cyclic deformation of Ni3(Al,Nb) single crystals at ambient and elevated temperatures

Acta meta[l. Vol. 35, No. 9, pp. 2371-2383, 1987 Printed in Great Britain. All rights reserved

Copyright 0

OOOI-6160/87 $3.00 + 0.00 1987 Pergamon Journals Ltd

CYCLIC DEFORMATION OF Ni,(Al, Nb) SINGLE CRYSTALS AT AMBIENT AND ELEVATED TEMPE~TURES N. R. BONDA,? D. P. POPE and C. LAIRD Department

of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104-6272, U.S.A. (Received 8 August 1986)

Abstract-In order to study the cyclic deformation of an alloy crystal and the asymmetry in the flow stress of the y’ phase, Ni,(Al, Nb) crystals have been cycled in strain control at room temperature, 400 and 700°C. The orientation of the crystals has been a major variable studied. At all temperatures, cyclic hardening has been found ~nsiderable and at the two lower tem~ratures, the asymmetry has been found to follow the predictions of the model by Paidar et ai. [Acta metalt. 32, 435 (1984)j which is based on the increase of the dislocation friction stress by thermally activated cross slip onto [OOl]planes. Moreover, TEM observations of the dislocation structures are consistent with the model. At 7OOC, a dominance of the tensile stress in the asymmetry was observed rather surprisingly. The model of Paidar et al. does not apply at this high temperature because dislocation climb and cube slip occurs, and no asymmetry is expected. Cracking and life behavior are also reported. R&u&--Dans le but d’etudier la deformation cyclique d’un cristal d’alliage, et l’asymetrie de la contrainte d’ecoulement de la phase y’, nous avons soumis des cristaux de Ni,(Al, Nb) L des cycles de deformation a la temperature ambiante, B 400 et a 7OO”C,l’orientation de ces cristaux constituant la principale variable etudiee. Pour toutes les temperatures, le durcissement cyclique est considerable, et pour ies deux temperatures les plus basses, l’asymetrie suit les previsions du modele de Paidar et al. fAc?u me&Z. 32, 435 (1984)] modele base sur l’accroissement de la contrainte de frottement des dislocations provoque par le glissement d&e, thermiquement active, sur les plans {OOI}.En outre, les observations en MET des structures de dislocations sont compatibles avec ce modele. A 7OO”C,nous avons observe avec quelque surprise que la contrainte de traction contrcilait l’asymetrie. Le modtle de Paidar et col. ne s’applique pas a cette temperature elevee parce qu’il y a montee des dislocations et glissement cubique, et qu’on ne s’attend a aucune asymetrie. Nous traitons egalement de la fissuration et de la duree de vie, Zusammenfassung-Zur Untersuchung der zyklischen Verformung eines Legierungskristalles und der Asymmetrie in der FlieDspannung der y'-Phasewurden Ni,(Al, Nb)-Kristalle verschiedenster Qrientierung dehnungskontrolliert bei Raumtemperatur, 400 und 700°C zyklisch verformt. Bei samtlichen Temperaturen war die zyklische Verfestigung ~tr~chtlic~ bei den beiden niedrigeren Temperaturen folgte die Asummetrie den Voraussagen des Modelles von Paidar et al. [Acfa metall. 32,435 (1984)] Dieses beruht auf dem Anstieg der Reibungsspannung fiir Versetzungen, hervorgerufen von der therm&h aktivierten Quergleitung auf die [OOl]-Ebenen. Die elektronenmikroskopischen Ergebnisse zur Versetzungsstruktur sind mit diesem Model1 such vertraglich. Bei 700°C wurde tiberraschenderweise beobachtet, da8 die Zugspannung in der Asytnmetrie dominierte. Das Model1 kann bei dieser hohen Temperatur nicht angewendet werden, da Versetzun~klette~ und kubische Gleitung auftreten. Eine Asymmetrie wird eigentlich nicht erwartet. Auf RiB- und S~ndard~itverhalten wird ebenfalls eingegangen.

1. INTRODUCTION The y ’ phase (N&(Al, X) has been a material of considerable engineering interest in recent years since many nickel-base superalloys depend for their

high temperature strength on precipitation of the 7’ phase in Josolid solution. This y’ phase has very unusual monotonic properties such as: (I) a positive temperature dependence of the yield stress showing a peak at some intermediate temperature [I, 21, (2) a breakdown of Schmid’s law [3] and (3) a tensioncompression asymmetry in the yield stress [4,5]. -.tPresent address: Department of Metallurgical Engineering, Ohio State University, USA.

Columbus,

OH 43210,

These anomalous properties are believed to be associated with the ordered structure of y’ and many attempts have been made to understand their origin. The y’ phase has the Ll, ordered structure in which the face-centered sites are occupied by Ni atoms, and the corner sites by AI atoms. A perfect dislocation in this ordered lattice of Burgers vector ]iOl] constitutes the so-called superlattice dislocation and is believed to consist of two ordinary 1/2[iOl] dislocations joined by an anti-phase boundary (APB). Westbrook first observed the anomafous strength increase of N&AI with temperature by measuring hot-hardness f6] and proposed a strain aging mechanism to explain the behaviour. Since then, the temperature and orientation dependence of the flow stress ofv’ phase alloys have been studied extensively

2371

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OF Ni,(Al, Nb) CRYSTALS

and the phenomena have been repeatedly reviewed [7-91. Several theories have been put forward to explain the anomalous peak in the flow stress of these high APB energy Ll, ordered alloys, such as:

Dislocation structures in these specimens were also studied and are reported in a companion paper [16].

(1) Diffusive mechanism, proposed by Flinn [l] in which dislocations are dissociated on (111) planes at low temperatures, but as the temperature is raised, diffusive mechanisms allow climb of one dislocation so that the pair is now separated by a low energy ABP on the (010) plane and is therefore immobilized (APB’s on (010) planes are expected to have a low energy since there are no nearest neighbor violations across such faults); (2) The cube slip mechanism [2], which implies that cube-slip occurs because octahedral slip is abnormally difficult due to Kear-Wilsdorf locks (in the Kear-Wilsdorf mechanism [lo], pinning of screw dislocations occurs due to cross slip from (111) planes where dislocations are mobile, to (010) planes where they are immobile. The driving force for cross slip is the difference in APB energy on the two planes); and (3) the cross-slip mechanism, proposed by Takeuchi and Kuramoto [3], based on the dynamic interaction between primary dislocations on {11 l} planes and jogged segments (with respect to slip on { 111)) which have cross-slipped onto (010) planes as a result of thermal activation. An increase in temperature promotes more cross-slip and therefore a higher flow stress. The decrease in the flow stress at high temperatures was attributed [3] to macroscopic slip on {OOl} planes. In addition, it was found that Schmid’s law did not hold, i.e. the larger the stress component on the (010) cross-slip plane the higher the critical resolved shear stress for [iOl](l 11) slip.

