- Email: [email protected]
The asymmetry of the flow stress in Ni3(Al,Ta) single crystals
Acra meroll. Vol. 32, No. 3, pp. 449-456, 1984 Printed in Great Britain. All rights reserved
Copyright
OOOI-6160/84 53.00 +O.OO C 1984 Pergamon Press Ltd
THE ASYMMETRY OF THE FLOW STRESS IN Ni, (Al, Ta) SINGLE CRYSTALS Y. UMAKOSHI’, D. P. POPE* and V. VITEK’ Science and Engineering, Osaka University, Osaka 565, Japan and *Department of Materials Science and Engineering and LRSM, University of Pennsylvania, 3231 Walnut Street, Philadelphia, PA 19104, U.S.A.
‘Department
of Materials
Abstract-Flow stress measurements were performed on single crystalline Ni,(Al, Ta) as a function of temperature, orientation, strain rate and sense of the applied uniaxial stress to check the predictions of the Paidar er al. model [ha merall. 32,435 (1984)]. It was found that the critical resolved shear stress (CRSS) for (11 l)[TOl] slip depends not only on the test temperature and orientation of the samples, as other investigators have previously observed, but also on the sense of the applied stress. The orientation dependence of the tension/compression asymmetry, including the regions where the asymmetry is a maximum (positive), a minimum, and where it disappears, is as predicted by the model. The applied stress changes the activation enthalpy of cross slip primarily through its effect on constricting the Shockley partials during cross slip and only secondarily on directly promoting (111) to (010) cross slip. A maximum attainable CRSS for (111) [TO11slip, the saturation stress, is also in agreement with the model. It was also found that the CRSS for (11 l)[TOl] slip is strain rate independent, but the CRSS for (OOl)[TlO]slip shows a strong positive strain rate dependence. The temperature at which the peak in the flow stress vs temperature curve occurs increases with increasing strain rate and decreases with increasing ratio of RSS on (OOl)[TlO] divided by that on (lll)[TOl]. When the deformation occurs by (OOl)[TlO] slip the stress-strain curve exhibits clearly defined, continuous yield points. R&urn&-Nous avons effect& des mesures de la contrainte d’ecoulement sur des monocristaux de Ni,(Al, Ta) en fonction de la temperature, de l’orientation, de la vitesse de deformation et du sens de la contrainte uniaxiale appliqute afin de verifier les previsions du modele de Paidar ef al. [Acra metall. 32, 435 (1984)]. Nous avons trouve que la fission critique reduite (CCR) pour le glissement (111) [TO]]dtpendait non seulement de la temperature de l’essai et de l‘orientation des echantillons, comme d’autres auteurs l’avaient deja signale, mais egalement du sens de la contrainte appliquee. La variation de l’asymetrie traction/compression en fonction de l’orientation, y compris dans les regions ou l’asymttrie est maximale (positive), minimale ou s’annule, correspondait aux previsions du modtle. La contrainte appliquie modifie l’enthalpie d’activation du glissement divie essentiellement par son effet sur la constriction des partielles de Shockley au tours du glissement d&vie, et seulement secondairement en favorisant le glissement d&e, (010) par rapport au glissement d&vie (111). La valeur maximale de la CCR que l’on peut atteindre pour le glissement (11 l)[TOl], cad la contrainte de saturation, est egalement en accord avec le modele. Nous avons egalement trouve que la CCR pour le glissement (11 l)[TOl] ne dipendait pas de la vitesse de deformation, mais que la CCR pour le glissement (OOl)[TOl] prtsentait une forte variation positive en fonction de la vitesse de deformation. La temperature du pit des courbes de la contrainte d’ecoulement en fonction de la temperature augmentait avec la vitesse de deformation et elle diminuait lorsqu’on on augmentait le rapport de la CCR de (00l)[Tl0] sur la CCR de (lll)[TOl]. Lorsque la deformation se produisait par glissement (OOl)[TlO], la courbe contraintedeformation prisentait des limites elastiques continues, bien dtfinies. Zuaammenfasaung-An Einkristallen Ni,(Al,Ta) wird die Fliegspannung in Abhlngigkeit von Temperatur, Orientierung, Abgleitgeschwindigkeit und Vorzeichen der angelegten einachsigen Spannung gemessen, urn die Aussagen des Modelles von Paidar et al. [Acra metal/. 32,435 (1984)] zu priifen. Die kritische FlieBspannung im System (11 l)[TOl] hangt nicht nur von der Versuchstemperatur und der Orientierung der Probe ab, wie andere Autoren berichtet haben, sondern such von Vorzeichen der angelegten Spannung. Die Orientierungsabhiingigkeit der Zug/Druck-Asymmetrie-einschliet3lich der Orientienmgen, bei denen die Asymmetrie maximal, minimal oder gerade Null ist-stimmen mit den Voraussagen des Modelles i&rein. Die iiullere Spannung veriindert die Aktivierungsenthalpie der Quergleitung iiberwiegend durch ihren EinfluB auf das Einschniiren der aufgespaltenen Versetzungen wiihrend des Quergleitens und nur in zweiter Linie durch direkte Einwirkung auf die Quergleitung von (111) nach (010). Die maximal erhaltbare kritische FEeDspannung bei (11 l)[TOl]-Gleitung, d.h. die Sittigungsspannung, stimmt ebenfalls mit dem Model1 iiberein. Die kritische FlieDspannung in (111) [TO]] war unabhangig von der Abgleitgeschwindigkeit. Dagegen zeigt diejenige fur Gleitung in (OOl)[~lO] eine starke positive Abhiingigkeit. Die Temperatur, bei dem ein Maximum in der Temperaturabhiingigkeit der Fliegspannungauftritt, nimmt mit ansteigender Abgleitgeschwindigkeit zu und sinkt mit zunehmendem Quotienten aus den FlieDspannungen im (001)[Tl0]- und (11 l)[TOl]-Gleitsystem. Rei Gleitung auf (OOl)[TlO] weist die Verformungskurve wohldefinierte kontinuierliche FlieBeinsHtze auf.
