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Anisotropy of the critical resolved shear stress of a superalloy containing 6 vol.% L12-ordered γ′-precipitates
Ac'ta metall, mawr. Vol. 43. No. 9, pp. 3295-3300, 1995
Pergamon
0956-7151(95)00046-1
Elsevier Science Ltd Copyright ~ 1995 Acta Metallurgica Inc. Printed in Great Britain. All rights reserved 0956-7151/95 $9.50 + 0.00
AN1SOTROPY OF THE CRITICAL RESOLVED S H E A R STRESS OF A S U P E R A L L O Y C O N T A I N I N G 6 VOL.% L1 e-ORDERED 7'-PRECIPITATES J. JOCKWEG and E. NEMBACH Institut fflr Metallforschung, Liniversitfit Mfinster, Wilhelm-Klemm-Strasse 10, D-48149 Mfinster, Germany lReceived 3 December 1994: m revised /brm 10 Januao' 1995)
Abstract Single crystals of the ;.'-strengthened nickel-base superalloy NIMONIC PEI6 have been compression tested in the temperature range 683 1143 K. Four different orientations of the specimens have been studied: [0 0 1],[/23].[011] and [T11]. They were either in the homogenized, single-phase state or in the peak-aged state. The critical resolved shear stress (CRSS) of the homogenized specimens was isotropic at 683 K. The CRSS of the peak-aged specimens, containing 6 vol.% of Lie-long-range ordered )"-precipitates of 25 nm radius, was anisotropic at 683 K and at 989 K: the [001]-orientated specimens were the softest ones, the CRSS increased as the orientation moved towards [01 l] or [111]. This is the same orientation dependence found for the CRSS of single-phase Ll_,-ordered materials. The interpretation of the anisotropy of the CRSS of NIMONIC PEI6 follows that given for single-phase Ll2-1ong-range ordered materials. Zusammenfassung An Einkristatlen der 7"-geh/irteten NickeI-Basis-Superlegierung N1MONIC PE16 wurden zwischen 683 und 1143 K Druckversuche ausgefiihrt. Vier verschiedene Orientierungen wurden untersucht: [001].[T23],[01 I] und [11l]. Die Proben waren entweder im homogenisierten, einphasigen Zustand oder im optimal gealterten. In letzterem enthiehen sie 6 Vol.% Ll:-ferngeordnete 7'-Ausscheidungen wm 25 nm Radius. Die kritiscbe Schubspannung der homogenisierten Proben war bei 683 K isotrop. Die der optimal gealterten war anisotrop bei 683 und 989 K: die [001]-orientierten Proben waren am weichsten: die kfitische Schubspannung stieg an, wenn die Orientierung auf [011] oder [TI 1] zuwanderte. Das ist dieselbe Orientierungsabh~ingigkeit, die man ffir einphasige Ll~,-ferngeordnete Materialien beobachtet. Die Anisotropie der kritischen Schubspannung yon NIMONIC PE16 wird folglich fihnlich ,~ie die yon cinphasigen Ll:-Materialien gedeutet.
l. 1NfRODU('TION Intermetallic phases with the long-range ordered Ll:-crystal structure are k n o w n to have an a n o m a l o u s plastic behaviour: (i) The critical resolved shear stress (CRSS) does not decrease monotonically as the d e f o r m a t i o n t e m p e r a t u r e Tt~ is raised, but it has a m a x i m u m . The peak t e m p e r a t u r e T> which depends on the material, on the orientation of the specimen a n d on the strain rate is a r o u n d 1000 K. (ii) The CRSS is anisotropic, i.e. Schmid's law is not followed. (iii) The CRSS depends on the direction of the deformation, it is different l\>r tension a n d compression Iesls. By far the most extensively studied L l,-material is Ni~A1. The N i - a t o m s occupy the laces of the f.c.c. L1,-elementary cell and the Al-atoms its corners. Let a~, be the lattice constant. The Burgers vector of a perfect dislocation in Ll,-materials is of the type a0(110). It dissociates into two dislocations of the type (a()/2)(l10) which is the s t a n d a r d type in the f.c.c.
crystal structure. There is an antiphase b o u n d a r y between these two (a0/2)(110) dislocations. Each of them splits further into two Shockley partial dislocations of the type (a0/6)(112) with a complex stacking fault in between. All three of the a b o v e - m e n t i o n e d anomalies have been interpreted on the basis of Kear a n d Wilsdorf's [1] original idea. The primary slip planes in Lie-materials are of the type {111}. But since the specific antiphase b o u n d a r y energy is lower o n { 100}t h a n on { 111 }-planes [2, 3] there is a tendency of screw dislocations to cross slip thermally activated from ~111 }- o n t o { 100}-planes. Baluc et al. [4] f o u n d for the respective specific antiphase b o u n d a r y energies of NLAI [0.111 + 0.015] and [0.090 _+ 0.005] J / m 2. If, by thermal activation, a short segment of a (a0/'2)(110)screw dislocation leaves its original {111 }-glide plane and cross slips o n t o a [100}-plane, this segment becomes a h i n d r a n c e to the glide of the remainder of the screw dislocation: this segment acts as a pinning centre. Detailed models to explain the three a b o v e - m e n t i o n e d anomalies have been developed by Takeuchi a n d K u r a m o t o [5], Lall et al. [6], P a i d a r et ell. [7] a n d Mills a n d C h r z a n [8]. A review has
3295
3296
JOCKWEGand NEMBACH:
CRITICAL RESOLVED SHEAR STRESS OF AN ALLOY
been published by Pope and Ezz [9]. In contrast to pure f.c.c, metals or disordered f.c.c, solid solutions, which are softened by cross slip, kl,-long-range ordered materials are strengthened by it. Thus, all factors which raise the probability of { 111 } --+{ 100}-cross slip in the latter class of materials, increase their C R S S - - p r o v i d e d TD is below Tp. Such factors are: high Tm a high Schmid factor (SF) of the { 100}-cross-slip-plane and a high force which presses the two Shockley partial dislocations of the leading (ao/2)(llO)-screw dislocation together. The latter forces derive from the externally applied stress acting on the edge components of the Shockley partials [6]. The latter two factors are quantified by the parameters N and Q, respectively: SF~(010)[i01]} N = SF{(1 ll)[T01]}
(la)
SF{(111)[121]} Q = SF{(Ill)[T01]}"
(lb)
The orientation of the specimen is supposed to lie in the triangle [001], [011] and [TI 1]. Then the primary slip system is (lll)[T01]. Its SF is the denominator of equations (1). The numerator of N is the SF of the cross slip system and the numerator of Q is the SF which governs the compression of the Shockley partials. A theoretical analysis of compression tests yields the following results for the dependence of the CRSS z,. on N and Q [6, 10]:
?z,/?N > 0
(2a)
Fr~Q < 0.
