and holdingtime8bull66

Lesoult 70 applied a square root law solution toestimate the time required for interlayer melting whena pure metal interlayer was used in a binary eutecticalloy system However MacDonald and Eagar65 havepointed out that Lesoults assumption that the final

Zhou et a Modelling of transient liquid phase bonding 185

width of the liquid zone equals the interlayer width(when melting of the interlayer is completed) is doubt-ful since base metal dissolution occurs when theinterlayer melts In this connection Liu et al76 devel-oped a model that accounts for base metal meltingduring liquid formation They used a general errorfunction solution to describe the solute distributionin the liquid zone when modelling stage 11-2a (thedissolution stage when three metallurgical phasesexist) and assumed that there was no solute diffusioninto the base metal These assumptions are question-able The error function solution is really only appli-cable for infinite or semi-infinite media and the liquidzone is very thin in comparison with the solutediffusion rate in the liquid during TLP bondingFurthermore solute diffusion into the base metal canaffect the process kinetics during stage II of TLPbonding

In summary analytical methods are difficult toapply during modelling of the dissolution stage duringTLP bonding It is shown in the section Comparisonof numerical and analytical output below thatnumerical methods are more eflfective when solvingthis particular problemIsothermal solidificationSolute distribution in the liquid can be considereduniform during the isothermal solidification stage ofTLP bonding6667and therefore solute diffusion inthe liquid can be ignored In addition the base metalcan be assumed to be semi-infinite because solutediffusion in the solid is relatively slow The isothermalsolidification stage during TLP bonding can beanalytically modelled as a single phase diffusioncontrolled moving interface problem (see Fig 5)

Lynch et al77 first linked interface movement withthe mass balance at the liquidsolid interface butfailed to provide an analytical solution for thisproblem Tuah-Poku et al8 proposed a method forestimating the completion time required to the iso-thermal solidification stage of TLP bonding In theirtreatment the problem was simplified to a half semi-infinite base metal with a surface on which the soluteconcentration was maintained at CaL Consequentlyan error function solution can be employed todescribe the solute distribution in the base metal

C(y t) = CaL + CaL err[(4~)12J (11)

where CaL is the solute concentration in solid atthe interface The total solute amount M that hasentered the base metal at time t can be calculatedfrom the relation

(Dst)12

Mt = 2CaL ---- bull (12)

If the amount of solute diffused into the base metalduring the heating and dissolution stages is ignoredthe total amount of solute diffused into the base metalequals the original solute content of the filler metal ie

(Dst)12

CF ~ = 4CaL ---- bullbull (13)

where CF is the solute content in the filler metal and

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186 Zhou et al Modelling of transient liquid phase bonding

C

oo t=o-t

IIIIII

CM

CLa

Cal

o y(t) Wmax2

Centre l1ne ofJo1nt

5 Concentration profile along specimen lengthduring isothermal solidification stage

VJiO the initial width of the filler metal The completiontime for isothermal solidification can therefore becalculated using the relation

n (CFWO)2ts=- - (14)16Ds CcxL

Similar treatments of this problem have been reportedby Ikawa et al22 Nakao et al31 and Onzawa et al49

A more rigorous treatment of the problem waspresented by Lesoult His derivation is almost ident-ical with that described by Danckwerts when hederived a general solution for unsteady state linearheat conduction or diffusion A general error functionsolution is assumed in the solid phase

Cs(y t) = Ai + A2 erfL (Dt) 12] (15)

where A1 and A2 are constants determined by thespecific boundary conditions When y ~ 00

Cs(oo t) = A1 + A2 = CM bull bull bull bull bull bull bull (16)

and at the moving interface

Cs(yen t) = Ai + A2 err[ 2(D~)12] = CaL (17)

Since equation (17) has to be satisfied for all valuesof t Y must be proportional to t12 ie

Y = K( 4Dst)12 (18)

where K is a constant The mass balance at the

International Materials Reviews 1995 Vol 40 No5

interface produces the relation

(CLcx - CcxL) dYd(t) = Ds(iJC~(Y t))t Y y=Y(t)

Solving equations (15) and (19) leads to

K(1 + erf K)n12 CcxL - CM

exp(-K2) CLa-CcxL

(19)

(20)

y

Similar solutions were derived by Sakamoto et al79and Ramirez and Liu80 It is worth noting that in thederivations of Lesoult and Liu et al76 the termexp( - K2) is higher than the fraction indicated inequation (20) Also Le Blanc and Mevrel used anidentical derivation procedure to obtain a formulationwhich accounts for boron consumption as a result ofboride formation during TLP bonding of nickel basesuperalloy base material

The completion time for isothermal solidificationduring TLP bonding can be calculated using therelation

W~axt ----s - 16K2Ds

(21)

where Wmax is the maximum liquid width calculatedusing the mass balance method

Derivation of equation (14) depends on the assump-tion that the solute distribution is given by equa-tion (11) and this is only exact for a stationaryinterface Since the liquidsolid interface migratesduring TLP bonding it is important to determine theconditions when this assumption can be appliedSolving equations (15)-(17) we obtain

CM - CaL CM - CaLCS(Y t) = CM- 1- erf(K) + 1- erf(K)

X err[ 2 (Dt)12 ] (22)

K is the factor related to the solute distribution inequation (20) and therefore when K ~ 0 anderf(K) ~ 1 equation (22) becomes

Cs(Y t) = CL + (CM- Cd erf[ 2(Dt)12 ] (23)

This is identical to equations (3) and (11) It followsthat the solute distribution in the solid can becalculated using equation (11) when K is very small

Homogenisation stageEquation (8) was used by Ikawa et al22 to model thesolute distribution during homogenisation of TLPbonded nickel base superalloy material In their for-mulation h was half the maximum liquid width atthe end of the base metal dissolution period and Coequalled CLa The solute concentration attained itsmaximum value at the centreline of the specimen(x = 0) when

Cmax = C(O t) = CM + (Co - CM)

x err[ 4 (Dt)12 ] (24)

When examining the aluminium redistribution during

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90 ------------------

bull80 bullbullcP-

o bull0 70)(

c0bullbullbullc5

60

50 -J--------r-------r-------r---o 100 200

Holding time ks

bull experimental test resultscalculated results

6 Calculated and experimentally measuredaluminium concentrations at the joint centrelineduring homogenisation of TLP bonded nickelbase superalloy material using MBF-80filler metal at 1453K (after Ref 12) c isconcentration of aluminium at time t Cb isaluminium concentration in base metal

homogenisation of nickel base superalloy materialNakao et al31 observed close agreement between theresults calculated using equation (24) and the experi-mental values (for much of the homogenisationperiod) However there was a distinct differencebetween the analytical calculations and the experi-mental values during the early stages of the homo-genisation treatment (see Fig 6) Nakao et al12

suggested that this difference was due to a criticalassumption in the analytical results (that the alumin-ium concentration in the joint centreline was uniformat the beginning of the homogenisation period)

Zhou67 also used equation (24) to model the homo-genisation stage during TLP bonding In that studyh was half the filler metal thickness (~2) and Cothe initial solute concentration in the filler metal CFbull

This particular approach has the advantage that themaximum liquid width need not be calculated usingequation (24)

Numerical simulation of TLP bondingNakagawa et al66 modelled dissolution behaviourduring TLP bonding of Nickel 200 base metal usingNi-P and Ni-Cr-P filler metals This research con-firmed the critical effect that both the filler metalthickness and the heating rate between the filler metalmelting temperature and the bonding temperaturehad on the base metal dissolution process An explicitfinite difference method was employed to calculatesolute diffusion in liquid and solid phases and astepwise mechanical mass balance method wasused to determine solidliquid interface movementHowever the approach of Nakagawa et al hadinherent problems since the exact location of thesolidliquid interface could be determined using thestepwise mass balance technique and extremely long

20

15

10

05 0 Experimental- Calculated

o~ 0 - 3 10 - 2 10 - 1 1 00 10 1

2Dtl

300 7 Comparison of calculated and experimentalresults during TLP bonding of single crystalnickel (after Ref 67)

calculation times were required when the whole TLPbonding process was modelled

These problems were overcome by developing afully implicit finite difference model that simulatedthe TLP bonding process in a continuous mannerFigure 7 compares the calculated and experimentaltest results during TLP bonding of single crystalnickel The results are in excellent agreement and ashort computation time is required This numericalmodel output can be used to

(i) predict the completion times required fordissolution isothermal solidification andhomogenisation

(ii) predict the solute concentration distributionboth in the solid phase and in the liquid phasethroughout TLP bonding (see Figs 8-10)these results cannot be calculated usinganalytical methods

(iii) select the optimum filler metal (chemistrythickness) and bonding temperature which willensure that the TLP bonding operation iscompleted in a reasonable time frame

(iv) examine diffusion controlled two phasemoving interface problems other than TLPbonding for example the fully implicit finitedifference model has been applied to the solu-tion treatment of thin multilayer a and f3 brassdiffusion couples81-83

Figure 11 shows the influence of changes in the equi-librium solute content in solid at the bonding tem-perature CaL on the completion times required forbase metal dissolution isothermal solidification andhomogenisation CaL can be varied by altering thesolute content in the filler metal or by changing thebonding temperature Increasing the CaL valuedecreases the time required for completion of iso-thermal solidification and also the time required forhomogenisation Thus the time required for com-pletion of the entire TLP bonding process (dissolu-tion isothermal solidification and homogenisation)will not be affected by an increase in the CaL value

It has been suggested that selection of the optimumbonding temperature during TLP bonding dependson the interplay of increasing solute diffusivity anddecreasing equilibrium solute concentration in the