1. INTRODUCTION In the previous paper [l] an explicit expression for the activation enthalpy for cross slip of 1/2[TOl] super449
partial dislocations from (111) to (010) planes in Ll, ordered alloys was derived. There were two parts to this derivation: the first part was concerned with the
450
UMAKOSHI
et al.:
FLOW
STRESS IN Ni,(Al,
cross slip of an undissociated superpartial, and the second part was concerned with the effects of core dissociation on the cross slip event. In the first part of the derivation the cross slip energy of a critical length of undissociated superpartial was calculated, based on three separate assumptions: (i) the antiphase boundary (APB) energy on (111) planes, y, , is higher than that on (010) planes, y,,, and therefore there is a natural tendency for superpartial dislocations to undergo this cross slip. This difference in APB energies was first pointed out by Flinn [2] and was subsequently used in the cross slip models of Kear and Wilsdorf [3], Thornton et al. [4] and Takeuchi and Kuramoto [5] (TK). (ii) Cross slip from (Ill) to (010) planes is aided by the resolved shear stress (RSS) for 1/2[TOl](OlO) slip, r,,,, as first proposed by TK [5]. (iii) Energy stored in the superpartial pair that can be released during cross slip is available for reducing the activation energy. This energy becomes available if the superpartial pair is compressed or extended before cross slip but has its stress-free width afterwards. The second part of the derivation includes the effects of the width of the core of the superpartials and employs the Escaig [6,7] analysis for cross slip in f.c.c. metals. In this analysis the energy, W, to form a constriction on the dissociated dislocation is determined by the degree of increase or decrease of the width of splitting into Shockley partials on the primary (111) plane and the secondary (111) plane compared to the width of splitting with no applied stress. The degree of the change of the dissociation width is, in turn, determined by the RSS on the edge components of the Shockley partials on these two planes. Such an analysis is applicable to Ll, alloys because the results of computer simulations of 1/2[TOl] dislocation cores in Liz alloys by Yamaguchi et al. (81and Paidar ef al. [9] have shown that the cores of 1/2[TOl] super-partial dislocations can always be regarded as dissociated on (111) or (171) into a pair of either well separated or overlapping l/6 ( 112) type partials, independent of whether the APB lies on (111) or (010). That is, the core of a 1/2[TOl] dislocation is dissociated on the (111) plane before cross slip and is dissocated on the (111) or (171) plane after cross slip to the cube plane. The distance, w, that the dislocation segment cross clips on the (010) plane must be an integral multiple of b/2, where b = 1/2[701], since after a jump of b/2 the core dissociates on the (171) plane, and after a jump of b it dissociates on (11 l), etc. The activation enthalpy depends on the length of this jump, but it was shown [l] that the minimum enthalpy jump is the one of length b/2. This was called the 01 jump and the activation enthalpy is &1 = Mb {h + c + Kktph -[(l/J3
whereA4is pb2/2n,
- Y~IY, + N I tphl)b/Rl”2P p
(1)
is the (isotropic) shear modulus; which depend on the width of the stress-free superpartial core; tphis r,,,b/y,; and K h and K are parameters
Ta) SINGLE
CRYSTALS
is an orientation-dependent parameter which measures the difference in Shockley partial spacing on the initial, (111) and final, (1 f 1), planes; N is the ratio of The physical meaning of the &h to 7phph; R = Mpi,. individual terms in equation (1) is as follows: the term h + c is a constant which depends on the width of the stress-free superpartials and involves the energy per unit length of a kink. The term Kktph is a measure of the change in activation enthalpy due to stressinduced differences in superpartial core widths on the (111) and (lT1) planes. K depends on the orientation of the tensile axis, but it does not change sign when the sense of the applied stress is changed and k is a constant. Consequently only tphchanges sign when the sense of the applied stress is changed and therefore this term, Kkt,,, gives rise to a tension/compression asymmetry of the flow stress. Included in K is a constant, K, which measures the relative importance of the RSS on the edge components of the Shockley partials on the primary and secondary { 111) planes, 7@ and rIe, respectively [ 11. When K = 1, rpp and T,~have an equal effect on the activation enthalpy, and when K = 0, only TV is important. K can be determined from experiment as described below. K is related to K by K=[l-~(N+,/3)(271’-J3)/ (3N - J3)J3lQ
(2)
where Q = r,/r,h, a factor which depends on orientation, but not on the sense of the applied stress. This definition is different from the one in Ref. [lo]. The term l/J3 - yO/y, in equation (1) is a measure of the APB energy gained by cross slip from (111) to (010). N It,,,,1 is a measure of the work done by the applied stresses when cross slip to (010) occurs. Note that N is always a positive number [lo] and that this term is, therefore, always positive, i.e. it does not change sign with changes in the sense of the applied stress. In summary, Ho, is a combination of three terms, a constant term, a term which depends on the orientation and sense of the applied stress, and a term which depends only on the orientation, but not the sense, of the applied stress. Ho, was then used to predict the flow stress, tph,by using the TK [5] model Irphl =A exp]-H,,/X,T]
(3)
where A is a constant, kB is the Boltzman constant and T is the absolute temperature. It was shown [1] that if equation (1) is expanded in a Taylor series in tpDand if quadratic and higher order terms in tphare neglected, then an equation similar to equation (4) of TK [5] is obtained. However, in the present case we obtain not only the term involving stress driven cross slip from (111) to (OlO), the most important part of the Takeuchi and Kuramoto theory [S], but we also obtain a term that depends on the sense of the applied stress. That is, the TK [5] result is a special case of the Paidar et al. [l] result.
UMAKOSHI
et al.:
FLOW
STRESS IN Ni,(Al,
Ta)
SINGLE
CRYSTALS
451
Table I. Schmid factors and Schmid factor ratios of siimplcs __ Deformed at a strain rate of 1.3 x 10-‘/s
Deformed at a strain rate of 6.5 x 10-‘/s
Sample A-l A-2 B-l C-l D-l D-2 E-l E-2 A-3 B-2 c-2 D-3 E-3
(I I I)[TOl]
(010)[T01]
1.34 1.34
36.3 51.8 7.16 4.32 11.73 13.94 1.41 1.56
0.4267 0.4438 0.4897 0.4886 0.4269 0.4336 0.3599 0.3797
0.0347 0.0686 0.2306 0.3559 0.3822 0.3771 0.4774 0.4639
4.98 1.31 2.41 12.46 I .28
51.84 4.76 4.32 12.49 1.29
0.4438 0.4699 0.4886 0.4224 0.3411
0.0686 0.2103 0.3559 0.3806 0.4817
Miller indices :
::;;t
1 7 :
2.30 2.41
: T
T 1 T i
t
:::I:
N = S.F. for {OlO)[~OI]~S.F. for (f 1I)[TOi], Q = SF. for fll I)[I%]:S.F.
Paidar er al. [l] used equation (1) to fit the recent results of Ezz et at. [ll] to show that the observed tension/compression asymmetry of the CRSS for (11 l)[TOl] slip can be explained by this model. Wowever, in addition to explaining the results of Ezz et al. f lo], namely that (i) the CRSS for (11 I)[fOl] slip measured in tension exceeds that measured in compression for samples near [OOl] and (ii) the opposite occurs for samples oriented near [Ol l] and {Tl 11, the Paidar ef al. model also predicts that: (i) The maximum separation along the temperature axis between the tensile and compressive flow stress curves should occur for samples oriented near (0111. (ii) If it is assumed that in equation (2) 0 d K d 1, then the tension/compression asymmetry must disappear somewhere between (0011 and the great circle joining [012] to [i13]. The [012]-[T13] great circle is the & = 0 curve in Ref. [IO]. The orientations at which this occurs provide a measure of K. This will occur when K = 0, equation (2). Finally, Paidar er al. 111introduced the concept of a saturation stress, the stress at which the rates of pinning and unpinning are equal. The unpinning can occur in the following way: if the leading super-partial undergoes two successive cross slip jumps of length b/2 on (010) (or one of length b), then the leading and trailing superpartials are dissociated on parallel (111) planes. If the density of kinks on the dislocation line is sufficiently high, then adjacent kinks lying on (010) which are of edge o~entation can annihilate each other, leaving two long straight superpartials on parallel (111) planes. This dislocation pair can then move until the trailing superpartial encounters the original (010) cross slip plane. At certain combinations of stress and temperature this trailing superpartial can cross slip to the plane of the leading superpartial, thereby freeing the dislocation. Whether or not such a saturation stress will be observed depends upon the relative rates of thermally activated pinning and unpinning. The experimentally observable features of such a saturation stress are: (i) { 111) slip above the peak in the CRSS vs temperature plot, or
(aol)lTW--.-.-~ 0.0532 0.0809 0.2903 0.4090 0.3828 0.3788 0.4877 0.4936 0.0808 0.3064 0.4090 0.3807 0.4834
,v
Q
0.2102 0.1982 0.0540 -0.0795 - 0.2368 -0.2205 -0.1957 -0.1816
0.0813 0.1545 0.4709 0.7284 0.8953 0.8697 1.3265 1.2218
0.4926 0.4466 0 1103 -0.1727 -0.5547 -0.5085 -0.5437 -0.4782
0.1982 0.0537 -0.0795 -0.2428 -0.1952
0.1546 0.4475 0.7284 0.9010 1.4120
0.4466 0.1143 -0.1627 -0.5748 -0.5723
(1 I l)(m)
for (11 l)[~Ol].
(ii) A combination of {l 11) and jOlO} slip below the peak with a slow rate of increase with temperature of the CRSS. The theory predicts that for [I1 l] oriented samples the saturation stress should be lowest and the temperature at which the saturation stress occurs should also be lowest, while those for [loo] samples should be the highest, and those for [01 l] samples should be intermediate. The purpose of the experiments reported here is to check the applicability of the Paidar et al. [I] model to the behavior of single crystalline Ni,(Al, Ta).
