intrinsic and extrinsic fracture resistance in lamellar tial alloys

$: Intrinsic and extrinsic fracture resistance in lamellar TiAl alloys$
Acta Materialia 52 (2004) 4601–4614

www.actamat-journals.com

Intrinsic and extrinsic fracture resistance in lamellar TiAl alloys

K.S. Chan a,*, P. Wang b, N. Bhate b,c, K.S. Kumar b

a Southwest Research Institute, P.O. Drawer 28510, 6220 Culebra Road, San Antonio, TX 78228-0510, USAb Division of Engineering, Brown University, Providence, RI 02912, USA

c Currently at General Electric Global Research Center, Niskayuna, NY 12309, USA

Received 21 January 2004; accepted 11 June 2004

Available online 17 July 2004

Abstract

The roles of colony boundary and crack orientations in the fracture resistance of two-phase lamellar TiAl alloys (Ti–46.5Al and

Ti–47Al–2Nb–1.6Cr–1V, all in at.%) were investigated. In situ fracture testing of single-colony thick compact-tension specimens was

performed at ambient temperature in a scanning electron microscope equipped with a loading stage. Near-tip micrographs of kink

or twist cracks approaching a colony boundary were obtained as a function of applied loads and subsequently analyzed using a

machine-vision-based stereoimaging technique to determine the displacement and strain fields. Metallographic and fractographic

techniques were utilized to measure the kink and twist angles of the crack as well as the orientation of the colony boundary. The

stress intensity factors of the kink and twist cracks were computed using a 2D boundary-integral-equation method and a 3D finite-

element method. Comparison of the computed stress intensity factors against those deduced from the near-tip strain field indicates

that the intrinsic fracture resistance in the lamellar colonies of the TiAl alloys is relatively low (about 3 MPapm, but its apparent

value can be increased as the result of shear ligament bridging. The magnitude of shear ligament toughening is strongly influenced by

the kink and twist angles of the crack, as well as the orientation of the colony boundary.

� 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Fracture toughness; Titanium aluminides; Lamellar cracking; Grain boundary

1. Introduction

It is well known that the fracture toughness of la-

mellar TiAl alloys arises mostly from extrinsic tough-

ening mechanism that involves bridging of crack

surfaces in the crack-wake by intact ligaments, whose

plastic deformation provides enhanced fracture resis-

tance [1–10]. In particular, the fracture toughness of

lamellar TiAl alloys have been found to increase with

increasing colony size because of the tendency to formlarger crack-wake ligaments in coarse-grained materials

[5]. Furthermore, the fracture toughness is insensitive to

the colony or grain size when the ligament widths are

constant or comparable [5]. The crack-wake ligaments

can be formed by three means: (1) interface decohesion

within the same colony; (2) interface delamination in a

* Corresponding author.

E-mail address: [email protected] (K.S. Chan).

1359-6454/$30.00 � 2004 Acta Materialia Inc. Published by Elsevier Ltd. A

doi:10.1016/j.actamat.2004.06.026

neighboring colony; (3) cracking at colony boundaries.

Fracture of the crack-wake ligaments can occur byshear, tension, or a combination of bending and shear.

Fracture anisotropy [11,12] in an individual lamellar

colony appears to play a significant role in interface

decohesion. Yamaguchi and coworkers [11,12] mea-

sured the fracture toughness of individual colonies of

lamellar TiAl alloys and PST crystals. Their results in-

dicated that fracture along the lamellar interface occurs

at about 4 MPapm. In contrast, translamellar fracture

occurs at 15 MPapm and 20 MPa

pm in the ‘‘crack

divider’’ and ‘‘crack arrestor’’ orientations, respectively.

Thus, ligament formation by interface delamination can

be attributed, at least partly if not totally, to the low

fracture toughness exhibited by this mode of interface

cracking. For ligaments formed by interface delamina-

tion, the resulting ligaments must be broken via transl-

amellar fracture, which often occurs by shear, and isaccompanied by larger plastic dissipation and exhibits a

higher fracture resistance.

ll rights reserved.

mail to: [email protected]

4602 K.S. Chan et al. / Acta Materialia 52 (2004) 4601–4614

Another important contributor to the fracture resis-

tance in lamellar TiAl alloys is the colony boundary [13].

In a recent study, Chan et al. [13], showed that interla-

mellar cracking within a colony in binary Ti–46.5Al

occurs at a fracture toughness as low as 2–4 MPapm,

but its value can be drastically increased when the main

crack encounters and arrests at a colony boundary. The

specimens used in this study were relatively thick and

contained several colonies in the through-thickness di-

rection. The presence of multiple colonies and colony

boundaries made it difficult to discern unambiguously

the various effects imparted by colony orientation,

cracking mode, and colony boundary on the fractureresistance of lamellar TiAl alloys.

To resolve these outstanding questions, a subsequent

study by Wang et al. [14], focused on the effects of col-

ony boundary resistance to quasi-static crack growth by

utilizing single-colony specimens in the through-thick-

ness direction. Such a specimen geometry was desirable

for isolating the effect of colony boundary on fracture

resistance since the crack would encounter a single col-ony boundary in the through-thickness direction as it

propagated across the width of the test specimen. In

addition, the orientation of the colony boundary could

be determined easily by identifying the orientations of

the surface colonies alone. The results of these experi-

ments indicated that under certain conditions, the col-

ony boundaries could arrest an advancing crack and

provide a significant resistance to crack growth. Withinindividual colonies, a crack propagated with minimal

resistance. Crack propagation across the colony

boundary ranged from being continuous with minimal

accompanying slip or microcracking at the boundary to

crack arrest, multiple crack renucleation, ligament for-

mation and subsequent failure of the bridging ligaments.