Three Ni,(Al, Nb) single crystals, one supplied by Pratt and Whitney Co. and two supplied by General Electric Co. were used in this investigation. The chemical composition of these single crystals, according to the suppliers, is 75 at.% Ni, 20 at.% Al and 5 at.% Nb. Wet chemical analysis by a specialist firm (International Testing Laboratory, Newark, N.J.) showed deviations from this composition by several percent but repeat analyses were found to vary around the suppliers’ composition. The composition is therefore considered “as received”. The as received crystals were homogenized at 1100°C for 3 days in an argon atmosphere, a process which was checked as satisfactory by EDAX analysis. The specimen design for room temperature testing is shown in Fig. 1. For tests at elevated temperature, the design is essentially the same except they have longer threaded lengths (28.6mm) to accommodate heaters which were screwed onto the threads at each end of the specimens. Specimens for elevated temperature tests were made out of the GE single crystals. Because of the limited size of these single crystals, it was not possible to machine specimens with orientations far removed from that of the growth axis [OOl]. All cyclic tests were performed using a CGS servohydraulic system under fully reversed plastic strain control at 0.1-0.2 Hz frequency. A sine wave loading signal was selected. Tests at room temperature were performed in air. At elevated temperature, tests

Since the introduction of these theories, much research work has been done to elaborate on them, and one of the most interesting discoveries has been the observation of the tension-compression asymmetry briefly noted above and which can be predicted from the cross-slip mechanism [1 1, 121. Such an observation naturally stimulated research into cyclic deformation [13-151. In an attempt to further the understanding of the cyclic deformation behavior of y ’ phase at different temperatures, cyclic tests have been carried out on Ni,(Al, Nb) single crystals at room temperature, 400 and 700°C (near the temperature corresponding to the peak in the flow stress). Since the monotonic properties are orientation dependent, the orientation effect on the cyclic behavior and tension-compression asymmetry have been studied. Results of cyclic hardening measurements, the observation of cracks on the surfaces of fatigued specimens and fatigue lives are reported in this paper.

2. EXPERIMENTAL

IT 17.5mm

l-

Fig. 1. Specimen design for fatigue testing at room temperature. Note the grooves in the shoulders for positioning the extensometer.

BONDA et al.:

CYCLIC DEFORMATION

performed in a high purity argon atmosphere. Elongation was measured with an Instron clip-on type extensometer which was attached across the shoulders (in the grooves) of the specimen. Thus the total strain was measured across the specimen shoulders, but the plastic strain was assumed to be limited within the gage length. This assumption seems justified because of the high strength of these specimens and the low plastic strains used in this study. To measure elongation in the elevated temperature tests, a scissors-type coupling was introduced between the Instron extensometer and the sample to protect it from the high temperature. Hysteresis loops were obtained by recording the load and elongation signals on a digitizing memory oscilloscope (Tektronix 5223). The hysteresis loop of each cycle during the entire test was observed and the loop width (which is a measure of plastic strain) was controlled manually be adjusting the total strain. Periodically, these loops were recorded on an X-Y recorder. Some of the specimens were tested by an incremental multiple step method 1171. A step test ceases to give valid info~ation about cyclic hardening if a crack develops in the specimen. Most cyclic tests were discontinued before complete failure to study strain localization and cracking behavior on the surface and to investigate the dislocation structures by TEM. The orientations of the specimens were dete~ined by X-ray Laue diffraction technique.

itr

were

3. RESULTS

2373

OF Ni,(AI, Nb) CRYSTALS

Sri (c) 7oo”c 713 ‘\ 0:: \ \ c ‘\, \t A\\ &\ \ \ A 001 ’ 012

011

Fig. 2. Orientations of the monocrystalline specimens arranged in the regions A, B and C of the standard triangle.

3.1. Cyclic ~lardeni~g beha~~or Table 1 shows the orientations of the specimens used in this investigation and the temperature at which they were tested. Specimens 2, 3 and 4 were machined from the single crystals supplied by Pratt and Whitney and the remaining specimens were machined from the single crystals supplied by General Electric Corp. The orientations of these specimens are also shown in the OOl-Oll-111 standard triangle in Fig. 2. The orientations were divided Table I. Orientations of the fatigue specimens and their test temperatures Specimen

1 2” 3” 46 5 6 7 8 9 10 11 12 13 14 I5

Orientation

f, 1.6,12.3 T, I .o,3.4 T, I .4,6.2 T, I .o,5.3 i, 1.7, 3.8 T, 2.0,4.5 T, t.5,25.8 f, 4.2,47.6 T, 4.0, 38.0 T, 1.4,3.8 T, 1.2,3.4 f, 2.2, 28.6 T, 9.0, 128.6 7,l.l. 3.3 T, 1.2, 3.8

Test temperature (“ct R.T. R.T. R.T. R.T. R.T. R.T. 400 400 400 400 400 700 700 700 700

aMachined from the crystal supplied by PW, the remaining from the crystals supplied by GE.

into three regions A, B and C as shown in Fig. 2. Region A is near (OOl), C is near the 012-113 great circle and B is between these two. These three regions are specified because the tensio~ompression asymmetry behavior is predicted to be different in each region [12]: Specimens of orientations in regions A and C were tested at 400 and 700°C. At room temperature, specimens having orientations in region B were also tested. 3. I. 1. Room temperature results. Cyclic hardening curves of specimens I and 2 which were tested by the multiple step method are shown in Fig. 3. To demonstrate the asymmetry expected in y ’ single crystals, tensile and compressive stresses are shown separately in the cyclic hardening curves. Normally the cyclic hardening curve is conventionally shown as the average of these stresses. The orientation of specimen 1 is in the region A and that of specimen 2 is in the region C (see Fig. 2 and Table 1). Specimen 1 was saturated at y,, (plastic shear strain amplitude) of 5.3 x lo-‘, 7.0 x 10s5, 8.8 x low5 and 1.3 x lO--4 and developed a crack at 1.75 x IO-“ before it reached saturation (Fig. 3). Specimen 2 developed cracks during the test with y,, 8.8 x lo-‘. Values of yp, vs the saturation stresses, averaged for tension and compression for both step tests, are shown in Table 2.