(2b)
and
The variations of N and Q with the orientation of the specimen is shown in Table 2. It is emphasized that though favourable values of N and Q may raise the probability of cross slip, thermal activation is needed to make screw dislocations actually cross slip and increase re. Therefore Or~/OTL~becomes positive at elevated temperatures. Yoo [1 l] has discussed the effects of the elastic anisotropy on the probability of cross slip. Relations (2) and the values given for N and Q in Table 2 explain the experimentally observed anisotropy of r~ of Ll:-materials: r~ of compression tested specimens increases as their orientation moves away from [001] towards [0l 1] or IT11]. Relation (2b) also explains the tension~compression asymmetry. Since nickel-base superalloys are strengthened by coherent precipitates of the 7'-phase which has the L12-structure, the question arises whether these alloys also exhibit the anomalous plastic behaviour described above. The disordered or short-range ordered solid solution matrices of these ;"-strengthened superalloys have the f.c.c, crystal structure. Heredia and Pope [12] investigated these aspects for a ~,'-strengthened superalloy. Shah and Duhl [13] and Caron and Khan [14] have published similar studies. The CRSS of the
Table 1. Overallcomposition of NIMONIC PEI6, of the 5/-particles and of its matrix, at.%. after Ref. [17] Elements Ni Fe Cr Mo AI Ti Overall 41.6 34.6 17.6 2.0 2.6 1.5 ;"-Particles 72.1 3.2 1.0 10.4 13.3 Matrix 39.6 36.6 18.7 2.1 2.1 0.7
superalloys showed anisotropies analogous to those of single-phase Ll:-materials. The results of an experimental study of the anisotropy of the CRSS of the commercial nickel-base superalloy N I M O N I C PE16 are presented below. Its spherical 7'-particles are small and their volume fraction is low: 50 nm diameter and 0.061, respectively. This contrasts with the materials studied by Heredia and Pope whose respective parameters were larger by the factors 8 and 10. Shah and Duhl's and Caron and Khan's i,'-particle dispersions were similar to or even coarser than those of Heredia and Pope. Since the CRSSs of pure copper [15] and of single-phase f.c.c, solid solutions of nickel-cobalt [16] are known to be anisotropic, a possible anisotropy of the CRSS of'),'-strengthened N I M O N I C PE16 single crystals may also reflect possible plastic anisotropies of the matrix. Therefore, this superalloy has also been studied in the homogenized, single-phase state. 2. EXPERIMENTAL METHODS AND RESULTS A polycrystalline rod of N I M O N I C PE 16 has been supplied by Glossop Superalloys Ltd, Glossop, U.K. The overall composition is given in Table 1. The low concentrations of C and Si have been disregarded. The nominal orientations of the specimens are listed in Table 2, their individual orientations deviated up to A (Table 2) from the nominal ones. The variation of the orientation within an individual specimen due to small angle boundaries was about _+ 1. fit and O are the respective averages over all specimens used in the present investigation. Their dimensions were 3.9 mm in diameter and 13.6mm in length. After crystal growth all specimens were homogenized for 4 h at 1473 K. One group of specimens was compression tested in this state. The other was heat treated for 2 h at 979 K, subsequently subjected to an Ostwald ripening treatment of 51.4 h duration at 1079 K and then compression tested. The purpose of the 979 K treatment was to enhance the nucleation of the 7'-particles. The specimens were sealed in argon-filled quartz ampoules: tubes of N I M O N I C PE16 prevented direct contact between the specimens and the
Table 2. Nominal specimenorientation, maximum deviation k from it. resolvedstrain rate a. ,~ and O [equations (1)] are the respective averages over the range k Oricntation A( ) d(104/s) ~V O [001] 12 1.37 0.14 0.43 [i231 3 1.33 0.90 - 0.33 [011] 3 1.46 0.86 054 IT11] 3 2.11 1.62 0.55
JOCKWEG and NEMBACtt:
CRITICAL RESOLVED SHEAR STRESS OF AN ALLOY
ampoules. In this way possible contaminations have been avoided. At the end of the treatments the ampoules were water quenched without breaking them. The resulting ;"-particle dispersions were: homogenized specimens: 7'-particle-strengthened specimens:
. l = 0.0,
5
I
4-
z
3
,-1
2
_ . . . . . . .
--
a)
0
0.1
I
0
0
0.2
0.3
I
1
,"
I
I
i
0.1
0.2
0.3
L
i
I
0
0.1
0.2
0.3
d [mm] Fig. 1. Load L versus the travel d of the cross-head of the testing machine. The dashed lines indicate the extrapolation scheme used for the derivation of the CRSS. (a) Peak-aged [001] specimen. 7], = 683 K, (b) peak-aged [011] specimen, TD= 1143 K and (c) homogeneous [011] specimen, TD = 1090 K.
2.1. Results/or the homogenized specimens The results for the CRSS of homogeneous, <-free specimens are compiled in Table 3. Up to 1090 K, the plastic deformation was discontinuous, Fig. l(c) shows an example. The peak-to-peak excursion of the discontinuities increased with TD. At 683 K, it amounted to less than 0.5% of the CRSS. Therefore defining the CRSS not on the basis of the peaks of the
C R S S (MPa)
IT t i]
-
c)
Table 3. CRSS o f the homogeneous specimens
[001] [T231 101I]
_
0.061, r = 25 nm.
,/'and r are the volume fraction and the average radius of the spherical, coherent 7'-particles. The second group of specimens was in the peak-aged state, i.e. their CRSS was the maximum possible at the givenf. The compositions of the ?"-particles and of the matrix are listed in Table 1. Since f is very low, the matrix composition is nearly the same as the overall composition. The specimens were compression tested at temperatures TD between 683 and 1143 K. TD was stabilized within +_4 K. For TD ~< 989 K, which is the most interesting temperature range, the ensuing errors in the CRSS are negligible. A protective argon atmosphere prevented oxidation. The technical strain rate was 6.1 x 10 5/s. The resulting resolved strain rates are given in Table 2. Their average was 1.6 x 10 +/s, the maximum difference from this average was 35%. The CRSS was derived from the intersection of the linearly extrapolated elastic and first plastic part of the ++load versus elongation" curve. This is demonstrated in Fig. 1. If this curve was discontinuous, the second straight line was drawn through the peaks ot" the curve [Fig. l(c)]. Each specimen's individual Schmid factor was inserted. The results for the CRSSs are presented in Tables 3 and 4. Each entry is the average over 3-5 specimens, the standard deviation of the average is also given. Since the orientations of individual specimens deviated from the nominal orientations by angles up to A quoted in Table 2, the 3-5 specimens used [br one data point were chosen such that these specimens were representative of all specimens homogenized for the respective orientation. Thus the scatter of the orientations and possible minor differences in the quality and thermal history of individual single crystals raise only the standard deviation of the CRSS, but do not lead to systematic variations of the CRSS with To or with the nominal orientation of the specimens. Standard deviations are equivalent to 68% confidence limits.