The cracking modes in these single-colony thick lamellar

TiAl specimens were complex and involved Mixed-Mode I, II, and III components. Consequently, only a

few specimens with simpler crack geometries were ana-

lyzed to obtain the corresponding stress intensity factors

and the elastic energy release rates as a function of crack

extension. Because of the presence of intact bridging

ligaments in the crack-wake, the observed fracture re-

sistance was considered extrinsic properties that arose

from crack-tip shielding mechanisms, while the intrin-sic fracture resistance of the lamellar colonies was not

determined.

In this paper, we present the results of an investiga-

tion whose goal was to determine the intrinsic fracture

resistance in single-colony thick specimens of lamellar

TiAl alloys. First, we will describe the experimental

procedure for obtaining the near-tip strain field ahead of

a quasi-static crack in a TiAl sheet using an in situloading stage inside a scanning electron microscope

(SEM) [15], as well as a local strain measurement tech-

nique known as the stereoimaging technique [16] and its

implementation via the machine-vision-based DISMAP

system [17]. Second, we will present the analytical

methods for computing the stress intensity factors and

the elastic energy release rates applied to the crack due

to the external load. The intrinsic fracture resistance ofthe lamellar TiAl colonies is then deduced by comparing

the measured near-tip strain field against that computed

from the applied load. The results are then utilized to

assess the effects of colony orientation, cracking mode

and colony boundary on the fracture resistance of la-

mellar TiAl colonies.

2. Experimental procedure

The Ti–46.5 at.% Al alloy examined in this study was

the same alloy studied in earlier investigations [13,14].

As described in detail earlier [13,14], the TiAl was cast

and forged into a pancake disk. Blocks of material

from the as-forged disk were heat-treated at 1440 �C for

6–10 h to grow the colonies and subsequently furnace-cooled to obtain a fully lamellar structure with an av-

erage colony size of 2–4 mm. The large colony sizes were

chosen so that the crack-tip plastic zone would reside

entirely within a single colony prior to crack extension.

Thin strips of dimensions of 22 mm� 22 mm� 1.25 mm

were cut from the blocks by electro-discharge machining

(EDM). The surfaces of the strips were ground, polished

and examined by optical microscopy. Single-colonythick compact-tension (CT) specimens, Fig. 1(a), were

prepared from the strips after careful consideration of

the notch orientation with respect to the orientations of

the lamellar platelets and colony boundaries. The CT

specimens were 19.8 mm in width, 19.05 in height, and

�1 mm in thickness. For comparison purposes, a mul-

ticomponent TiAl alloy (Ti–47Al–2Nb–1.6Cr–1V) from

a previous study [5] was also investigated. A block ofthis alloy was heat-treated to grow large colonies (2–4

mm colony size) with a fully lamellar microstructure

using an identical procedure (1440 �C for 6–10 h) as that

used for Ti–46.5Al. Fig. 1(b) and (c) shows the lamellar

microstructures of Ti–46.5Al and Ti–47Al–2Nb–1.6Cr–

1V, respectively.

The test specimens were fatigue-precracked under

compression/compression cyclic loading at ambienttemperature. The fatigue crack was subsequently loaded

at R ¼ 0:1 to extend the crack-tip outside the compres-

sive fatigue zone. The cracked specimens were then in-

crementally loaded at small increments of K levels (�0.5

MPapm or less) within a SEM equipped with a loading

stage [15]. High-resolution still photographs of the near-

tip regions were taken as a function of K level and crack

extension. Uncracked ligaments between the main crackand the microcracks were identified. The widths of in-

dividual ligaments were measured from the SEM mi-

crographs. Micrographs of the near-tip region under

Fig. 1. Fracture toughness specimen and microstructure of TiAl alloys: (a) single-colony thick compact-tension specimen; (b) lamellar Ti–46.5Al;

(c) lamellarTi–47Al–2Nb–1.6Cr–1V.

K.S. Chan et al. / Acta Materialia 52 (2004) 4601–4614 4603

loaded and unloaded conditions constituted a stereo-

pair micrographs [16]. The stereo-pair micrographs wereanalyzed using a machined-vision-based DISMAP sys-

tem to determine the near-tip displacement and strain

fields [17]. The near-tip displacements and strains were

then utilized to deduce the local stress intensity factors

and compared to those computed on the basis of the

applied load and crack geometry.

Fig. 2. A schematic illustration of the parameters, a;b, and / describing the l

inclination. From Wang et al. [14].

The orientation of the lamellae in a colony was

characterized in terms of three angles: (1) an in-planekink angle (a) measured with respect to the initial

crack or notch tip; (2) a through-thickness twist angle

(b) measured with respect to the normal of the crack

plane; (3) a colony boundary inclination angle (/)measured also with respect to the crack-plane normal.

It is noted that the colony boundary inclination angle

amellar orientation with respect to the notch and the colony boundary


/ in this paper corresponds to the inclination angle hin the paper by Wang et al. [14]. These three angles are

shown schematically in Fig. 2. Furthermore, positive

and negative notations were used to describe clockwise

and counterclockwise deviations. The lamellar misori-entation across a colony boundary was then described

through Da and Db using the a and b values for the

two adjacent colonies under consideration. These in-

formation, reported earlier, were used to define the

cracking modes and to compute the relevant stress

intensity factors using two different fracture mechanics

analysis codes, including a two-dimensional boundary-

integral-equations code dubbed BIE/CRX [18] and athree-dimensional finite-element code named FRAC3D

[19].