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25 ----------------- 20cac Uquid Solid0 bullbull 15e bullbullbull bullc bullbullbullbullBc 10 ------ --~---I0 I() I

oS II

5 i 0165I

(5 Time=O s 336 s() I

I

---00 10 20 30 40 50

Distance from liquid centreline JU11

8 Change in solute concentration profile duringbase metal dissolution stage (after Ref 68)

solid However this idea is based wholly on aconsideration of the isothermal solidification stageduring TLP bonding the critical homogenisationstage during TLP bonding is not taken into accountSince variation of the equilibrium solute concen-tration in the solid has no influence on the timerequired for completion of the whole TLP bondingoperation the highest possible bonding temperatureshould be selected during joining This will increasethe rate of solute diffusion into the base metal Inpractice the maximum bonding temperatures will belimited by the need for compatibility with the heattreatment requirements of the base materialComparison of numerical and analytical outputIn the analytical approach it -is assumed that move-ment of the solidliquid interface Y during isothermalsolidification obeys a parabolic law

Y = 2f3(t12) = 2K(Dst)12 (25)

where the constant f3 defines the rate of interfacemovement During numerical calculations f3 isevaluated using the relation

f3 = ~ = (t)12 dY (26)2 d(t12) dt

The f3 parameter is a particularly useful means of

15 I-

10 bullbullbullbull-- bullbullbullbull---r--7-----I I Liquid e Solidimiddot

1900 5 Tlme=3365

i --- _--_1

5 -3200 s

10 4020 30

Distance from liquid centreline JU11

9 Change in solute concentration profile duringisothermal solidification stage (after Ref 68)

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fI 10 Time=7000 scac0ca bullbullbullbullbullbullbullbulla-C 9200 S bullbullbullbullbullbullB 05c0()

oS(5()

000 200 400 600 800

Distance from joint centreline JU11

10 Change in solute concentration profile duringhomogenisation stage (after Ref 68)

comparing the output of analytical and numericalcalculations Figure 12 shows the variation of thef3 parameter during base metal dissolution and sub-sequent isothermal solidification for a hypotheticalTLP bonding situation The value of f3decreasesprogressively and approaches zero when base metaldissolution is almost completed In fact f3 decreasesto a value of -0185 urn S-12 and this is identicalto the analytical solution (equation (20)) Thus theisothermal solidification stage during TLP bondingcan be readily estimated using an analytical solutionfor example Fig 13 shows the results when nickelbase material is TLP bonded using Ni-B filler metalIn direct contrast base metal dissolution depends ona non-parabolic relation and no single value of f3 cancharacterise solidliquid interface movement

The remarkable difference between the output ofnumerical and analytical solutions during base metaldissolution and isothermal solidification occurs be-cause the analytical calculations assume that solutediffusion occurs wholly in solid state and that liquidphase is not formed during the joining operation

o Dissolution ~Ifla Homogenisation

105 -----------------

Solidificationbull Total

en 103cDEi= 102

101

100

50200

Cal al

11 Effect of solidus composition at bondingtemperature CaL on completion times requiredfor dissolution isothermal solidification andhomogenisation (after Ref 68)

100

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10

8

0 6~1 4rS

2

0

-210- 1 10deg0- 2

Numerical

Analytical

Eo+~~ Isothermal solidification

Bonding time s

12 Comparison between numerical and analyticalcalculated p values where the constant pdefines the rate of interface movement (afterRef 67)

Figure 14 compares the results of analytical andnumerical calculations of the homogenisation stageduring TLP bonding Numerical and analyticalresults are in close agreement during part of thehomogenisation stage although differences are appar-ent early and late in the processing cycle The devi-ation between the numerical and analytical resultslate in the homogenisation stage (in Fig 14) resultsfrom the semi-infinite test specimen assumption inthe analytical calculations

It can be concluded therefore that simple analyti-cal solutions can be used to estimate the completiontimes for isothermal solidification and for estimatingthe solute concentration at the joint centreline Itshould be noted that the error function required inthe analytical solution must be found by solvingequation (20) numerically Also direct parameterinput into a numerical program can permit readyprediction of the completion times for dissolutionisothermal solidification or homogenisation (for anychosen bonding temperature and filler metal-basemetal combination)

Modelling of real systemsMuch research to date on modelling of TLP bond-ing has involved two aspects The first aspect is

e 30=1-c~ 20i~u 10Q)

w

00

Bonding temperature K

bull 1393bull 1433

bull 1473

40Holding time S

13 Relation between holding time at differentbonding temperatures and eutectic widthduring TLP bonding of nickel base materialusing Ni-B filler metal (after Ref 31)

20 60 80

Zhou et al Modelling of transient liquid phase bonding 189

Isothermalsolidification I Homogenisation

gtltDissolution-1lt

AnaJytimiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot bullNumerical bull

Bonding time s

14 Calculated changes in solute concentration atspecimen centreline during TLP bonding(after Ref 68)

one-dimensional modelling only However whenTuah-Poku et al8 compared their analyticallycalculated and experimental completion times forisothermal solidification during TLP bonding of silverusing copper filler metal they observed a markeddifference in these results They suggested that thisdifference might be due to liquid penetration at grainboundaries in the base metal (this increased the solidiliquid interfacial area for solute diffusion) This effecthas been confirmed in research by Kokawa et al85

and Saida et al86 (Fig 15) With this in mind onedimensional modelling results are really only usefulwhen single crystal or very coarse grained polycrystalsubstrates are joined using TLP bonding

The second aspect is the solution of a two phasemoving interface problem in a simple binary alloysystem eg pure nickel base material bonded using aNi-P interlayer The implicit assumptions are thatlocal equilibrium exists at the migrating interfaceduring TLP bonding and that formation of an inter-mediate phase does not occur during isothermalsolidification However this is an approximation sincelocal equilibrium is generally not attained at the solidiliquid interface Furthermore direct experimentalevidence has been presented by Gale and Wallach64

E 301

- ~C1) 0gt-

20 -~uC1)-sC1)

~ 10 -0

s-C~

0 0

A Single-crystal+ Coarse grain (d=34mm)

o Fine grain high purity (d=33JUTl)

A 0 Fine grain low purity (d=40JUTl)+o

o A+o

J J

300 400200

Holdingtime ~s

15 TLP bonding of nickel base metals withdifferent grain sizes d is mean grain sizebefore TLP bonding (after Refs 85 86)

100

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190 Zhou et at Modelling of transient liquid phase bonding

L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

International Materials Reviews 1995 Vol 40 No5

L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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30

~ 20

5

~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

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236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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186 Zhou et al Modelling of transient liquid phase bonding

C

oo t=o-t

IIIIII

CM

CLa

Cal

o y(t) Wmax2

Centre l1ne ofJo1nt

5 Concentration profile along specimen lengthduring isothermal solidification stage

VJiO the initial width of the filler metal The completiontime for isothermal solidification can therefore becalculated using the relation

n (CFWO)2ts=- - (14)16Ds CcxL

Similar treatments of this problem have been reportedby Ikawa et al22 Nakao et al31 and Onzawa et al49

A more rigorous treatment of the problem waspresented by Lesoult His derivation is almost ident-ical with that described by Danckwerts when hederived a general solution for unsteady state linearheat conduction or diffusion A general error functionsolution is assumed in the solid phase

Cs(y t) = Ai + A2 erfL (Dt) 12] (15)

where A1 and A2 are constants determined by thespecific boundary conditions When y ~ 00

Cs(oo t) = A1 + A2 = CM bull bull bull bull bull bull bull (16)

and at the moving interface

Cs(yen t) = Ai + A2 err[ 2(D~)12] = CaL (17)

Since equation (17) has to be satisfied for all valuesof t Y must be proportional to t12 ie

Y = K( 4Dst)12 (18)

where K is a constant The mass balance at the

International Materials Reviews 1995 Vol 40 No5

interface produces the relation

(CLcx - CcxL) dYd(t) = Ds(iJC~(Y t))t Y y=Y(t)

Solving equations (15) and (19) leads to

K(1 + erf K)n12 CcxL - CM

exp(-K2) CLa-CcxL

(19)

(20)

y

Similar solutions were derived by Sakamoto et al79and Ramirez and Liu80 It is worth noting that in thederivations of Lesoult and Liu et al76 the termexp( - K2) is higher than the fraction indicated inequation (20) Also Le Blanc and Mevrel used anidentical derivation procedure to obtain a formulationwhich accounts for boron consumption as a result ofboride formation during TLP bonding of nickel basesuperalloy base material

The completion time for isothermal solidificationduring TLP bonding can be calculated using therelation

W~axt ----s - 16K2Ds

(21)

where Wmax is the maximum liquid width calculatedusing the mass balance method

Derivation of equation (14) depends on the assump-tion that the solute distribution is given by equa-tion (11) and this is only exact for a stationaryinterface Since the liquidsolid interface migratesduring TLP bonding it is important to determine theconditions when this assumption can be appliedSolving equations (15)-(17) we obtain

CM - CaL CM - CaLCS(Y t) = CM- 1- erf(K) + 1- erf(K)

X err[ 2 (Dt)12 ] (22)

K is the factor related to the solute distribution inequation (20) and therefore when K ~ 0 anderf(K) ~ 1 equation (22) becomes

Cs(Y t) = CL + (CM- Cd erf[ 2(Dt)12 ] (23)

This is identical to equations (3) and (11) It followsthat the solute distribution in the solid can becalculated using equation (11) when K is very small

Homogenisation stageEquation (8) was used by Ikawa et al22 to model thesolute distribution during homogenisation of TLPbonded nickel base superalloy material In their for-mulation h was half the maximum liquid width atthe end of the base metal dissolution period and Coequalled CLa The solute concentration attained itsmaximum value at the centreline of the specimen(x = 0) when

Cmax = C(O t) = CM + (Co - CM)

x err[ 4 (Dt)12 ] (24)

When examining the aluminium redistribution during

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Zhou et al Modelling of transient liquid phase bonding 187

