Brittle-to-ductile transition in NiAl single crystals

BRITTLE-TO-DUCTILE TRANSITION IN NiAl SINGLE

CRYSTAL

F. EBRAHIMI and S. SHRIVASTAVA

Materials Science and Engineering Department, University of Florida, Gainesville, FL 32611, U.S.A.

(Received 14 August 1997; accepted 10 October 1997)

AbstractÐThe brittle-to-ductile transition (BDT) of NiAl single crystals was studied as a function of dis-placement rate and prestraining using double-notched tensile specimens loaded along a h110i orientationwith the crack front parallel to a h001i direction. The tensile properties were also evaluated as a functionof strain rate and test temperature. For specimens tested, the BDT coincided with the onset of net-sectionyielding. It has been found that decreasing the applied displacement rate reduced the BDT temperatureand strain hardening rate without a�ecting the low temperature toughness and yield strength signi®cantly.Prestraining improved the low temperature toughness level but increased the BDT temperature. It has beenshown that fracture in NiAl single crystal occurs by development of microcracks on slip bands and theirsubsequent instability. The e�ects of displacement rate and prestraining are discussed in terms of the plastic¯ow mechanisms and their e�ects on crack initiation and propagation processes. It has been suggested thatthe cross-slip of screw dislocations at elevated temperatures and low strain rates retards plastic strain local-ization, and hence, toughness is improved. # 1998 Acta Metallurgica Inc.

1. INTRODUCTION

Crystalline materials that cleave show a brittle-to-

ductile transition (BDT) upon an increase in the

test temperature. The BDT is conventionally

de®ned as a sharp increase in the material's tough-

ness which is evaluated at the point of crack

instability. This sudden increase in toughness is

usually a result of non-linearity in the load±displa-

cement curve which is initiated by either slow crack

growth or gross yielding (non-contained yielding)

followed by unstable fracture. However, BDT can

also be achieved within the linear-elastic fracture

mechanics frame as long as the specimen size is

increased with an elevation in the test temperature.

In this case the BDT is more gradual in nature.

The brittleness of a material can be viewed as

either a low, lower-shelf toughness or a high,

brittle-to-ductile transition temperature (BDTT) as

depicted schematically in Fig. 1. In semi-brittle ma-

terials, local plasticity always precedes unstable

fracture, even at low test temperatures [1, 2].

Because of the blunting of the original crack tip,

microcracking usually precedes unstable fracture,

i.e. sharp microcracks form at or ahead of the

blunted crack tip. In single phase materials intergra-

nular microcracking, shear decohesion, and clea-

vage microcracking owing to the intersection of

twins or slip bands are examples of crack initiation

processes. These microcracks have to reach a criti-

cal length (or velocity) in order to cause the global

instability of the specimen. The gradual increase in

toughness as a function of temperature within the

lower shelf region is usually due to a decrease of

the yield strength which reduces the probabilities of

microcracking and its subsequent instability. Any

factor that a�ects these probabilities will also

change the variation of toughness with temperature

in this regime. The BDT arises from the interven-

tion of either ductile fracture or gross yielding. The

BDT has been studied extensively in steels, in which

case it is often associated with the development of

slow crack growth prior to unstable fracture [3, 4].

The slow crack grows by microvoid coalescence

mechanism in steels; however, the mechanism of un-

stable crack propagation can be cleavage, quasi-

cleavage or microvoid coalescence, depending on

the microstructure and deformation behavior of the

steel. An increase in the crack tip opening displace-

ment for ductile crack initiation indeed results in a

higher BDT temperature in steels [4]. In single-

phase materials, where microvoid initiation occursby mechanisms such as decohesion at dislocation

cell boundaries or intersection of slip bands [4, 5],

the toughness at the point of ductile crack initiation

can be relatively high. Hence, gross yielding is

expected to precede the initiation of slow crack

growth in the absence of environmental e�ects.

