Plastic Properties of a Mg-Al-Ca Alloy Reinforced with ShortSaffil Fibers

ZUZANKA TROJANOVA, KRISTIAN MATHIS, PAVEL LUKAC, MILOS JANECEK,and GERGELY FARKAS

AX41 magnesium alloy was reinforced with short Saffil fibers using squeeze cast technology.Samples of the composite were deformed in compression at elevated temperatures. The workhardening rate as a function of the flow stress in the matrix was investigated. A model takinginto account two hardening and two softening processes was used for analyzing of experimentalcurves. Parameters of the model follow different temperature dependences. Possible hardeningand softening processes are discussed.

DOI: 10.1007/s11661-013-2120-1� The Minerals, Metals & Materials Society and ASM International 2013

I. INTRODUCTION

MAGNESIUM alloys reinforced with short ceramicfibers exploit a comparatively high stiffness of ceramicfibers and plasticity of metallic matrix.[1] Such materialshave unique and desirable mechanical and thermalproperties.[2] Metal matrix composites (MMCs) havehigher moduli,[3,4] higher strength,[5,6] more enhancedfatigue properties,[7] and lower thermal expansion[8]

than their metallic counterparts. On the other hand,plasticity of MMCs is lower especially at lower temper-atures. MMC can be processed with conventionaltechniques; but in some cases, they are manufacturedby relatively complicated and expensive methods.[9] Thepotential to use the materials’ architecture methods fortailoring of physical and mechanical properties of MMCis highly attractive. While, during straining, the rein-forcing phase is deformed only elastically, plasticdeformation occurs in the matrix. The deformationprocesses in the matrix are influenced by the presence ofthe reinforcing phase (fibers or particles). Manyattempts have been made to find the relationshipbetween mechanical properties and possible effects ofthe reinforcing phase. fibers or particles may influencenot only the microstructure and dislocation substructureof the MMCs, but also the deformation processesthemselves.[10–13]

The main objective of this study is to investigate thedeformation behavior of an AX41 magnesium alloyreinforced by short Saffil fibers and to estimate possibledeformation mechanisms operating in the matrix duringplastic deformation.

II. EXPERIMENTAL

Magnesium alloy AX41 (4 wt pct Al, 1 wt pct Ca,balance Mg) was reinforced with 13 vol pct of shortAl2O3 (Saffil�) fibers. Composites were prepared by thesqueeze casting technology. The preforms consisting ofAl2O3 short fibers showing a planar isotropic fiberdistribution and a binder system (containing Al2O3 andstarch) were preheated to ~1273 K (1000 �C) and theninserted into a preheated die [573 K to 633 K (300 �C to360 �C)]. Preforms were infiltrated by the liquid alloyusing two-stage application of the pressure. Compositeswere not thermally treated. The mean Saffil fiber lengthand fiber diameter measured after squeeze casting were78 and about 3 lm, respectively. Samples for deforma-tion tests were cut from the bulk composite so that thefiber’s plane was parallel to the stress axis. Compressiontests were carried out in an INSTRON 1186 universaltesting machine with the displacement control at anominal strain rate of 8.3 9 10�5 s�1 in a wide temper-ature range from room temperature (RT) to 573 K(300 �C). The temperature in the furnace was keptwithin an accuracy of ±1 �C. The dimensions of thecompression samples were 5 9 5 9 10 mm3. Micro-structures of composites were examined using the lightmicroscope OLYMPUS.