3. Computation of stress intensity factors

In previous work, Chan and Cruse [20] computed the

stress intensity factors for an inclined crack in a com-pact-tension specimen of a Ni-based single-crystal su-

peralloy. The stress intensity factors were reported for

Mixed-Mode I and II cracks with various in-plane kink

angles (a) ranging from 0� to 90�. For this crack ge-

a

αα

a'= ρ + a cos

ρ

W

P

P

ρ /W =0.3

a/W

0.0 0.1 0.2 0.3 0.4 0.5 0.6

0

10

20

30

40

KIα = 0α = 20˚α = 30˚α = 45˚α = 60˚α = 70˚

KII

α = 0α = 20˚α = 30˚α = 45˚α = 60˚α = 70˚

Kb

W/P

?

(a)

(b)

Fig. 3. Stress intensity factor solutions via the 2D BIE/CRX code: (a) BIE/C

46.5Al; (b) plot of binary correction factors, KbpW =P , as a function of a=W ;

ometry, the Mode I component was the dominant one

while the Mode II component was relatively small and

could be ignored. Based on these results, Chan and

Cruse computed the boundary-correction factors for

individual cracking modes of a Mixed-Mode I and IIcrack. Furthermore, Chan and Cruse [20] suggested an

approximate method for computing the individual Kcomponents in a Mixed-Mode I, II, and III crack with a

twist angle b as follows [20,21]:

KI ¼P cos2 b

bffiffiffiffiffiW

p f1a0

W

� �; ð1Þ

KII ¼P cos2 b

bffiffiffiffiffiW

p f2a0

W

� �ð2Þ

and

KIII ¼P cos b sin b

bffiffiffiffiffiW

p f3a0

W

� �; ð3Þ

where the boundary-correction factors f1ða0=W Þ and

f2ða0=W Þ were obtained from the BIE/CRX results. The

Mode III boundary-correction factor, f3ða0=W Þ, was notdetermined but was set equal to f1ða0=W Þ on the basis

that the Mode I boundary-correction factor can be

higher than that for a Mode III crack by no more

α

∆∆

a'/W = (ρρ +a cos αα /Wρ /W = 0.3

a'/W

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Kb

W/P

0

10

20

30

40

ASTM Mode I Crack

KI

α = 0α = 20˚α = 30˚α = 45˚α = 60˚α = 70˚

KII

α = 0α = 20˚α = 30˚α = 45˚α = 60˚α = 70˚

(c)

RX mesh of an inclined crack in a compact-tension specimen of Ti–

(c) plot of boundary correction factor, KbpW =P , as a function of a0=W .


than 15% for a variety of crack geometries includ-

ing center-crack, edge-crack, and double-edge-crack

configurations.

The range of a=W ratios utilized in the present in-

vestigation differed from those examined by Chan andCruse [20]. Because of this, it was necessary to compute

the boundary-correction factors using the pertinent a=Wratios, crack geometry, elastic properties for TiAl, and

the BIE/CRX code. Fig. 3(a) presents an example of a

BIE mesh utilized for an inclined crack with an in-plane

kink angle of a in a compact-tension specimen of width

W and a notch length q. The crack length a is measured

from the tip of the notch. The projected crack length a0

computed according to [20,21]

a0 ¼ qþ a cos a ð4Þfor a specified kink angle a. For computing the KI and

the KII solutions for the inclined crack, q=W was taken

Fig. 4. Stress intensity factor solutions via the 3D FRAC3D code: (a) schemat

specimen of Ti–46.5Al; (b) ryy stress distribution; (c) eyy strain distribution.

to be equal to 0.3 and the kink angle a was varied from

0� to 70�. Results of the boundary-correction factors

(fiða=W Þ and fiða0=W ), i ¼ 1 and 2) are plotted as

functions of a=W and a0=W in Fig. 3(b) and (c), re-

spectively. The results indicate that the KII component isgenerally small compared to the KI component of the

inclined crack. A comparison of Fig. 3(b) and (c) reveals

that the projected crack length dose a better job in

collapsing the K solutions for the different kink angles.

Fig. 3(c) also shows that the KI solutions for an inclined

crack with a6 30� can be computed on the basis of the

ASTM Mode I crack solution, as pointed out earlier by

Chan and Cruse [20].The validity of the methodology based on Eqs. (1)–

(3), for computing the K solutions for Mixed-Mode I,

II, and III cracks was evaluated by performing 3D

finite element crack analysis using a relatively new

code named FRAC3D [19]. In these calculations, the

ics of an inclined, Mixed-Mode I, II, and III crack in a compact-tension

Table

1

Acomparisonofstress

intensity

factorsolutionsobtained

using2D

BIE

/CRX,3D

FRAC3D,andanalyticalsolutionsfitted

to2D

BIE

/CRX

results(Eqs.(1)–(3))

Crack

Geometry

2D

BIE

/CRX

result

3D

FRAC3D

result

Analyticalsolutions

Eq.(1)

Eq.(2)

Eq.(3)

Case

number

a (�)

b (�)

Notch

length

(q)

(mm)

Crack

length

(a)

(mm)

a0¼

qþacosa

(mm)

Width

(W)

(mm)

Thickness

(b)(m

m)

a0=W

KI

bpW=P

KII

bpW=P

KI

bpW=P

KII

bpW=P

KIII

bpW=P

KI

bpW=P

KII

bpW=P

KIII

bpW=P

10

07.1374

2.54

9.6774

15.875

1.2192

0.610

14.78

015.72

00

14.20

00

230

07.1374

2.54

9.3371

15.875

1.2192

0.588

13.24

2.13

13.90

2.22

013.14

2.13

0

30

30

7.1374

2.54

9.6774

15.875

1.2192

0.610

––

11.27

0.10

4.01

10.65

06.15

430

30

7.1374

2.54

9.3371

15.875

1.2192

0.588

––

12.10

1.20

4.13

9.86

1.60

5.69


specimen was assumed to be isotropic and the elastic

constants of TiAl alloy were used. The stress intensity

factors were evaluated using enriched crack-tip

elements, which are finite elements that contain ana-

lytic asymptotic crack-tip displacement and strainfields in addition to regular shape function terms. The

advantage of the enriched crack-tip element formula-

tion is that complex 3D problems can be solved

without having to generate specialized crack-tip meshes

and without having to post-process the finite element

solution to obtain the stress intensity factors.