90 ------------------

bull80 bullbullcP-

o bull0 70)(

c0bullbullbullc5

60

50 -J--------r-------r-------r---o 100 200

Holding time ks

bull experimental test resultscalculated results

6 Calculated and experimentally measuredaluminium concentrations at the joint centrelineduring homogenisation of TLP bonded nickelbase superalloy material using MBF-80filler metal at 1453K (after Ref 12) c isconcentration of aluminium at time t Cb isaluminium concentration in base metal

homogenisation of nickel base superalloy materialNakao et al31 observed close agreement between theresults calculated using equation (24) and the experi-mental values (for much of the homogenisationperiod) However there was a distinct differencebetween the analytical calculations and the experi-mental values during the early stages of the homo-genisation treatment (see Fig 6) Nakao et al12

suggested that this difference was due to a criticalassumption in the analytical results (that the alumin-ium concentration in the joint centreline was uniformat the beginning of the homogenisation period)

Zhou67 also used equation (24) to model the homo-genisation stage during TLP bonding In that studyh was half the filler metal thickness (~2) and Cothe initial solute concentration in the filler metal CFbull

This particular approach has the advantage that themaximum liquid width need not be calculated usingequation (24)

Numerical simulation of TLP bondingNakagawa et al66 modelled dissolution behaviourduring TLP bonding of Nickel 200 base metal usingNi-P and Ni-Cr-P filler metals This research con-firmed the critical effect that both the filler metalthickness and the heating rate between the filler metalmelting temperature and the bonding temperaturehad on the base metal dissolution process An explicitfinite difference method was employed to calculatesolute diffusion in liquid and solid phases and astepwise mechanical mass balance method wasused to determine solidliquid interface movementHowever the approach of Nakagawa et al hadinherent problems since the exact location of thesolidliquid interface could be determined using thestepwise mass balance technique and extremely long

20

15

10

05 0 Experimental- Calculated

o~ 0 - 3 10 - 2 10 - 1 1 00 10 1

2Dtl

300 7 Comparison of calculated and experimentalresults during TLP bonding of single crystalnickel (after Ref 67)

calculation times were required when the whole TLPbonding process was modelled

These problems were overcome by developing afully implicit finite difference model that simulatedthe TLP bonding process in a continuous mannerFigure 7 compares the calculated and experimentaltest results during TLP bonding of single crystalnickel The results are in excellent agreement and ashort computation time is required This numericalmodel output can be used to

(i) predict the completion times required fordissolution isothermal solidification andhomogenisation

(ii) predict the solute concentration distributionboth in the solid phase and in the liquid phasethroughout TLP bonding (see Figs 8-10)these results cannot be calculated usinganalytical methods

(iii) select the optimum filler metal (chemistrythickness) and bonding temperature which willensure that the TLP bonding operation iscompleted in a reasonable time frame

(iv) examine diffusion controlled two phasemoving interface problems other than TLPbonding for example the fully implicit finitedifference model has been applied to the solu-tion treatment of thin multilayer a and f3 brassdiffusion couples81-83

Figure 11 shows the influence of changes in the equi-librium solute content in solid at the bonding tem-perature CaL on the completion times required forbase metal dissolution isothermal solidification andhomogenisation CaL can be varied by altering thesolute content in the filler metal or by changing thebonding temperature Increasing the CaL valuedecreases the time required for completion of iso-thermal solidification and also the time required forhomogenisation Thus the time required for com-pletion of the entire TLP bonding process (dissolu-tion isothermal solidification and homogenisation)will not be affected by an increase in the CaL value

It has been suggested that selection of the optimumbonding temperature during TLP bonding dependson the interplay of increasing solute diffusivity anddecreasing equilibrium solute concentration in the

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188 Zhou et al Modelling of transient liquid phase bonding

25 ----------------- 20cac Uquid Solid0 bullbull 15e bullbullbull bullc bullbullbullbullBc 10 ------ --~---I0 I() I

oS II

5 i 0165I

(5 Time=O s 336 s() I

I

---00 10 20 30 40 50

Distance from liquid centreline JU11

8 Change in solute concentration profile duringbase metal dissolution stage (after Ref 68)

solid However this idea is based wholly on aconsideration of the isothermal solidification stageduring TLP bonding the critical homogenisationstage during TLP bonding is not taken into accountSince variation of the equilibrium solute concen-tration in the solid has no influence on the timerequired for completion of the whole TLP bondingoperation the highest possible bonding temperatureshould be selected during joining This will increasethe rate of solute diffusion into the base metal Inpractice the maximum bonding temperatures will belimited by the need for compatibility with the heattreatment requirements of the base materialComparison of numerical and analytical outputIn the analytical approach it -is assumed that move-ment of the solidliquid interface Y during isothermalsolidification obeys a parabolic law

Y = 2f3(t12) = 2K(Dst)12 (25)

where the constant f3 defines the rate of interfacemovement During numerical calculations f3 isevaluated using the relation

f3 = ~ = (t)12 dY (26)2 d(t12) dt

The f3 parameter is a particularly useful means of

15 I-

10 bullbullbullbull-- bullbullbullbull---r--7-----I I Liquid e Solidimiddot

1900 5 Tlme=3365

i --- _--_1

5 -3200 s

10 4020 30

Distance from liquid centreline JU11

9 Change in solute concentration profile duringisothermal solidification stage (after Ref 68)

International Materials Reviews 1995 Vol 40 No5

fI 10 Time=7000 scac0ca bullbullbullbullbullbullbullbulla-C 9200 S bullbullbullbullbullbullB 05c0()

oS(5()

000 200 400 600 800

Distance from joint centreline JU11

10 Change in solute concentration profile duringhomogenisation stage (after Ref 68)

comparing the output of analytical and numericalcalculations Figure 12 shows the variation of thef3 parameter during base metal dissolution and sub-sequent isothermal solidification for a hypotheticalTLP bonding situation The value of f3decreasesprogressively and approaches zero when base metaldissolution is almost completed In fact f3 decreasesto a value of -0185 urn S-12 and this is identicalto the analytical solution (equation (20)) Thus theisothermal solidification stage during TLP bondingcan be readily estimated using an analytical solutionfor example Fig 13 shows the results when nickelbase material is TLP bonded using Ni-B filler metalIn direct contrast base metal dissolution depends ona non-parabolic relation and no single value of f3 cancharacterise solidliquid interface movement

The remarkable difference between the output ofnumerical and analytical solutions during base metaldissolution and isothermal solidification occurs be-cause the analytical calculations assume that solutediffusion occurs wholly in solid state and that liquidphase is not formed during the joining operation

o Dissolution ~Ifla Homogenisation

105 -----------------

Solidificationbull Total

en 103cDEi= 102

101

100

50200

Cal al

11 Effect of solidus composition at bondingtemperature CaL on completion times requiredfor dissolution isothermal solidification andhomogenisation (after Ref 68)

100

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10

8

0 6~1 4rS

2

0

-210- 1 10deg0- 2

Numerical

Analytical

Eo+~~ Isothermal solidification

Bonding time s

12 Comparison between numerical and analyticalcalculated p values where the constant pdefines the rate of interface movement (afterRef 67)

Figure 14 compares the results of analytical andnumerical calculations of the homogenisation stageduring TLP bonding Numerical and analyticalresults are in close agreement during part of thehomogenisation stage although differences are appar-ent early and late in the processing cycle The devi-ation between the numerical and analytical resultslate in the homogenisation stage (in Fig 14) resultsfrom the semi-infinite test specimen assumption inthe analytical calculations

It can be concluded therefore that simple analyti-cal solutions can be used to estimate the completiontimes for isothermal solidification and for estimatingthe solute concentration at the joint centreline Itshould be noted that the error function required inthe analytical solution must be found by solvingequation (20) numerically Also direct parameterinput into a numerical program can permit readyprediction of the completion times for dissolutionisothermal solidification or homogenisation (for anychosen bonding temperature and filler metal-basemetal combination)

Modelling of real systemsMuch research to date on modelling of TLP bond-ing has involved two aspects The first aspect is

e 30=1-c~ 20i~u 10Q)

w

00

Bonding temperature K

bull 1393bull 1433

bull 1473

40Holding time S

13 Relation between holding time at differentbonding temperatures and eutectic widthduring TLP bonding of nickel base materialusing Ni-B filler metal (after Ref 31)

20 60 80

Zhou et al Modelling of transient liquid phase bonding 189

Isothermalsolidification I Homogenisation

gtltDissolution-1lt

AnaJytimiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot bullNumerical bull

Bonding time s

14 Calculated changes in solute concentration atspecimen centreline during TLP bonding(after Ref 68)

one-dimensional modelling only However whenTuah-Poku et al8 compared their analyticallycalculated and experimental completion times forisothermal solidification during TLP bonding of silverusing copper filler metal they observed a markeddifference in these results They suggested that thisdifference might be due to liquid penetration at grainboundaries in the base metal (this increased the solidiliquid interfacial area for solute diffusion) This effecthas been confirmed in research by Kokawa et al85

and Saida et al86 (Fig 15) With this in mind onedimensional modelling results are really only usefulwhen single crystal or very coarse grained polycrystalsubstrates are joined using TLP bonding

The second aspect is the solution of a two phasemoving interface problem in a simple binary alloysystem eg pure nickel base material bonded using aNi-P interlayer The implicit assumptions are thatlocal equilibrium exists at the migrating interfaceduring TLP bonding and that formation of an inter-mediate phase does not occur during isothermalsolidification However this is an approximation sincelocal equilibrium is generally not attained at the solidiliquid interface Furthermore direct experimentalevidence has been presented by Gale and Wallach64

E 301

- ~C1) 0gt-

20 -~uC1)-sC1)