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175

CYCLIC DEFORMATION

T

-

125

Table 2. Plastic strain amplitude vs average saturation stresses for specimens 1 and 2

_

c

C{

(0) 8

’

’

’

5.3x10-5 ’ ’

’

I

OF Ni,(Al, Nb) CRYSTALS

Plastic shear strain amplitude

Specimen

’

Specimen 1

5.3 x 7.0 x 8.8 x 1.3 x 1.75 x 3.6 x 5.5 x 7.2 x 8.8 x

Specimen 2

200’

’

’

’

’

’

’

’

’

’

’

350

I

,

,

,

,

,

I

,

I

,

,

(

,

:,p,

;;; 1

500

1500

1000

Number

1 275

751

I

of

I

I 2000

Cycles

I

Number

(0

I 3000

2500

2000

-

I 1000

1

I 4000

I

Average saturation shear stress (MPa)

10-S 10-S 10-S 10-d 10-d 1O-5 10-s lo-’ 10-S

172.7 196.2 234. I 299.7 3 11.4 (peak stress) 176.5 199.0 230.5 252.2 (peak stress)

Specimens 3 and 4 have orientations in region B, i.e. in between the orientations of specimens 1 and 2. These show no asymmetry which agrees with the prediction. Specimens 5 and 6 had orientations in region C and both showed C > T asymmetry. For cyclic tests in normal metals, a difference in tensile and compressive stresses of up to 5%, almost exclusively C > T, is usually observed. For example, in copper single crystals, Finney [18] observed C > T by about 4%. The reason for this regular asymmetry is not known. In the light of this common behavior, it is rather difficult to justify the asymmetries observed for specimens 2, 5 and 6 which have a difference of about 5%. Therefore, in spite of the consistent C > T

R.T.

I 5000

6000

of Cycles

Fig. 3. Cyclic hardening curves for specimen (l), (a) to (e), and specimen (2) (f), tested by the multiple step test method at the plastic shear strain amplitudes indicated. The specimen number indicates the orientation, keyed to Table 1. T-tensile stress; C*ompression stress; the same conventions are used in later figures.

1001

’

I

’ 2000

!

.

I

4000

Number

6000

of

I

100

Cycles

(b)

Aside from the considerable hardening shown in these tests, an important feature of Fig. 3 is that the

tensile stress (T) is greater than the compressive stress (C) for specimen 1, whereas the compressive stress is greater than the tensile stress for specimen 2. This demonstrated that the expected asymmetry is observed in cyclic deformation and the sense of the asymmetry for specimens 1 and 2 is in agreement with the predictions of the Paidar et al. model [12] for monotonic deformation. In addition to these multiple step tests, specimens 3-6 were tested by the constant amplitude method to find more evidence for the asymmetry. Cyclic hardenine curves for these tests are shown in Fig. 4.

1001

1

’

’ 2000

’

Number

’ 4000

of

t

’ 6000

1 6OOC

Cycles

Fig. 4. Cyclic hardening curves obtained at room temperature in constant amplitude tests for specimens 3 and 4 (a), and for specimens 5 and 6(b).

BONDA

et al.:

CYCLIC

DEFORMATION

OF Ni,(Al,

2375

Nb) CRYSTALS

Table3. The plastic shear strain and asymmetry ofcyclictests at room temperature with parameters N and Q Specimen 1

2 3 4 5 6

Y”,

5.3x 10-sto 1.75x 10-5 3.6-8.8x 10-S 8.5x 10ms 8.5x 10-s 4.0 x 10-5 2.0 x 10-s

Asymme~

Orientation

N

T>C

A

0.21

0.35

C>T T=C T=C

C B 3

0.48 0.37 0.33 0.64 0.63

0.08 0.19 0.21 -0.06 -0.05

C>T

c

C>T

c

0

T = Tensile stress; C = Compressive stress

asymmetry for these specimens, the asymmetries are considered to be very small. But for specimen 1, where T > C by up to 18%, the asymmetry is rather large and therefore considered as convincing evidence for- the asymmetry due to the model predicted by Paidar et al. Values of y,,, the as~metry in the tensile and compressive stresses of the hardening curves and orientation parameters N and Q for specimens l-6 are tabulated in Table 3. N is defined as the ratio of the shear stress on the cube cross slip system to the shear stress on the primary octahedral slip system (N = (OlO)[iOl]/(l lI)[iOl]) and Q is defined as the ratio of the shear stress that constricts the superpartials on the primary slip system to the shear stress on the primary octahedral slip system (Q =(lll)[l~l]/(lll)[~OlJ). N and Q are important parameters when dealing with the effect of orientation on flow stress and asymmetry. The results shown in Table 3 confirm that asymmetry in cyclic deformation falls in line with the predictions for monotonic defo~ation. Cyclic stress strain curves (CSSC), based on cyclic multiple step tests, for specimens 1 and 2 are shown

1 i

3MF *c(5)

in Fig. 5. Note that the CSSC of specimen 2 lies above that of specimen 1 and therefore indicates an effect of orientation. In these CSSCs, the peak stresses are indicated since the hardening curves are nonstandard in not showing saturation. However, saturation appears to be nearly attained especially for specimen 2, by the time the specimen fractured, The strain range of these CSSCs is limited by the development of cracks at 1.75 x 10e4 and 9.8 x low5 respectively. In spite of the fact that single crystals were employed for testing and strain localization is common in this material, no evidence was detected of a plateau in the CSSCs within the strain range tested. The slope change in the CSSC of specimen 1 could be caused by the fact that a major crack formed during the last step and it is possible that the specimen could have hardened further in the absence of this crack. The peak stresses of specimens 3, 4 and 5 vs their yp, are also shown in Fig. 5. As noted, these stresses are far above those of the CSSCs of specimen 1 and 2 which indicates that the saturation stresses are also cyclic history dependent besides being orientation dependent.

a0

(4)

2o01

L j

’ 600

’

I

16’2

171 IS] 191

’ 1500

’

1000

Number

Q) 240m e z a 200 ..

------2.3X1O-5 -4.6X165 --

-9.0x10-5 ’

2000 2500

1 3000

of Cycles

(b)

1

4

1 6 Shear

’ ’ ’ 8 10 12 Plastic Strain,

’ ’ 14 16 yp*105

’ 18

1 20

Fig. 5. Cyclic stress-strain curves for Ni,(Al, Nb) at room temperature and for various crystalline orientations identified by specimen number and region (letters) of the stereographic projection.

,601

1

100

200

300

Number

400

500

600

700

of Cycles

Fig. 6. Cyclic hardening curves for Ni,(AI, Nb) at 400°C for specimens: (a) in the A region of orientation, (b) in the C region of orientation.