The brittle-to-ductile transition of materials has

been found to be dependent on displacement rate,

specimen geometry, and prestraining. It is well

known that BDTT of steels increases with an

increase in the displacement rate [6]. This e�ect has

been recently investigated in other materials [7±10].In general, the e�ect of displacement rate is

explained in terms of local plastic yielding which is

controlled by the number and velocity of dislo-

cations near the crack tip. A reduction in the speci-

Acta mater. Vol. 46, No. 5, pp. 1493±1502, 1998# 1998 Acta Metallurgica Inc.

Published by Elsevier Science Ltd. All rights reservedPrinted in Great Britain

1359-6454/98 $19.00+0.00PII: S1359-6454(97)00370-4

1493

men dimensions decreases the total number of the

microcracks near the crack tip, as well as allowing

gross yielding to precede unstable cracking at lower

test temperatures, thus decreasing BDTT [3].

Increasing the notch root radius modi®es the stress

distribution ahead of the notch and may lead to a

lower BDTT [11]. The e�ect of prestraining depends

on the nature of the material. If the introduction of

dislocations increases the yield strength of the ma-

terial considerably, then the BDTT will be

increased. For example a cold worked steel shows a

higher BDTT than it does in the annealed con-

dition. However, in materials with a low density of

mobile dislocations, prestraining may result in a re-

duction of yield strength and hence, in improvement

of the toughness [12]. For example, prestraining sili-

con has been shown to reduce hardness and

increase room temperature toughness [13], as well

as decreasing the BDTT by changing the shape of

the toughness vs temperature curve [14].

The intermetallic NiAl has been considered to

have a poor room temperature fracture toughness

which makes it unsuitable for high temperature

structural applications [15]. In polycrystalline form

NiAl has a lower-shelf toughness of 10±15 MPa�m1/

2 and a BDT temperature around 4008C [16]. NiAl

has a B2 crystal structure and its slip vector is

ah100i [17], except when it is loaded uniaxially

along a h100i direction [18]. The preferred slip

planes are {001} and {011} planes; however, {013}

and {015} slip planes have also been

observed [19, 20]. The a h100i slip directions result

in only three independent slip systems. The multi-

plicity of slip planes does not increase the number

of independent slip systems, however, it facilitates

cross-slip by so-called ``pencil'' glide [21]. A lack of

enough slip systems to accommodate the strain

incompatibility between the grains leads to for-

mation of intergranular microcracks and develop-

ment of high internal hydrostatic stress components

that provide the driving force for intergranular

crack propagation [16]. This material fractures by

microvoid coalescence at high temperatures, wherestress-assisted di�usion can cause coalescence of

vacancies [16]. However, the BDT in polycrystallineNiAl was found to be associated with gross yield-ing, which occurred at a lower temperature than

that at which cracking by microvoid coalescencewas possible. The low lower-shelf toughness and thehigh BDT temperature of the polycrystalline NiAl

has been attributed to the plasticity-induced inter-granular microcracking and the existence of high in-ternal stresses arising from incompatibility between

grains [16].The lower-shelf fracture toughness of single-crys-

talline NiAl depends on the crystallographic orien-tation and heat treatment, and its value varies

between 4 and 15 MPa�m1/2 [22]. This range oftoughness is comparable to the lower shelf of b.c.c.single crystals such as molybdenum [9]. The limited

work on BDT of NiAl single crystal indicates aBDTT/Tm ratio of 0.22 to 0.35 (transition tempera-ture range of 1508C±4008C [22, 23]), which is much

higher than the ratio for metallic single crystalssuch as Mo (BDTT/Tm=0.05±0.07 [9]) but muchlower than covalently bonded single crystals such as

Si (BDTT/Tm=0.46±0.58 [7]). The BDT in siliconis strongly strain-rate dependent, and it correspondswith non-linearity in load±displacement curveowing to gross plasticity [7]. Models based on dislo-

cation nucleation [25] as well as dislocationmotion [26] have been proposed to explain theshielding and blunting of the crack tip in Si which

drop the stress intensity factor at the crack tipbelow that necessary for breaking atomic bonds. Incontrast to Si, the yield strength of Mo does not

drop very fast with temperature and it is less tem-perature sensitive within the BDT regime.Accordingly, the BDTT of Mo is not stronglydependent on the applied displacement rate [9]. The

BDT in this material has been explained by plas-ticity-enhanced microcleavage [2, 9]. The purpose ofthis paper is to understand the mechanism(s) of

BDT in NiAl single crystals oriented along a h110iorientation.