~ 10 -0

s-C~

0 0

A Single-crystal+ Coarse grain (d=34mm)

o Fine grain high purity (d=33JUTl)

A 0 Fine grain low purity (d=40JUTl)+o

o A+o

J J

300 400200

Holdingtime ~s

15 TLP bonding of nickel base metals withdifferent grain sizes d is mean grain sizebefore TLP bonding (after Refs 85 86)

100

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190 Zhou et at Modelling of transient liquid phase bonding

L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

International Materials Reviews 1995 Vol 40 No5

L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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30

~ 20

5

~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

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4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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Zhou et al Modelling of transient liquid phase bonding 187

90 ------------------

bull80 bullbullcP-

o bull0 70)(

c0bullbullbullc5

60

50 -J--------r-------r-------r---o 100 200

Holding time ks

bull experimental test resultscalculated results

6 Calculated and experimentally measuredaluminium concentrations at the joint centrelineduring homogenisation of TLP bonded nickelbase superalloy material using MBF-80filler metal at 1453K (after Ref 12) c isconcentration of aluminium at time t Cb isaluminium concentration in base metal

homogenisation of nickel base superalloy materialNakao et al31 observed close agreement between theresults calculated using equation (24) and the experi-mental values (for much of the homogenisationperiod) However there was a distinct differencebetween the analytical calculations and the experi-mental values during the early stages of the homo-genisation treatment (see Fig 6) Nakao et al12

suggested that this difference was due to a criticalassumption in the analytical results (that the alumin-ium concentration in the joint centreline was uniformat the beginning of the homogenisation period)

Zhou67 also used equation (24) to model the homo-genisation stage during TLP bonding In that studyh was half the filler metal thickness (~2) and Cothe initial solute concentration in the filler metal CFbull

This particular approach has the advantage that themaximum liquid width need not be calculated usingequation (24)

Numerical simulation of TLP bondingNakagawa et al66 modelled dissolution behaviourduring TLP bonding of Nickel 200 base metal usingNi-P and Ni-Cr-P filler metals This research con-firmed the critical effect that both the filler metalthickness and the heating rate between the filler metalmelting temperature and the bonding temperaturehad on the base metal dissolution process An explicitfinite difference method was employed to calculatesolute diffusion in liquid and solid phases and astepwise mechanical mass balance method wasused to determine solidliquid interface movementHowever the approach of Nakagawa et al hadinherent problems since the exact location of thesolidliquid interface could be determined using thestepwise mass balance technique and extremely long

20

15

10

05 0 Experimental- Calculated

o~ 0 - 3 10 - 2 10 - 1 1 00 10 1

2Dtl

300 7 Comparison of calculated and experimentalresults during TLP bonding of single crystalnickel (after Ref 67)

calculation times were required when the whole TLPbonding process was modelled

These problems were overcome by developing afully implicit finite difference model that simulatedthe TLP bonding process in a continuous mannerFigure 7 compares the calculated and experimentaltest results during TLP bonding of single crystalnickel The results are in excellent agreement and ashort computation time is required This numericalmodel output can be used to

(i) predict the completion times required fordissolution isothermal solidification andhomogenisation

(ii) predict the solute concentration distributionboth in the solid phase and in the liquid phasethroughout TLP bonding (see Figs 8-10)these results cannot be calculated usinganalytical methods

(iii) select the optimum filler metal (chemistrythickness) and bonding temperature which willensure that the TLP bonding operation iscompleted in a reasonable time frame

(iv) examine diffusion controlled two phasemoving interface problems other than TLPbonding for example the fully implicit finitedifference model has been applied to the solu-tion treatment of thin multilayer a and f3 brassdiffusion couples81-83

Figure 11 shows the influence of changes in the equi-librium solute content in solid at the bonding tem-perature CaL on the completion times required forbase metal dissolution isothermal solidification andhomogenisation CaL can be varied by altering thesolute content in the filler metal or by changing thebonding temperature Increasing the CaL valuedecreases the time required for completion of iso-thermal solidification and also the time required forhomogenisation Thus the time required for com-pletion of the entire TLP bonding process (dissolu-tion isothermal solidification and homogenisation)will not be affected by an increase in the CaL value

It has been suggested that selection of the optimumbonding temperature during TLP bonding dependson the interplay of increasing solute diffusivity anddecreasing equilibrium solute concentration in the

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25 ----------------- 20cac Uquid Solid0 bullbull 15e bullbullbull bullc bullbullbullbullBc 10 ------ --~---I0 I() I

oS II

5 i 0165I

(5 Time=O s 336 s() I

I

---00 10 20 30 40 50

Distance from liquid centreline JU11

8 Change in solute concentration profile duringbase metal dissolution stage (after Ref 68)

solid However this idea is based wholly on aconsideration of the isothermal solidification stageduring TLP bonding the critical homogenisationstage during TLP bonding is not taken into accountSince variation of the equilibrium solute concen-tration in the solid has no influence on the timerequired for completion of the whole TLP bondingoperation the highest possible bonding temperatureshould be selected during joining This will increasethe rate of solute diffusion into the base metal Inpractice the maximum bonding temperatures will belimited by the need for compatibility with the heattreatment requirements of the base materialComparison of numerical and analytical outputIn the analytical approach it -is assumed that move-ment of the solidliquid interface Y during isothermalsolidification obeys a parabolic law

Y = 2f3(t12) = 2K(Dst)12 (25)

where the constant f3 defines the rate of interfacemovement During numerical calculations f3 isevaluated using the relation

f3 = ~ = (t)12 dY (26)2 d(t12) dt

The f3 parameter is a particularly useful means of

15 I-

10 bullbullbullbull-- bullbullbullbull---r--7-----I I Liquid e Solidimiddot

1900 5 Tlme=3365

i --- _--_1

5 -3200 s

10 4020 30

Distance from liquid centreline JU11

9 Change in solute concentration profile duringisothermal solidification stage (after Ref 68)

International Materials Reviews 1995 Vol 40 No5

fI 10 Time=7000 scac0ca bullbullbullbullbullbullbullbulla-C 9200 S bullbullbullbullbullbullB 05c0()

oS(5()

000 200 400 600 800

Distance from joint centreline JU11

10 Change in solute concentration profile duringhomogenisation stage (after Ref 68)

comparing the output of analytical and numericalcalculations Figure 12 shows the variation of thef3 parameter during base metal dissolution and sub-sequent isothermal solidification for a hypotheticalTLP bonding situation The value of f3decreasesprogressively and approaches zero when base metaldissolution is almost completed In fact f3 decreasesto a value of -0185 urn S-12 and this is identicalto the analytical solution (equation (20)) Thus theisothermal solidification stage during TLP bondingcan be readily estimated using an analytical solutionfor example Fig 13 shows the results when nickelbase material is TLP bonded using Ni-B filler metalIn direct contrast base metal dissolution depends ona non-parabolic relation and no single value of f3 cancharacterise solidliquid interface movement

The remarkable difference between the output ofnumerical and analytical solutions during base metaldissolution and isothermal solidification occurs be-cause the analytical calculations assume that solutediffusion occurs wholly in solid state and that liquidphase is not formed during the joining operation

o Dissolution ~Ifla Homogenisation

105 -----------------

Solidificationbull Total

en 103cDEi= 102

101

100

50200

Cal al

11 Effect of solidus composition at bondingtemperature CaL on completion times requiredfor dissolution isothermal solidification andhomogenisation (after Ref 68)

100

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10

8

0 6~1 4rS

2

0

-210- 1 10deg0- 2

Numerical

Analytical

Eo+~~ Isothermal solidification

Bonding time s

12 Comparison between numerical and analyticalcalculated p values where the constant pdefines the rate of interface movement (afterRef 67)

Figure 14 compares the results of analytical andnumerical calculations of the homogenisation stageduring TLP bonding Numerical and analyticalresults are in close agreement during part of thehomogenisation stage although differences are appar-ent early and late in the processing cycle The devi-ation between the numerical and analytical resultslate in the homogenisation stage (in Fig 14) resultsfrom the semi-infinite test specimen assumption inthe analytical calculations

It can be concluded therefore that simple analyti-cal solutions can be used to estimate the completiontimes for isothermal solidification and for estimatingthe solute concentration at the joint centreline Itshould be noted that the error function required inthe analytical solution must be found by solvingequation (20) numerically Also direct parameterinput into a numerical program can permit readyprediction of the completion times for dissolutionisothermal solidification or homogenisation (for anychosen bonding temperature and filler metal-basemetal combination)

Modelling of real systemsMuch research to date on modelling of TLP bond-ing has involved two aspects The first aspect is

e 30=1-c~ 20i~u 10Q)

w

00

Bonding temperature K

bull 1393bull 1433

bull 1473

40Holding time S

13 Relation between holding time at differentbonding temperatures and eutectic widthduring TLP bonding of nickel base materialusing Ni-B filler metal (after Ref 31)

20 60 80

Zhou et al Modelling of transient liquid phase bonding 189

Isothermalsolidification I Homogenisation

gtltDissolution-1lt

AnaJytimiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot bullNumerical bull

Bonding time s

14 Calculated changes in solute concentration atspecimen centreline during TLP bonding(after Ref 68)

one-dimensional modelling only However whenTuah-Poku et al8 compared their analyticallycalculated and experimental completion times forisothermal solidification during TLP bonding of silverusing copper filler metal they observed a markeddifference in these results They suggested that thisdifference might be due to liquid penetration at grainboundaries in the base metal (this increased the solidiliquid interfacial area for solute diffusion) This effecthas been confirmed in research by Kokawa et al85

and Saida et al86 (Fig 15) With this in mind onedimensional modelling results are really only usefulwhen single crystal or very coarse grained polycrystalsubstrates are joined using TLP bonding