2. EXPERIMENTAL Single crystals of Ni,(Al, Ta) were grown using a modified Bridgeman method and homogenized at 1450 I( for 10 days in a purified argon atmosphere. The chemical compositions were 76.3 wt.?; Ni, 9.6 wt% Al and 14.1 wt% Ta. Oriented samples with lo/32 NC threads, a 6.5mm gauge length and a 2.5 mm gauge diameter were manufactured from the homogenized single crystals by grinding and were subsequently electrolytically polished in a 30”/, nitric acid-methanol solution to remove surface damage. The specimens were then annealed for 5 hr at 1173 K in purified argon atmosphere and slowly cooled in the furnace to room temperature. Some of the specimens were given a final electropolish in the above electrolyte before deformation to prepare surfaces suitable for slip trace analysis. The Miller indices of the sample axes are given in Table 1. Some Schmid factors for various slip systems and the ratios of some Schmid factors are also listed. The orientations of these samples are also shown in Fig. 1 in the standard (OOl]-[Ol l]-[Tl l] unit triangle. Tension and compression tests were conducted on an Instron Universial Testing Machine at a nominal strain rate of 1.3 x lo-‘s-’ at temperatures from 77 to 1200 K. Some of the tests were carried out at a strain rate of 6.5 x 10m3/s in order to determine the strain rate dependence of the flow stress. Tests at 77 K were performed with the samples immersed in
452
UMAKOSHI
et al.:
FLOW STRESS IN Ni,(Al, Ta) SINGLE CRYSTALS
001 012 011 Fig. I. The orientations of the samples tested in this study. The unit triangle is divided into three regions in which the core constriction effect is expected to be different, ref. [I 11.
liquid nitrogen. Tests at temperatures in the range 293-12OOK were carried out under vacuum. The same sample was repeatedly deformed at different temperatures to eliminate errors due to variations between samples. A given sample was first deformed in tension to a 0.2% nominal plastic strain and then deformed in compression at the same temperature, and then it was tested in the reverse sequence at the next temperature, thus eliminating the effects of different deformation sequences. Some of the flow stresses were checked with virgin samples. Slip lines were photographed on samples deformed in tension using an optical microscope equipped for Nomarski interference contrast, and the operative slip systems were determined by measuring the angle between the tensile axis and the tangent to the slip line for different rotations about the deformation axis. 3. RESULTS Temperature and orientation dependence of the CRSS
The temperature and orientation dependence of the CRSS for (lll)[TOl] and (OOl)[TlO] slip measured at a strain rate of 1.3 x 10e3 s-’ are shown in Fig. 2(a)-(e). In all samples except sample E, deformation at temperatures below the peak temperature occurred by {111) ( 110) slip. In sample E, the sample oriented near [Ill], deformation occurred in this temperature range by a combination of (11 l)[TOl] and (OOl)[TlO] slip. Consequently the curves labeled “CRSS for (lll)[TOl]” are appropriate for all samples except sample E for temperatures below the peak. Above the peak all samples except sample A, the near - [OOl] sample, deformed by (OOl)[TlO] slip, and therefore the CRSS for this system is appropriate in that temperature regime. (The CRSS for (11 l)[TOl] slip is therefore shown as a dotted line in this temperature range.) Sample A deformed by (11 l)[‘fOl] slip over the entire temperature range. Examples of slip traces are shown in Fig. 3(a)-(d). In Fig. 2(a)-(e) the symbols without arrows denote the CRSS measured on samples that were deformed a number of times at a series of temperatures, and the symbols with arrows indicate data obtained on virgin samples.
As expected, the CRSS of the virgin samples was generally lower than that of the work hardened, multiply-deformed samples. The main features of Fig. 2(a)-(e) are: (i) the CRSS for (11 l)[TOl] slip increases with increasing temperature for all orientations; (ii) the CRSS for (11 l)[TOl] slip as measured in tension is in general, different from that measured in compression; (iii) the magnitude and sign of this tension/compression asymmetry is strongly orientation dependent. Sample A is stronger in tension than compression, the reverse is true for C, D and E, and the asymmetry nearly disappears for sample B. Sample D, which is approximately 50% stronger in compression than tension at 400 K, shows the largest asymmetry; (iv) the slope of the CRSS vs temperature curves at temperatures below the peak temperature is orientation-dependent -note the rather flat slope of Fig. 2(e) compared to the others; (v) above the peak temperature there is little or no tension/compression asymmetry, even in sample A which deformed by {11I} (110) slip in this temperature range; (vi) the transition from octahedral to cube slip occurred at or near the peak temperature in samples B, C and D. In sample A cube slip was not observed and in sample E cube and octahedral slip were observed at temperatures well below the peak temperature. Strain rate effects
The CRSS of samples measured at the higher strain rate of 6.5 x 10-3s-’ is shown in Fig. 4(a)-(c). Comparison of Figs 2 and 4 shows that the magnitude of the CRSS for (11 l)[TOl] slip, both in tension and compression, is largely strain rate independent, but the flow stress for (OOl)[TOl] slip is strain rate dependent. For example, the CRSS for (OOl)[TlO] slip of samples of orientation C is substantially higher at the higher strain rate. The effects of orientation, sense of the applied stress, and strain rate on the CRSS for (11 l)[TOl] and (OOl)[TlO] slip are shown in Fig. 5. It is seen that the CRSS for (OOl)[TlO] slip is independent of the orientation and sense of the applied stress, but it increases with increasing strain rate. Since the CRSS for (11 l)[TOl] slip is largely strain rate-independent, only the dependence on crystal orientation and sense of the applied stress are shown in this figure, measured at a strain rate of 1.3 x lo-' s-‘. Note that the CRSS for (11 I)[TOl] slip as measured in tension first decreases, then increases as N increases. As will be discussed later, this observation cannot be explained using the TK model. In Fig. 6 the effects of strain rate, sample orientation and sense of the applied stress on the peak temperature are shown. The peak temperature depends strongly on the ratio of the Schmid factor for ‘(OlO)[TOlJ slip to that for (11 l)[TOl] slip, but it increases only slightly with increased strain rate, and appears to be almost independent of sense of the applied stress.
UMAKOSHI
et al.:
FLOW
STRESS IN Ni,(AI. Ta) SINGLE
CRYSTALS
453
(d) 500 A
I
0
200
I
400
600
Temperature
1
0
I
1
800
1000
I 1200
I
0
200
1
600
I
800
Temperature
(K)
1
f
10001200
(K)
(e)
(b)
I
t
400
I
200
I
400
1
600
1
I
1000
1200
I
800
Temperature
(K
1
1 0
I
200
I
400
I
600
Temperature
I
600
I
1000
I 1200
CK 1
Ic)
I
200
I
400
I
600
Temperature
1
800
I
1000
I 1200
(K)
fig. 2. (a)-(e) The temperature dependence of the CRSS for (I I l)[TOl] and (~l)[TlO] and compression measured at a strain rate of I .3 x 10m3SK’.
Stresf-strain
curves
Stress-strain curves measured in tension, for samples which deformed by (11 l)[TOl] slip at 600 K and for samples deformed by (00 1)[Tlo] slip at 995 K, are shown in Fig. 7. At 600 K samples A, B and C show only parabolic work hardening, similar to b.c.c. metals at low temperatures, while sample E shows a three stage work hardening curve, similar to that seen in f&c. materials. The shape of the curve for sample D is intermediate between the two. Samples deformed
slip in tension
at 995 K show clearly defined, continuous yield point phenomena. Note that the curve for sample B shows two such yield points. 4. DISCUSSION Tensionlcompres~ion asymmerry of the CR.!% ,for (1 I l)[;TOl] slip
The experimental results shown in Figs 2 and 4 are in complete agreement with the model of Paidar et al. [l] and with the previous resuhs of Ezz er a/. [I I]. The
454
UMAKOSHI
ci al.:
FLOW STRESS IN Ni,(Al.Ta)
SINGLE CRYSTALS (a)
(b) I
0
200
I
I
I
400 600 600 Temperature (K
I
I
1000 1200
)
(b) 500
c
Fig. 3. Slip traces produced by deformation at (a) 1200 K, (b) and (c) 780 K. 100
CRSS measured in tension exceeds that measured in compression for orientations near [OOl], and the reverse is true for orientations near [ill] and [Oll]. This has previously been observed by Ezz et al. [I I] and it is predicted by the model. The most important results of the present work are:
I
0
200
/
I
I
I
400 600 600 Temperature (K
I
1000 1200
I
(cl
(i) The CRSS for (I 1l)[iOl] slip is independent of the sense of the applied stress for samples of orientation B. This is within the range of orientations at which the disappearance of the tension/compression asymmetry was predicted by the model [l]. (ii) The tension compression asymmetry is very large for samples oriented near [Ol I]. e.g. at 400 K the CRSS measured in compression is approximately 50% higher than the value obtained in tension. This is also as predicted by the model [l]. The present data also allow us to determine the relative importance of T,,,, the stress driving (010) cross slip, and 5Pcand T,,, the stresses which change the width of the core dissociation. We will call these the “cross slip” and the “constriction” effects, respectively. This can be done by referring to the top two curves in Fig. 5. The curve for the compression tests shows that the CRSS for (11 l)[TOl] slip increases with increasing N in the same manner as predicted by the TK theory: however the CRSS measured in tension decreases with N, for N less than about 0.9. opposite to that predicted by the TK theory. These tensile test results indicate that the
I 0
I
I
I
I
200
400
600
000
Temperature
1
I
1000 ,200
(K)
Fig. 4. (a)-(c) The temperature dependence of the CRSS for (11 l)[TOI] and (OOl)[TlO]slip measured in tension and compression at a strain rate of 6.5 x IO-) s-‘.