Orientation
].f /.]"
r = 0.0 nm 1
f=
I
--
3297
683 K 47.5 4__(17 43,4 + 0 7 44.3 + (13 43.3±13
989 K
1040 K
42.7 ± 3.4 68.9 _+ 0.8 42.4 + 0,6 79.9 = 2.5 44.8 ± 0.7 78.0 - 2.1 63.5+_4.1 74.5+1.9 Discontinuous glide
1090 K
1143 K
77.0 + 1.5 80.1) ± 1.0 88,7 + 0.2 99.3±4.5
71.4 ± 5.3 82.9 + 1.4 85.6 _4_4.2 75.2_+5.4 Yield point
3298
JOCKWEG and NEMBACH:
Oricntation [0011 [T23l [011t [ill I
CRITICAL RESOLVED SHEAR STRESS OF AN ALLOY
Table 4. CRSS of the peak-aged specimens CRSS (MPa) 683 K 989 K 1040 K 1090 K 128.0 + 3.0 127.7 + 1.9 125.4 -+ 1.5 90.9 + 1.2 129.7 + 2.5 133.6 + 0.3 133.9 + 2.7 106.4 + 1.7 130.3_+ 1.2 135.5_+1.3 135.4_+1.6 110.0_+4.2 135.5+0.1 137.1_+0.5 124.9_+3.7 97.4+0.3 Yield point
load versus elongation curve [Fig. l(c)] but, for example, on the basis of the average load would not change the results. At 1143 K there were minor yield points. The increase of the CRSS for TD > 989 K is caused by the precipitation of very small 7'-particles during heating of the specimens up to TD and during their elastic deformation. The presence of these ";'-precipitates has been proved for a specimen deformed at 1090 K by observing the L l,-superlattice reflections in the transmission electron microscope, after cooling the specimen to ambient temperature. About one half of the total time which the specimen was at or above 989 K. was spent prior to its plastic deformation, the other half was needed for cooling it down to ambient temperature. The lower CRSSs found at TD = 1143 K are due to the partial dissolution of the fine ?"-precipitates. The solvus temperature of the 7'-phase in N I M O N I C PE 16 is around 1150 K [18]. In the temperature range 989 K ~< Tu ~ 1143 K, the growth of the ","-precipitates and their possible later dissolution depend critically on the heating rate of the specimens. Since this rate could not be controlled precisely, the data taken for the homogenized specimens at TD ~> 989 K are not considered any further.
2.2. Results jor the peak-aged specimens The results obtained for the peak-aged specimens are given in Table 4. Except at TL~= 683 K [Fig. l(a)], there were yield points [Fig. l(b)]. The two highest deformation temperatures are above the temperature at which the ;.,'-particles had been grown (1079 K). Therefore changes in their dispersion during heating and during the elastic deformation are possible. In a first order approximation these changes can be estimated on the basis of the )"-particle growth observed for unstressed specimens.
3. DISCUSSIONS In an earlier investigation [18] the CRSSs of middle-orientated single crystals of N I M O N I C P E I 6 have been measured at 500 K. The CRSS of homogenized specimens and of those having the same )"-particle dispersion as the present peak-aged ones were 47.5 and 130.9 MPa, respectively. This is in good agreement with the present data taken for the [123] orientation at 683 K: (43.4 + 0.7) and (129.7 _+ 2.5) MPa. The present Tv is 183 K higher than the former. The CRSS averaged over the four orientations of the homogeneous, ;,'-free specimens is 43.6 MPa at 683 K,
1143 K 60.8 + 2.4 73.0 + 0.6 75.4_+0.7 64.9+0.5
the average over the four standard deviations amounts to 0.7 MPa. The CRSSs measured for the four orientations fall within the range of (43.6 _+ 0.7) MPa. Evidently the C R S S of the homogeneous specimens is isotropic, i.e. Schmid's law is followed. Though the precipitation of some ),'-particles at 989 K prevented the experimental p r o o f of the plastic isotropy at 989 K, it can be assumed that the CRSS of the homogeneous specimens is isotropic at 989 K as well as at 683 K. Consequently, any anisotropy of the peak-aged, ,/'-strengthened specimens observed at these two temperatures is not caused by their matrices, whose composition is nearly the same as that of the homogeneous specimens (Table 1). In order to demonstrate the anisotropies and temperature dependencies of the CRSSs of the peak-aged specimens, the data presented in Table 4 are repeated in Table 5 in normalized form. The CRSS measured at TD for the orientation [hkl] is divided by the CRSS found at 683 K for the [001] specimens. At 683 and 989 K, the C R S S increases as the orientation varies from [001] through [i23] to [011] or []'11]. This anisotropy is higher at 989 K than at 683 K (Table 5). The plastic anisotropy of the compression tested N I M O N I C PE16 single crystals is the same as that quoted in Section 1 for compression tested singlephase L12-materials. Evidently the two-phase NIM O N I C PE16 single crystals reflect the C R S S anisotropy of their hardening L1 :-ordered 7'-particles. It is quite remarkable that this is the case in spite of their small size (r = 25nm) and their low volume fraction ( J = 0.061). Evidently screw dislocations can cross slip in these small 7'-precipitates. This will be discussed further below. The anisotropy apparent at and above 1040 K probably reflects the different temperature dependencies of the CRSSs of the four orientations [5, 9, 12, 13]. Since the 7'-precipitates are spherical they cannot induce a simple geometric anisotropy as cuboidal precipitates may do. Concerning the specimens with the [ i l l ] orientation, some caution is appropriate. Their resolved strain rate is 50% higher than that of the specimens with the other Table 5. Normalized (to [001], Tt, = 683 K) CRSS of the peak-aged specimens Normalized CRSS Orientation [001] [T23] [011] [111]
683 K
989 K
1040 K
1090 K
1143 K
1.00 1.01 1.02 1.04
1.00 1.04 1.06 1.07
0.98 1.05 1.06 0.98
0.71 0.83 0.86 0.76
0.48 0.57 0.59 0.51