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Nb) CRYSTALS

Table 4. Plastic shear strain amplitude, asymmetry, N and Q for tests at 400°C Specimen

1.1

2.3 x 4.6 x 9.0 x 4.2 x 1.3 x

I

8 9 10 I1

Asymmetry

Orientation

N

0

T>C T>C T>C C>T C>T

A A A C c

0.10

0.47 0.45 0.43 -0.01 0.00

IO-’ 10m5 10-s IO-’ 10-a

0.14 0.17 0.59 0.58

Table 5. Plastic shear strain amulitude. asvmmetrv. N and 0 for the tests at 700°C Specimen

% 4 x 10-S 4 x 10-S 4 x 10-S 1 x 10-d

12 13 14 15

Asymmetry

Orientation

N

Q

T>C T>C T>C T>C

A A

0.13 0.11 0.56 0.51

0.45 0.49 0.01 0.06

3.1.2. Hardening results at 400°C. Cyclic hardening curves of specimens 7, 8 and 9 (orientations in region A) are shown in Fig. 6(a). All these specimens showed T > C by about 1620%. Cyclic hardening curves of specimens 10 and 11 (orientations in region C) are shown in Fig. 6(b) and those specimens showed C > T by about 7%. All these specimens developed cracks at the ends of the tests. Also, only specimen 7 reached saturation but specimens 8-l 1 developed cracks before they reached saturation. Therefore no CSSC could be plotted for tests at this temperature within the strain range investigated. Table 4 shows the values of yp,, asymmetry, N and Q for the tests on specimens 7-l 1. Asymmetries observed at this temperature are consistent with those observed at room temperature and therefore are in agreement with the model by Paidar et al. Note that the cyclic hardening curves at this temperature started at higher stresses (around 275(a) 4

700%

400-

‘A’

,

1200

1400

4.0x10-5

,_______------___

-- T

---*

I

I

I

0

1121 I131

1

2001 1

200

400

600

Number

600

of

1 1000

Cycles

325

MPa) compared to those at room temperature (100-l 50 MPa) for similar plastic strain amplitudes. This indicates that the pinning of screw dislocations (and therefore the action of an anomalous strength increase with temperature) occurs almost from the beginning of the cycling. This is attributed to higher thermal activation at 400°C. 3.1.3. Hardening results at 700°C. Cyclic hardening curves of specimens 12 and 13 (orientations in region A) are shown in Fig. 7(a) and those of specimens 14 and 15 (orientations in region C) are shown in Fig. 7(b). The hardening rate is high in the first lo&200 cycles and the specimens then saturated. However, they all developed cracks at the ends of these tests, so it was not possible to continue testing with steps of higher amplitude. Therefore no CSSC is available. As shown in Fig. 7 and Table 5, all cyclic hardening curves showed T > C asymmetry, irrespective of their orientations, N and Q. This is not in agreement with the Paidar et al. model since it predicts C > T for specimens 14 and 15, if pinning of screw dislocations is an effective strength increasing mechanism at this temperature. However, around 700°C cube slip was usually observed to operate for the orientations in region C, in which case no asymmetry aside from the usual compressive bias should be expected. In either case, the T > C asymmetry for specimens 14 and 15 is difficult to explain. These results cannot be considered in disagreement with the predictions of Paidar et al., because the specifics of the model may not apply at such a high temperature. 3.2. Surface observation of fatigued specimens

(b) ____---__

Number

‘-7

of

1 l.oXl64rl5)

Cycles

Fig. 7. Cyclic hardening curves for Ni,(Al, Nb) at 700°C for specimens: (a) in the A region of orientation; (b) in the C region of orientation.

Cyclic tests were discontinued before complete failure and this permitted surface observation of the specimens tested at room temperature, 400°C and 700°C. The results are reported as follows: 3.2.1. Stage I cracks at room temperature. All cracks on the surfaces of the specimens tested at room temperature were found to be of the stage I type on crystallographic {111) planes, irrespective of the orientation and test amplitude of the specimens. Fig. 8(a) shows one of these cracks on the surface of a specimen tested at a yp, of 2 x 10m4for about 2000 cycles (specimen 6). This crack is considered to be in the early stages of propagation. The central region of

BONDA et al.:

CYCLIC DEFORMATION

OF Ni,(Al, Nb) CRYSTALS

2377

Fig. 8. Stage I crack in Ni,(Al, Nb) tested at y,, = 2 x lo-’ for about 2050 cycles (specimen 6) at room temperature. (a) Short crack in early stages of propagation; (b) view of central region of crack at higher magnification. In this later figures, the stress axis is horizontal.

Fig. 9. Stage I crack on specimen 5 tested at yP1= 4 x tom5 for about 6700 cycles at room temperature. (b) A detail from (a), region X, indicating signs of plastic deformation on the fracture surface.

the crack is shown magnified in Fig. 8(b) and a part of its fracture surface is visible. Absence of evidence of large plastic deformation on the fracture surface indicates that stage I cracks in these crystals nucleate in a narrow band. The mechanism of stage I crack nucleation in these crystals is not known, but one possible mechanism is weakening of a slip band in a local region which is caused by strain localization due to cyclic deformation. Stage I cracks were also found to nucleate at casting pores on the surface. As is well known in this type of material, surface pores act as stress raisers and thus become the potential sites for crack nucleation. Internal pores can have a similar effect on crack nucleation, but the investigation done in the present work was not sufficient to support this. The stage I cracks nucleated in these crystals at the pores do not necessarily have to be fatal always, but they could be fatal in the absence of larger cracks. The shear stress was found to play a major role in the crack propagation process. This can be seen in a specimen tested at a yP, of 4 x 10m5 for about 6700 cycles (specimen 5). A stage I crack on its surface is shown in Fig. 9(a). A view of an area near X in this figure is shown in Fig. 9(b) at higher magnification. This shows a part of the fracture surface. The appearance of this fracture surface indicates that plastic

deformation occurred on this surface during fracture; this emphasizes the role of shear stress in the crack propagation process. Therefore, even though some of the cracks appear crystallographic enough to be of the cleavage type (which may suggest that they propagate in one or a few applications of tensile stress) they are actually stage I cracks, propagated in a cyclic manner by localized plastic deformation. The orientations of the specimens and the strain amplitude of the test (within the range tested) were found to have no effect on the cracking behavior. 3.2.2. Stage I cracks at 400°C. Cracks on the surface of specimens tested at 400°C were also found to be of stage I type. Figure 10(a) shows a typical stage I crack on the surface of a specimen tested at yP, of 4 x lo-’ for about 600 cycles (specimen IO). This crack has propagated entirely on one crystallographic {1 I l} plane. Even though it seems sharp enough to look like a cleavage crack there is evidence of considerable plastic deformation on its fracture surface which emphasizes that it too is a regular stage I crack. Evidence for the plastic deformation on the fracture surface is shown in Fig. 10(b). indicating the nature of the fracture surface along the band. This fracture surface is inclined to the plane of the figure. Rubbing due to the cyclic shear stress occurred in the area A, but the rough surface on either side of this

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CYCLIC DEFORMATION

OF Ni,(Al, Nb) CRYSTALS

Fig. 10. Sharp stage I crack in specimen 10 tested at yr, = 4.2 x 10m5for about 600 cycles at 400°C. (a) Apparent curvature of the crack is caused by the cylindrical form of the gage section; (b) Area near x seen at higher magnification.