constriction effect is large enough to offset the cross slip effect at 400 K if N is less than 0.9. This is also in qualitative agreement with the theory [l], c.f. Fig. 11 of Ref. [I 1. The constriction effect reaches a maximum for N = 0.87, at the [Ol l] orientation, and then rapidly decreases for higher values of N, while the
UMAKOSHI
et al.:
FLOW STRESS IN Ni,(Al, Ta) SINGLE CRYSTALS
455
A Tension . Camp, 6 5xlQ3s-'
I
I
1
05
IO
I5
N
Fig. 5. The effects of orientation and sense of the applied stress and the effectof strain rate on the CRSS for (11 l)[TOl] slip at 400 K and for (OOl)[TlO]slip at 1000K.
cross slip effect increases continuously with increasing N for all N. Another way of comparing the present data with the model [l] is shown in Fig. 8. The difference between the tensile and compressive values of the CRSS at 4OOK, normalized to the tensile value, is plotted as a function of N. It is seen that the difference is zero for N = 0.42. Since the model predicts that the asymmetry disappears for K = 0 in equation (2), the value of K can be determined to be 0.32. This means that TVis more important than T,!~ in determining the constriction effect. Saturation stress The model developed in the previous paper [l] predicts that there should be a maximum possible CRSS for (11 l)[TOl] slip at any given sample orientation and temperature. Such a saturation stress has clearly been reached in the near-[0011 oriented samples, Figs 2(a) and 4(a), because the slip still occurs on (11 l)[TOl] at temperatures above the peak temperture. Also for samples oriented near [Tl l] a saturation stress appears to have been reached. At temperatures below the peak temperature the stress and 1200 r o Tension .
l
Comp.
I
3 x Io-3s-’
Shear
strain
Fig. 7. Shear stress-shear strain curves for samples deformed by (11 l)[TOl] slip at 600 K and for samples deformed by (OOl)[~lO] slip at IOOOK.
temperature are not high enough to cause massive (OOl)[TlO] slip, consequently both (111) and (001) slip are observed. However the CRSS for (11 l)[TOl] slip is quite high, e.g. compare Fig. 2(e) with Fig 2(a)-(d). Consequently we conclude that a saturation stress has also been reached for samples of this orientation. Note also that the saturation stress and temperature are higher for the near-[0011 sample than for the near-[Tl l] sample, which is also in qualitative agreement with the model. Strain rate effects The physical basis of the TK model for (I 1l)[‘fOl] slip can be approximately described in the following way. The flow stress at any temperature is determined by the density of cross-siipped segments which form pinning points on dislocations. This density of pinning points is expected to be independent of dislocation velocity for small changes in the velocity. Hence one would expect that there be very little strain rate sensitivity of the CRSS for (11 l)[TOl] slip, which has, indeed, been observed in the present experiments. The mechanism controlling the rate of (OOl)[‘f lo] slip, the cube slip mode at high temperatures, is quite different, however. The cores of these dislocations do not lie on the (001) slip plane [8,9], and therefore 06 t
A Tension 65x
b camp.
-=-I
4
700 $ a
;lWIl
01400K
_'-01400;
6 =I~xIO-~ i="'""T
600 0
4004
05 Schmid
05
I.0
1.5
Fig. 6. The variation of the pea: temperature with N, sense of the applied stress, and strain rate.
factor
IO
I.5
rat~o,~010~~01]~~1II~[i0l]
Fig. 8. Orientation dependence of the tension/compression flow stress asymmetry for samples deformed at 400K. rl. and tc are the CRSS for (11 l)[TOl] slip as measured in tension and compression, respectively.
456
UMAKOSHI ef al.: FLOW STRESS IN N&(AI, Ta) SINGLE CRYSTALS
these dislocations are expected to move by a thermally activated process, similar to that observed in b.c.c. materials at low temperatures. Consequently a fairly high positive strain rate dependence of the CRSS for (OOl)[Tlo] slip is expected, exactly as observed, c.f. Fig. 5. The dependence of the peak temperature on orientation, Fig. 6, is qualitatively what is expected based on the changes in slip system that occur at this temperature. The peak temperature marks the transition between slip predominately on (11 l)[TOl] at lower temperatures to slip predominately on (OOl)[TlO] at higher temperatures. The higher the ratio of the Schmid factor for the cube slip system to that for the octahedral system the lower should be the temperature of the transition. It is seen in Figure 6 that this has, indeed, been observed. Furthermore, since the CRSS for slip on (OOl)[TlO] has a positive strain rate dependence while that for (11 l)[TOl] slip has almost none, an increased strain rate is expected to shift the peak to higher temperatures. This is also what is observed.
Stress-strain
curves
The difference in shape of the stress-strain curves for the two slip systems, Fig. 7, is very striking. The shape of the curves at 1000 K, showing the pronounced smooth yield point, and sometimes more than one, is very similar to that observed in materials like LiF [ 121in which dislocation motion is thermally activated and the mobile dislocation density is related to the total density.
SUMMARY AND CONCLUSIONS The results of the experiments on N&(Al, Ta) are in complete agreement with the predictions of the model developed by Paidar et al. [l]. The most important observations are: (1) The CRSS for (11 l)[TOl] slip depends not only on the temperature and sample orientation but also on the sense of the applied stress. (2) Samples near [OOl] are stronger in tension than in compression, while the reverse is true for samples near [Ill] and (0111. (3) Samples near [Ol l] are much stronger in compression than in tension. (4) The asymmetry of the CRSS disappears for samples oriented between [OOl] and the [012]-[T13] great circle. (5) From the fact that the asymmetry disappears at the orientation indicated in No. 4 above, it can be concluded that the constriction stress on the primary octahedral slip plane, (11 l), has a larger effect on the activation enthalpy for cross slip than does the
constriction stress on the secondary octahedral slip plane, (lTl). (6) In this material the effects of stress-driven core constriction are more important in determining the CRSS for (11 l)[TOl] slip than are the effects of stress driven cross slip from (111) to (010). That is, the Escaig effect is more important than the TK effect. (7) A saturation stress is observed for samples of [Ill] and [OOl] orientation. The relative values of these stresses and the temperature at which they occur are in agreement with the model. The following observations were also made which cannot be qualitatively analysed using the Paidar et al. [l] model but support its basic assumptions, namely thermally activated formation of obstacles for (I 1l)[TOl] slip and thermally activated motion of sessile dislocations in the case of (OOl)[TlO] slip. (1) The CRSS (11 l)[TOl] slip is strain rate independent. (2) The CRSS for (OOl)[TlO] slip shows a large positive strain rate dependence. (3) The peak temperature increases with increasing strain rate and decreases with increasing RSS on (OOl)[TlO] relative to that on (lll)[TOl]. (4) When the sample deforms by (OOl)[TlO] slip, the stress-strain curve shows clearly defined continuous yield points. Acknowledgements-Support for this program was provided bv the NSF under arant no. DMR-7905556. Research facilities were provided by the Laboratory for Research on the Structure of Matter at the University of Pennsylvania, supported by the NSF MRL program under grant no. DMR-8216718. The single crystalline Ni,(Al, Ta) was gratiously supplied by Dr Dilip Shah of the Pratt and Whitney Aircraft Corp., Middletown, CT.
REFERENCES 1. V. Paidar, D. P. Pope and V. Vitek, Acra metal/. 32,435 (1984). 2. P. A. Flinn, Trans. T.M.S.-A.I.M.E. 218, 145 (1960). 3. B. H. Kear and H. G. F. Wilsdorf, Trans. T.M.S.A.I.M.E. 22.4, 382, (1962). 4. P. H. Thornton, R. G. Davies and T. L. Johnston, Metall. Trans. lA, 207 (1970). 5. S. Takeuchi and E. Kuramoto, Acta metall. 21, 415
(1973). 6. B. Escaig, .I. Phys. 29, 225 (1968). 7. B. Es&g, in Dislocation Dynamics, p, 655 (edited by A. R. Rosenfield, G. T. Hahn, A. L. Bement Jr and R. I. Jaffee). McGraw-Hill, New York (1968). 8. M. Yamaguchi, V. Paidar, D. P. Pope and V. Vitek, Phil. Mag. 45, 861 (1982).
9. V. Paidar, M. Yamaguchi, D. P. Pope and V. Vitek, Phil. Mag. 45, 883 (1982).
10. C. Lall, S. Chin and D. P. Pope, Metall. Trans. lOA, 1323 (1979). 11. Salah S. Exe, D. P. Pope and V. Paidar, Acta metall. 30, 921. (1982).