The FRAC3D code was applied to compute the

Mode I, II, and III stress intensity factors for an in-clined crack in a compact tension specimens subjected

to a remotely applied load. Schematics of an inclined

crack with a kink angle a and a twist angle b is shown

in Fig. 4(a), while the ryy stress fields and the eyystrain fields of a stressed crack are illustrated in

Fig. 4(b) and (c), respectively. Four different sets of

crack angles of a and b were used in these computa-

tions. As summarized in Table 1, both a and b wereset to zero for the Mode I crack in Case 1. For the

Mixed-Mode I and II crack in Case 2, a was set to

30� while b was taken to be zero. Similarly, a was

taken to be zero and b ¼ 30� for the Mixed-Mode I

and III crack in Case 3. In contrast, both a and bwere taken to be 30� for the Mixed-Mode I, II, and

III crack in Case 4. The computed K values of the 3D

crack generally showed slight variations along thecrack front. Consequently, the local K values along

the crack front were averaged and used in the com-

putation of the boundary-correction factors. Results

of the boundary-correction factors for these four

crack problems are presented in Table 1. These results

are also compared against those obtained from the 2D

BIE/CRX code, approximate solutions based on Eqs.

(1)–(3), as well as those based on the 3D center cracksolution reported in the literature [22].

For isotropic materials under the plane stress condi-

tion, the elastic energy release rate, G, is related to stress

intensity factors according to

G ¼ 1

EK2

I

�þ K2

II þ1

1� mK2

III

�; ð5Þ

where E is Young’s modulus, and m is Poisson’s ratio.

An equivalent stress intensity factor, Keq, can then be

defined in the terms of the elastic energy release rate G to

give

Keq ¼ ðEGÞ1=2 ¼ K2I

�þ K2

II þ1

1� mK2

III

�1=2

ð6Þ

in terms of individual K components. Eq. (5) indicates

that Keq equals to KI, KII, and ð1=1� mÞ1=2 KIII for Mode

I, II, and III cracks, respectively. The stress intensityfactors for mixed mode cracks in TiAl alloys were

computed in terms of Eqs. (1)–(3) using measured values

, MP

am

8

10

12

Binary Ti-46.5AlSingle Colony-Thick Specimens

Ti-47Al-2Nb-1.6Cr-1V


of the crack length, crack angles, specimen geometry,

and the applied load. Once the individual K components

were obtained, the corresponding energy release rate

and the equivalent K, Keq, values were computed via

Eqs. (5) and (6), respectively.

Twist Angle, Deg.

0 10 20 30 40 50

Ki =

(EG

i)1/2

0

2

4

6

Fig. 6. Initiation toughness, K i, at the onset of crack extension for

individual single-colony thick specimens plotted as a function of the

twist angle.

4. Results

In a previous study [14], the fracture resistance in

single-colony thick TiAl alloys was characterized by

measuring the applied load as a function of crack ex-

tension. The fracture load is plotted as a function of thetwist angle as shown in Fig. 5, which shows substantial

variations. Because of complex crack geometry, the re-

sults of the applied load for individual specimens were

reported, but the corresponding applied stress intensity

factors were reported for only for specimens that ex-

hibited a rather simple crack geometry. Using the pre-

viously reported fracture loads, crack dimensions and

orientations, and the critical Mode I, II, and III stressintensity factors, the elastic energy release rate and the

equivalent stress intensity factor were obtained via Eqs.

(5) and (6). Results of critical values of GE at crack

extension are shown in parentheses in Fig. 5 while the

corresponding critical Keq values are plotted as a func-

tion of the twist angle in Fig. 6, which shows large

variations of Keq values with the twist angle without an

obvious pattern or trend.To better understand the observed fracture behavior,

crack-tip strain measurements were obtained for Ti–

Fig. 5. A plot of the load required to advance the precrack versus the

lamellae inclination angle b in Colony 1 for several specimens. Values

in parentheses correspond to GE in MPa2 m, where G is strain energy

release rate, and E is elastic modulus. The hatched region corresponds

to the lowest set of initiation loads independent of b. The accuracy of

the load measurements is �5 N, and the accuracy of the twist angle is

�3�. From Wang et al. [14].

46.5Al and Ti–47Al–2Nb–1.6Cr–1V at selected K levels.

Summaries of the crack angles, crack length, applied

load, specimen dimensions are presented in Table 2. The

individual K components computed based on the ap-

plied loads and the pertinent crack geometries are also

presented in Table 2, together with the equivalent stress

intensity factor, Keq, computed based on individual Kcomponents, elastic properties, and Eq. (6). The vonMises effective strains measured by the DISMAP system

[17] at a 1 lm distance ahead of the crack-tip are also

reported in Table 2.