2. MATERIALS AND EXPERIMENTALPROCEDURES

Stoichiometric NiAl single crystals studied in thisinvestigation were grown using a modi®edBridgeman technique. The as-grown crystals were

homogenized in an argon atmosphere at 13008C forthree hours and were cooled to room temperatureat a rate of 2.48C/min to eliminate the thermal

vacancies generated at high temperatures. The crys-tal orientation was determined using the Laue back-scattered X-ray technique.

Tensile and fracture toughness tests were per-formed using a closed loop hydraulic testing system.The high temperature tests were conducted in aclosed furnace, with tungsten mesh as heating el-

Fig. 1. A schematic showing how the room temperature(RT) toughness can be improved by shifting the BDTTbelow RT and/or increasing the lower-shelf toughness level.

F. EBRAHIMI and S. SHRIVASTAVA: BRITTLE-TO-DUCTILE TRANSITION1494

Fig. 2. Schematic showing the geometry and crystallographic orientation of the specimens used for ten-sile and fracture toughness testings.

Fig. 3. Tensile engineering stress±strain curves at a strain rate of (a) 5�10ÿ3/s, (b) 5�10ÿ5/s, and (c)5� 10ÿ6/s.

F. EBRAHIMI and S. SHRIVASTAVA: BRITTLE-TO-DUCTILE TRANSITION 1495

ement, under a constant ¯ow of oxygen-getteredargon gas. The specimens were soaked at the test

temperature for an hour before testing. Tensile testswere conducted in the temperature range of roomtemperature to 3008C at approximate strain rates of

5�10ÿ3/s, 5�10ÿ5/s, and 5� 10ÿ6/s. Three displa-cement rates viz, 10ÿ2 mm/s, 2�10ÿ4 mm/s, and2�10ÿ5 mm/s were used for establishing the BDT.

A double-notched tension specimen was used forcharacterizing the BDT as shown in Fig. 2. Thisgeometry was adopted primarily because it allows auniform prestraining to be performed prior to mak-

ing notches. The notches were introduced using aslow speed saw with a diamond wafering blade of300 mm thickness. Specimens with the same geome-

try and dimensions as shown in Fig. 2, but in an``un-notched'' form, were used for tensile testing.Prestraining was performed at a strain rate of

5�10ÿ4/s at 2008C to a level of 10% strain. Atthese conditions the specimen showed adequatemaximum uniform strain [23]. The specimens werecooled to room temperature under ¯owing argon

after unloading. The specimens were notched afterprestraining. Fracture toughness testing of pre-strained specimens were conducted at the displace-

ment rate of 10ÿ3 mm/s.The apparent fracture toughness, KJC, was calcu-

lated using the following equations [27, 28]:

KJC � �YPfa1=2�=BW � �JpE �1=2

Y � 1:99� 0:76�a=W � ÿ 8:48�a=W �2 � 27:32�a=W �3

Jp � 2Ap=B�W ÿ a�where Pf is the load at the point of unstable frac-ture, a is the crack length, B is the thickness, W is

the width, and Ap is the area under the plasticregime of the load±displacement curve.

3. RESULTS

3.1. Tensile testing

Engineering stress±strain curves for the threestrain rates tested are shown in Fig. 3, and the ten-sile properties are summarized in Table 1. The yieldstrength decreased considerably with test tempera-

ture; however, the e�ect of strain rate was not as

signi®cant. Figure 4 presents ¯ow stress as a func-

tion of temperature at various strain rates. These

curves show that initially the strain hardening rate

is very high, as re¯ected in the large di�erence in

the ¯ow stress values at 0.2% and 3% strain levels.