12. W. G. Johnston and J. J. Gilman, I. appl. Phys. 38, 129 (1959).
Copyright
OOOI-6160/84 53.00 +O.OO C 1984 Pergamon Press Ltd
THE ASYMMETRY OF THE FLOW STRESS IN Ni, (Al, Ta) SINGLE CRYSTALS Y. UMAKOSHI’, D. P. POPE* and V. VITEK’ Science and Engineering, Osaka University, Osaka 565, Japan and *Department of Materials Science and Engineering and LRSM, University of Pennsylvania, 3231 Walnut Street, Philadelphia, PA 19104, U.S.A.
‘Department
of Materials
Abstract-Flow stress measurements were performed on single crystalline Ni,(Al, Ta) as a function of temperature, orientation, strain rate and sense of the applied uniaxial stress to check the predictions of the Paidar er al. model [ha merall. 32,435 (1984)]. It was found that the critical resolved shear stress (CRSS) for (11 l)[TOl] slip depends not only on the test temperature and orientation of the samples, as other investigators have previously observed, but also on the sense of the applied stress. The orientation dependence of the tension/compression asymmetry, including the regions where the asymmetry is a maximum (positive), a minimum, and where it disappears, is as predicted by the model. The applied stress changes the activation enthalpy of cross slip primarily through its effect on constricting the Shockley partials during cross slip and only secondarily on directly promoting (111) to (010) cross slip. A maximum attainable CRSS for (111) [TO11slip, the saturation stress, is also in agreement with the model. It was also found that the CRSS for (11 l)[TOl] slip is strain rate independent, but the CRSS for (OOl)[TlO]slip shows a strong positive strain rate dependence. The temperature at which the peak in the flow stress vs temperature curve occurs increases with increasing strain rate and decreases with increasing ratio of RSS on (OOl)[TlO] divided by that on (lll)[TOl]. When the deformation occurs by (OOl)[TlO] slip the stress-strain curve exhibits clearly defined, continuous yield points. R&urn&-Nous avons effect& des mesures de la contrainte d’ecoulement sur des monocristaux de Ni,(Al, Ta) en fonction de la temperature, de l’orientation, de la vitesse de deformation et du sens de la contrainte uniaxiale appliqute afin de verifier les previsions du modele de Paidar ef al. [Acra metall. 32, 435 (1984)]. Nous avons trouve que la fission critique reduite (CCR) pour le glissement (111) [TO]]dtpendait non seulement de la temperature de l’essai et de l‘orientation des echantillons, comme d’autres auteurs l’avaient deja signale, mais egalement du sens de la contrainte appliquee. La variation de l’asymetrie traction/compression en fonction de l’orientation, y compris dans les regions ou l’asymttrie est maximale (positive), minimale ou s’annule, correspondait aux previsions du modtle. La contrainte appliquie modifie l’enthalpie d’activation du glissement divie essentiellement par son effet sur la constriction des partielles de Shockley au tours du glissement d&vie, et seulement secondairement en favorisant le glissement d&e, (010) par rapport au glissement d&vie (111). La valeur maximale de la CCR que l’on peut atteindre pour le glissement (11 l)[TOl], cad la contrainte de saturation, est egalement en accord avec le modele. Nous avons egalement trouve que la CCR pour le glissement (11 l)[TOl] ne dipendait pas de la vitesse de deformation, mais que la CCR pour le glissement (OOl)[TOl] prtsentait une forte variation positive en fonction de la vitesse de deformation. La temperature du pit des courbes de la contrainte d’ecoulement en fonction de la temperature augmentait avec la vitesse de deformation et elle diminuait lorsqu’on on augmentait le rapport de la CCR de (00l)[Tl0] sur la CCR de (lll)[TOl]. Lorsque la deformation se produisait par glissement (OOl)[TlO], la courbe contraintedeformation prisentait des limites elastiques continues, bien dtfinies. Zuaammenfasaung-An Einkristallen Ni,(Al,Ta) wird die Fliegspannung in Abhlngigkeit von Temperatur, Orientierung, Abgleitgeschwindigkeit und Vorzeichen der angelegten einachsigen Spannung gemessen, urn die Aussagen des Modelles von Paidar et al. [Acra metal/. 32,435 (1984)] zu priifen. Die kritische FlieBspannung im System (11 l)[TOl] hangt nicht nur von der Versuchstemperatur und der Orientierung der Probe ab, wie andere Autoren berichtet haben, sondern such von Vorzeichen der angelegten Spannung. Die Orientierungsabhiingigkeit der Zug/Druck-Asymmetrie-einschliet3lich der Orientienmgen, bei denen die Asymmetrie maximal, minimal oder gerade Null ist-stimmen mit den Voraussagen des Modelles i&rein. Die iiullere Spannung veriindert die Aktivierungsenthalpie der Quergleitung iiberwiegend durch ihren EinfluB auf das Einschniiren der aufgespaltenen Versetzungen wiihrend des Quergleitens und nur in zweiter Linie durch direkte Einwirkung auf die Quergleitung von (111) nach (010). Die maximal erhaltbare kritische FEeDspannung bei (11 l)[TOl]-Gleitung, d.h. die Sittigungsspannung, stimmt ebenfalls mit dem Model1 iiberein. Die kritische FlieDspannung in (111) [TO]] war unabhangig von der Abgleitgeschwindigkeit. Dagegen zeigt diejenige fur Gleitung in (OOl)[~lO] eine starke positive Abhiingigkeit. Die Temperatur, bei dem ein Maximum in der Temperaturabhiingigkeit der Fliegspannungauftritt, nimmt mit ansteigender Abgleitgeschwindigkeit zu und sinkt mit zunehmendem Quotienten aus den FlieDspannungen im (001)[Tl0]- und (11 l)[TOl]-Gleitsystem. Rei Gleitung auf (OOl)[TlO] weist die Verformungskurve wohldefinierte kontinuierliche FlieBeinsHtze auf.
1. INTRODUCTION In the previous paper [l] an explicit expression for the activation enthalpy for cross slip of 1/2[TOl] super449
partial dislocations from (111) to (010) planes in Ll, ordered alloys was derived. There were two parts to this derivation: the first part was concerned with the
450
UMAKOSHI
et al.:
FLOW
STRESS IN Ni,(Al,
cross slip of an undissociated superpartial, and the second part was concerned with the effects of core dissociation on the cross slip event. In the first part of the derivation the cross slip energy of a critical length of undissociated superpartial was calculated, based on three separate assumptions: (i) the antiphase boundary (APB) energy on (111) planes, y, , is higher than that on (010) planes, y,,, and therefore there is a natural tendency for superpartial dislocations to undergo this cross slip. This difference in APB energies was first pointed out by Flinn [2] and was subsequently used in the cross slip models of Kear and Wilsdorf [3], Thornton et al. [4] and Takeuchi and Kuramoto [5] (TK). (ii) Cross slip from (Ill) to (010) planes is aided by the resolved shear stress (RSS) for 1/2[TOl](OlO) slip, r,,,, as first proposed by TK [5]. (iii) Energy stored in the superpartial pair that can be released during cross slip is available for reducing the activation energy. This energy becomes available if the superpartial pair is compressed or extended before cross slip but has its stress-free width afterwards. The second part of the derivation includes the effects of the width of the core of the superpartials and employs the Escaig [6,7] analysis for cross slip in f.c.c. metals. In this analysis the energy, W, to form a constriction on the dissociated dislocation is determined by the degree of increase or decrease of the width of splitting into Shockley partials on the primary (111) plane and the secondary (111) plane compared to the width of splitting with no applied stress. The degree of the change of the dissociation width is, in turn, determined by the RSS on the edge components of the Shockley partials on these two planes. Such an analysis is applicable to Ll, alloys because the results of computer simulations of 1/2[TOl] dislocation cores in Liz alloys by Yamaguchi et al. (81and Paidar ef al. [9] have shown that the cores of 1/2[TOl] super-partial dislocations can always be regarded as dissociated on (111) or (171) into a pair of either well separated or overlapping l/6 ( 112) type partials, independent of whether the APB lies on (111) or (010). That is, the core of a 1/2[TOl] dislocation is dissociated on the (111) plane before cross slip and is dissocated on the (111) or (171) plane after cross slip to the cube plane. The distance, w, that the dislocation segment cross clips on the (010) plane must be an integral multiple of b/2, where b = 1/2[701], since after a jump of b/2 the core dissociates on the (171) plane, and after a jump of b it dissociates on (11 l), etc. The activation enthalpy depends on the length of this jump, but it was shown [l] that the minimum enthalpy jump is the one of length b/2. This was called the 01 jump and the activation enthalpy is &1 = Mb {h + c + Kktph -[(l/J3