III. RESULTS AND DISCUSSION

A. Stress–Strain Curves

The microstructure of the sample before deformationis shown in Figure 1. It can be seen that some fibers arebroken as a consequence of the squeeze casting proce-dure. The cut has been performed in the fibers plane; 2Drandom distribution of fibers is clearly visible. The truestress–true strain (r vs e) curves obtained at varioustemperatures are shown in Figure 2. It is obvious thatthe deformation (flow) stress decreases with the increas-ing test temperature, and simultaneously, the elongationto failure increases. At and greater than 473 K (200 �C),the work hardening rate decreases with strain. The

ZUZANKA TROJANOVA and PAVEL LUKAC, Professors,KRISTIAN MATHIS and MILOS JANECEK, Associate Professors,and GERGELY FARKAS, Doctoral Student are with the Depart-ment of Physics of Materials, Faculty of Mathematics and Physics,Charles University in Prague, Ke Karlovu str. 5, 121 16 Praha 2, CzechRepublic. Contact e-mail: ztrojan@met.mff.cuni.cz

Manuscript submitted March 13, 2013.Article published online November 23, 2013

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 45A, JANUARY 2014—29

temperature dependence of the compressive yield stressr02 (determined as the flow stress at e = 0.002) esti-mated at various temperatures for the composite andunreinforced alloy is shown in Figure 3. The tempera-ture variation of the compressive yield stress of theunreinforced AX41 alloy is also plotted in Figure 3. Thereinforcing effect of fibers is about 100 MPa at RT, andit decreases with the increasing test temperature up to67.5 MPa at 573 K (300 �C). The difference between thestress necessary for deformation of the composite andthe stress acting in the unreinforced alloy is a complexvalue containing various contributions to the fibershardening: (a) load transfer of the applied stress to thewell-bonded fibers, DrLT

[14–17]; (b) an increase of thedislocation density accommodating the thermal stressesat the fiber/matrix interface that are induced because ofa large difference in the coefficients of thermal expansion(CTE) between matrix and fibers, DrCTE

[18]; (c) increasein grain boundary area due to grain refinement—theHall–Petch strengthening DrHP

[19]; (d) Orowan strength-ening, DrOR,

[20]; (e) generation of geometrically neces-sary dislocations which accommodate the fiber/matrixinterface during plastic deformation, DrGEO,

[21]; and (f)residual thermal stresses remaining in the matrix when

stresses exceeding the yield stress are accommodatedwithin the newly created dislocations, DrTH.

[8] The loadtransfer mechanism may be calculated (if the all fibersare aligned in the stress direction) as[14]

rLT ¼ rA 1þ Lþ dð Þv4L

� �fþ rAð1� fÞ; ½1�

where rA is the stress for the unreinforced alloy, L isthe fiber length in the stress direction, d is the fiberdiameter, v is a fibers aspect ratio: v = L/d, and f isthe volume fraction of reinforcing fibers in the matrix.Equation [1] expresses the stress which is necessary fordeformation of a composite if all other strengtheningmechanisms are not present or if they are negligible.The effect of the load is based on the existence of shearstresses at the interface between the matrix and thereinforcing phase fibers (particles). It is calculated con-sidering the perfect or nearly perfect bonding betweenthe both components of the composite. The contribu-tion to the load transfer can be calculated according to

DrLT ¼ rALþ dð Þv4L

f; ½2�

using the stress rA estimated for various temperatures.[22]

As in this case all fibers are not aligned into the stressdirection, they are only randomly distributed in the fibersplane; only a component of this stress DrLTÆb wasapplied, where b is a mean value of the direction cosines.The stress rC necessary for the composite deformation

may be expressed as

rC¼rAþDrLTþDrORþDrCTEþDrHPþDrGEOþDrTH:

½3�

Note that the plus sign in this case has only formalmeaning, because in fact, we do not know exactly howto combine the individual strengthening terms.[23] Someauthors express the stress of the composite as square ofthe quadratic sum of the above mentioned contribu-tions. In fact, the effect of several mechanisms may besynergetic. An analysis of the individual strengtheningterms in the fiber-reinforced magnesium alloy-basedcomposites has shown that the load transfer and

Fig. 1—Light micrograph showing the microstructure of the as pre-pared composite.

Fig. 2—True stress–true strain curves of samples deformed in com-pression at various temperatures.

Fig. 3—Temperature dependence of the yield stress estimated forcomposite and unreinforced alloy.