JOCKWEG and NEMBACH: CRITICAL RESOLVED SHEAR STRESS OF AN ALLOY orientations (Table 2). This may affect the CRSS of the [Tll] specimens in the 1% range [5,9]. Except for the [001] orientation, the actual orientations of the specimens deviate by no more than 3c from the nominal orientations (Table 2). No systematic variation of the CRSS with the actual orientation of the nominal [001] specimens has been found. Hence, the CRSSs quoted in Tables 3-5 are representative of the listed orientations. In contrast to the present results, Heredia and Pope [12] found that their [T11] compression specimens were the softest for 600 K ~< T~, ~< 800 K. The authors interpreted this as being due to the fact that for this orientation the (010) [1"01]slip system is favoured at all TD, because its Schmid factor is high. This is evident from the high value listed for :gT [equation (la)] in Table 2. It must be remembered that r a n d f o f Heredia and Pope's material were approx. 8 and 10 times as large as the present values, respectively. Shah and Duhl [13] investigated even coarser ;,'-particle dispersions. The CRSSs of the peak-aged [T23]-, [011]- and IT11]-orientated specimens show maxima at TD = 989 or 1040 K (Table 4). If the error limits are taken into consideration, this statement may hold for the [001] specimens too. Such maxima of the CRSS are common for single-phase Ll:-materials (Section l); evidently peak-aged NIMONIC PE16 single crystals reflect the CRSS maxima of their hardening L1,-ordered ?,'-particles. It cannot, however, be excluded that the volume fraction of the )"-particles increased and even some new, very small ones formed during heating and deforming the specimens elastically. The equilibrium ``,'-volume fraction at 1040 K is estimated to be 0.083 instead of 0.061 at 1079 K, which is the temperature at which the original ;"-dispersion had been grown. The above rationalization of (1) the anisotropy of the CRSS of peak-aged NIMONIC PE16 single crystals and (2) the anomalous temperature variation of their CRSS has been based on the analogous behaviour of single-phase Ll~-materials: {111}~{100} cross slip of a short screw dislocation segment reduces the mobility of the remainder of the dislocation in the primary {lll~j slip plane. A prerequisite of this rationalization is, of course, that the screw dislocation can cross slip in the small Ll:-ordered ,"-precipitates present in peak-aged NIMONIC PEI6. Their average radius is only 25 nm. The following two observations indicate that {1ll}~.{100} cross slip is actually possible in these small ,"-particles: (i) Mills and Chrzan [8] estimated the probability P of ~lll}~ftl001• cross slip of screw dislocations in single-phase Eli-materials as a function of the length / of the cross-slipped screw dislocation segment. P(I) was found to be high for l ~ 100 nm. (ii) Koizumi el al. [19] studied the formation of kink pairs in materials whose CRSS is governed
3299
by the Peierls potential. These authors found for the length of the double kink in the saddle point configuration about 40b; b is the length of the Burgers vector. At Tv = 1090 K the CRSSs of all peak-aged specimens are below the respective 1040 K values. The equilibrium ",,'-volume fraction at 1090 K is estimated to be 0.052, i.e. 0.009 below that of 1079 K at which temperature the original 7'-dispersion had been produced. Even if the 7'-volume fraction reached its 1090 K equilibrium value during heating and deforming the specimens elastically, it is questionable whether this decrease in f is sufficient to explain the decrease of the CRSS by about 23% between 1040 and 1090 K. The low CRSSs found at TD = 1143 K are probably caused by the partial dissolution of the 7'-particles during heating and deforming the specimens elastically. The 7'-solvus temperature of NIMONIC PE16 is around 1150 K [18]. At 1143 K the CRSSs of the peak-aged specimens are still more than 40% above the respective values measured for the homogeneous specimens at 683 K. Evidently there is still 7'-hardening at 1143 K. No under-aged NIMONIC PEI6 single crystals have been studied because their fine ;,'-particles are highly prone to Ostwald ripening during heating and during the elastic deformation. During Ostwald ripening the growth rate of the average 7'-particle radius r is roughly proportional to 1/r ~ [ 18, 20, 21], i.e. small particles grow fast. Moreover peak-aged specimens have the additional advantage that their CRSS is independent of r, it depends only on the volume fraction [18]. Thus some coarsening of the ,"-particles of peak-aged specimens does not affect their CRSS. 4. CONCLUSIONS The CRSS of peak-aged, 7'-hardened (r = 25 nm, f = 0.061) NIMONIC PE16 single crystals is anisotropic when compression tested at 683 and 989 K. The CRSS increases as the orientation of the specimens moves from [001] through [123] to [011] or [111]. Since the CRSS of homogeneous, ;"-particlefree NIMONIC PE16 single crystals is isotropic, it is concluded that the CRSS of the peak-aged crystals reflects the asymmetry of their hardening ``"-phase, which has the long-range ordered Ll_,-structure. The analogue applies to the anomalous temperature dependence of the CRSS of NIMONIC PEI6: the CRSSs of the peak-aged specimens with [123] , [011] and [il 1] orientations have maxima at 989 or 1040 K. Fruitful discussions with Professor Dr S. Takeuchi, Tokyo, Japan, Professor Dr M. J. Mills, Livermore, U.S.A. and Dipl.-Phys. A. Nitz, Miinster, are gratefully acknowledged. Dipl.-Phys. A. Kalogeridis is thanked for proving, by electron diffraction, that the originally homogeneous NIMONIC PEI6 specimens contained ;,'-precipitates after the deformation at 1090 K. Acknowledgements
3300
J O C K W E G and N E M B A C H :
C R I T I C A L R E S O L V E D S H E A R STRESS O F AN A L L O Y
REFERENCES 1. B. H. Kear and H. G. F. Wilsdorf, Trans. AIME224, 382 (1962). 2. A. J. C. Wilson, Proc. R. Soc. Lond. AI81, 36(I {1943). 3. P. A. Flinn, Trans. A I M E 218, 145 (1960). 4. N. Baluc. H. P. Karnthaler and M. J. Mills, Phil. Ma~. A 64, 137 (1991). 5. S. Takeuchi and E. Kuramoto. Acta metall. 21, 415 (1973). 6. C. Lall, S. Chin and D. P. Pope. Metall. Trans. A 10A, 1323 (1979). 7. V. Paidar, D. P. Pope and V. Vitek, Acta metall. 32,435 (1984). 8. M. J. Mills and D. C. Chrzan, Acta metall, mater. 40, 3051 (1992). 9. D. P. Pope and S. S. Ezz, b~t. Metal. Rev. 29, 136 (1984). 10. Y. Umakoshi, D. P. Pope and V Vitek, Acta metall. 32, 449 (1984).