whereA4is pb2/2n,
- Y~IY, + N I tphl)b/Rl”2P p
(1)
is the (isotropic) shear modulus; which depend on the width of the stress-free superpartial core; tphis r,,,b/y,; and K h and K are parameters
Ta) SINGLE
CRYSTALS
is an orientation-dependent parameter which measures the difference in Shockley partial spacing on the initial, (111) and final, (1 f 1), planes; N is the ratio of The physical meaning of the &h to 7phph; R = Mpi,. individual terms in equation (1) is as follows: the term h + c is a constant which depends on the width of the stress-free superpartials and involves the energy per unit length of a kink. The term Kktph is a measure of the change in activation enthalpy due to stressinduced differences in superpartial core widths on the (111) and (lT1) planes. K depends on the orientation of the tensile axis, but it does not change sign when the sense of the applied stress is changed and k is a constant. Consequently only tphchanges sign when the sense of the applied stress is changed and therefore this term, Kkt,,, gives rise to a tension/compression asymmetry of the flow stress. Included in K is a constant, K, which measures the relative importance of the RSS on the edge components of the Shockley partials on the primary and secondary { 111) planes, 7@ and rIe, respectively [ 11. When K = 1, rpp and T,~have an equal effect on the activation enthalpy, and when K = 0, only TV is important. K can be determined from experiment as described below. K is related to K by K=[l-~(N+,/3)(271’-J3)/ (3N - J3)J3lQ
(2)
where Q = r,/r,h, a factor which depends on orientation, but not on the sense of the applied stress. This definition is different from the one in Ref. [lo]. The term l/J3 - yO/y, in equation (1) is a measure of the APB energy gained by cross slip from (111) to (010). N It,,,,1 is a measure of the work done by the applied stresses when cross slip to (010) occurs. Note that N is always a positive number [lo] and that this term is, therefore, always positive, i.e. it does not change sign with changes in the sense of the applied stress. In summary, Ho, is a combination of three terms, a constant term, a term which depends on the orientation and sense of the applied stress, and a term which depends only on the orientation, but not the sense, of the applied stress. Ho, was then used to predict the flow stress, tph,by using the TK [5] model Irphl =A exp]-H,,/X,T]
(3)
where A is a constant, kB is the Boltzman constant and T is the absolute temperature. It was shown [1] that if equation (1) is expanded in a Taylor series in tpDand if quadratic and higher order terms in tphare neglected, then an equation similar to equation (4) of TK [5] is obtained. However, in the present case we obtain not only the term involving stress driven cross slip from (111) to (OlO), the most important part of the Takeuchi and Kuramoto theory [S], but we also obtain a term that depends on the sense of the applied stress. That is, the TK [5] result is a special case of the Paidar et al. [l] result.
UMAKOSHI
et al.:
FLOW
STRESS IN Ni,(Al,
Ta)
SINGLE
CRYSTALS
451
Table I. Schmid factors and Schmid factor ratios of siimplcs __ Deformed at a strain rate of 1.3 x 10-‘/s
Deformed at a strain rate of 6.5 x 10-‘/s
Sample A-l A-2 B-l C-l D-l D-2 E-l E-2 A-3 B-2 c-2 D-3 E-3
(I I I)[TOl]
(010)[T01]
1.34 1.34
36.3 51.8 7.16 4.32 11.73 13.94 1.41 1.56
0.4267 0.4438 0.4897 0.4886 0.4269 0.4336 0.3599 0.3797
0.0347 0.0686 0.2306 0.3559 0.3822 0.3771 0.4774 0.4639
4.98 1.31 2.41 12.46 I .28
51.84 4.76 4.32 12.49 1.29
0.4438 0.4699 0.4886 0.4224 0.3411
0.0686 0.2103 0.3559 0.3806 0.4817
Miller indices :
::;;t
1 7 :
2.30 2.41
: T
T 1 T i
t
:::I:
N = S.F. for {OlO)[~OI]~S.F. for (f 1I)[TOi], Q = SF. for fll I)[I%]:S.F.
Paidar er al. [l] used equation (1) to fit the recent results of Ezz et at. [ll] to show that the observed tension/compression asymmetry of the CRSS for (11 l)[TOl] slip can be explained by this model. Wowever, in addition to explaining the results of Ezz et al. f lo], namely that (i) the CRSS for (11 I)[fOl] slip measured in tension exceeds that measured in compression for samples near [OOl] and (ii) the opposite occurs for samples oriented near [Ol l] and {Tl 11, the Paidar ef al. model also predicts that: (i) The maximum separation along the temperature axis between the tensile and compressive flow stress curves should occur for samples oriented near (0111. (ii) If it is assumed that in equation (2) 0 d K d 1, then the tension/compression asymmetry must disappear somewhere between (0011 and the great circle joining [012] to [i13]. The [012]-[T13] great circle is the & = 0 curve in Ref. [IO]. The orientations at which this occurs provide a measure of K. This will occur when K = 0, equation (2). Finally, Paidar er al. 111introduced the concept of a saturation stress, the stress at which the rates of pinning and unpinning are equal. The unpinning can occur in the following way: if the leading super-partial undergoes two successive cross slip jumps of length b/2 on (010) (or one of length b), then the leading and trailing superpartials are dissociated on parallel (111) planes. If the density of kinks on the dislocation line is sufficiently high, then adjacent kinks lying on (010) which are of edge o~entation can annihilate each other, leaving two long straight superpartials on parallel (111) planes. This dislocation pair can then move until the trailing superpartial encounters the original (010) cross slip plane. At certain combinations of stress and temperature this trailing superpartial can cross slip to the plane of the leading superpartial, thereby freeing the dislocation. Whether or not such a saturation stress will be observed depends upon the relative rates of thermally activated pinning and unpinning. The experimentally observable features of such a saturation stress are: (i) { 111) slip above the peak in the CRSS vs temperature plot, or
(aol)lTW--.-.-~ 0.0532 0.0809 0.2903 0.4090 0.3828 0.3788 0.4877 0.4936 0.0808 0.3064 0.4090 0.3807 0.4834
,v
Q
0.2102 0.1982 0.0540 -0.0795 - 0.2368 -0.2205 -0.1957 -0.1816
0.0813 0.1545 0.4709 0.7284 0.8953 0.8697 1.3265 1.2218
0.4926 0.4466 0 1103 -0.1727 -0.5547 -0.5085 -0.5437 -0.4782
0.1982 0.0537 -0.0795 -0.2428 -0.1952
0.1546 0.4475 0.7284 0.9010 1.4120
0.4466 0.1143 -0.1627 -0.5748 -0.5723
(1 I l)(m)
for (11 l)[~Ol].
(ii) A combination of {l 11) and jOlO} slip below the peak with a slow rate of increase with temperature of the CRSS. The theory predicts that for [I1 l] oriented samples the saturation stress should be lowest and the temperature at which the saturation stress occurs should also be lowest, while those for [loo] samples should be the highest, and those for [01 l] samples should be intermediate. The purpose of the experiments reported here is to check the applicability of the Paidar et al. [I] model to the behavior of single crystalline Ni,(Al, Ta).
2. EXPERIMENTAL Single crystals of Ni,(Al, Ta) were grown using a modified Bridgeman method and homogenized at 1450 I( for 10 days in a purified argon atmosphere. The chemical compositions were 76.3 wt.?; Ni, 9.6 wt% Al and 14.1 wt% Ta. Oriented samples with lo/32 NC threads, a 6.5mm gauge length and a 2.5 mm gauge diameter were manufactured from the homogenized single crystals by grinding and were subsequently electrolytically polished in a 30”/, nitric acid-methanol solution to remove surface damage. The specimens were then annealed for 5 hr at 1173 K in purified argon atmosphere and slowly cooled in the furnace to room temperature. Some of the specimens were given a final electropolish in the above electrolyte before deformation to prepare surfaces suitable for slip trace analysis. The Miller indices of the sample axes are given in Table 1. Some Schmid factors for various slip systems and the ratios of some Schmid factors are also listed. The orientations of these samples are also shown in Fig. 1 in the standard (OOl]-[Ol l]-[Tl l] unit triangle. Tension and compression tests were conducted on an Instron Universial Testing Machine at a nominal strain rate of 1.3 x lo-‘s-’ at temperatures from 77 to 1200 K. Some of the tests were carried out at a strain rate of 6.5 x 10m3/s in order to determine the strain rate dependence of the flow stress. Tests at 77 K were performed with the samples immersed in
452
UMAKOSHI
et al.:
FLOW STRESS IN Ni,(Al, Ta) SINGLE CRYSTALS
001 012 011 Fig. I. The orientations of the samples tested in this study. The unit triangle is divided into three regions in which the core constriction effect is expected to be different, ref. [I 11.