However, the strain hardening rate decreased sig-

ni®cantly at higher strain levels as indicated by the

small di�erence in the ¯ow stress at 2% and 3%

Table 1. Tensile properties of NiAl single crystal

Strain rate(sÿ1)

Temperature(8C)

Yieldstrength(MPa)

Fracturestress(MPa)

Ductility(%)

5� 10ÿ3 20 110 211 5.8100 83 151 5.8200 69 168 9.1

5� 10ÿ5 20 98 189 6.3100 75.5 186 10.0200 56 Ð 61300 28 Ð >63

5� 10ÿ6 20 94 163.5 6.9100 84 192 11.0200 56 Ð >56

Fig. 4. E�ect of temperature on ¯ow stress at a strain rateof (a) 5� 10ÿ3/s, (b) 5� 10ÿ5/s, and (c) 5� 10ÿ6/s.


strain levels. Table 2 presents an estimate of the in-

itial strain hardening rate for various temperaturesand strain rates tested. The strain hardening rate

decreased signi®cantly with a reduction in the strainrate. The e�ect of temperature on strain hardeningrate was not as signi®cant and the strain hardening

rate remained almost constant at the lowest strainrate tested.

Figure 5 presents yield stress as a function of theapplied strain rate. The strain rate sensitivity values

calculated from these curves are given in Table 3.The negative strain rate sensitivity observed at

1008C and low strain rates suggests the occurrenceof dynamic strain aging at this temperature. The ac-

tivation energy for yielding was estimated based onthe data at room temperature and 2008C test tem-

peratures. The 1008C temperature results wereexcluded because of the occurrence of dynamic

strain aging. The activation energy, Q, was calcu-lated from:

Q � �ÿR log�_e2=_e1�=�1=T2 ÿ 1=T1��swhere _e is strain rate, T is temperature, s is the

¯ow stress, and R gas constant. The subscripts 1and 2 refer to 258C and 2008C test temperatures.

Within the stress range of 70 to 90 MPa, the acti-vation energy was found to be 97 kJ/mol and inde-pendent of the stress level.

The specimens that did not show plastic instabil-

ity (necking) broke near the shoulder where thecross-section area changed drastically. At 2008C,

where the specimens necked before fracture, themaximum uniform strain was reduced considerablywith a decrease in the applied strain rate from

5�10ÿ5 to 5�10ÿ6. The tensile ductility in speci-mens fractured in the specimen's shoulder was inthe range of 5±11% but it increased drastically

(>60%) in specimens that did not break in theshoulder area. This transition was not observed inthe specimens tested at 5�10ÿ3/s, suggesting thatthe transition temperature should be above 2008C.Analysis of the slip traces on both sides of speci-

mens that showed signi®cant ductility has revealedthat {100} and {110} slip planes as well as various

{hk0} planes were activated [20]. The wavy natureof the slip lines as shown in Fig. 6 indicated exten-sive cross-slip of dislocations between the slip

planes.

3.2. Fracture toughness testing

The e�ect of displacement rate on the BDT isshown in Fig. 7. All specimens tested, except for thespecimen tested at 2508C at the displacement rate

of 2� 10ÿ5 mm/s, broke in an unstable manner

Table 2. Strain hardening rate$ (MPa) as a function of tempera-ture and strain rate

208C 1008C 2008C

5� 10ÿ3 sÿ1 1546 1172 10565� 10ÿ5 sÿ1 1240 900 10265� 10ÿ6 sÿ1 604 784 686

$Strain hardening rate was de®ned as: (s5%ÿs0.2%)/0.048, wheres5% and s0.2% are the ¯ow stress at 5% and 0.2% strain, re-spectively.

Fig. 5. E�ect of strain rate on yield strength at di�erenttest temperatures.