11. M. H. Yoo, Scripta metall. 20, 915 (1986). 12. F. E. Heredia and D. P. Pope, Acta metall. 34, 279 (1986). 13. D. M. Shah and D. N. Duhl, Superalloys (edited by M. Gell et al.), p. 105. AIME, Warrendale, Pa (1984). 14. P. Caron and T Khan, Proc. 1st A S M Eur. Technical Cot!/. (edited by T. Khan), p. 59 (1987). 15. J. Diehl, Z. Metallkde. 47, 33l (1956). 16. W. Pfeiffer and A. Seeger, Phvsica status solidi 2, 668 (1962). 17. W. Mangen, E. Nembach and H. Schfifer, Mater. Sci. Engng 70, 205 (1985). 18. E. N e m b a c h and G. Neite, Prog. Mater. Sci. 29, 177 (1985). 19. H. Koizumi, H. O. K. Kirchner and T. Suzuki, Acta metall, mater. 41, 3483 (1993). 20. C. Wagner, Z. Elektrochem. 65, 581 (1961). 21. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961).
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AN1SOTROPY OF THE CRITICAL RESOLVED S H E A R STRESS OF A S U P E R A L L O Y C O N T A I N I N G 6 VOL.% L1 e-ORDERED 7'-PRECIPITATES J. JOCKWEG and E. NEMBACH Institut fflr Metallforschung, Liniversitfit Mfinster, Wilhelm-Klemm-Strasse 10, D-48149 Mfinster, Germany lReceived 3 December 1994: m revised /brm 10 Januao' 1995)
Abstract Single crystals of the ;.'-strengthened nickel-base superalloy NIMONIC PEI6 have been compression tested in the temperature range 683 1143 K. Four different orientations of the specimens have been studied: [0 0 1],[/23].[011] and [T11]. They were either in the homogenized, single-phase state or in the peak-aged state. The critical resolved shear stress (CRSS) of the homogenized specimens was isotropic at 683 K. The CRSS of the peak-aged specimens, containing 6 vol.% of Lie-long-range ordered )"-precipitates of 25 nm radius, was anisotropic at 683 K and at 989 K: the [001]-orientated specimens were the softest ones, the CRSS increased as the orientation moved towards [01 l] or [111]. This is the same orientation dependence found for the CRSS of single-phase Ll_,-ordered materials. The interpretation of the anisotropy of the CRSS of NIMONIC PEI6 follows that given for single-phase Ll2-1ong-range ordered materials. Zusammenfassung An Einkristatlen der 7"-geh/irteten NickeI-Basis-Superlegierung N1MONIC PE16 wurden zwischen 683 und 1143 K Druckversuche ausgefiihrt. Vier verschiedene Orientierungen wurden untersucht: [001].[T23],[01 I] und [11l]. Die Proben waren entweder im homogenisierten, einphasigen Zustand oder im optimal gealterten. In letzterem enthiehen sie 6 Vol.% Ll:-ferngeordnete 7'-Ausscheidungen wm 25 nm Radius. Die kritiscbe Schubspannung der homogenisierten Proben war bei 683 K isotrop. Die der optimal gealterten war anisotrop bei 683 und 989 K: die [001]-orientierten Proben waren am weichsten: die kfitische Schubspannung stieg an, wenn die Orientierung auf [011] oder [TI 1] zuwanderte. Das ist dieselbe Orientierungsabh~ingigkeit, die man ffir einphasige Ll~,-ferngeordnete Materialien beobachtet. Die Anisotropie der kritischen Schubspannung yon NIMONIC PE16 wird folglich fihnlich ,~ie die yon cinphasigen Ll:-Materialien gedeutet.
l. 1NfRODU('TION Intermetallic phases with the long-range ordered Ll:-crystal structure are k n o w n to have an a n o m a l o u s plastic behaviour: (i) The critical resolved shear stress (CRSS) does not decrease monotonically as the d e f o r m a t i o n t e m p e r a t u r e Tt~ is raised, but it has a m a x i m u m . The peak t e m p e r a t u r e T> which depends on the material, on the orientation of the specimen a n d on the strain rate is a r o u n d 1000 K. (ii) The CRSS is anisotropic, i.e. Schmid's law is not followed. (iii) The CRSS depends on the direction of the deformation, it is different l\>r tension a n d compression Iesls. By far the most extensively studied L l,-material is Ni~A1. The N i - a t o m s occupy the laces of the f.c.c. L1,-elementary cell and the Al-atoms its corners. Let a~, be the lattice constant. The Burgers vector of a perfect dislocation in Ll,-materials is of the type a0(110). It dissociates into two dislocations of the type (a()/2)(l10) which is the s t a n d a r d type in the f.c.c.
crystal structure. There is an antiphase b o u n d a r y between these two (a0/2)(110) dislocations. Each of them splits further into two Shockley partial dislocations of the type (a0/6)(112) with a complex stacking fault in between. All three of the a b o v e - m e n t i o n e d anomalies have been interpreted on the basis of Kear a n d Wilsdorf's [1] original idea. The primary slip planes in Lie-materials are of the type {111}. But since the specific antiphase b o u n d a r y energy is lower o n { 100}t h a n on { 111 }-planes [2, 3] there is a tendency of screw dislocations to cross slip thermally activated from ~111 }- o n t o { 100}-planes. Baluc et al. [4] f o u n d for the respective specific antiphase b o u n d a r y energies of NLAI [0.111 + 0.015] and [0.090 _+ 0.005] J / m 2. If, by thermal activation, a short segment of a (a0/'2)(110)screw dislocation leaves its original {111 }-glide plane and cross slips o n t o a [100}-plane, this segment becomes a h i n d r a n c e to the glide of the remainder of the screw dislocation: this segment acts as a pinning centre. Detailed models to explain the three a b o v e - m e n t i o n e d anomalies have been developed by Takeuchi a n d K u r a m o t o [5], Lall et al. [6], P a i d a r et ell. [7] a n d Mills a n d C h r z a n [8]. A review has
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CRITICAL RESOLVED SHEAR STRESS OF AN ALLOY
been published by Pope and Ezz [9]. In contrast to pure f.c.c, metals or disordered f.c.c, solid solutions, which are softened by cross slip, kl,-long-range ordered materials are strengthened by it. Thus, all factors which raise the probability of { 111 } --+{ 100}-cross slip in the latter class of materials, increase their C R S S - - p r o v i d e d TD is below Tp. Such factors are: high Tm a high Schmid factor (SF) of the { 100}-cross-slip-plane and a high force which presses the two Shockley partial dislocations of the leading (ao/2)(llO)-screw dislocation together. The latter forces derive from the externally applied stress acting on the edge components of the Shockley partials [6]. The latter two factors are quantified by the parameters N and Q, respectively: SF~(010)[i01]} N = SF{(1 ll)[T01]}
(la)
SF{(111)[121]} Q = SF{(Ill)[T01]}"
(lb)
The orientation of the specimen is supposed to lie in the triangle [001], [011] and [TI 1]. Then the primary slip system is (lll)[T01]. Its SF is the denominator of equations (1). The numerator of N is the SF of the cross slip system and the numerator of Q is the SF which governs the compression of the Shockley partials. A theoretical analysis of compression tests yields the following results for the dependence of the CRSS z,. on N and Q [6, 10]:
?z,/?N > 0
(2a)
Fr~Q < 0.