liquid nitrogen. Tests at temperatures in the range 293-12OOK were carried out under vacuum. The same sample was repeatedly deformed at different temperatures to eliminate errors due to variations between samples. A given sample was first deformed in tension to a 0.2% nominal plastic strain and then deformed in compression at the same temperature, and then it was tested in the reverse sequence at the next temperature, thus eliminating the effects of different deformation sequences. Some of the flow stresses were checked with virgin samples. Slip lines were photographed on samples deformed in tension using an optical microscope equipped for Nomarski interference contrast, and the operative slip systems were determined by measuring the angle between the tensile axis and the tangent to the slip line for different rotations about the deformation axis. 3. RESULTS Temperature and orientation dependence of the CRSS
The temperature and orientation dependence of the CRSS for (lll)[TOl] and (OOl)[TlO] slip measured at a strain rate of 1.3 x 10e3 s-’ are shown in Fig. 2(a)-(e). In all samples except sample E, deformation at temperatures below the peak temperature occurred by {111) ( 110) slip. In sample E, the sample oriented near [Ill], deformation occurred in this temperature range by a combination of (11 l)[TOl] and (OOl)[TlO] slip. Consequently the curves labeled “CRSS for (lll)[TOl]” are appropriate for all samples except sample E for temperatures below the peak. Above the peak all samples except sample A, the near - [OOl] sample, deformed by (OOl)[TlO] slip, and therefore the CRSS for this system is appropriate in that temperature regime. (The CRSS for (11 l)[TOl] slip is therefore shown as a dotted line in this temperature range.) Sample A deformed by (11 l)[‘fOl] slip over the entire temperature range. Examples of slip traces are shown in Fig. 3(a)-(d). In Fig. 2(a)-(e) the symbols without arrows denote the CRSS measured on samples that were deformed a number of times at a series of temperatures, and the symbols with arrows indicate data obtained on virgin samples.
As expected, the CRSS of the virgin samples was generally lower than that of the work hardened, multiply-deformed samples. The main features of Fig. 2(a)-(e) are: (i) the CRSS for (11 l)[TOl] slip increases with increasing temperature for all orientations; (ii) the CRSS for (11 l)[TOl] slip as measured in tension is in general, different from that measured in compression; (iii) the magnitude and sign of this tension/compression asymmetry is strongly orientation dependent. Sample A is stronger in tension than compression, the reverse is true for C, D and E, and the asymmetry nearly disappears for sample B. Sample D, which is approximately 50% stronger in compression than tension at 400 K, shows the largest asymmetry; (iv) the slope of the CRSS vs temperature curves at temperatures below the peak temperature is orientation-dependent -note the rather flat slope of Fig. 2(e) compared to the others; (v) above the peak temperature there is little or no tension/compression asymmetry, even in sample A which deformed by {11I} (110) slip in this temperature range; (vi) the transition from octahedral to cube slip occurred at or near the peak temperature in samples B, C and D. In sample A cube slip was not observed and in sample E cube and octahedral slip were observed at temperatures well below the peak temperature. Strain rate effects
The CRSS of samples measured at the higher strain rate of 6.5 x 10-3s-’ is shown in Fig. 4(a)-(c). Comparison of Figs 2 and 4 shows that the magnitude of the CRSS for (11 l)[TOl] slip, both in tension and compression, is largely strain rate independent, but the flow stress for (OOl)[TOl] slip is strain rate dependent. For example, the CRSS for (OOl)[TlO] slip of samples of orientation C is substantially higher at the higher strain rate. The effects of orientation, sense of the applied stress, and strain rate on the CRSS for (11 l)[TOl] and (OOl)[TlO] slip are shown in Fig. 5. It is seen that the CRSS for (OOl)[TlO] slip is independent of the orientation and sense of the applied stress, but it increases with increasing strain rate. Since the CRSS for (11 l)[TOl] slip is largely strain rate-independent, only the dependence on crystal orientation and sense of the applied stress are shown in this figure, measured at a strain rate of 1.3 x lo-' s-‘. Note that the CRSS for (11 I)[TOl] slip as measured in tension first decreases, then increases as N increases. As will be discussed later, this observation cannot be explained using the TK model. In Fig. 6 the effects of strain rate, sample orientation and sense of the applied stress on the peak temperature are shown. The peak temperature depends strongly on the ratio of the Schmid factor for ‘(OlO)[TOlJ slip to that for (11 l)[TOl] slip, but it increases only slightly with increased strain rate, and appears to be almost independent of sense of the applied stress.
UMAKOSHI
et al.:
FLOW
STRESS IN Ni,(AI. Ta) SINGLE
CRYSTALS
453
(d) 500 A
I
0
200
I
400
600
Temperature
1
0
I
1
800
1000
I 1200
I
0
200
1
600
I
800
Temperature
(K)
1
f
10001200
(K)
(e)
(b)
I
t
400
I
200
I
400
1
600
1
I
1000
1200
I
800
Temperature
(K
1
1 0
I
200
I
400
I
600
Temperature
I
600
I
1000
I 1200
CK 1
Ic)
I
200
I
400
I
600
Temperature
1
800
I
1000
I 1200
(K)
fig. 2. (a)-(e) The temperature dependence of the CRSS for (I I l)[TOl] and (~l)[TlO] and compression measured at a strain rate of I .3 x 10m3SK’.
Stresf-strain
curves
Stress-strain curves measured in tension, for samples which deformed by (11 l)[TOl] slip at 600 K and for samples deformed by (00 1)[Tlo] slip at 995 K, are shown in Fig. 7. At 600 K samples A, B and C show only parabolic work hardening, similar to b.c.c. metals at low temperatures, while sample E shows a three stage work hardening curve, similar to that seen in f&c. materials. The shape of the curve for sample D is intermediate between the two. Samples deformed
slip in tension
at 995 K show clearly defined, continuous yield point phenomena. Note that the curve for sample B shows two such yield points. 4. DISCUSSION Tensionlcompres~ion asymmerry of the CR.!% ,for (1 I l)[;TOl] slip
The experimental results shown in Figs 2 and 4 are in complete agreement with the model of Paidar et al. [l] and with the previous resuhs of Ezz er a/. [I I]. The
454
UMAKOSHI
ci al.:
FLOW STRESS IN Ni,(Al.Ta)
SINGLE CRYSTALS (a)
(b) I
0
200
I
I
I
400 600 600 Temperature (K
I
I
1000 1200
)
(b) 500
c
Fig. 3. Slip traces produced by deformation at (a) 1200 K, (b) and (c) 780 K. 100
CRSS measured in tension exceeds that measured in compression for orientations near [OOl], and the reverse is true for orientations near [ill] and [Oll]. This has previously been observed by Ezz et al. [I I] and it is predicted by the model. The most important results of the present work are:
I
0
200
/
I
I
I
400 600 600 Temperature (K
I
1000 1200
I
(cl
(i) The CRSS for (I 1l)[iOl] slip is independent of the sense of the applied stress for samples of orientation B. This is within the range of orientations at which the disappearance of the tension/compression asymmetry was predicted by the model [l]. (ii) The tension compression asymmetry is very large for samples oriented near [Ol I]. e.g. at 400 K the CRSS measured in compression is approximately 50% higher than the value obtained in tension. This is also as predicted by the model [l]. The present data also allow us to determine the relative importance of T,,,, the stress driving (010) cross slip, and 5Pcand T,,, the stresses which change the width of the core dissociation. We will call these the “cross slip” and the “constriction” effects, respectively. This can be done by referring to the top two curves in Fig. 5. The curve for the compression tests shows that the CRSS for (11 l)[TOl] slip increases with increasing N in the same manner as predicted by the TK theory: however the CRSS measured in tension decreases with N, for N less than about 0.9. opposite to that predicted by the TK theory. These tensile test results indicate that the
I 0
I
I
I
I
200
400
600
000
Temperature
1
I
1000 ,200
(K)
Fig. 4. (a)-(c) The temperature dependence of the CRSS for (11 l)[TOI] and (OOl)[TlO]slip measured in tension and compression at a strain rate of 6.5 x IO-) s-‘.