The second aspect is the solution of a two phasemoving interface problem in a simple binary alloysystem eg pure nickel base material bonded using aNi-P interlayer The implicit assumptions are thatlocal equilibrium exists at the migrating interfaceduring TLP bonding and that formation of an inter-mediate phase does not occur during isothermalsolidification However this is an approximation sincelocal equilibrium is generally not attained at the solidiliquid interface Furthermore direct experimentalevidence has been presented by Gale and Wallach64

E 301

- ~C1) 0gt-

20 -~uC1)-sC1)

~ 10 -0

s-C~

0 0

A Single-crystal+ Coarse grain (d=34mm)

o Fine grain high purity (d=33JUTl)

A 0 Fine grain low purity (d=40JUTl)+o

o A+o

J J

300 400200

Holdingtime ~s

15 TLP bonding of nickel base metals withdifferent grain sizes d is mean grain sizebefore TLP bonding (after Refs 85 86)

100

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L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

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L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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30

~ 20

5

~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

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4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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25 ----------------- 20cac Uquid Solid0 bullbull 15e bullbullbull bullc bullbullbullbullBc 10 ------ --~---I0 I() I

oS II

5 i 0165I

(5 Time=O s 336 s() I

I

---00 10 20 30 40 50

Distance from liquid centreline JU11

8 Change in solute concentration profile duringbase metal dissolution stage (after Ref 68)

solid However this idea is based wholly on aconsideration of the isothermal solidification stageduring TLP bonding the critical homogenisationstage during TLP bonding is not taken into accountSince variation of the equilibrium solute concen-tration in the solid has no influence on the timerequired for completion of the whole TLP bondingoperation the highest possible bonding temperatureshould be selected during joining This will increasethe rate of solute diffusion into the base metal Inpractice the maximum bonding temperatures will belimited by the need for compatibility with the heattreatment requirements of the base materialComparison of numerical and analytical outputIn the analytical approach it -is assumed that move-ment of the solidliquid interface Y during isothermalsolidification obeys a parabolic law

Y = 2f3(t12) = 2K(Dst)12 (25)

where the constant f3 defines the rate of interfacemovement During numerical calculations f3 isevaluated using the relation

f3 = ~ = (t)12 dY (26)2 d(t12) dt

The f3 parameter is a particularly useful means of

15 I-

10 bullbullbullbull-- bullbullbullbull---r--7-----I I Liquid e Solidimiddot

1900 5 Tlme=3365

i --- _--_1

5 -3200 s

10 4020 30

Distance from liquid centreline JU11

9 Change in solute concentration profile duringisothermal solidification stage (after Ref 68)

International Materials Reviews 1995 Vol 40 No5

fI 10 Time=7000 scac0ca bullbullbullbullbullbullbullbulla-C 9200 S bullbullbullbullbullbullB 05c0()

oS(5()

000 200 400 600 800

Distance from joint centreline JU11

10 Change in solute concentration profile duringhomogenisation stage (after Ref 68)

comparing the output of analytical and numericalcalculations Figure 12 shows the variation of thef3 parameter during base metal dissolution and sub-sequent isothermal solidification for a hypotheticalTLP bonding situation The value of f3decreasesprogressively and approaches zero when base metaldissolution is almost completed In fact f3 decreasesto a value of -0185 urn S-12 and this is identicalto the analytical solution (equation (20)) Thus theisothermal solidification stage during TLP bondingcan be readily estimated using an analytical solutionfor example Fig 13 shows the results when nickelbase material is TLP bonded using Ni-B filler metalIn direct contrast base metal dissolution depends ona non-parabolic relation and no single value of f3 cancharacterise solidliquid interface movement

The remarkable difference between the output ofnumerical and analytical solutions during base metaldissolution and isothermal solidification occurs be-cause the analytical calculations assume that solutediffusion occurs wholly in solid state and that liquidphase is not formed during the joining operation

o Dissolution ~Ifla Homogenisation

105 -----------------

Solidificationbull Total

en 103cDEi= 102

101

100

50200

Cal al

11 Effect of solidus composition at bondingtemperature CaL on completion times requiredfor dissolution isothermal solidification andhomogenisation (after Ref 68)

100

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10

8

0 6~1 4rS

2

0

-210- 1 10deg0- 2

Numerical

Analytical

Eo+~~ Isothermal solidification

Bonding time s

12 Comparison between numerical and analyticalcalculated p values where the constant pdefines the rate of interface movement (afterRef 67)

Figure 14 compares the results of analytical andnumerical calculations of the homogenisation stageduring TLP bonding Numerical and analyticalresults are in close agreement during part of thehomogenisation stage although differences are appar-ent early and late in the processing cycle The devi-ation between the numerical and analytical resultslate in the homogenisation stage (in Fig 14) resultsfrom the semi-infinite test specimen assumption inthe analytical calculations

It can be concluded therefore that simple analyti-cal solutions can be used to estimate the completiontimes for isothermal solidification and for estimatingthe solute concentration at the joint centreline Itshould be noted that the error function required inthe analytical solution must be found by solvingequation (20) numerically Also direct parameterinput into a numerical program can permit readyprediction of the completion times for dissolutionisothermal solidification or homogenisation (for anychosen bonding temperature and filler metal-basemetal combination)

Modelling of real systemsMuch research to date on modelling of TLP bond-ing has involved two aspects The first aspect is

e 30=1-c~ 20i~u 10Q)

w

00

Bonding temperature K

bull 1393bull 1433

bull 1473

40Holding time S

13 Relation between holding time at differentbonding temperatures and eutectic widthduring TLP bonding of nickel base materialusing Ni-B filler metal (after Ref 31)

20 60 80

Zhou et al Modelling of transient liquid phase bonding 189

Isothermalsolidification I Homogenisation

gtltDissolution-1lt

AnaJytimiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot bullNumerical bull

Bonding time s

14 Calculated changes in solute concentration atspecimen centreline during TLP bonding(after Ref 68)

one-dimensional modelling only However whenTuah-Poku et al8 compared their analyticallycalculated and experimental completion times forisothermal solidification during TLP bonding of silverusing copper filler metal they observed a markeddifference in these results They suggested that thisdifference might be due to liquid penetration at grainboundaries in the base metal (this increased the solidiliquid interfacial area for solute diffusion) This effecthas been confirmed in research by Kokawa et al85

and Saida et al86 (Fig 15) With this in mind onedimensional modelling results are really only usefulwhen single crystal or very coarse grained polycrystalsubstrates are joined using TLP bonding

The second aspect is the solution of a two phasemoving interface problem in a simple binary alloysystem eg pure nickel base material bonded using aNi-P interlayer The implicit assumptions are thatlocal equilibrium exists at the migrating interfaceduring TLP bonding and that formation of an inter-mediate phase does not occur during isothermalsolidification However this is an approximation sincelocal equilibrium is generally not attained at the solidiliquid interface Furthermore direct experimentalevidence has been presented by Gale and Wallach64

E 301

- ~C1) 0gt-

20 -~uC1)-sC1)

~ 10 -0

s-C~

0 0

A Single-crystal+ Coarse grain (d=34mm)

o Fine grain high purity (d=33JUTl)

A 0 Fine grain low purity (d=40JUTl)+o

o A+o

J J

300 400200

Holdingtime ~s

15 TLP bonding of nickel base metals withdifferent grain sizes d is mean grain sizebefore TLP bonding (after Refs 85 86)

100

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190 Zhou et at Modelling of transient liquid phase bonding

L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

International Materials Reviews 1995 Vol 40 No5

L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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30

~ 20

5

~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

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4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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10

8

0 6~1 4rS

2

0

-210- 1 10deg0- 2

Numerical

Analytical

Eo+~~ Isothermal solidification

Bonding time s

12 Comparison between numerical and analyticalcalculated p values where the constant pdefines the rate of interface movement (afterRef 67)

Figure 14 compares the results of analytical andnumerical calculations of the homogenisation stageduring TLP bonding Numerical and analyticalresults are in close agreement during part of thehomogenisation stage although differences are appar-ent early and late in the processing cycle The devi-ation between the numerical and analytical resultslate in the homogenisation stage (in Fig 14) resultsfrom the semi-infinite test specimen assumption inthe analytical calculations

It can be concluded therefore that simple analyti-cal solutions can be used to estimate the completiontimes for isothermal solidification and for estimatingthe solute concentration at the joint centreline Itshould be noted that the error function required inthe analytical solution must be found by solvingequation (20) numerically Also direct parameterinput into a numerical program can permit readyprediction of the completion times for dissolutionisothermal solidification or homogenisation (for anychosen bonding temperature and filler metal-basemetal combination)

Modelling of real systemsMuch research to date on modelling of TLP bond-ing has involved two aspects The first aspect is

e 30=1-c~ 20i~u 10Q)

w

00

Bonding temperature K

bull 1393bull 1433

bull 1473

40Holding time S

13 Relation between holding time at differentbonding temperatures and eutectic widthduring TLP bonding of nickel base materialusing Ni-B filler metal (after Ref 31)

20 60 80

Zhou et al Modelling of transient liquid phase bonding 189

Isothermalsolidification I Homogenisation

gtltDissolution-1lt

AnaJytimiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddotmiddot bullNumerical bull

Bonding time s

14 Calculated changes in solute concentration atspecimen centreline during TLP bonding(after Ref 68)

one-dimensional modelling only However whenTuah-Poku et al8 compared their analyticallycalculated and experimental completion times forisothermal solidification during TLP bonding of silverusing copper filler metal they observed a markeddifference in these results They suggested that thisdifference might be due to liquid penetration at grainboundaries in the base metal (this increased the solidiliquid interfacial area for solute diffusion) This effecthas been confirmed in research by Kokawa et al85

and Saida et al86 (Fig 15) With this in mind onedimensional modelling results are really only usefulwhen single crystal or very coarse grained polycrystalsubstrates are joined using TLP bonding