Fig. 11. Fracture surface of specimen 9 tested at yr, = 9 x 10m5 at 400°C showing fatigue striations on two { 111) planes. Cycles to failure = 450 cycles. (b) shows a detail from the left hand fracture in (a).

area in the band indicates that plastic deformation

1 x 10e4 for about 530 cycles. The orientations of these cracks wander with respect to the stress axis, which suggests that they are stage II cracks. It can be seen from Fig. 12 that the crack orientations tend to be stage I-like, but they are not sufficiently crystallographic to be considered stage I cracks. Therefore, it is suggested that the cracks at 700°C are of the stage II type because of the distinct difference of their nature from the stage I cracks observed at room temperature and at 400°C. In Fig. 12, some openings can be seen along the traces of the cracks. A close observation indicates that these openings are formed by the shear of the top and bottom portions of the specimen across the crack (“closure induced by crack roughness”). This shearing is suggested to occur from the complex state of stress at the crack tip which may develop as the crack becomes larger.

occurred in the process of fracture. More evidence for the stage I cracks and their cyclic growth can be found in a specimen which was tested at yr, of 9 x 10m5 for about 450 cycles (specimen 9). This specimen fractured completely during the test. The fracture surface of this specimen is shown in Fig. 11(a). As can be seen in this figure, fatigue crack propagation occurred on two crystallographic {11l} planes, as confirmed by measuring the angle between these two planes. It was found to be 70” as expected. The stage I fracture covered almost the entire fracture surface. Final fracture occurred at the vertex of the fracture surface. In this figure and in Fig. 11(b), striations and beach marks are shown. Striations are not typical of stage I fracture surfaces and they indicate that stage II crack propagation occurred on a {111) plane. Similar to the behavior observed at room temperature, orientation was found to have no effect on the cracking behavior at 400°C. 3.2.3. Crack propagation at 700°C. Surface cracks at this temperature were found to be significantly different from the stage I cracks observed in specimens tested at room temperature and at 400°C. Typical cracks on the surface of specimen 15 are shown in Fig. 12. This specimen was tested at yD,of

3.3. Fat&e

lives

Although establishing the fatigue fracture behavior of these y’ phase single crystals was not one of the aims of the present investigation, the specimens nevertheless developed cracks during the cyclic tests, and one of them ran to complete fracture. It is of value to record this behavior. The number of cycles at which cracks were observed to develop (N,) (by the

BONDA

et al.:

CYCLIC

DEFORMATION

OF Ni,(Al,

Nb) CRYSTALS

2319

012 Fig. 13. The predictions of the model by Paidar ef nl. [l2] for the orientation dependence of the tension/compression asymmetry in the flow stress of Ni,Al.

those observed at room temperature. It was also observed (not evident from Table 6) that cracks propagated much faster at 400 and 700°C compared to behavior at room temperature. Since the stresses in the cyclic hardening curves are higher at 400 and 700°C due to the anomalous behavior of the y ’ phase, once strain localization occurs, cracks nucleate and propagate more easily at these temperatures because of the high stress intensity. This is suggested to be the main reason for the lower lives of single crystals at elevated temperatures. Fig. 12. Stage II cracks visible at the gage surface of specimen 15 tested at 7 = 1 x 10e4 for 530 cycles at 7OO”C, illustrating typical crack morphology.

of the hysteresis loop), the total number of cycles (A’,), the various temperatures of the tests, and yp, are summarized in Table 6. As can be noted from Table 6, the N, of these specimens were lower at 400 and 700°C compared to shape

change

Table

6. Lwes of Ni,(AI, Nb) single crystal specimens different temrxratures and YY.,

Specimen

Test temperature

I”

Room

2”

Room

3 4 5 6 I 8 9d IO II I2 13 14 15

Room Room 400°C 4oo‘c 400°C 400 ‘C 400’ c 700 c 700-c 700°C 7OO‘C

Yp1 5.3 x 7.0 x 8.8 x I.3 x I.8 x 3.6 x 5.5 x 7.2 x 8.8 x 8.5 x 8.5 x 4.0 x 2.0 x 2.3 x 4.6 x 9.0 x 4.2 x 1.3 x 4.0x 4.0 x 4.0 x 1.0 x

IO 5 10-s IO-’ 10-d 10~’ IO-’ 10-5 IO 5 IO ’ 10m5 IO-’ 10-s 10-d IO-’ IO-’ 10-S IO-’ 10-d 10 5 10-s 10-S 1om4

N, 2200b 2OOb 1600b 2400b 500 5000b 3600b 3200b 1500 4800 6700 6400 2050 2500 1800 300 570 550 1000 800 800 500

tested

at

N,

600

2400 5400 7200 6700

1920 450 600 II60 1250 900 530

(“multiple step tests; bsaturation, no cracks; ‘total number of cycles experienced by the crystals without complete fracture, but very close to fracture; %omplete fracture).

4. DISCUSSION 4.1.

Cyclic deformation

behaoior and asymmetry

The research reported here has emphasized cyclic hardening and asymmetry in Ni, (Al, Nb). It is appropriate to consider other research which has been done in response to the theories of the so-called anomalous temperature effect outlined in the introduction. For example, Mulford and Pope [19] observed that the micro-yield strength (tp, = 5 x 10m5) is temperature independent up to 870°C and suggested that the strain in the micro-yield region is carried by a small density of mobile edge dislocations. La11 et al. [I I] modified the Takeuchi and Kuramoto theory and predicted tension-compression asymmetry in the yield stress of y ‘-phase alloys depending on the crystallographic orientations. Based on the study of dislocation core configuration in Ll, ordered alloys [20,21], Paidar et al. [ 121 modeled the cross-slip process and predicted the tension-compression asymmetry in y’-phase alloys as shown in Fig. 13; i.e. for orientation near [OOl], the tensile flow stress is greater than the compressive flow stress (T > C), near the [012]-[i13] great circle, but on the [OOl] side, T = C; and C > T for the other regions of orientation in the standard triangle. These predictions have been confirmed by the experimental results of Ezz et ul. [4] and Umakoshi et al. [5]. So far, the pinning of screw dislocations by cross-slip appears to provide a valid mechanism for the strength increase of the 7’ phase with temperature. However, recent work by Veyssiere et al. [22] and Veyssiere [23] indicated support for

2380

BONDA et al.:

CYCLIC DEFORMATION

the earlier predictions of Flinn’s theory [l]. Based on a TEM study using weak beam technique, these workers concluded that at intermediate temperatures, the influence of cross-slip and climb dissociation would be superimposed, and that the lower the temperature, the stronger is the role played by the cross-slip. The temperature and orientation dependence of the monotonic flow stress and the deformation behavior of Ni, Al single crystals have been studied very extensively [l-12, 19-231, but the effect of anomalous behavior in cyclic deformation has not been studied in detail. Doherty et al. [24] found that fatigue life of alloyed y’ in pulsating stress controlled tests was independent of temperature below 800°C; whereas the fatigue life in strain controlled tests decreased with temperature. The difference in behavior was attributed to a temperature dependent differential dislocation mobility [19]. Nothing was mentioned about whether tension-compression asymmetry was observed in these fatigue tests. Jablonski and Sargent [ 131observed a particularly large asymmetry (T > C) in the cyclic hardening behavior of y + y’ alloy crystals having an [OOl] orientation and cycled at 760°C and under strain control. But later, Anton [14] argued that the asymmetry observed by Jablonski and Sargent was due to an experimental error. More recently, Ezz and Pope [ 151performed fatigue tests on y’ single crystals and observed that cyclic hardening and asymmetry are orientation-dependent. In addition to this they also observed that a plastic strain of more than 1 x 10m4 is needed to cause asymmetry. Based on this observation they suggested that the amount of plastic strain amplitude in the fatigue tests influences the asymmetry (because the flow stress temperature anomaly of N&Al has been shown to disappear in the micro-yield region [19]). In the results described here, the orientation dependence of the tension and compression stress asymmetry is in agreement with the predictions of the model suggested by Paidar et al. for monotonic deformation, but only for the cyclic tests at room temperature and 400°C. At 7OO”C, tensile stresses were found to be greater than compressive stresses for all the specimen orientations tested in the present study. Comparing with the results of Ezz et al. [4] who performed yield stress measurements on the same materials they found that T > C at about 700°C for samples oriented near [OOl], the same result as found in this study, but for a sample located on the [012l_[T13] great circle, 700°C is above the peak temperature and hence the Paidar et al. model does not apply. Paidar [25] has recently proposed a theory which is applicable for temperatures above the peak temperature for thermally activated motion of [IlO] screw dislocations on (001) planes. In this theory it is assumed that the dislocation core lies alternately on (111) and (1 li) planes, and thermal activation is required to bring about the transformation. Unfortunately, the theory predicts that any asym-

OF Ni,(Al, Nb) CRYSTALS

metry in this temperature range should be of the type C > T, opposite to what has been observed in the present study. This model is also not applicable to the present study since, as is described in the next paragraph and in Ref. [16], edge dislocations seem to dominate in the deformation of this material at 700°C. To explain the cyclic deformation behavior and asymmetry observed, dislocation structures in these fatigued specimens (reported in a companion paper [16]) were studied in detail by using TEM. Briefly, the dislocation structures in a specimen tested at room temperature were found to contain a small density of edge dislocation dipoles and a relatively large density of screw dislocations. These screw dislocations were observed as dipoles as well as single unit dislocations proving that they were a great deal less mobile than regular screw dislocations. Thus it was clearly demonstrated that both edge and screw dislocations participate in the cyclic hardening of y ’ phase single crystals at room temperature even at small plastic strain amplitudes. This may be the reason for the observation of asymmetry at plastic strains which were previously considered as micro-plastic strains by Ezz and Pope [15]. These workers, as noted above, observed that a plastic strain of 1 x 10m4is needed to cause asymmetry. However, the results obtained here show that the asymmetry exists in the fatigue tests using microplastic strain amplitudes because a large amount of cyclic hardening occurred in all these tests (see Figs 3 and 4). Such a hardening cannot be explained by the movement of a small density of mobile edge dislocation during cycling at these strain ranges. Furthermore, in copper single crystals, it is well established that to and fro motion of edge dislocations causes them to be trapped as dipoles and this reduces the density of mobile dislocations. This in turn causes cyclic hardening in copper. As evidenced by the dislocation structures, a similar trapping of edge dislocations occurs in these y ’ crystals which would prevent them from carrying any more plastic deformation. In that case screw dislocations would be forced to participate in the deformation and to accommodate a large cumulative plastic strain. TEM study supports the participation of screw dislocations. Once they participate, pinning of these screw dislocations by the Kear-Wilsdorf mechanism can occur even at room temperature (the anomalous strength increase with temperature was observed between 77 and 298 K in this phase). But the amount of pinning will be much less than at elevated temperatures. Once pinning of screw dislocations occurs, asymmetry is expected depending an orientation. Pinning of screw dislocations can also explain the large cyclic hardening observed in these tests. From these considerations, it is suggested that the mechanisms of monotonic and cyclic deformation are different in the micro-yield regions. The discrepancy between the observations of the present study and those of Ezz and Pope is un-

BONDA et al.: CYCLIC DEFORMATION OF Ni,(Al, Nb) CRYSTALS

explained. Ezz and Pope performed their particular fatigue test under total strain control. In this test, the plastic strains decreased continuously due to cyclic hardening during the test. It is not known whether this will have any effect on the asymmetry behavior, but it very well may have an effect. In monotonic deformation of the y ’ phase, the yield strength was found to be o~entation dependent besides being temperature dependent [3-5,7,9, 11, 191. This is due to the fact the pinning of screw dislocations is aided by the resolved shear stress on the cube slip plane and the constriction stress on the superpartials. A similar dependency of cyclic deformation on the orientation can be seen by the difference in the saturation stresses and in the CSSCs for two specimens which have different orientations (Fig. 5). The saturation stresses were found to be higher for the specimen having higher N and Q ratios which could be caused by more pinning of screw dislocations with increasing N and Q. During saturation the reversible plastic strains are speculated to be carried [l] by the “flip-flop” motion of edge dipoles as the cyclic stress drives them from one 45” equilibrium position to the other, [2] the bowing of the unpinned segment of screw dislocation dipoles and [3] the regular glide of unpinned single unit screw dislocations. It was also observed in the present study that the saturation stresses are strain history dependent for Ni,(Al, Nb) single crystals as seen in Fig. 5, i.e. the saturation stress is different for a multiple step test and a constant amplitude test for the same yp,. Saturation stresses were found to be higher for constant amplitude tests. This could be due to the participation in the deformation of a larger population of screw dislocations in the constant amplitude tests compared to that in multiple step tests. Specimens 3 and 4 were tested at the same ypl and have orientations in region B. But as noted in Fig. 4, the cyclic hardening for specimen 3 is slightly larger than that of specimen 4. These specimens also have similar values of N and Q. One difference between these two specimens is the ratio # of the Schmid factor for the second most highly stressed system as compared to that of the primary system. This ratio is 1.0 for specimen 3 and 0.94 for specimen 4. Such a small difference is not expected to cause a major change in hardening behavior. Besides, the effect of this ratio on cyclic hardening should be opposite to that found in specimens 3 and 4, according to a previous study of copper single crystals by Cheng 1171.He also observed that this ratio has no effect on hardening below yp, of 8 x lob4 which is a much “smaller“ strain in copper crystals than it is for Ni)(Al, Nb) single crystals. The reason for the difference in the hardening behavior of specimens 3 and 4 is not known and the difference is too large to be attributed to scatter. Specimens 5 and 6 have similar values of N, Q and d, and were tested at different yp,. As shown in