constriction effect is large enough to offset the cross slip effect at 400 K if N is less than 0.9. This is also in qualitative agreement with the theory [l], c.f. Fig. 11 of Ref. [I 1. The constriction effect reaches a maximum for N = 0.87, at the [Ol l] orientation, and then rapidly decreases for higher values of N, while the
UMAKOSHI
et al.:
FLOW STRESS IN Ni,(Al, Ta) SINGLE CRYSTALS
455
A Tension . Camp, 6 5xlQ3s-'
I
I
1
05
IO
I5
N
Fig. 5. The effects of orientation and sense of the applied stress and the effectof strain rate on the CRSS for (11 l)[TOl] slip at 400 K and for (OOl)[TlO]slip at 1000K.
cross slip effect increases continuously with increasing N for all N. Another way of comparing the present data with the model [l] is shown in Fig. 8. The difference between the tensile and compressive values of the CRSS at 4OOK, normalized to the tensile value, is plotted as a function of N. It is seen that the difference is zero for N = 0.42. Since the model predicts that the asymmetry disappears for K = 0 in equation (2), the value of K can be determined to be 0.32. This means that TVis more important than T,!~ in determining the constriction effect. Saturation stress The model developed in the previous paper [l] predicts that there should be a maximum possible CRSS for (11 l)[TOl] slip at any given sample orientation and temperature. Such a saturation stress has clearly been reached in the near-[0011 oriented samples, Figs 2(a) and 4(a), because the slip still occurs on (11 l)[TOl] at temperatures above the peak temperture. Also for samples oriented near [Tl l] a saturation stress appears to have been reached. At temperatures below the peak temperature the stress and 1200 r o Tension .
l
Comp.
I
3 x Io-3s-’
Shear
strain
Fig. 7. Shear stress-shear strain curves for samples deformed by (11 l)[TOl] slip at 600 K and for samples deformed by (OOl)[~lO] slip at IOOOK.
temperature are not high enough to cause massive (OOl)[TlO] slip, consequently both (111) and (001) slip are observed. However the CRSS for (11 l)[TOl] slip is quite high, e.g. compare Fig. 2(e) with Fig 2(a)-(d). Consequently we conclude that a saturation stress has also been reached for samples of this orientation. Note also that the saturation stress and temperature are higher for the near-[0011 sample than for the near-[Tl l] sample, which is also in qualitative agreement with the model. Strain rate effects The physical basis of the TK model for (I 1l)[‘fOl] slip can be approximately described in the following way. The flow stress at any temperature is determined by the density of cross-siipped segments which form pinning points on dislocations. This density of pinning points is expected to be independent of dislocation velocity for small changes in the velocity. Hence one would expect that there be very little strain rate sensitivity of the CRSS for (11 l)[TOl] slip, which has, indeed, been observed in the present experiments. The mechanism controlling the rate of (OOl)[‘f lo] slip, the cube slip mode at high temperatures, is quite different, however. The cores of these dislocations do not lie on the (001) slip plane [8,9], and therefore 06 t
A Tension 65x
b camp.
-=-I
4
700 $ a
;lWIl
01400K
_'-01400;
6 =I~xIO-~ i="'""T
600 0
4004
05 Schmid
05
I.0
1.5
Fig. 6. The variation of the pea: temperature with N, sense of the applied stress, and strain rate.
factor
IO
I.5
rat~o,~010~~01]~~1II~[i0l]
Fig. 8. Orientation dependence of the tension/compression flow stress asymmetry for samples deformed at 400K. rl. and tc are the CRSS for (11 l)[TOl] slip as measured in tension and compression, respectively.
456
UMAKOSHI ef al.: FLOW STRESS IN N&(AI, Ta) SINGLE CRYSTALS
these dislocations are expected to move by a thermally activated process, similar to that observed in b.c.c. materials at low temperatures. Consequently a fairly high positive strain rate dependence of the CRSS for (OOl)[Tlo] slip is expected, exactly as observed, c.f. Fig. 5. The dependence of the peak temperature on orientation, Fig. 6, is qualitatively what is expected based on the changes in slip system that occur at this temperature. The peak temperature marks the transition between slip predominately on (11 l)[TOl] at lower temperatures to slip predominately on (OOl)[TlO] at higher temperatures. The higher the ratio of the Schmid factor for the cube slip system to that for the octahedral system the lower should be the temperature of the transition. It is seen in Figure 6 that this has, indeed, been observed. Furthermore, since the CRSS for slip on (OOl)[TlO] has a positive strain rate dependence while that for (11 l)[TOl] slip has almost none, an increased strain rate is expected to shift the peak to higher temperatures. This is also what is observed.
Stress-strain
curves
The difference in shape of the stress-strain curves for the two slip systems, Fig. 7, is very striking. The shape of the curves at 1000 K, showing the pronounced smooth yield point, and sometimes more than one, is very similar to that observed in materials like LiF [ 121in which dislocation motion is thermally activated and the mobile dislocation density is related to the total density.
SUMMARY AND CONCLUSIONS The results of the experiments on N&(Al, Ta) are in complete agreement with the predictions of the model developed by Paidar et al. [l]. The most important observations are: (1) The CRSS for (11 l)[TOl] slip depends not only on the temperature and sample orientation but also on the sense of the applied stress. (2) Samples near [OOl] are stronger in tension than in compression, while the reverse is true for samples near [Ill] and (0111. (3) Samples near [Ol l] are much stronger in compression than in tension. (4) The asymmetry of the CRSS disappears for samples oriented between [OOl] and the [012]-[T13] great circle. (5) From the fact that the asymmetry disappears at the orientation indicated in No. 4 above, it can be concluded that the constriction stress on the primary octahedral slip plane, (11 l), has a larger effect on the activation enthalpy for cross slip than does the
constriction stress on the secondary octahedral slip plane, (lTl). (6) In this material the effects of stress-driven core constriction are more important in determining the CRSS for (11 l)[TOl] slip than are the effects of stress driven cross slip from (111) to (010). That is, the Escaig effect is more important than the TK effect. (7) A saturation stress is observed for samples of [Ill] and [OOl] orientation. The relative values of these stresses and the temperature at which they occur are in agreement with the model. The following observations were also made which cannot be qualitatively analysed using the Paidar et al. [l] model but support its basic assumptions, namely thermally activated formation of obstacles for (I 1l)[TOl] slip and thermally activated motion of sessile dislocations in the case of (OOl)[TlO] slip. (1) The CRSS (11 l)[TOl] slip is strain rate independent. (2) The CRSS for (OOl)[TlO] slip shows a large positive strain rate dependence. (3) The peak temperature increases with increasing strain rate and decreases with increasing RSS on (OOl)[TlO] relative to that on (lll)[TOl]. (4) When the sample deforms by (OOl)[TlO] slip, the stress-strain curve shows clearly defined continuous yield points. Acknowledgements-Support for this program was provided bv the NSF under arant no. DMR-7905556. Research facilities were provided by the Laboratory for Research on the Structure of Matter at the University of Pennsylvania, supported by the NSF MRL program under grant no. DMR-8216718. The single crystalline Ni,(Al, Ta) was gratiously supplied by Dr Dilip Shah of the Pratt and Whitney Aircraft Corp., Middletown, CT.
REFERENCES 1. V. Paidar, D. P. Pope and V. Vitek, Acra metal/. 32,435 (1984). 2. P. A. Flinn, Trans. T.M.S.-A.I.M.E. 218, 145 (1960). 3. B. H. Kear and H. G. F. Wilsdorf, Trans. T.M.S.A.I.M.E. 22.4, 382, (1962). 4. P. H. Thornton, R. G. Davies and T. L. Johnston, Metall. Trans. lA, 207 (1970). 5. S. Takeuchi and E. Kuramoto, Acta metall. 21, 415
(1973). 6. B. Escaig, .I. Phys. 29, 225 (1968). 7. B. Es&g, in Dislocation Dynamics, p, 655 (edited by A. R. Rosenfield, G. T. Hahn, A. L. Bement Jr and R. I. Jaffee). McGraw-Hill, New York (1968). 8. M. Yamaguchi, V. Paidar, D. P. Pope and V. Vitek, Phil. Mag. 45, 861 (1982).
9. V. Paidar, M. Yamaguchi, D. P. Pope and V. Vitek, Phil. Mag. 45, 883 (1982).
10. C. Lall, S. Chin and D. P. Pope, Metall. Trans. lOA, 1323 (1979). 11. Salah S. Exe, D. P. Pope and V. Paidar, Acta metall. 30, 921. (1982).
12. W. G. Johnston and J. J. Gilman, I. appl. Phys. 38, 129 (1959).