30—VOLUME 45A, JANUARY 2014 METALLURGICAL AND MATERIALS TRANSACTIONS A

increased dislocation density are the main contributorsto the total stress necessary for the composite deforma-tion. Other terms (contributions) are not significant;they exhibit only units of MPa.[6,24] Subtracting the loadtransfer contribution, (i.e., independent of the disloca-tion density), we obtain the flow stress acting in thematrix. Note that this stress, rm, is not identical with theflow stress in the unreinforced alloy. Figure 4 shows theflow stress rm as a function of strain for various testtemperatures.

B. Work Hardening Rate

The work hardening rate in the matrix hm = drm/deas a function of the stress in the matrix rm is shown inFigure 5 for various temperatures. The work hardeningrate decreases with the increasing matrix stress for allthe straining test temperatures. The stress necessary forcontinuous deformation increases with strain up to themaximum stress and then it decreases. The hm vs rm

curves in Figure 5 were plotted corresponding torm = hm according to Considere criterion for uniformdeformation. A number of authors have modeled thestress dependence of the strain hardening rate of metallicmaterials.[25–30] They used different assumptions. It isgenerally accepted that during deformation, the dislo-

cation density changes due to accumulation (storage) ofdislocations, interaction between dislocations, staticrecovery and dynamic recovery. In the dislocationtheory of strain hardening, the increase in flow stresswith strain is due to the dislocation storage. Thedislocation accumulation rate depends inversely on themean free path of dislocations. On the other hand, themean free path may increase, at certain temperatures,because of cross slip and/or climb of dislocations.Annihilation of dislocations—the so-called dynamicrecovery (depends strongly on temperature and strainrate)—can also occur. Therefore, the evolution ofdislocations with strain is associated with their storageand annihilation.The evolution of the dislocation density q (accumu-

lation) with the shear strain c can be expressed as

dq=dcð Þh¼ 1=bLð Þ; ½4�

where L is the mean free path of dislocations, and bthe Burgers vector magnitude of movable dislocations.Kocks[25] has assumed that the dislocation mean freepath is proportional to the average spacing betweenforest dislocations. He also considered that disloca-tions can annihilate, which cause a decrease in the dis-location density. The decrease of the dislocationdensity with shear strain can be expressed as

dq=dcð Þr¼ Lrq=bð Þ; ½5�

where Lr is the dislocation segment recovered in onerecovery event, and it depends on the testing tempera-ture and strain rate. The evolution of dislocation den-sity can be described by the following equation:

ðdq=dcÞ ¼ ðdq=dcÞh�ðdq=dcÞr ¼ c1q1=2�c2q; ½6�

where c1 and c2 are the coefficients describing a storagerate and a dynamic recovery rate, respectively. Equation[6] may also be used for polycrystals if the Taylor factoris known. Strain is used instead of the shear strain.In our case—the composite—we have to consider

different obstacles for dislocation motion in the matrix.There are (a) impenetrable obstacles such as grains,precipitates, short fibers, clusters of impurities, and (b)dislocations in different slip systems—the dislocationforest. The moving dislocations can cross slip and orlocally climb. We can use the model of Lukac andBalık[29] who considered the dislocation density as themain structural parameter controlling hardening andsoftening during plastic straining. Considering twohardening and two softening processes, it is possible towrite the equation for the evolution of the dislocationdensity with strain in the following form:

@q@e¼ K1 þ K2q

1=2 � K3q� K4q2: ½7�

The first two terms in Eq. [7] are due to multiplicationof dislocations at both impenetrable (nondislocation)obstacles and forest dislocations. K1 = 1/bs, where s isthe spacing between impenetrable obstacles; and K2 is acoefficient of the dislocation multiplication intensity due

Fig. 4—Stress acting in the matrix depending on strain obtained forvarious temperatures.