(2b)
and
The variations of N and Q with the orientation of the specimen is shown in Table 2. It is emphasized that though favourable values of N and Q may raise the probability of cross slip, thermal activation is needed to make screw dislocations actually cross slip and increase re. Therefore Or~/OTL~becomes positive at elevated temperatures. Yoo [1 l] has discussed the effects of the elastic anisotropy on the probability of cross slip. Relations (2) and the values given for N and Q in Table 2 explain the experimentally observed anisotropy of r~ of Ll:-materials: r~ of compression tested specimens increases as their orientation moves away from [001] towards [0l 1] or IT11]. Relation (2b) also explains the tension~compression asymmetry. Since nickel-base superalloys are strengthened by coherent precipitates of the 7'-phase which has the L12-structure, the question arises whether these alloys also exhibit the anomalous plastic behaviour described above. The disordered or short-range ordered solid solution matrices of these ;"-strengthened superalloys have the f.c.c, crystal structure. Heredia and Pope [12] investigated these aspects for a ~,'-strengthened superalloy. Shah and Duhl [13] and Caron and Khan [14] have published similar studies. The CRSS of the
Table 1. Overallcomposition of NIMONIC PEI6, of the 5/-particles and of its matrix, at.%. after Ref. [17] Elements Ni Fe Cr Mo AI Ti Overall 41.6 34.6 17.6 2.0 2.6 1.5 ;"-Particles 72.1 3.2 1.0 10.4 13.3 Matrix 39.6 36.6 18.7 2.1 2.1 0.7
superalloys showed anisotropies analogous to those of single-phase Ll:-materials. The results of an experimental study of the anisotropy of the CRSS of the commercial nickel-base superalloy N I M O N I C PE16 are presented below. Its spherical 7'-particles are small and their volume fraction is low: 50 nm diameter and 0.061, respectively. This contrasts with the materials studied by Heredia and Pope whose respective parameters were larger by the factors 8 and 10. Shah and Duhl's and Caron and Khan's i,'-particle dispersions were similar to or even coarser than those of Heredia and Pope. Since the CRSSs of pure copper [15] and of single-phase f.c.c, solid solutions of nickel-cobalt [16] are known to be anisotropic, a possible anisotropy of the CRSS of'),'-strengthened N I M O N I C PE16 single crystals may also reflect possible plastic anisotropies of the matrix. Therefore, this superalloy has also been studied in the homogenized, single-phase state. 2. EXPERIMENTAL METHODS AND RESULTS A polycrystalline rod of N I M O N I C PE 16 has been supplied by Glossop Superalloys Ltd, Glossop, U.K. The overall composition is given in Table 1. The low concentrations of C and Si have been disregarded. The nominal orientations of the specimens are listed in Table 2, their individual orientations deviated up to A (Table 2) from the nominal ones. The variation of the orientation within an individual specimen due to small angle boundaries was about _+ 1. fit and O are the respective averages over all specimens used in the present investigation. Their dimensions were 3.9 mm in diameter and 13.6mm in length. After crystal growth all specimens were homogenized for 4 h at 1473 K. One group of specimens was compression tested in this state. The other was heat treated for 2 h at 979 K, subsequently subjected to an Ostwald ripening treatment of 51.4 h duration at 1079 K and then compression tested. The purpose of the 979 K treatment was to enhance the nucleation of the 7'-particles. The specimens were sealed in argon-filled quartz ampoules: tubes of N I M O N I C PE16 prevented direct contact between the specimens and the
Table 2. Nominal specimenorientation, maximum deviation k from it. resolvedstrain rate a. ,~ and O [equations (1)] are the respective averages over the range k Oricntation A( ) d(104/s) ~V O [001] 12 1.37 0.14 0.43 [i231 3 1.33 0.90 - 0.33 [011] 3 1.46 0.86 054 IT11] 3 2.11 1.62 0.55
JOCKWEG and NEMBACtt:
CRITICAL RESOLVED SHEAR STRESS OF AN ALLOY
ampoules. In this way possible contaminations have been avoided. At the end of the treatments the ampoules were water quenched without breaking them. The resulting ;"-particle dispersions were: homogenized specimens: 7'-particle-strengthened specimens:
. l = 0.0,
5
I
4-
z
3
,-1
2
_ . . . . . . .
--
a)
0
0.1
I
0
0
0.2
0.3
I
1
,"
I
I
i
0.1
0.2
0.3
L
i
I
0
0.1
0.2
0.3
d [mm] Fig. 1. Load L versus the travel d of the cross-head of the testing machine. The dashed lines indicate the extrapolation scheme used for the derivation of the CRSS. (a) Peak-aged [001] specimen. 7], = 683 K, (b) peak-aged [011] specimen, TD= 1143 K and (c) homogeneous [011] specimen, TD = 1090 K.
2.1. Results/or the homogenized specimens The results for the CRSS of homogeneous, <-free specimens are compiled in Table 3. Up to 1090 K, the plastic deformation was discontinuous, Fig. l(c) shows an example. The peak-to-peak excursion of the discontinuities increased with TD. At 683 K, it amounted to less than 0.5% of the CRSS. Therefore defining the CRSS not on the basis of the peaks of the
C R S S (MPa)
IT t i]
-
c)
Table 3. CRSS o f the homogeneous specimens
[001] [T231 101I]
_
0.061, r = 25 nm.
,/'and r are the volume fraction and the average radius of the spherical, coherent 7'-particles. The second group of specimens was in the peak-aged state, i.e. their CRSS was the maximum possible at the givenf. The compositions of the ?"-particles and of the matrix are listed in Table 1. Since f is very low, the matrix composition is nearly the same as the overall composition. The specimens were compression tested at temperatures TD between 683 and 1143 K. TD was stabilized within +_4 K. For TD ~< 989 K, which is the most interesting temperature range, the ensuing errors in the CRSS are negligible. A protective argon atmosphere prevented oxidation. The technical strain rate was 6.1 x 10 5/s. The resulting resolved strain rates are given in Table 2. Their average was 1.6 x 10 +/s, the maximum difference from this average was 35%. The CRSS was derived from the intersection of the linearly extrapolated elastic and first plastic part of the ++load versus elongation" curve. This is demonstrated in Fig. 1. If this curve was discontinuous, the second straight line was drawn through the peaks ot" the curve [Fig. l(c)]. Each specimen's individual Schmid factor was inserted. The results for the CRSSs are presented in Tables 3 and 4. Each entry is the average over 3-5 specimens, the standard deviation of the average is also given. Since the orientations of individual specimens deviated from the nominal orientations by angles up to A quoted in Table 2, the 3-5 specimens used [br one data point were chosen such that these specimens were representative of all specimens homogenized for the respective orientation. Thus the scatter of the orientations and possible minor differences in the quality and thermal history of individual single crystals raise only the standard deviation of the CRSS, but do not lead to systematic variations of the CRSS with To or with the nominal orientation of the specimens. Standard deviations are equivalent to 68% confidence limits.