2381

Fig. 4(b), the hardening rate of specimen 6 (ypl= 2 x 10m4) is much higher than that of specimen 5 (Y,~= 4 x lo-s). This indicates that the higher the y,,,, the higher the cyclic hardening rate which is normally observed in cyclic tests. In these y’ crystals this could be due to pinning of a larger number of screw dislocations at the higher strain amplitude. At 4OO”C, the amount of pinning by screw dislocations involving the Kear-Wilsdorf mechanism increases due to the greater capacity for thermal activation. This is confirmed by the large number of long straight screw dislocations observed in a specimen cycled at 400°C [16]. It is therefore concluded that the Kear-Wilsdorf mechanism plays a major role in cyclic hardening at 400°C. The specimen tested at 4OO”C, for which the dislocation structures were reported [16], was cycled at y,, of 4.6 x 10m5.This is normally considered as a micro-plastic strain amplitude. However, clear indications of screw dislocation pinning at this ypl confirm that the mechanisms of cyclic and monotonic deformation are different in this region of strain amplitudes. We attribute the difference. to the large cumulative plastic strains in cyclic tests. Therefore, the observed tensioncompression asymmetry is not surprising in cyclic tests even at small plastic strains. In Fig. 6, the cyclic hardening of specimen 10 would reasonably be expected to be lower than that of specimen 11 since the latter was tested at larger yp,. Both specimens have similar values of N and Q, and have different Q,values. But this should cause an even larger amount of hardening in specimen 11 since its value is 0.94 compared to 0.87 for specimen 10. The reason for this discrepancy is not known. However, high temperature testing in controlled environment is difficult and there may have been an undetected experimental problem. The model suggested by Paidar ef al. [12] requires pinning of the screw dislocations by cross slip onto (001) as the mechanism for the strength increase with increasing temperature. The dislocation structures observed in the specimens tested at room temperature and 400°C indicated that the strength increase occurs by this mechanism at both temperatures. But at 7OO”C,the dislocation structures contained long edge dislocations as well as long screw dislocations [16]. Therefore it is suggested that the climb of edge dislocations also plays a major role in increasing the strength at 700°C. Because of this the model of Paidar et al. is not applicable at 700°C or only partially so. The climb process depends on thermal activation and the availability of vacancies and it does not depend on the stress or the orientation dependence of the yield stress. Climb is believed to occur at elevated temperature as shown by Veyssi&re [22,23]. Some direct evidence for this climb process was also found in this investigation f16] in the specimen tested at 700°C. Also it was shown in monotonic deformation that cube slip occurs near the peak temperature in the

2382

BONDA et al.: CYCLIC DEFORMATION OF Ni,(Al, Nb) CRYSTALS

strength versus temperature curve if the resolved shear stress on the cube planes is high enough [ll]. In that case no asymmetry is expected near this temperature range except for the special conditions assumed by Paidar [25] and mentioned above. Since these conditions do not apply for the present investigation, the reason for the T > C asymmetry for the specimens tested at 700°C is not known. 3.2. Surface observation of fatigued specimens All cracks on the surfaces of the specimens tested at room temperature and at 400°C were found to be of stage I type. These cracks usually propagate on crystallographic {111) planes. They are believed to nucleate in a narrow band and one factor in the mechanism for this nucleation is weakening of the material in the slip band which is caused by strain localization due to cyclic deformation. Even though some of the cracks appear to be of the cleavage type, evidence of plastic deformation on the fracture surface, and propagation of these cracks on {111) planes in the normal cyclic manner emphasized that these are actually regular stage I cracks. Stage I cracks were also observed to nucleate at casting pores and these can cause failure in the absence of larger cracks formed from persistent slip bands. Some of these results are in line with those of Gabb et al. [26] who reported fracture modes for Rene N4. However, the small stage II regions reported by them near the crack initiation sites were not observed here and they did not find striations of the type reported in Fig. 11. The orientation of the specimen has been found to have no effect on cracking behavior. This result is to be expected since the orientation of the specimen affects only the amount of pinning of screw dislocations, but does not change the deformation behavior in general. The striations observed on the stage I fracture surface of a specimen tested at 400°C not only confirms the role of the shear stress in the crack propagation process but also suggests that normal stresses at the crack tip also influence the crack growth process. Gel1 and Leverent [27] observed striations on a portion of the stage I fracture surface in an alloy containing y + y’. If shear stresses were only important, then they felt that features on the fracture surface would be obliterated by rubbing. Since similar features are observed on the fracture surface in the present study, the model suggested by Gel1 and Leverant might be applicable to the y ’ phase alloy here. In this model [28], the reversed deformation ahead of a crack or defect is suggested to weaken the atomic bonds across the slip plane. After sufficient weakening in a local area at the crack tip, a normal stress mode of separation is supposed to occur at the maximum stress in a cycle. However, no one appears to have a clear idea about the details of this mechanism. The mechanism suggested by Gel1 and Leverant may be possible when the plastic deformation at the

crack tip is limited. The friction stress of screw dislocations in y ’ crystals is high at 400°C due to increased pinning by cross slip. Therefore, the plastic deformation could be limited, even in the low amplitude tests performed in the present study. Therefore, the model suggested by Gel1 and Leverent can be considered a possible mechanism for the propagation of stage I cracks in these y’ crystals. The model suggested by Gel1 and Leverant can explain the preservation of striations on the stage I fracture surface, but it does not explain the mechanism of formation of these striations. These striations may form in the manner explained by Kaplan and Laird 1191. These workers proposed that the plastic blunting process occurs within a single slip band during stage I growth, rather than on two gross bands as in stage II when the acting stress is greater. The openings of the crack required to define the striations may occur by secondary slip within the band. Evidence of such slip has been discovered recently by TEM in PSB’s formed in planar slip Cu-16 at.% Al alloy [30]. In contrast to the cracks observed in specimens tested at room temperature and 4OO”C, those of specimens tested at 700°C were found to be of the stage II type. Stage II cracks have been observed by many workers in y + y’ alloys at temperatures above 900°C but not between 700 and 900°C where stage I growth has usually been observed. Plastic blunting has often been suggested as the propagation mechanism for stage II growth. In the present study the observation of stage II growth at the unusually low temperature of 700°C appears to indicate a difference from the previous observations. The reason for this difference has not been proved, but may be explained by the fact that the crystals studied here were less complicated than commercial crystals studied earlier, and therefore could deform more easily on more than one system. In high strain fatigue, stage II growth of cracks occurs almost immediately after crack nucleation. The reason for this is the homogeneous deformation at the crack tip. Since slip can occur on {111} and {OOl} at temperatures near 700°C the deformation would be more homogeneous at the crack tip compared to that at ambient temperatures where slip occurs only on (111) planes. The dislocation structures reported for the specimens tested at room temperature, 400 and 700°C confirm this difference in slip activity [16]. Therefore homogeneous deformation at the crack tip is believed to be the cause for stage II crack propagation in specimens tested at 700°C. 5. CONCLUSIONS Based on the present investigation of the cyclic hardening behavior of Ni,(Al, Nb) single crystals, the following conclusions can be drawn: 1. The mechanism of the cyclic hardening of Ni, (Al, Nb) single crystals varies with temperature,

et al.:

BONDA

and

this variation

behavior

of the

2. A large specimens

is attributed

y’ phase

amount

tested

with

of cyclic

at room

by

due

to trapping

form

dipoles.

small

plastic

the Thus

strain

to the anomalous

hardening

occurs

and

deformation amplitudes

even

due to pinning

Kear-Wilsdorf

of edge

DEFORMATION

temperature.

temperature

small plastic strain amplitude dislocations

CYCLIC

in the at very

of screw

mechanism screw

is different

Nb) CRYSTALS

provided testing facility support 16718. The active support of working on ordered compounds, especially valuable, as was the Whitney and General Electric single crystals.

2383

under Grant No. DMR-82the LRSM thrust group including V. Vitek, was generosity of the Pratt & Corporations in providing

and

dislocations

in cyclic

OF Ni,(Al,

tests from

to at that

in monotonic tests in the micro-plastic regions in which the micro-plastic strains are believed to be carried by a small density of mobile edge dislocations. 3. The stress levels in the cyclic stress-strain curves at room temperature depend on orientation and straining history. These differences are attributed to the difference in the amount of pinning of screw dislocations depending on such factors. The range of measurable CSSCs is limited by the development of cracks. No CSSCs were established at 400 and 700°C since cracks developed during the first step of the multiple step test. 4. Asymmetry of tension and compression stresses is observed in the cyclic hardening curves of specimens tested at room temperature, 400 and 700°C. Asymmetries at room temperature and 400°C are consistent with the model suggested by Paidar et al. for monotonic deformation. At 7OO”C, a T > C asymmetry is observed for all orientations tested in the present study. This observation differs from the predictions of the model [12] which really no longer applies at high temperature because cube slip and the climb of edge dislocations are activated. A more recent model designed to explain high temperature measurements [25] also does not apply. 5. Cracks in specimens tested at room temperature and 400°C are of the stage I type. These cracks nucleate in narrow bands indicating strain localization by cyclic deformation. The stage I cracks propagated in a cyclic manner on crystallographic { Ill} planes. At 700°C the cracks were found to be of stage II type. This difference is attributed to the possibility of octahedral and cube slip at the crack tips of the tested crystals at 700°C. 6. The lives of Ni,(Al, Nb) single crystals, based on the failure criterion that a large crack was present, implying complete separation would follow rapidly, are found to be low, especially at 400 and 700°C. This is attributed to higher cyclic stresses at elevated temperatures (due to the anomalous temperature effect) and therefore faster crack nucleation and propagation once strain localization occurred. Acknowledgements-This work was supported by the Army Research Office under Grants No. DAAG-29-82-K0014 and 84-K0068. We are grateful for this support and also to the Laboratory for Research on the Structure of Matter, which

REFERENCES 1. P. A. Flinn, Trans. Metall. Sot. A.I.M.E. 218, 145 (1960). 2. S. M. Copley and B. H. Kear, Trans. Metall. Sot. A.I.M.E. 239, 971 (1967). Acta melall. 21, 1375 3. S. Takeuchi and E. Kuramoto. (1973). 4. S. S. Ezz. D. P. Pope and V. Paidar, Acia me/all. 30,921 (1982). 5. Y. Umakoshi, D. P. Pope and V. Vitek, AC/a metall. 32, 447 (1984). 6. J. H. Westbrook, Trans. Merail. Sot. A.I.M.E. 209, 898 (1957). 7. S. J. Liang and D. P. Pope, Acia mefall. 25,485 (1977). 8. D. P. Pope and V. Vitek, Structure and Properties of Crystal Defects (edited by V. Paidar and C. Leicek). p. -37. Elsevier, Amsterdam (1983). 9. D. P. Pooe and S. S. Ezz. Int. Merall. Rev. 29. 136 (1984). I 10. B. H. Kear Acia mefall. 12, 555 (1964). 11. C. Lall, S. Chin and D. P. Pope, Mefall. Trans. IOA, 1323 (1979). 12. V. Paidar, D. P. Pope and V. Vitek, Acfa metall. 32,435 (1984). 13. D. A. Jablonski and S. Sargent, Scripta metall. 15, 1003 (1981). 14. D. L. Anton, Scripra metall. 16, 479 (1982). IS. S. S. Ezz and D. P. Pope, Scripta metall. 19, 741 (1985). 16. N. R. Bonda. D. P. Pope and C. Laird, The Dislocation Structures of Ni,(Al, Nb) Single Crystals Fatigued at Ambient and Elevated Temperatures (1985). 17. A. S. Cheng, Ph.D. thesis, Univ. of Pennsylvania, Philadelphia, Pa (1981). 18. J. M. Finney, Ph.D. thesis, Univ. of Pennsylvania, Philadelphia,-Pa (1974). 19. R. A. Mulford and D. P. Pove Acta merall. 21. 1375 (1973). V. Paidar, D. P. Pope and V. Vitek, Phil 20. M. Yamaguchi, Mag. 45, 867 (1982). D. P. Pope and V. Vitek, 21. V. Paidar, M. Yamaguchi, Phil. Mag. 45, 883 (1982). 22. P. Veyssiere. D. L. Guan and J. Rabier. Phil. Mag. A 49, 45 (1984). 23. P. Veyssiere, Phil. Msg. A 50, 189 (1984). 24. J. E. Doherty, A. F. Giamei and B. H. Kcar, Mefall. Trans. 6A, 219 (1975). 25. V. Paidar, in Dislocation in Solid.7 (edited by H. Suzuki, T. Ninomiya, K. Somino and S. Takeuchi), pp. 73-76. Univ. of Tokyo Press, Tokyo (1985). 26. T. P. Gabb, J. Gayda and R. V. Miner. Meiall. Tram 17A, 497 (1986). 27. M. Gel1 and G. R. Leverant, Acta merall. 16,553 (1968). 28. M. Gel1 and G. R. Leverant, Trans. T.M.S.-A.I.M.E. 242, 1869 (1968). 29. H. 1. Kaplan and C. Laird. Trans. T.M.S.-A.I.M.E., 239, 1017 (1967). 30. L. Buchinger, A. S. Cheng, S. Stanzl and C. Laird, Mater. Sci. Engng 80, 155 (1986).