Fig. 5—Work hardening rate in the matrix depending on the truestress in the matrix.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 45A, JANUARY 2014—31

to interaction with forest dislocations. Annihilation ofdislocations due to both cross slip and dislocation climb(negative terms in Eq. [7]) may be considered as thedominant softening process K3 and K4 are coefficients ofdislocation recovery intensity due to cross slip and climbof dislocations, respectively. Both coefficients K3 and K4,depend on temperature and strain rate.[29]

The flow stress, r, acting in ductile polycrystallinematrix is related to the total dislocation density, q, as

r ¼ awGbq1=2; ½8�

where a is a dislocation interaction parameter (for hex-agonal metals estimated by Lavrentev et al.[31],a = 0.35 ); w is the Taylor factor; w(Mg) = 4.5[32]

G = 17 GPa is the shear modulus. Using Eqs. [7] and[8], we obtain the stress dependence of the strain hard-ening rate, h = dr/de, in the following form:

h ¼ A= r� ry

� �þ B� C r� ry

� ��D r� ry

� �3; ½9�

where the parameter A is connected with the interactionof moving dislocations with impenetrable obstacles. Asmentioned above, such impenetrable obstacles can bethe grain boundaries, incoherent precipitates, and nat-urally the reinforcing fibers or particles. The parameterB relates to the work-hardening due to the interactionwith forest dislocations, C relates to recovery due tocross slip, the parameter D is connected with climb ofdislocations, and ry is the applied yield stress. Both Cand D, being related to the thermally activated pro-cesses, are expected to increase with the increasingtemperature. The hm vs rm curves introduced in Figure 5are fitted to Eq. [9] with the aim to estimate thecorresponding parameters A, B, C, and D.

C. Hardening Parameters

The temperature dependence curve of the A param-eter is shown in Figure 6. The parameter can beexpressed in the following form:

A ¼ awGð Þ2b=2s: ½10�

where the s value computed from the experimentalparameter A, using A = 200,000 MPa2 as estimated atroom temperature, ranges from 1 to 2 lm, which issignificantly lower than the grain size (25 ± 3 lm).

An observed decrease in the temperature dependenceof A parameter implies that the strengthening effect ofimpenetrable obstacles is weaker at elevated tempera-tures, and the effective spacing between impenetrableobstacles increases. The mean spacing between theimpenetrable obstacles is obtained from

1=s ¼ 1=dþ 1=Ltw þ 1=Lf þ 1=Ldp þ � � � ; ½11�

where d is the grain size, Ltw is the distance betweentwins, and Ldp is the mean spacing between pile-ups.

We should consider additional impenetrable obstaclesfor the dislocation motion such as incoherent precipi-tates in the matrix, twins, and dislocation pile-upsformed at grain boundaries and fibers. Microstructure

of the matrix alloy consists of a grains with the Mg17Al12intermetallic phase surrounded by smaller particles ofAl2Ca.

[33] As reported by Trojanova et al.,[34] twopronounced maxima of acoustic emission were observedat the very beginning of straining if AX61 magnesiumalloy samples were deformed in compression at roomtemperature. Those authors explained these maxima bythe twinning activity. Decreasing reinforcing effect ofnondislocation obstacles with the increasing tempera-ture may be caused by the releasing of bonding at theinterface matrix-fiber (-precipitate). Dislocations frompile-ups can climb along the fibers.[24] Therefore, thelonger the average free path of dislocations ; the longerthe s is. The intensity of climb increases with theincreasing temperature, and parameter A should de-crease with the increasing temperature in this tempera-ture range as observed experimentally (Figure 8). It isimportant to note that the temperature at which theparameter A starts to decrease is the same as thetemperature at which the parameter D starts to increasewith the increasing temperature.It is well known that the low symmetry of hexagonal

crystallographic structure does not produce the fiveindependent slip systems that are necessary, accordingto von Mises criterion, for the compatible deformation.In this particular case, additional deformation modemay be the deformation twinning allowing for theaccommodation of strain along c-axes. In general,twinning enables a rapid reorientation of grains, andso the twinning areas can continue to deform due to thesoft basal slip mode. The 10�11

� �compressive twinning

occurs first, and then, these compression twins may bere-twinned by the 10�12

� �secondary twinning. The

shear strain caused by 10�11� �

compression twins mayinduce strain incompatibility with the neighboringmatrix. The 10�12

� �secondary twins then accommodate

the strain incompatibility caused by the preceding10�11� �

compression twins.[35] The activity of twinningdecreases with the increasing deformation temperature;for temperatures higher than 473 K (200 �C), it is notsignificant.[36] Annihilation (detwinning) of twins mayalso occur.The temperature dependence of parameter B (see

Figure 7) reflects a possible influence of temperature onthe formation of the dislocation-type obstacles and

Fig. 6—Temperature dependence of the parameter A.