The crack-tip strain measurements for Crack 7 (Table

2), which was a Mixed-Mode I, II, and III crack sub-

jected to an applied Keq of 2.94 MPapm, are presented

in Fig. 7. Fig. 7(a) shows the crack-tip region at maxi-

mum load. The measured crack-tip displacements weresuperimposed on the crack-tip region and are shown in

Fig. 7(b). The near-tip strains are shown in terms of

Mohr’s circles of strain in Fig. 7(c). The diameter of an

individual circle indicates the magnitude of the strains at

the point where the center of the circle is located. In

addition, the von Mises effective strains are plotted as a

function of distance from the crack-tip in Fig. 7 for

angular orientations, h, 45� and )45�, where h is theangular orientation of a point measured from the crack-

tip. Using the applied Keq value, the crack-tip strain

distributions corresponding to the HRR field [23–25]

were computed for the same angular orientations and

the corresponding plastic mode mixity factor, MP. The

value of MP is zero for a pure Mode II crack, and

MP ¼ 1 for a pure Mode I crack [25]. Because of the

small strain values, the near-tip strain field appeared tobe mostly elastic. Thus, the plastic mode mixity factor

was taken to be the same as the elastic mode mixity

factor and was computed as [25]

MP ¼ 2

ptan�1 KII

KI

� �ð7Þ

Table

2

Asummary

ofcrack

angles,crack

geometry,andstress

intensity

factor(K

I,K

II,K

III,K

eq)computedbasedontheapplied

load(P)aswellasthecrack-tip

strain

andK

eqvalues

determined

from

the

DISMAPstrain

measurements

Alloy

Crack

geometry

Applied

stress

intensity

factors

Localvalues

from

DISMAP

results

Crack

number

Dataset

number

a (�)

b (�)

a (mm)

f1

f2

P (Nt)

b (mm)

W (mm)

KI

(MPapm)

KII

(MPapm)

KIII

(MPapm)

Keq

(MPapm)

Crack-tip

strain

(%)

Keq

(MPapm)

Ti–46.5Al

1Set

1582

43

10

1.049

5.16

1.16

124

1.19

15.9

4.25

0.96

0.00

4.36

1.54

2.94

Ti–47Al–2Nb–1.6Cr–1V

3Set

1581

23

30

0.292

5.60

0.70

305

1.40

15.9

7.27

0.91

4.20

8.35

6.78

2.94


3Set

1583

23

30

1.034

7.00

1.06

128

1.39

15.9

3.83

0.58

2.21

4.40

3.54

–


7Set

1579

14

45

0.130

5.36

0.57

131

1.39

15.9

2.00

1.00

2.00

2.94

5.39

2.94


8Set

1578

11

01.514

7.42

0.00

170

1.33

15.9

7.55

0.00

0.00

7.54

2.08

2.94


or

MP ¼ 2

ptan�1 KIII

KI

� �; ð8Þ

where KI, KII and KIII are the Mode I, II and III compo-

nents of a mixed-mode crack. The MP values for the

mixed-mode cracks investigated ranged from 0.5 to 0.9.Solutions of the HRR fields for mixed mode cracks are

available for selected MP values only. We have selected

MP ¼ 0:67 and 0.83 to perform the strain distribution

because they were closest to theMP value of 0.7 and 0.86

computed on the basis of the applied KI and KII values.

The computed and measured strain distributions for

Crack 7 are compared in Fig. 8, which shows reasonable

agreement despite scatter in the experimental strainmeasurements. This agreement of the measured and

computed strain distributions indicates that local and

global K levels are equivalent and suggest the absence of

any shielding mechanism at the crack-tip. Thus, the

fracture resistance measured on this crack, which is about

3 MPapm, represents the intrinsic property of the TiAl

colony in this particular crack geometry and orientation.

For comparison, the crack-tip strain measurementsfor Crack 3 (Table 2), which was a Mixed-Mode I, II,

and III crack subjected to an applied Keq level of 8.35

MPapm, are presented in Fig. 9. The crack-tip region

at the maximum K level is shown in Fig. 9(a), where the

measured crack-tip displacement field is superimposed

at the crack-tip in Fig. 9(b). The corresponding crack-tip

strains are presented in terms of Mohr’s circles of strain

in Fig. 9(c). The measured von Mises effective strains areplotted as a function of distance ahead of the crack-tip

in Fig. 10. The computed strains for the HRR field at

Keq ¼ 8:35 MPapm are considerable higher than the

measured values. This over prediction of the near-tip

strains suggests that crack-tip shielding might be present

in this crack configuration. The local K level required to

match the measured near-tip strains was about 2.94

MPa/m, as shown in Fig. 10. Using the same procedure,the local K levels for Cracks 1 and 8 were deduced to

be 2.94 MPapm and the results are summarized in

Table 2. The discrepancy between the applied Keq value

(8.35 MPapm) and the local Keq value (2.94 MPa

pm)

suggested the presence of a shielding mechanism in

Crack 3. Similar observations were made in Cracks 1

and 8.

Previous investigations [1–10] have identified that theshielding mechanisms in lamellar TiAl alloys include

various types of ligament bridging in the crack-wake

and the resistance of colony boundary against crack

renucleation and propagation into neighboring colonies.

Previous work [10] has also shown that the fracture

toughness of TiAl alloys increases with the width of

bridging or shear ligaments in the crack-wake. Moti-

vated by the previous findings, the width of ligaments inthe crack-wake were measured from SEM micrographs

Fig. 7. Near-tip displacement and strain fields for Crack 7 in Ti–47Al–2Nb–1.6Cr–1V subjected to an applied Keq of 2.94 MPapm: (a) crack-tip at

Keq ¼ 2.94 MPapm; (b) displacement field superimposed on the crack-tip region; (c) near-tip strain field in terms of Mohr’s circle of strains.


of all test specimens investigated in the current and

previous study. The critical Keq values are plotted as a

function of ligament width in Fig. 11. In some cases

critical Keq value showed considerable scatter at a given

value of ligament width. Under this circumstance, the

average Keq value is shown with the corresponding errorbars (�standard deviations). In general, Fig. 11 shows

that the critical value of Keq, which is a measure of the

fracture toughness, increases with increasing widths of

the ligaments in the crack-wake. The experimental trend

line shown in Fig. 11 has been obtained by a least-square

regression analysis of the experimental data excluding

the two highest toughness values. Thus, the deduced

experimental trend is conservative.