The second aspect is the solution of a two phasemoving interface problem in a simple binary alloysystem eg pure nickel base material bonded using aNi-P interlayer The implicit assumptions are thatlocal equilibrium exists at the migrating interfaceduring TLP bonding and that formation of an inter-mediate phase does not occur during isothermalsolidification However this is an approximation sincelocal equilibrium is generally not attained at the solidiliquid interface Furthermore direct experimentalevidence has been presented by Gale and Wallach64

E 301

- ~C1) 0gt-

20 -~uC1)-sC1)

~ 10 -0

s-C~

0 0

A Single-crystal+ Coarse grain (d=34mm)

o Fine grain high purity (d=33JUTl)

A 0 Fine grain low purity (d=40JUTl)+o

o A+o

J J

300 400200

Holdingtime ~s

15 TLP bonding of nickel base metals withdifferent grain sizes d is mean grain sizebefore TLP bonding (after Refs 85 86)

100

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L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

International Materials Reviews 1995 Vol 40 No5

L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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30

~ 20

5

~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

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4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

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and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

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2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

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1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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190 Zhou et at Modelling of transient liquid phase bonding

L1quid phase DL

Solid phase

16 Schematic showing factors in two dimensionalmodel of TLP bonding (Dl Ds Dgb and Dintare diffusion coefficients in liquid solid grainboundary and liquidsolid interface regionsrespectively)

for the formation at the bonding temperature of anintermediate phase (Ni3B) during TLP bonding ofnickel base material using Ni-Si-B filler metal Inaddition it has been reported that partial or completehomogenisation can occur in some regions of NiAljNi-Si-BNiAI joints while isothermal solidification isstill taking place in adjacent regions1718

Effect of base metal grain boundaries on processkineticsSince TLP bonding is a diffusion controlled processany factor that affects diffusion will alter the processkinetics during the joining operation When singlecrystal base material is TLP bonded solute transportdepends on volume diffusion in the solid and in theliquid However when a polycrystalline base metal isTLP bonded solute diffusion will depend on anumber of factors (see Fig 16)

1 Orain boundary diffusion diffusivity is muchhigher at grain boundary regions than in the bulkmaterial when the temperature T is in the rangeT lt 05-075Tm (where Tm is the equilibrium meltingtemperature K)87 At such temperatures the DgbD1ratio is 105 or higher where Dgb and D1 are thediffusion coefficients in the grain boundary regionand the lattice respectively

2 Interface curvature liquidsolid interface curva-ture promotes interfacial diffusion which is faster thanin the bulk base material

3 Changes in the solidliquid interfacial area sinceTLP bonding is essentially a homogenisation processin which solute continuously diffuses from the liquidzone into the base metal solid increasing the solidiliquid interfacial area (as a result of liquid penetrationand grain boundary grooving) will increase thetransport area for solute diffusion8586

4 Grain boundary migration grain boundarymigration (as a result of grain growth during the TLPbonding operation) will mean that the solute hasmore chance of intersecting with grain boundariesThis will affect the solute diffusion rate and thereforethe process kinetics

International Materials Reviews 1995 Vol 40 No5

L

ce-ca

--1bullbullbull-------1------- b

a isothermal solidification stage b exchange experiment model

17 Development of grain boundary model foranalysing TLP bonding

5 Segregation to grain boundaries factors such asgrain boundary segregation will influence the grainboundary free energy and solute diffusivity

Grain boundary diffusion model Diffusion alongstationary and moving grain boundaries has beenextensively modelled eg by Fisher91 Whipple92Suzuoka Glaeser and Evans Mishin andRazumovskii Cermak and Zhou and North9798In this connection only Zhou and North9798 havedirectly examined the effects of base material grainboundaries on solute diffusion and isothermalsolidification during TLP bonding

The rate of isothermal solidification during TLPbonding depends on the amount of solute that diffusesacross the interface between the liquid and the basemetal and therefore

[Wmax - W(t)JCLct = 2M(t) (27)

where W is the liquid width during TLP bondingWmax the maximum liquid width CLa the soluteconcentration in liquid at the interface during iso-thermal solidification and M(t) the amount of solutethat diffuses into the base metal in an exchangeexperiment (see Fig 17) It follows that the processkinetics during isothermal solidification can be effec-tively described using M(t) the amunt of solutediffused rather than W(t) the liquid width presentduring TLP bonding In other words calculating thechange in the amount of solute diffused with pro-cessing time provides a useful indication of the processkinetics during TLP bonding With this in mind anumerical model was developed that accounted forthe influence of high solute diffusivity at grain bound-ary regions and of grain boundary migrationon the total amount diffused during the isothermalsolidification stage of TLP bonding9798

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~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

20

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

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4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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~Dlt um18 Effect of grain size and of Dgbl D on Mpl Ms

ratio (D is lattice diffusion coefficient Mp istotal amount diffused into polycrystallinematerial and Ms is total amount diffused insingle crystal base metal) (after Ref96)

The influence of grain boundary diffusivity and ofgrain size on the ratio of MpMs is shown in Fig 18where Mp is the total amount diffused into a polycrys-talline material and M the total amount diffused ina single crystal base metal It is apparent that theinfluence of grain boundary regions on solutediffusion depends on the grain size and on the Dgb D1ratio (where Dgb is the grain boundary diffusioncoefficient and D1 the lattice diffusion coefficient) Thecontribution resulting from grain boundary diffusionincreases when the grain size becomes smaller Aspointed out earlier the DgbD1 ratio is 105 or higherat temperatures in the range T lt 0middot5-0~75Trn (whereTm is the equilibrium melting temperature of thematerial in kelvin) The influence of grain boundarieson diffusional transport will be much greater underthese conditions However at high temperatures(Tgt 0middot75Tm) the DgbD1 ratio is 103 or less andconsequently Fig 18 indicates that the contributionresulting from grain boundary diffusion will be muchless In this context the bonding temperature duringTLP bonding of nickel base superalloy base materialis typically around 1373 K and the TbTm ratio isconsequently about 0middot8 As a result there will be arelatively small contribution resulting from grainboundary diffusion when nickel base superalloymaterial is TLP bonded

The influence of grain boundary migration on theMvMp ratio is shown in Fig 19 where M is thetotal amount diffused into a polycrystalline materialthat contains migrating grain boundaries and M thetotal amount diffused into a polycrystalline materialwhen the grain boundaries are stationary Grainboundary migration speeds up mass transfer duringpart of the holding period and during this periodmore diffusion occurs when the grain size the rate ofthe grain boundary migration and the Dgb D1 ratioare increased

Liquid penetration model A detailed explanation ofthe grain boundary grooving phenomenon was firstproposed by Mullins8899 The kinetics of grain bound-ary grooving were analysed when a bicrystal con-

Zhou et al Modelling of transient liquid phase bonding 191

12 ---------------~

d=40JLm DgtIDl=lOsV=10-llms I

d=40Jlrn DgJD=lOSV=5xlO-12ms I

10 -+-~-==-----r========~o10 5 10

19 Effect of grain boundary migration on Myl Mpratio (My is total amount diffused intopolycrystalline material containing migratinggrain boundaries Mp is total amount diffusedinto polycrystalline material when grainboundaries are stationary) (after Ref 69)

tacted a saturated fluid phase (liquid or gas) atsufficiently high temperature Grooving occurred asa result of surface diffusion volume diffusion in thefluid and evaporationcondensation Gjostein 100 andRobertson confirmed Mullins theoretical predic-tions when examining grain boundary grooving inthe copper-liquid lead system Further support wasprovided by Allenl when examining chromiummolybdenum and tungsten alloyed with rhenium Hoand WeatherlyP applied Mullins model to a solid-solid system and Robertson extended Mullinsanalysis of grain boundary grooving to the case wherethe groove angle varied Also Hardy et ai10S general-ised Mullins theory to the entire range of dihedralangle values through the use of a boundary integralformulation of the free boundary problem Hackneyand Ojard 106 examined grain boundary groovingcaused by evaporation or by surface diffusion in afinite system and Srinivasan and Trived 107 evaluatedgrooving produced by the concomitant action ofsurface and volume diffusion Finally Vogel andRadke combined volume diffusion in the melt andgrain boundary diffusion into one mathematical for-mulation to explain the formation of deep channel-like grooves at grain boundary intersections with asolidj1iquid interface (during isothermal solidificationof Al-bicrystal couples in contact with an In-AImelt) Their model is essentially an extension ofMullinss derivation for grain boundary groovingresulting from the combined action of volume andgrain boundary diffusion

As pointed out in the section Effect of base metalgrain boundaries on process kinetics above thedriving force for interface migration emanates frominterfacial curvature Consequently a flat interfacethat has no intersection with a grain boundary willnot migrate This is a quite different situation fromthat during TLP bonding The driving force forinterface migration during TLP bonding results fromthe concentration gradient in each phase andinterface migration will occur even when the interface

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

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4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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192 Zhou et al Modelling of transient liquid phase bonding

E 251c~ SolidBasisen 15=a8

~oSUquid5

5-20 -1 0

Grain boundary

Time=11s

2s

1s

o 10

Distance from grain boundary um20 Evolution of profile of liquidsolid interface

during dissolution stage (after Ref 69)

is flat and there is no grain boundary intersection(eg in a single crystal bonding situation) The mater-ial transport mechanisms comprise volume diffusionin each phase interfacial diffusion and grain bound-ary diffusion The classical grain boundary groovingtheories proposed by Mullins8899 involve extremelycomplex analytical solutions As a result it is difficultto apply Mullins derivations during TLP bondingsince several diffusion mechanisms operate and finitegeometries exist With this in mind a numerical modelwas developed that predicts the extent of interfacemigration under the combined driving forces ofconcentration and interfacial curvature gradients