32—VOLUME 45A, JANUARY 2014 METALLURGICAL AND MATERIALS TRANSACTIONS A

interactions between dislocations. Another possibilityfor fulfilling von Mises criterion is the activity ofnonbasal slip systems such as prismatic and pyrami-dal.[37,38] nonbasal dislocations with the Burgers vectorof the ha+ ci type were observed in hcp magnesiumalloys by several authors.[39–42] Moving dislocations inthe basal plane—hai dislocations—may interact withdislocations in the second order pyramidal slip systems,in which ha+ ci dislocations are moving.[43] The fol-lowing dislocation reaction may occur:

1

32�1�13�

þ 1

3�2110�

! 0001h i: ½12�

Dislocations on the left-hand side of the equation areglissile hai (in the basal plane) and ha+ ci (in thepyramidal plane); the product of the reaction is immobile(sessile) hci dislocation and the Burgers vector perpendic-ular to the basal plane. Another dislocation reactionbetween glissile pyramidal dislocations and the glissilebasal hai dislocations produces sessile ha+ ci dislocations:

1

32�1�13�

þ 1

3�12�10�

! 1

311�23�

: ½13�

Two glissile hc+ ai dislocations may interact accord-ing to the reaction:

1

32�1�13�

þ 1

3�12�1�3�

! 1

311�20�

½14�

and produce a sessile hai type dislocation lying along theintersection of the second-order pyramidal planes. It isobvious from the dislocation reactions that the interac-tions between ha+ ci and hai dislocations producesessile dislocations and contribute to the hardening inthe matrix—obstacles for moving dislocation are cre-ated. The activation of the pyramidal slip systems ispossible if the resolved shear stress in the system reachesits critical stress. With the increasing temperature thecritical resolved shear stress rapidly decreases. Enhancedactivity of the nonbasal slip systems especially attemperatures greater than 473 K (200 �C) causes theobserved influence of temperature on the B parameter.

The activities of nonbasal dislocations, including ha+ cidislocations, in magnesium alloys are often discussedand documented in the literature.[39–42]

D. Softening Parameters

Figures 8 and 9 illustrate the temperature variations ofthe softening parameters C and D. While the parameterC reflects the intensity of the dynamic recovery processdue to cross slip, the D parameter corresponds to theactivity of climb process. Both mechanisms are thermallyactivated and can be characterized by the activationvolume and activation energy. In this connection, it isinteresting to note that Trojanova et al.[44] measured theinternal stress and the activation parameters on the samecomposite as in this study. They found that the internalstress estimated from the stress relaxation tests rapidlydecreases with the increasing deformation temperature.This decrease in the internal stress indicates a decrease inthe dislocation density. The values of the activationvolumes are of the order of 101 to 102 b3 and theestimated values of the activation energy are the same asfound for the monolithic alloy (about 1 eV). Trojanovaet al.[44,45] concluded that the main thermally activatedprocess is most probably that of the glide of dislocationsin the noncompact planes i.e., prismatic and pyramidal.Couret and Caillard[46,47] studied prismatic glide inmagnesium in a wide temperature range using TEM.They showed that screw dislocations with the Burgersvector 1=3 11�20

�were able to glide on prismatic planes.