Table 3. Strain rate sensitivity, m$, as a function of temperature

Temperature 8C

Strain rate sensitivity

high strain rates low strain rates

20 0.024 0.014100 0.022 ÿ0.045200 0.047 0

$m = ln(s2/s1)/ln� _"2= _"1�, where s is the yield strength, _" is thestrain rate, and subscripts 1 and 2 refer to the two levels ofstrain rate.

Fig. 6. SEM micrograph showing the relationship betweenthe slip traces on faces of a tensile specimen loaded to a

strain of 25% at 2008C.


without a noticeable slow crack growth. The BDT

temperature, as de®ned by the temperature at which

toughness increases drastically with temperature, co-

incided with the onset of nonlinearity in the load±displacement curve [20]. This nonlinearity is due to

the net-section yielding of the specimen. Table 4

compares the actual load at the onset of nonlinear-

ity, Py, with that predicted based on the net-section

area, Anet. The results indicate that the constraint

factor, L = Py/syAnet, is about 1.4±1.5 in specimens

tested. Decreasing the displacement rate reduced theBDTT without improving the low temperature

toughness level (lower-shelf toughness) noticeably.

The activation energy for BDTT was estimated

by plotting the displacement rate as a function ofthe inverse of temperature at the point where un-

stable fracture correspond with net-section yielding

as shown in Fig. 8. For comparison the curves

at KJC=25, 50, 100 and 150 MPa�m1/2 are also

included. The activation energy values calculated

are presented in Table 5. The activation energy

values increased with an increase in the apparent K

value. Note that the activation energy correspond-ing to BDT is signi®cantly smaller than the value

for yielding (48 kJ/mol for BDT vs 97 kJ/mol for

tensile yielding).

The e�ect of prestraining on BDT behavior isshown in Fig. 9. The average lower-shelf toughness

was increased from 4.9 MPa�m1/2 to 8.5 MPa�m1/2;

however, the BDTT was shifted to a higher tem-

perature upon prestraining. Similar to the as-hom-ogenized specimens, the BDTT corresponded to theonset of net-section yielding.

3.3. Fractography

Unstable fracture occurred by cleavage fracture in

all notched and un-notched specimens and no micro-void coalescence mechanism was observed. The pro-cesses of crack initiation and propagation have beenpresented in detail elsewhere [20] and here only sali-

ent features are presented. At all conditions cracknucleation occurred by shear decohesion along con-centrated slip bands. Figure 10 presents three

examples of microcracking: at the notch tip (lowtemperature, below net-section yielding), ahead butnear the notch (intermediate temperature, above net-

section yielding but below general yielding), and inthe mid-section of a specimen (high temperature,above general yielding). The crack initiation andpropagation was found to start invariably near the

sides of the specimens as shown in Fig. 11. Asdemonstrated in Fig. 12, the plane stress conditionnear the surface enhanced localized plastic defor-

mation which is the pre-curser to crack initiationand propagation in NiAl single crystals.

4. DISCUSSION

Based on the fractographic analysis, cleavage

microcracks are produced by slip decohesion on theslip planes in NiAl single crystals. It should benoted that {100} and {110} planes act as both slip

and cleavage planes in this material. The micro-cracks formed preferentially near the sides of the

Fig. 7. Fracture toughness as a function of test tempera-ture at di�erent applied displacement rate [21].

Table 4. A comparison of load at the onset of non-linearity,Py(N), with P = syAnet(N). The values in the parenthesis are the

plastic constraint factor, L

5� 10ÿ3 sÿ1 5� 10ÿ5 sÿ1 5�10ÿ6 sÿ1

208C a a Py=623,P = 480 (1.3)

1008C a Py=534,P = 383 (1.4)

Py=445,P = 414 (1.1)

2008C Py=489,P = 351 (1.4)

Py=427,P = 285 (1.5)

Py=423,P = 285 (1.5)

aFracture occurred within the linear portion of the load±displace-ment curve.

Fig. 8. Ln displacement rate vs reciprocal of absolute tem-perature at various stress intensity factor, K, levels.