Ikeuchi et al69 simulated liquidsolid interfacemigration at grain boundary regions during TLPbonding of nickel base metal using Ni-19 at-Pfiller metal Figures 20 and 21 show the evolution ofthe liquidsolid interface profile at the bonding tem-perature Based on Fig 20 the liquidsolid interfaceis almost planar during the base metal dissolutionstage and liquid penetration at the grain boundaryregion is only apparent near the end of the dissolutionprocess From Fig21 it can be seen that liquidpenetration is more pronounced when the holdingtime increases during the isothermal solidification

3 25 Grain boundary

5 -t----r----r---- - --- bull-20 -10 10o

Distance from grain boundary um21 Evolution of profile of liquidsolid interface

during isothermal solidification stage (afterRef 69)

International Materials Reviews 1995 Vol 40 No5

300 YgbYint=2

sect 25 6 YgbYint=3

E a 19bYint= 1

CD 20~cai5 Solid 150

8-~ 10

Liquid Grain boundary

20 5-20 -10 0 10 20

Distance from grain boundary J1I11

22 Effect of grain boundary energy on profile ofliquidsolid interface during isothermalsolidification (after Ref 69)

stage The penetration depth increases to more than10lm large enough to be clearly observed usingconventional optical microscopy and scanning elec-tron microscopy These indications correspond wellwith the experimental results observed by Saidaet al86 In this connection Kokawa et al85 indicatedthat liquid penetration could not be observed duringthe dissolution process but became more pronouncedwhen the holding time increased during the isothermalsolidification stage of TLP bonding

The horizontal broken lines in Fig 21 indicate thecalculated displacement of the liquidsolid interfacewhen the effects of grain boundary related factors areneglected It is clear that the width of the liquid phasein the bulk region far from the grain boundary(represented by the width at the symmetry axis) issmaller when the influence of grain boundary energyand liquidsolid interfacial energy are taken intoaccount Thus the isothermal solidification processin the bulk material is accelerated when the effectsof the grain boundary energy and the liquidsolidinterfacial energy are taken into account

The influence of the grain boundary energy onliquid penetration at the grain boundary region isillustrated in Fig 22 In this figure the liquidsolidinterfacial energy is maintained at 0middot424 J m -2 andthe grain boundary energy is varied from 0middot424 to0middot848 J m - 2 It has already been indicated that theenergy of a large angle grain boundary is 0middot848 J m - 2

(Ref 109) The penetration depth increases and theangle at which the liquidsolid interface intersects thegrain boundary becomes sharper when the grainboundary energy increases Kokawa et al85 corrobor-ated these findings during TLP bonding of nickelusing Ni-19 at-P filler metal

Microstructural development inmulticomponent systemsDirect experimental evidence for the formation of anintermediate phase at the bonding temperature hasbeen presented by Gale and Wallach64 During TLPbonding of nickel base metal using N-Si- B fillermetal Ni3 B formed in substrate material immediatelyadjacent to the original solidliquid interface (see

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

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Zhou et a Modelling of transient liquid phase bonding 193

o Ni Substrate 0 Ni3B Precipitates bull Liquid Interlayer

a

00000aoooao()QOOQOOOOOO

b c

a initial as melted geometry b formation of Ni3B during early stages of bonding c Ni3B present after completion of isothermal solidification

23 Schematic showing formation of Ni3B during isothermal holding of NiNi-Si-BNi bonds attemperature below the Ni-B binary eutectic temperature

Fig 23) Boride formation only commenced oncemelting of the interlayer had been completed and wasobserved in NiNi-Si-BNi joints held at temper-atures (eg 1065degC) below the Ni-B binary eutectictemperature (1093-1095degC (Ref 110)) In contrastwhen bonding temperatures (eg 1150degC) in excess ofthe Ni-B binary eutectic temperature were employedextensive liquation of the substrates was observedOnce formed borides precipitated at the bondingtemperature remained stable with further change inholding time (Fig 24) Following completion of iso-thermal solidification the borides could be observedas a near continuous band demarcating the originalposition of the solidliquid interface

Gale and Wallach64 proposed the following mech-anism for the formation of borides at the bondingtemperature in NiNi-Si-BNi joints They envisageda situation where local equilibrium was not developedacross the solidliquid interface and in such circum-stances boron was free to diffuse from the interlayerinto the base material immediately after melting ofthe substrates Given that interstitial diffusion ofboron in nickel is considerably more rapid thansubstitutional diffusion of silicon the initially boronfree substrates would be converted into a binary Ni-Balloy Continued boron diffusion would rapidly resultin a substrate boron concentration in excess of theboron solubility in nickel (0middot3 at-oo at the Ni-B

24 Microstructure of NiNi-Si-BNi bond held attemperature of 1065degCfor 2 h Ni3B precipitatespresent after completion of isothermalsolidification (a Ni substrate b Ni3 Bprecipitates c isothermally resolidified joint)(after Ref 64)

eutectic temperature of 1093-1095degC (Ref 110))Subsequent events would depend on the bondingtemperature selected When a bonding temperaturegreater than the Ni-B binary eutectic temperature isemployed liquation of the substrate would beexpected In contrast the use of a bonding temper-ature below the binary Ni-B eutectic temperaturewould result in the isothermal formation of boridesThese predictions correlated with experimental obser-vations of NiNi-Si-BNi joints produced both aboveand below the Ni-B binary eutectic temperature

In NiAlNi-Si-BNi joints Orel et al17 observedthat boride formation and liquation within the nickelsubstrate proceeded in a manner similar to that inthe NiNi-Si-BNi system (see Figs 25 and 26)However in the NiAI substrate there was no evidenceof either the anomalous formation of borides at thebonding temperature or excessive liquation Insteadboride formation in the NiAI substrate was entirelyconsistent with precipitation on cooling from thebonding temperature Orel et al17 associated theseobservations with a lower boron diffusivity in NiAIthan Ni Based on the boride precipitation distancefrom the bondline the apparent boron diffusivity inNiAI (tVI0-12m2s-1) was estimated to be abouttwo orders of magnitude lower than in Ni(tV10-10 m2 s -1) In such circumstances anomalousboride formation and liquation dependent upon rapidboron diffusion in advance of the establishment oflocal solid-liquid equilibrium would only be expectedin the Ni substrate and not the NiAI substrate Hencemicrostructural development in the NiAlNi-Si-BNisystem occurs in a manner that is consistent with theprocesses proposed by Gale and Wallach64 forNiNi-Si-BNi joints

Le Blanc and Mevrel took boron consumptionresulting from boride formation into account whenthey modelled isothermal solidification during TLPbonding of nickel base superalloy material using aNi-Si-B filler metal They found that boron consump-tion as a result of boride formation accelerated theisothermal solidification process This particular studyemployed analytical solutions only and further workon numerical modelling of this aspect is required

SummaryAll analytical approaches to the modelling of TLPbonding have treated the joining process as a numberof discrete stages however this is not what actually

International Materials Reviews 1995 Vol 40 No5

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194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

References1 w JOST Diffusion in solids liquids gases 1960 New York

Academic Press2 J CRANK Free and moving boundary problems 1984Oxford

Oxford University Press3 R F SEKERKA C F JEANFILS and R W HECKEL in Lectures

on the theory of phase transformations (ed H I Aaronson)117-169 1975 New York AIME

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

International Materials Reviews 1995 Vol 40 No5

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

194 Zhou et al Modelling of transient liquid phase bonding

25 Microstructure of NiAINi-Si-BNi bondshowing Ni3B precipitation in Ni substratesample held at 1065degC for 5 min (a NiAIsubstrate b residual eutectic c proeutecticNi d Ni3B precipitates e Ni substrate)(after Ref 17)

occurs during the TLP bonding process Base metaldissolution can not be represented using a paraboliclaw However the isothermal solidification stage canbe readily characterised by assuming a linear relationbetween liquidsolid interface displacement and thesquare root of the holding time at the bondingtemperature Also an analytical solution can be usedto estimate the solute concentration at the specimencentreline following a given holding period duringthe homogenisation stage of TLP bonding

Numerical modelling has the advantage that itcan treat base metal dissolution liquid phase isother-mal solidification and solute homogenisation assequential steps It can therefore be readily appliedto two- or three-dimensional joining situations whencomponents with complex shapes are fabricatedLiquidsolid interface migration during base metaldissolution isothermal solidification and solute redis-tribution during homogenisation have been simulatedusing numerical modelling The optimum joiningparameters during TLP bonding have been quantitat-ively predicted and occur when the solute diffusivityin the liquid and solid phases is increased andwhen the highest bonding temperature is employedIn addition the total amount of solute diffused dur-ing TLP bonding and grain boundary evolutionhave been successfully characterised using numericalmodelling

Future requirementsFuture work on the modelling ofTLP bonding shouldinvolve the development of a general numerical modelthat encompasses all the transport mechanisms whichoccur during the TLP bonding process namelyvolume diffusion in each phase grain boundarydiffusion and interfacial diffusion The driving forcesfor diffusion consist of the concentration gradients inboth the liquid and solid phases the chemical poten-tial gradients that result from the liquidsolid interfa-cial curvature gradient and the grain boundary freeenergy balance at the grain boundary triple junction

International Materials Reviews 1995 Vol 40 No5

26 Microstructure of NiAINi-Si-BNi bondshowing liquation of Ni substrate sampleheld at 1150degC for 20 min (a NiAI sub-strate b Ni3AISi) c eutectic deposit in Nisubstrate d substrate Ni phase) (after Ref 17)

In addition other factors such as grain boundarysegregation will strongly affect the process kineticsduring TLP bonding In this respect it is worthnoting that a general model has already been devel-oped and has been successfully applied during solidstate diffusion bonding