Orientation
].f /.]"
r = 0.0 nm 1
f=
I
--
3297
683 K 47.5 4__(17 43,4 + 0 7 44.3 + (13 43.3±13
989 K
1040 K
42.7 ± 3.4 68.9 _+ 0.8 42.4 + 0,6 79.9 = 2.5 44.8 ± 0.7 78.0 - 2.1 63.5+_4.1 74.5+1.9 Discontinuous glide
1090 K
1143 K
77.0 + 1.5 80.1) ± 1.0 88,7 + 0.2 99.3±4.5
71.4 ± 5.3 82.9 + 1.4 85.6 _4_4.2 75.2_+5.4 Yield point
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JOCKWEG and NEMBACH:
Oricntation [0011 [T23l [011t [ill I
CRITICAL RESOLVED SHEAR STRESS OF AN ALLOY
Table 4. CRSS of the peak-aged specimens CRSS (MPa) 683 K 989 K 1040 K 1090 K 128.0 + 3.0 127.7 + 1.9 125.4 -+ 1.5 90.9 + 1.2 129.7 + 2.5 133.6 + 0.3 133.9 + 2.7 106.4 + 1.7 130.3_+ 1.2 135.5_+1.3 135.4_+1.6 110.0_+4.2 135.5+0.1 137.1_+0.5 124.9_+3.7 97.4+0.3 Yield point
load versus elongation curve [Fig. l(c)] but, for example, on the basis of the average load would not change the results. At 1143 K there were minor yield points. The increase of the CRSS for TD > 989 K is caused by the precipitation of very small 7'-particles during heating of the specimens up to TD and during their elastic deformation. The presence of these ";'-precipitates has been proved for a specimen deformed at 1090 K by observing the L l,-superlattice reflections in the transmission electron microscope, after cooling the specimen to ambient temperature. About one half of the total time which the specimen was at or above 989 K. was spent prior to its plastic deformation, the other half was needed for cooling it down to ambient temperature. The lower CRSSs found at TD = 1143 K are due to the partial dissolution of the fine ?"-precipitates. The solvus temperature of the 7'-phase in N I M O N I C PE 16 is around 1150 K [18]. In the temperature range 989 K ~< Tu ~ 1143 K, the growth of the ","-precipitates and their possible later dissolution depend critically on the heating rate of the specimens. Since this rate could not be controlled precisely, the data taken for the homogenized specimens at TD ~> 989 K are not considered any further.
2.2. Results jor the peak-aged specimens The results obtained for the peak-aged specimens are given in Table 4. Except at TL~= 683 K [Fig. l(a)], there were yield points [Fig. l(b)]. The two highest deformation temperatures are above the temperature at which the ;.,'-particles had been grown (1079 K). Therefore changes in their dispersion during heating and during the elastic deformation are possible. In a first order approximation these changes can be estimated on the basis of the )"-particle growth observed for unstressed specimens.
3. DISCUSSIONS In an earlier investigation [18] the CRSSs of middle-orientated single crystals of N I M O N I C P E I 6 have been measured at 500 K. The CRSS of homogenized specimens and of those having the same )"-particle dispersion as the present peak-aged ones were 47.5 and 130.9 MPa, respectively. This is in good agreement with the present data taken for the [123] orientation at 683 K: (43.4 + 0.7) and (129.7 _+ 2.5) MPa. The present Tv is 183 K higher than the former. The CRSS averaged over the four orientations of the homogeneous, ;,'-free specimens is 43.6 MPa at 683 K,
1143 K 60.8 + 2.4 73.0 + 0.6 75.4_+0.7 64.9+0.5
the average over the four standard deviations amounts to 0.7 MPa. The CRSSs measured for the four orientations fall within the range of (43.6 _+ 0.7) MPa. Evidently the C R S S of the homogeneous specimens is isotropic, i.e. Schmid's law is followed. Though the precipitation of some ),'-particles at 989 K prevented the experimental p r o o f of the plastic isotropy at 989 K, it can be assumed that the CRSS of the homogeneous specimens is isotropic at 989 K as well as at 683 K. Consequently, any anisotropy of the peak-aged, ,/'-strengthened specimens observed at these two temperatures is not caused by their matrices, whose composition is nearly the same as that of the homogeneous specimens (Table 1). In order to demonstrate the anisotropies and temperature dependencies of the CRSSs of the peak-aged specimens, the data presented in Table 4 are repeated in Table 5 in normalized form. The CRSS measured at TD for the orientation [hkl] is divided by the CRSS found at 683 K for the [001] specimens. At 683 and 989 K, the C R S S increases as the orientation varies from [001] through [i23] to [011] or []'11]. This anisotropy is higher at 989 K than at 683 K (Table 5). The plastic anisotropy of the compression tested N I M O N I C PE16 single crystals is the same as that quoted in Section 1 for compression tested singlephase L12-materials. Evidently the two-phase NIM O N I C PE16 single crystals reflect the C R S S anisotropy of their hardening L1 :-ordered 7'-particles. It is quite remarkable that this is the case in spite of their small size (r = 25nm) and their low volume fraction ( J = 0.061). Evidently screw dislocations can cross slip in these small 7'-precipitates. This will be discussed further below. The anisotropy apparent at and above 1040 K probably reflects the different temperature dependencies of the CRSSs of the four orientations [5, 9, 12, 13]. Since the 7'-precipitates are spherical they cannot induce a simple geometric anisotropy as cuboidal precipitates may do. Concerning the specimens with the [ i l l ] orientation, some caution is appropriate. Their resolved strain rate is 50% higher than that of the specimens with the other Table 5. Normalized (to [001], Tt, = 683 K) CRSS of the peak-aged specimens Normalized CRSS Orientation [001] [T23] [011] [111]
683 K
989 K
1040 K
1090 K
1143 K
1.00 1.01 1.02 1.04
1.00 1.04 1.06 1.07
0.98 1.05 1.06 0.98
0.71 0.83 0.86 0.76
0.48 0.57 0.59 0.51