Table 5. Activation energy calculated at various KJC values

K Level (MPa�m1/2)Activation energy

(kJ/mol)

Net section yielding 4825 5250 66100 79150 84


specimens tested, where the stress state is close tothe plane stress condition. This stress state enhances

shear localization and thus microcracking. The factthat unstable cracks always started from the sides

of the specimens suggests that microcrack for-mation is the main mechanism that controls the

apparent fracture toughness of the NiAl specimenstested. Consistently, the abrupt decrease in tensileductility with a reduction in temperature is attribu-

ted to the localization of plastic strain near the ten-sile specimen shoulders which causes crack

initiation and leads to a premature fracture.In contrast to the observations made for silicon

single crystals [14], the BDT temperature wasincreased with prestraining of the NiAl single crys-tal tested in this study. This contradiction may be

related to the di�erence in the prestraining pro-cedures. In the case of silicon, prestraining was con-

ducted after a sharp crack has been introduced bymicroindentation [14]. Since silicon single crystalshave a very low dislocation density, dislocations

formed upon prestraining are expected to be gener-ated from the crack tip. These dislocations reduce

the stress intensity factor at the crack tip duringlow temperature fracture toughness testing by

blunting the originally sharp crack tip and acting asshielding dislocations. In this study prestraining wasconducted prior to the introduction of the notches.

The random distribution of the dislocations and theabsence of a change in the notch tip geometry may

re¯ect why the BDTT was not improved in the caseof NiAl single crystal studied here. Furthermore,our recent results indicate that the toughness of sili-

con can also be improved by high temperature pre-straining performed prior to the introduction of

cracks [13]. We have also found that room tempera-ture hardness of silicon is reduced by prestraining.

This result suggests that the improvement of tough-ness and the reduction of BDTT in silicon are as-sociated with introduction of dislocation sources

upon prestraining. The increase in the BDTT of

NiAl with prestraining suggests that dislocationgeneration is not the mechanism that controls thetoughness of NiAl single crystals. Indeed, TEM stu-

dies have revealed that homogenized NiAl singlecrystals show small angle boundaries indicating thata reasonable number of dislocation sources exist in

this material [29]. Therefore, lack of enough dislo-cations is not a reason for the brittleness of NiAlsingle crystals. The e�ect of prestraining on BDT

behavior of NiAl is depicted in Fig. 13(a). Theincrease in the BDTT with prestraining can beattributed to the increase in the ¯ow stress which

Fig. 9. Brittle-to-ductile transition in as-homogenized andprestrained conditions [24].

Fig. 10. SEM micrographs showing microcracking in NiAlsingle crystals. (a) Microcracks at the notch tip. (b)Microcracks within the heavily deformed region ahead ofthe notch. (c) Microcracks in the middle of a specimen.


raises the load level, and hence the applied K (or J)

value at which net-section yielding occurs.

Therefore, the intervention of gross yielding is post-

poned to higher temperatures. In addition, the

increase in the stress distribution level in the plastic

zone increases the probability that microcracks may

lead to instability. The improvement of the room

temperature toughness with prestraining can be

attributed to the uniformity of deformation in theplastic zone. At low temperatures the toughness is

strongly dependent on the resistance to crack in-

itiation. The uniformity of deformation resulted

from prestraining retards plastic strain localization

and consequently for microcracking to occur larger

plastic strains are required. Apparently this e�ecto�sets the adverse e�ect of the high ¯ow stress, and

thus toughness is improved.

The results presented here indicated that BDT

temperature is reduced signi®cantly with decreasing

the applied displacement rate. This observation is

similar to the results reported for silicon. However,

in contrast to the behavior of silicon, within the

temperature range studied here, the yield strength

of NiAl is insensitive to the applied strain rate.Therefore, models that explain the displacement

rate dependency of BDTT based on the variation of

the yield strength are not applicable. Consistently,

the estimated activation energy for yielding was

found to be much higher than the activation energy

associated with BDT.