The colony size of the materials investigated in this

study was 2–4 mm, in a specimen thickness of 1 mm,

which was considerably larger than the plastic zone at

fracture (e.g., rp � 190 lm based on Keq ¼ 8:3 MPapm

and a yield stress of 350 MPa). Thus, the crack front in

the single-colony specimens interrogated only a single

lamellar colony until it encountered a colony boundary.

In contrast, previous studies [5,13] of multi-colony thick

specimens on the same alloys had a colony size of �600–

1400 lm and a specimen thickness of �4–5 mm. In these

Distance From Crack Tip, µµm

1 10 100

Mis

es E

ffec

tive

Str

ain

0.001

0.01

0.1

θ = 45˚_+

HRR Field, Mp=0.67

∆Keq = 2.94 MPa m

Ti-47Al-2Nb-1.6Cr-1V

θ = 45˚θ = - 45˚

Applied ∆ Keq = 2.94 MPa m

Fig. 8. Comparison of measured strains against those computed based

on the HRR field. The deduced near-tip Keq value is 2.94 MPapm,

which is in agreement with the applied Keq value.

Fig. 9. Near-tip displacement and strain fields for Crack 3 in Ti–47Al–2Nb–1

applied Keq ¼ 8.35 MPapm; (b) displacement field superimposed on the crac


cases, the crack front interrogated multiple lamellar

colonies and colony boundaries at all times. The possi-

ble dependence of the fracture toughness on the number

of lamellar colonies and colony boundaries encountered

by the crack front was investigated by plotting thecritical Keq versus specimen thickness normalized by the

colony size in Fig. 12(a) and (b) for Ti–46.5Al and Ti–

47Al–2Nb–1.6Cr–1V, respectively. The ratio of speci-

men thickness to colony size is a measure of the number

of colony boundaries encountered by a through-thick-

ness crack as it extends across the specimen width. This

ratio is one for single-colony thick specimens but is

greater than one for multi-colony thick specimens.Fig. 12 shows that the single-colony thick specimens

exhibit large variations in fracture resistance (K i) be-

cause of variations in the orientations of the crack,

colony, and colony boundary encountered by the crack

.6Cr–1V subjected to an applied Keq of 8.35 MPapm: (a) crack-tip at

k-tip region; (c) near-tip strain field in terms of Mohr’s circle of strains.

Distance Ahead of Crack Tip, µm

1 10 100

Mis

es E

ffec

tive

Str

ain

0.001

0.01

0.1

1

HRR Field, Mp = 0.83

∆Keq = 8.35 MPa m

∆Keq = 2.94 MPa m= 45˚

= 45˚

Ti-47Al-2Nb-1.6Cr-1VApplied Keq = 8.35 MPa m

= 45˚

Fig. 10. Comparison of measured strains against those computed

based on the HRR field. The deduced Keq value is 2.94 MPapm,

which is less than the applied Keq value of 8.35 MPapm.

Ligament Width, mm

0.0 0.2 0.4 0.6 0.8 1.00

10

20

30

40

50

60

EG

, MP

a2 m

Binary Ti-46.5Al

Experimental TrendLeast-Square Fit

Fig. 11. Plot of EG at fracture as a function of ligament width ob-

served in the crack-wake.

Specimen Thickness/Colony Size

0 2 4 6 8 10

Ki =

(E

Gi)1/

2 o

r

Kc=

(E

Gc)

1/2 , M

Pa

m

1

10

100Binary Ti-46.5Al

Ki in first colonyKC

Specimen Thickness/Colony Size

0 2 4 6 8 10

Ki =

(E

Gi)1/

2 o

r

Kc=

(E

Gc)

1/2 , M

Pa

m

1

10

100Ti-47Al-2Nb-1.6Cr-1V

Ki in first colonyKC at fracture

(b)

(a)

Fig. 12. Plot of initiation toughness, K i, at the onset of crack extension

and critical stress intensity factor, KC, at the onset of unstable fracture

as a function of the ratio of specimen thickness to the colony size in

lamellar TiAl alloys: (a) binary Ti–46.5 Al; (b) Ti–47Al–2Nb–1.6Cr–

1V [5].


front as its extends. Only K i values are shown in Fig. 12

because the crack geometry of the single-colony speci-

mens became too complex when the crack extended into

the neighboring colonies and further deflected to a dif-

ferent path. Many single-colony thick specimens were

tested because they showed a larger variation in the K i

value. These specimens showed a mean K i value of 2.85

MPapm with a standard deviation of 1.57 MPa

pm,

leading to a 55% variation (standard deviation/mean�100%). In contrast, fewer numbers of multi-colony thick

specimens were tested because they showed less scatter

and did not require a larger sampling size. When the

ratio of specimen thickness/colony size increases, the

number of colonies encountered by the crack front in-

creases which results in more statistical averaging of the

orientation of the colonies and their boundaries. Theconsequence is that the observed initiation toughness

value, K i, at the onset of crack extension for specimens

with larger values of the specimen thickness/colony ratio

shows somewhat less scatters (mean Ki ¼ 1:5 MPapm

with �0.3 MPapm standard deviation, and 29% vari-

ation at specimen thickness/colony size¼ 3.3; mean

K i ¼ 3.02 MPa with 0.88 MPapm standard deviation

and 20% variation at specimen thickness/colony

size¼ 7.4). The increased number of colony boundariesalong the crack front in the through-thickness direction