When complex alloys are TLP bonded much mod-elling research seems to have proceeded independentlyof detailed microstructural studies This has resultedin some of the basic assumptions in modelling notbeing supported by direct microstructural obser-vations in real joints In particular the key assump-tion that intermediate phase formation does not occurduring isothermal solidification is questionable Forexample it has been shown that an intermediatephase (Ni3B) forms at the bonding temperature whenNi and NiAljNi base materials are TLP bonded usingNi-Si-B interlayers With this in mind there is acritical need for research programmes where model-ling output is closely related to detailed micro-structural observations In this connection phasediagram and diffusivity data are essential require-ments for rigorous modelling when multi-elementcommercial substrates are bonded using filler metalswhich are available commercially This type of inform-ation is generally unavailable at present and mustbe developed if modelling and direct experimentalobservations are to be successfully linked

AcknowledgementThe authors would like to thank the Ontario Centerfor Materials Research for financial support in theprosecution of this research

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Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

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materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

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39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

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40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

International Materials Reviews 1995 Vol 40 No5

Pub

lishe

d by

Man

ey P

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hing

(c)

IOM

Com

mun

icat

ions

Ltd

4 A J HICKL and R W HECKEL Metall Trans 1975 6A431-440

5 R W HECKEL A J HICKL R J ZAEHRING and R A TANZILLIMetall Trans 1972 3 2565-2569

6 G V KIDSON and G D MILLER J Nucl Mater 19641261-697 w A KAYSSER W J HUPPMANN and G PETZOW Powder

Metall 1980 23 86-918 I TUAH-POKU M DOLLAR and T B MASSALSKIMetall Trans

198~ 19A675-68~9 D S DUVALL W A OWCZARSKI and D F PAULONIS Weld J

1974 53 203-21410 w A OWCZARSKI Weld J 196252 (2) 78s-83s11 E LUGSCHEIDER T SCHITTNY and E HALMOY Weld J 1989

68 (1) 9s-13s12 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Joining of advanced materials (ed T H North) 129-1441990 London Chapman and Hall

13 A E DRAY PhD dissertation University of Cambridge 198514 E R MADDRELL and E R WALLACH in Proc Conf Recent

trends in welding science and technology (ed S A Davidand J M Vitek) 1990 Materials Park OH ASMInternational

15 T J MOORE and J M KALINOWSKI in MRS Symp Proc onHigh temperature ordered intermetallic alloys V (ed I Bakeret al) Vol 288 1173-1178 1993 Pittsburgh PA MaterialsResearch Society

16 M J STRUM and G A HENSHALL in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 76-88 1994 Miami FL AmericanWelding Society

17 s V OREL L PAROUS and w F GALE Weld J 1995 74 (9)319s-324s

18 s V OREL L PAROUS and w F GALE in Proc Conf Advancedjoining technologies for new materials II (ed N F Floreand J O Stiegler) 5-9 1994 Miami FL AmericanWelding Society

19 R THAMBURAJ W WALLACE and J A GOLDAK Int Met Rev1983 28 (1) 1-22

20 G S HOPPIN and T F BERRY Weld J 197049 (11)505s-509s21 H lKAWA and Y NAKAO Trans Jpn Weld Soc 197783-822 H IKAWA Y NAKAO and T ISAI Trans Jpn Weld Soc 1979

10 (1) 24-2923 D S DUVALL W A OWCZARSKI D F PAULONIS and w H KING

Weld J 1970 49 (2) 41s-49s24 T ONZAWA A SUZAMURA and M w KO J Jpn Weld Soc

1989 7 (4) 38-45 (in Japanese)25 w A OWCZARSKI in Proc Conf Physical metallurgy of metal

joining (ed R Kossowsky and M E Glicksman) 1980Warrendale PA TMS-AIME

26 B JAHNKE and J DEMNY Thin Solid Films 1983110225-23527 T J MOORE and T K GLASGOW Weld J 1985 64 (8)

219s-226s28 G E SHEWARD High temperature brazing in controlled

atmospheres 1985 London Pergamon Press29 A SUZAMURA T ONZAWA and H TAMURA J Jpn Weld Soc

1985 3 (2) 85-91 (in Japanese)30 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANG and Y HORI

Q J Jpn Weld Soc 1988 6 519-52631 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG Trans

Jpn Weld Soc 1989 2060-6532 Y NAKAO K NISHIMOTO K SHINOZAKI and c Y KANG in

Proc Symp Superalloys (ed M Cieslak) 775-783 1989Warrendale PA TMS

33 A RABINKIN Weld J 1989 68 (10) 39-4534 K NISHIGUCHI Y TAKAKASHI and A SEO Q J Jpn Weld Soc

1990 8 336-34235 M NAKAHASHI M SHIROKANE and H TAKEDA J Jpn Weld

Soc 1990 54 (7) 826-831 (in Japanese)36 A LE BLANC and P MEVREL in Proc Conf High temperature

materials for power engineering (ed E Bachelet et al)1451-1460 1990 Dordrecht The Netherlands

37 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA Weld Int 19916 (4)270-277

38 T FUNAMOTO M KATO R KAJIWARA K YASUDA T SHIDAT MATSUDA and F MATSUDA J Jpn Weld Soc 1991 9 (3)47-54 (in Japanese)

39 Y NAKAO K NISHIMOTO K SHINOZAKI C Y KANGY C SHIGETA and H SHIGETA J Jpn Weld Soc 1991 9 (1)55-59 (in Japanese)

Zhou et a Modelling of transient liquid phase bonding 195

40 Y NAKAO and K SHINOZAKI Mater Sci Technol 1995 11(3) 304-311

41 R R WELLS and E B MIKUS Thin film diffusion brazing oftitanium members using copper intermediaries US Patent3417461 Northrop Hawthorne CA 1968

42 K c wu Weld J 1971 49 386s-393s43 R R WELLS Weld J 197655 (1) 20s-27s44 B NORRIS Designing with titanium 83-86 1986 London

The Institute of Metals45 Y KOMIZO F KASHIMOTO T TOMITA and K OGAWA Q J Jpn

Weld Soc 19908 197-20446 T FUNAMOTO H WACHIRKAJIWARAMKATOT MATSUZAKA

and T SHIDA J Jpn Weld Soc 1987 5 43-45 (in Japanese)47 J T NIEMANN and R A GARRET Weld J 1974 52 175-

18448 T ONZAWA A SUZAMURA J H KIM and K TAKAGAMI Weld

Int 1992 6 (9) 707-71249 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (4) 74-7850 T ONZAWA A SUZAMURA and J H KIM J Jpn Weld Soc

1990 8 (2) 122-12851 z LI Y ZHOU and T H NORTH J Mater Sci 1995 11

April 363-36952 K KURIYAMA PhD dissertation University of Cambridge

199253 T MOMONO S JACKSON and E R WALLACH in Proc Seminar

Joining of advanced materials Kobe Japan July 1993Technical Commission on Welding Metallurgy and InterfaceJoiningjJWES Research Commission on Welding of SpecialMaterials 68-73

54 z LI W FEARIS and T H NORTH Mater Sci Technol 199511 (4) 363-369

55 TFUN~IOTOHWACHIRKAJIWARAMKATOTMATSUZAKAand T SHlDA J Jpn Weld Soc 1988 6 (2) 23-29 (inJapanese)

56 L BERNSTEIN J Electrochem Soc 1966 113 1282-128857 L BERNSTEIN and H BARTHOLOMEW Trans AIME 1966

236405-41258 R E LOEHMANN in Surfaces and interfaces in ceramic and

ceramic-metal systems (ed J Pask and A Evans) 701-7111980 New York Plenum Press

59 w FEDUSKA Weld J 1958 37 (2) 62s-73s60 K P GROSSKURTH Prakt Metallogr 197411 249-25861 R JOHNSON Weld J 1981 60 10 185s-193s62 B GRUSHKO and B z WEISS Metall Trans 1984 15A

(4) 609-62063 A J MARKHAM PhD dissertation University of Cambridge

198864 w F GALE and E R WALLACH Me ta ll Trans 1991 22A

2451-245765 w D MacDONALD and T W EAGAR Annu Rev Mater Sci

1992 22 23-4666 H NAKAGAWA C H LEE and T H NORTH Metall Trans

1991 22A 543-55567 Y ZHOU PhD dissertation University of Toronto 199468 Y ZHOU and T H NORTH Z Metallkd 199485775-78069 K IKEUCHI Y ZHOU H KOKAWA and T H NORTH Metall

Trans 1993 23A (10) 2905-291570 G LESOULT 1976 cited in Ref 871 R F SEKERKA in Proc Conf Physical metallurgy of metals

joining (ed R Kossowsky and M E Glicksman) 1-3 1980St Louis MO TMS-AIME

72 T H NORTH K IKEUCHI Y ZHOU and H KOKAWA in ProcSymp The science of metal joining (ed M J Cieslak et al)83-91 1991 Warrendale PA TMS

73 J S LANGER and R F SEKERKA Acta Metall 1975 231225-1237

74 J CRANK The mathematics of diffusion 2nd edn 1975 NewYork Oxford University Press

75 P G SHEWMON Diffusion in solids 2nd edn 37-39 1989Warrendale PA TMS

76 s LIU D L OLSON G P MARTIN and G R EDWARDS Weld J1991 70 207s-215s

77 J F LYNCH L FEINSTEIN L HUGGINS and R A HUGGINS WeldJ 1959 37 85s-89s

78 P v DANCKWERTS Trans Faraday Soc 1950 46 701-71279 A SAKAMOTO C FUJIWARA T HATTORI and s SAKAI Weld J

1989 68 63-7180 J E RAMIREZ and s LIU Weld J 1992 71 365s-375s

International Materials Reviews 1995 Vol 40 No5

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

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Ltd

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