JOCKWEG and NEMBACH: CRITICAL RESOLVED SHEAR STRESS OF AN ALLOY orientations (Table 2). This may affect the CRSS of the [Tll] specimens in the 1% range [5,9]. Except for the [001] orientation, the actual orientations of the specimens deviate by no more than 3c from the nominal orientations (Table 2). No systematic variation of the CRSS with the actual orientation of the nominal [001] specimens has been found. Hence, the CRSSs quoted in Tables 3-5 are representative of the listed orientations. In contrast to the present results, Heredia and Pope [12] found that their [T11] compression specimens were the softest for 600 K ~< T~, ~< 800 K. The authors interpreted this as being due to the fact that for this orientation the (010) [1"01]slip system is favoured at all TD, because its Schmid factor is high. This is evident from the high value listed for :gT [equation (la)] in Table 2. It must be remembered that r a n d f o f Heredia and Pope's material were approx. 8 and 10 times as large as the present values, respectively. Shah and Duhl [13] investigated even coarser ;,'-particle dispersions. The CRSSs of the peak-aged [T23]-, [011]- and IT11]-orientated specimens show maxima at TD = 989 or 1040 K (Table 4). If the error limits are taken into consideration, this statement may hold for the [001] specimens too. Such maxima of the CRSS are common for single-phase Ll:-materials (Section l); evidently peak-aged NIMONIC PE16 single crystals reflect the CRSS maxima of their hardening L1,-ordered ?,'-particles. It cannot, however, be excluded that the volume fraction of the )"-particles increased and even some new, very small ones formed during heating and deforming the specimens elastically. The equilibrium ``,'-volume fraction at 1040 K is estimated to be 0.083 instead of 0.061 at 1079 K, which is the temperature at which the original ;"-dispersion had been grown. The above rationalization of (1) the anisotropy of the CRSS of peak-aged NIMONIC PE16 single crystals and (2) the anomalous temperature variation of their CRSS has been based on the analogous behaviour of single-phase Ll~-materials: {111}~{100} cross slip of a short screw dislocation segment reduces the mobility of the remainder of the dislocation in the primary {lll~j slip plane. A prerequisite of this rationalization is, of course, that the screw dislocation can cross slip in the small Ll:-ordered ,"-precipitates present in peak-aged NIMONIC PEI6. Their average radius is only 25 nm. The following two observations indicate that {1ll}~.{100} cross slip is actually possible in these small ,"-particles: (i) Mills and Chrzan [8] estimated the probability P of ~lll}~ftl001• cross slip of screw dislocations in single-phase Eli-materials as a function of the length / of the cross-slipped screw dislocation segment. P(I) was found to be high for l ~ 100 nm. (ii) Koizumi el al. [19] studied the formation of kink pairs in materials whose CRSS is governed
3299
by the Peierls potential. These authors found for the length of the double kink in the saddle point configuration about 40b; b is the length of the Burgers vector. At Tv = 1090 K the CRSSs of all peak-aged specimens are below the respective 1040 K values. The equilibrium ",,'-volume fraction at 1090 K is estimated to be 0.052, i.e. 0.009 below that of 1079 K at which temperature the original 7'-dispersion had been produced. Even if the 7'-volume fraction reached its 1090 K equilibrium value during heating and deforming the specimens elastically, it is questionable whether this decrease in f is sufficient to explain the decrease of the CRSS by about 23% between 1040 and 1090 K. The low CRSSs found at TD = 1143 K are probably caused by the partial dissolution of the 7'-particles during heating and deforming the specimens elastically. The 7'-solvus temperature of NIMONIC PE16 is around 1150 K [18]. At 1143 K the CRSSs of the peak-aged specimens are still more than 40% above the respective values measured for the homogeneous specimens at 683 K. Evidently there is still 7'-hardening at 1143 K. No under-aged NIMONIC PEI6 single crystals have been studied because their fine ;,'-particles are highly prone to Ostwald ripening during heating and during the elastic deformation. During Ostwald ripening the growth rate of the average 7'-particle radius r is roughly proportional to 1/r ~ [ 18, 20, 21], i.e. small particles grow fast. Moreover peak-aged specimens have the additional advantage that their CRSS is independent of r, it depends only on the volume fraction [18]. Thus some coarsening of the ,"-particles of peak-aged specimens does not affect their CRSS. 4. CONCLUSIONS The CRSS of peak-aged, 7'-hardened (r = 25 nm, f = 0.061) NIMONIC PE16 single crystals is anisotropic when compression tested at 683 and 989 K. The CRSS increases as the orientation of the specimens moves from [001] through [123] to [011] or [111]. Since the CRSS of homogeneous, ;"-particlefree NIMONIC PE16 single crystals is isotropic, it is concluded that the CRSS of the peak-aged crystals reflects the asymmetry of their hardening ``"-phase, which has the long-range ordered Ll_,-structure. The analogue applies to the anomalous temperature dependence of the CRSS of NIMONIC PEI6: the CRSSs of the peak-aged specimens with [123] , [011] and [il 1] orientations have maxima at 989 or 1040 K. Fruitful discussions with Professor Dr S. Takeuchi, Tokyo, Japan, Professor Dr M. J. Mills, Livermore, U.S.A. and Dipl.-Phys. A. Nitz, Miinster, are gratefully acknowledged. Dipl.-Phys. A. Kalogeridis is thanked for proving, by electron diffraction, that the originally homogeneous NIMONIC PEI6 specimens contained ;,'-precipitates after the deformation at 1090 K. Acknowledgements
3300
J O C K W E G and N E M B A C H :
C R I T I C A L R E S O L V E D S H E A R STRESS O F AN A L L O Y
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11. M. H. Yoo, Scripta metall. 20, 915 (1986). 12. F. E. Heredia and D. P. Pope, Acta metall. 34, 279 (1986). 13. D. M. Shah and D. N. Duhl, Superalloys (edited by M. Gell et al.), p. 105. AIME, Warrendale, Pa (1984). 14. P. Caron and T Khan, Proc. 1st A S M Eur. Technical Cot!/. (edited by T. Khan), p. 59 (1987). 15. J. Diehl, Z. Metallkde. 47, 33l (1956). 16. W. Pfeiffer and A. Seeger, Phvsica status solidi 2, 668 (1962). 17. W. Mangen, E. Nembach and H. Schfifer, Mater. Sci. Engng 70, 205 (1985). 18. E. N e m b a c h and G. Neite, Prog. Mater. Sci. 29, 177 (1985). 19. H. Koizumi, H. O. K. Kirchner and T. Suzuki, Acta metall, mater. 41, 3483 (1993). 20. C. Wagner, Z. Elektrochem. 65, 581 (1961). 21. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961).