The deformation is controlled by the thermally activatedglide of those screw dislocation segments. A singlecontrolling mechanism was identified as the Friedel–Escaig cross slip mechanism. This mechanism assumesdissociated dislocations on compact planes, like (0001),which are joined together along a critical length Lr

producing double kinks on noncompact planes. Theactivation volume is proportional to the critical lengthbetween two kinks. Typical values for the activationvolume of the Friedel–Escaig mechanism are 70 b3.[48]

The C parameter values estimated in magnesiumalloys[49,50] are insignificant at lower temperatures (val-ues of the order of units). On the other hand, the Cparameter values estimated in this study are about ten

Fig. 7—Temperature dependence of the parameter B. Fig. 8—Temperature dependence of the parameter C.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 45A, JANUARY 2014—33

times higher. Note that the C parameter depends notonly on temperature but also on the alloy composi-tion.[50] Plastic deformation in a composite begins in thevicinity of fibers where the dislocation density is higherthan elsewhere in the matrix. Dislocations cannot passthrough the fibers cutting them or leaving loops aroundthe fibers. Dislocation pile-ups are formed in the vicinityof fibers and/or grain boundaries. These dislocationscreating pile-ups at fibers can act as stress concentrators.This increased stress is the driving force for cross slip ofscrew dislocation components locally in the vicinity offibers. This is the most probable reason for the highervalues of parameter C that were found in the composite.Similarly, the D parameter estimated for the compositein the current study is substantially higher than in themonolithic alloy. The edge components of dislocationsstored in the vicinity of fibers may climb and thenannihilate in neighboring slip planes.[51] Climb andannihilation of dislocations can be supported by diffu-sion of vacancies in the thin layer at the matrix-fiberinterface. Shewfelt and Brown,[52] assuming that themetal-ceramic boundary is disordered and as such acts asa low energy channel for movement of atoms, modeledthe dislocation motion in the field of impenetrableobstacles. They showed that the number of obstaclesby-passed by local climb depends on the strain rate andtemperature. Therefore the incoherent matrix/fiber inter-faces serve as source or sink of vacancies. Enhancedvacancy flow may support edge dislocation climb. This isalso reason for the rapid increase of the D parameterwith the increasing temperature. The parameter D isproportional to the diffusion coefficient (rather pipediffusion). While the cross-slip mechanism is operating atall temperatures, climb of dislocations may be realizedonly at elevated temperatures when the diffusion con-trolled processes are enough effective. The exponentialincrease of the vacancy concentration with temperaturetogether with the diffusion flow in the interface is likelythe reason for the extensive climb process at tempera-tures higher than 423 K (150 �C). This temperature isabout 0.45 Tm, with Tm being the melting temperature.Temperatures higher than 0.4 Tm are considered as thetemperatures above which diffusion processes play animportant role. Intensive course of softening processes at

elevated temperatures is the reason for the rapid degra-dation of mechanical properties of magnesium alloy-based composites at elevated temperatures.

IV. CONCLUSIONS

Hardening and softening processes occurring in thecomposite matrix were analyzed in the current studyusing a model taking into account two hardening andtwo softening processes. Results of the investigation canbe summarized as follow:

� Ceramic fibers and twin interfaces are very effectivenondislocation obstacles for gliding dislocations;they have a substantial effect on hardening.

� Sessile dislocations formed in the reactions betweenbasal and pyramidal dislocations are the main dislo-cation-type obstacles for the slipping dislocations.

� Parameters responsible for recovery processes (crossslip and climb of dislocations) indicate massiveapplication of the softening processes at elevatedtemperatures, stronger than in the monolithic alloy.

� Dislocation pile-ups in the vicinity of fibers serve asstress concentrations and may supply the stress nec-essary for the constriction of the dissociated disloca-tions, thus to making the cross slip easier. The samedislocation pile-ups enable local climb of the edgedislocation components supported by enhanced va-cancy flow in the matrix–fiber interface.

� Rapid degradation of the composite mechanicalproperties at elevated temperatures is due to en-hanced softening conditioned on increased diffusion.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial sup-port of the Czech Grant Agency under the contractP108/12/J018. Thecurrent study is a part of the activi-ties of the Charles University Research Center ‘‘Phys-ics of Condensed Matter and Functional Materials.’’

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