Although the yield strength was found to be inde-

pendent of the applied strain rate, the strain hard-

ening rate was in¯uenced considerably (see Table 2).Slip trace analysis of NiAl tensile specimens loaded

in a h110i direction has revealed that double cross-

Fig. 11. SEM micrograph showing crack initiation site ina specimen fractured at 3508C at 10ÿ2 mm/s. The arrow in-

dicates the crack initiation site.

Fig. 12. SEM micrograph showing the extensive plastic de-formation and the Poisson's e�ect near the side of a speci-men fractured at 3508C at 10ÿ2 mm/s [21]. The arrow

indicates the crack initiation site.

Fig. 13. Schematics depicting the e�ects of (a) prestrainingand (b) displacement rate on BDT of NiAl single crystal


slip occurs at large applied strains (see Fig. 6).

TEM analysis of deformed NiAl samples usuallyreveals formation of dislocation loops [30]. Theseloops can develop by dislocations bowing out

between superjogs. One mechanism for formationof superjogs is the double cross-slip of screw com-ponent of dislocations. Thus, it is suggested that an

increase in the probability of cross-slip withdecreasing strain rate is responsible for the improve-

ment in the BDT temperature. Double cross-slipinhibits strain localization [31] in addition to limit-ing the maximum level of elastic stresses that

develop ahead of the dislocation pile-ups. The lessprobability of localization reduces the chance ofmicrocracking. Because of the relaxation of local

stresses by cross-slip, the probability that a micro-crack will become unstable is also reduced.Consequently, the temperature at which unstable

fracture occurs after gross yielding is lowered byreducing the applied displacement rate. This e�ect

is depicted schematically in Fig. 13(b).The lower-shelf toughness of the as-homogenized

specimens was found to be independent of the displa-

cement rate in this study. This observation is consist-ent with the results reported previously [32] where it

has been found that the fracture toughness of NiAlsingle crystals remained relatively constant for stressintensity rates up to about 100 MPa�m1/2/s (the high-

est displacement applied in this study corresponds toa stress intensity rate of approximately 1 MPa�m1/2/s). It should be noted that at very high strain rates

there will be not enough time for dislocation motion,and mechanisms other than shear localization maycontribute to the crack initiation process.

The nature of barriers to dislocation motion inNiAl has not been well understood. The results of

this study, consistent with many previously reportedinvestigations [33], suggest that dynamic strainaging (DSA) occurs in NiAl single crystals. The ac-

tivation energy for the onset of serration in the ten-sile stress±strain curves has been found to be within70 to 115 kJ/mole [33]. These values have been cor-

related with the activation energy for di�usion ofinterstitial atoms [34], however, the analysis of the

activation volume has suggested that impurity±dis-location interaction may not be the controllingmechanism at low temperatures [35]. DSA may

enhance plastic strain localization, however, for thecrystal tested in this study DSA was observed onlyat the lowest strain rate tested, which is much lower

than the strain rates achieved in the plastic zone ofnotched specimens. Therefore, it is concluded that

the occurrence of DSA is not responsible for BDTin NiAl single crystals.

The tri-axial stress state and the constraint at the

crack tip is expected to encourage slip by a h111idislocations. These dislocations have been found tobe activated near sharp crack tips, but due to the

high Peirels stress associated with them, they cannot move far from the crack tip [36]. TEM [36] and

slip line [19] analyses of indented NiAl single crys-

tals have also revealed that in spite of the hightriaxiality of the stress state, the a h100i are thedominant slip vectors. Therefore, it is concluded

that the activation of a h111i dislocations is not re-sponsible for BDT in NiAl single crystals.