provides a greater opportunity for crack kinking,

twisting, renucleation, and the function of crack-wake

bridging ligaments. Consequently, the critical stress in-

tensity factor at fracture is higher than the initiation

toughness. For both Ti–46.5Al and Ti–47Al–2Nb–

1.6Cr–1V, the KC value appears to be insensitive to the

specimen thickness to colony size ratio as long as theratio is equal to or greater than 3.3. Fig. 12 also shows

that for specimen thickness/colony size ratios greater

than 3.3, the difference between KC and K i is larger for

Ti–46.5Al than that for Ti–47Al–2Nb–1.6Cr–1V be-

cause of a high K i value for the latter alloy. For exam-

ple, the K i values are �2–3 MPapm(2.26� 1.02

MPapm, 45% variation) and the KC values are �25

MPapm (24.9� 9.8 MPa

pm, 39% variation) for Ti–

46.5Al with a thickness/colony size ratio >3. In com-

parison, the K i values are �15–23 MPapm

(Ki ¼ 20:9� 2:9 MPapm, 14% variation) and KC

re R

esis

tan

ce

Ti-47Al-2Nb-1.6Cr-1V (Type 2)

Ti-46.5Al (Type 1)

Interlamellar Cracking inUnfavorably Oreinted Colony (Type 3)

MicroscopicR-Curve Region

Ki,T1

Ki,T3

Ki,Ta


values are �25–44 MPapm (36.27� 6.6 MPa

pm, 18%

variation) for Ti–47Al–2Nb–1.6Cr–1V with a thickness/

colony size ratio >3. This behavior appears to be an

alloying effect but its origin has not been identified. One

possibility is that the colonies or interface boundariesare tougher for the multi-component alloy.

Crack Extension

Fra

ctu

Interlamellar Cracking inFavorably Oreinted Colony

SC MC

Ki,in

Fig. 13. Schematics of possible R-curves for small cracks in lamellar

TiAl alloys. SC and MC denotes single colony and multiple colonies at

the crack front, respectively.

5. Discussion

The cleavage energy values for (2 0 0), (0 0 2), (1 1 0),

and (1 1 1) planes in c-TiAl are 4.6, 5.6, 5.3, and 4.5 J/m2

[26], respectively. Using the elastic moduli reported by

Yoo and Yoshimi [26], the computed KC values for

cleavage on (2 0 0), (0 0 2), (1 1 0), and (1 1 1) planes are

0.93, 1.03, 1.13, and 1.47 MPapm, respectively. These

fracture toughness values are about 1/3 to 1/2 of that (»3MPa

pm) measured for interlamellar fracture in the

lamellar TiAl alloys. The higher KC value reflects the

presence of plastic deformation during interlamellar

fracture in TiAl alloys, as evidenced in Figs. 7–10.

One of the important findings of this investigation is

that the intrinsic fracture toughness values for interla-

mellar cracking in Ti–46.5Al and Ti–47Al–2Nb–1.6Cr–

1V are about 3 MPapm, which is comparable to those

measured (2–4 MPapm for interlamellar fracture in

TiAl single colonies [11,12]. The agreement can be un-

derstood on the basis that the plastic zone size and the

crack front in the single-colony thick encounter only a

single lamellar colony at the onset of crack extension.

Since the plastic zone is embedded entirely within a sin-

gle colony, the large variation in the K i values in the

single-colony thick specimens is unlikely the result of acolony size effect. Furthermore, the fracture toughness

of lamellar TiAl alloys has been shown to be indepen-

dent of the colony size when the colony size exceeds

about 500–700 lm [5,27]. When a colony size effect is

observed, the increase in fracture toughness with in-

creasing colony size is generally an indirect consequence

of the formation of larger crack-wake ligaments in

coarse-grained materials [5]. Instead, the large variationin the K i values in single-colony specimens appears to be

a manifestation of the effect of crystallographic orien-

tation on fracture toughness, since previous work on

PST crystals [11,12] have shown that the fracture

toughness of PST crystals varied from 3.5 MPapm to

17 MPapm, depending on the orientation of the crack

with respect to the crystallographic orientations of the

lamellar colony or PST crystal [11,12].Another important finding is that the effects of colony

orientation, cracking mode, and colony boundary can

be understood on the basis of the generation of crack-

wake ligaments that cause crack bridging and enhance

the apparent fracture resistance by reducing the near-tip

crack driving force, which is elastic energy release rate or

equivalent stress intensity factor because of local mixed-

mode loading at the crack-tip. Despite the intrinsic

fracture toughness is low (about 3 MPapm) for inter

lamellar fracture, the apparent or extrinsic fracture re-

sistance of single-colony thick lamellar TiAl specimens

can be quite high when bridging ligaments form in the

crack-wake, as reported earlier [1–10,13,14]. Recent

computations [28,29] have shown that the energy ex-pended in renucleating a crack across a boundary and

plastically deforming the ligament between the old

crack and the new crack is higher than that expended

in nucleating several parallel interlamellar cracks with-

in a single colony. Like other multicomponents alloys

[5], the fracture toughness of lamellar binary TiAl

alloy increases with increasing ligament width in the

crack-wake.Because of the presence of extrinsic mechanisms, the

fracture resistance of lamellar TiAl alloys is expected to

vary with crack size and, in particular, with the number

of colonies and colony boundaries encountered by the

crack front. Based on the results shown in Fig. 12, three

different types of resistance-curve (R-curve) are expectedand they are depicted in Fig. 13. The lower bound of the

R-curve corresponds to intrinsic fracture resistance byinterlamellar cracking in the absence of any ligament

formation in the crack-wake. An increase in the‘‘initia-

tion toughness’’ can result when a crack embedded in a

single lamellar colony extends into the neighboring

colonies and the crack front experiences the fracture

resistance of adjacent colonies. This increase in the

fracture resistance can develop with relatively small

crack extension and is manifest as a microscopic R-curve, as illustrated in Fig. 13. At least three different

microscopic R-curve behaviors can be induced by the

variation of the number and orientation of colonies and

colonial boundaries along a crack front. The first case,

which corresponds to that observed in Ti–46.5Al, and is

depicted as a dashed line in Fig. 13, involves only a small

increase in K i and a comparatively high KC at critical

fracture. The second case, which corresponds to thebehavior observed in Ti–47Al–2Nb–1.6Cr–1V and is

depicted as a solid line in Fig. 13, involves a substan-


tially higher increase in K i with only a slightly higher KC

value at fracture. The third type, shown as a dotted line

in Fig. 13, corresponds to a crack embedded in a la-

mellar colony unfavorably oriented for interlamellar

fracture. As the crack extends into the neighboringcolonies that are of lower fracture resistance, the energy

release rate of the crack would be sufficiently large to

cause unstable crack extension and a flat R-curve. All

three types of R-curve were observed in the lamellar Ti–

46.5Al and Ti–47Al–2Nb–1.6Cr–1V alloys investigated

in this study, as well as in other polycrystalline lamellar

TiAl alloys [3–7]. Emerging engineering TiAl alloys tend

to have a finer grain size than the materials investigatedin this study. Therefore, the engineering TiAl alloys are

likely to have a small single colony (SC) region and the

crack front is likely to encounter many colony or grain

boundaries even at small crack sizes.

Interlamellar fracture appears to be the weakest

fracture mode in the lamellar colonies of TiAl alloys.

For multicomponent Ti–47Al–2Nb–1.6Cr–1V alloys,

the fracture path has been identified to lie within the cphase, c=c interface [3,7], and along the a2=c interface

[3,8]. In contrast, the interlamellar fracture path in Ti–

46.5Al has been shown to lie within the a2 phase [30,31]or along the a2=c interface [14]. Thus, the difference in

the K i values observed in these two alloys might possibly

be related to the crack path or the fracture resistance of

the various interfaces. Furthermore, there exists a (1 1 1)

slip plane that is aligned either parallel or coplanar tothe interlamellar crack while the remaining (1 1 1) slip

planes, if activated, would produce translamellar slip.

Crack-tip strain measurements, shown in Table 2, indi-

cate that the maximum strain attained ahead of an in-

terlamellar crack was about 1.5–6.8% prior to the onset

of crack extension. The lack of slip activities in the

crack-tip region underscores the difficulties of disloca-

tions moving away from the crack-tip. A recent analysis[32] has demonstrated that the low dislocation mobility

in TiAl alloys might be caused by high stacking fault

energies, which dislocations must overcome in shearing

the ordered L1o structure. Besides stacking fault energy,

dislocation mobility also depends on the antiphase

boundary energy [33,34], complex fault energy [35,36],

dislocation core structure [35–37], dislocation interac-

tion with oxygen [38], as well as dislocation dissociation[39], jog formation [38], and twin interaction [40–42]. To

improve the intrinsic fracture resistance, one must pre-

vent or delay interlamellar fracture by enhancing dislo-

cation mobility and slip emission from the crack-tip.

One possible approach to reduce the stacking fault and

antiphase boundary energies in TiAl alloys is through

proper alloying additions. Unfortunately, the pertinent

alloy additions required to alter the stacking fault en-ergies and the propensity of the lamellar interface to

decohere have not been identified and must await future

research.

6. Conclusions

The conclusions reached in this investigation are as

follows:

1. The intrinsic fracture toughness is about 3 MPapm

for interlamellar cracking in single-colony thick spec-

imens of Ti–46.5Al and Ti–47Al–2Nb–1.6Cr–1V la-

mellar alloys.

2. Near-tip strain distribution for single-colony cracked

specimen shows the presence of one or more shielding

mechanisms at the crack-tip that reduce the crack

driving force and increase the apparent fracture resis-

tance in lamellar TiAl alloys.3. The fracture toughness of lamellar Ti–46.5Al alloy in-

creases with increasing widths of ligaments as the re-

sult of ligament bridging in the crack-wake.

4. Single-colony thick fracture specimens of Ti–46.5Al

exhibit a large variation in the critical elastic energy

release rate or equivalent stress intensity factor at

fracture because of large variations on crack orienta-

tion, colony orientation, and colony boundaries. Thefracture toughness variation decreases with increas-

ing ratios of specimen thickness to colony size be-

cause of improving statistical averaging along the

crack front.

5. The fracture resistance of lamellar TiAl alloys is

likely to vary with crack size as the number of colo-

nies and colony boundaries by the crack front in-

creases. A flat or a rising resistance-curve ispossible, but depend on the fracture response of the

lamellar colony where the crack is first initiated.

Acknowledgements

This effort was supported in part (K.S.K. and P.W.)

by the Materials Research Science and EngineeringCenter on Micro- and Nano-Mechanics of Materials at

Brown University (NSF Grant DMR-9632524). The

contribution of K.S.C. was supported by Southwest

Research Institute� (SwRI�). The technical assistance

provided by B. Chapa, SwRI, in performing in situ SEM

fracture testing is acknowledged. Finally we thank Dr.

A. Ayhan and Professor H. Nied for their assistance

with the FRAC3D code.

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