The analysis of the tensile results indicated that

the initial work hardening rate is relatively high inthe h110i oriented NiAl single crystal and it re-

sembles the stage II work hardening of f.c.c. singlecrystals. Upon straining, the work hardening ratedropped signi®cantly, which is similar to stage III

of strain hardening in f.c.c. crystals. The transitionstrain from the high strain hardening rate to thelow strain hardening rate regimes decreased at elev-

ated temperatures and low strain rates. These e�ectswere also manifested as a decrease in the maximum

uniform strain similar to observations made in f.c.c.materials. While the barrier to cross-slip in f.c.c.crystals is associated with dissociation of dislo-

cations and thus stacking fault energy, the instabil-ity of screw dislocations owing to elastic anisotropymay be responsible for the thermally activated

cross-slip in NiAl. It has been shown theoreticallythat the a h100i screw dislocations have a high elas-

tic energy and are unstable [37]. Consistently, theobservation of zig±zag dislocations in TEM foilshave been attributed to the fact that a h100i dislo-cations have minimum line tension at 458 on either{001} or {011} slip planes [36]. Based on the preced-ing discussion it is suggested that at large strains

the ¯ow stress of NiAl single crystal is controlledby the thermally activated cross-slip of screw dislo-cations. Considering that activation energy for plas-

tic deformation is stress dependent, the apparentlylow activation energy calculated for BDT is

suggested to be associated with the cross-slip of dis-locations in the heavily deformed regions in theplastic zone. As temperature is elevated above

BDTT, the apparent toughness becomes moredependent on the yielding of the whole cross-sectionarea rather than the activities near the notch tip.

Thus, the activation energy is increased to valuesclose to the value for yielding.

The low tensile ductility at low temperatures wasfound to be a result of premature fracture in thespecimen shoulder. Decreasing the cross-section of

the specimen in the mid-section by as much as 10%was unsuccessful in persuading the fracture to occurwithin the gauge length. These observations suggest

that NiAl single crystal shows an extreme notchsensitivity. This sensitivity can be attributed to two

e�ects. First, because of elastic anisotropy the elas-tic stress intensi®cation at the notches can be veryhigh for this orientation. This problem could have

been overcome by reducing the cross-section area ofthe gauge length signi®cantly. Secondly, when plas-tic deformation occurs it remains localized and does

not spread, thus crack initiation and propagationoccurs easily. A decrease in the strain hardening


rate and an increase in test temperature reduce theprobability of localization by allowing cross-slip of

dislocations to happen. Therefore, the ductilityincreases drastically if deformation becomes morehomogeneous.

5. CONCLUSIONS

E�ects of temperature, displacement rate, andprestraining on behavior of smooth and double-notched tensile specimens of NiAl single crystal

loaded along a h110i direction were evaluated.Based on the results of this study the following con-clusions have been made:

(1) Ductility and toughness of NiAl single crystalis controlled by the formation of cleavage micro-cracks on slip bands and their subsequent instabil-

ity. Factors that make the deformation moreuniform and/or decrease the stress distributionahead of the microcracks improve toughness.

(2) The high BDTT of NiAl single crystals is dueto an ease of plastic strain localization in this ma-terial which causes crack initiation by a slip decohe-sion mechanism.

(3) The h110i oriented NiAl single crystal deformssimilar to a f.c.c. crystal. Initially duplex slip causeshigh strain hardening and as cross-slip becomes

possible the strain hardening rate decreases signi®-cantly. The thermally activated cross-slip of screwdislocations reduces the slip localization tendency in

this material. The improvement of BDT due to a re-duction of the applied displacement rate is associ-ated with enhanced cross-slip of dislocations.(4) Prestraining retards strain localization at the

notch tip and thus improves low temperaturetoughness by reducing the probability of micro-cracking. The increase in BDT temperature owing

to prestraining arises from an increase in the ¯owstress which raises the stress distribution at themicrocrack tip and hence enhances the probability

of instability.

AcknowledgementsÐThe ®nancial support by the AirForce O�ce Of Scienti®c Research under URI Grant No.F49620-93-1-030 is gratefully acknowledged. The NiAlsingle crystals used in this study were kindly grown byM. J. Kaufman's research group.

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Brittle-to-ductile transition in NiAl single crystals