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Tension—compression asymmetry of the (001) single crystal nickel base superalloy SC16 under cyclic loading at elevated temperatures
Acta mater. Vol. 44. No. 10. pp. 3933 3942. 1996
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Pergamon PII
S 1359-6454(96)00050-X
Copyright ! 1996Acta MetallurgicaInc. Published b.~ ElsevierScience Lid Printed in Great Britain. All rights reserved 1359-6454'96$15.00 + 0.00
TENSION-COMPRESSION ASYMMETRY OF THE (001) SINGLE CRYSTAL NICKEL BASE SUPERALLOY SC16 UNDER CYCLIC LOADING AT ELEVATED TEMPERATURES F. JIAO, D. BETTGE, W. OSTERLE and J. ZIEBS Bundesanstalt ffir Materialforschung und -priifung. Laboratorium V.13-Elektronenmikroskopie, 12205 Berlin, Germany (Received 25 October 1995: in revised form 24 Janua o" 1996)
Abstract--Fully reversed low cycle fatigue tests were conducted on (001) oriented single crystals of the nickel base superalloy SC16 at a constant total strain range of 2.0%. The strain rates were varied from l0 -2 to 10-5 s -t at 750:C and the temperatures were changed from 650 to 950:C under the strain rate 10-~ s ~. During cycling under the high strain rates 10 z and 10-3 s ~at 750C or under the strain rate l0 -3 s -~ at 650°C, the SC16 single crystals show that the tensile stress (T) is higher than the compressive stress (C). During cycling under the low strain rates l0 -4 and l0 -5 s -~ at 750 C or under the strain rate 10 3 s-~ at 850°C, the cyclic tension-compression asymmetry of C > Twas observed. At 950:C under the strain rate 10-~s -~, no tension-compression asymmetry (T = C) was present during fatigue testing. The deformation mechanism corresponding to T > C determined by transmission electron microscopy (TEM) is that the 7' precipitates are sheared by pairs of a/2(110) matrix dislocations coupled by antiphase boundaries (APB) within 7' phase. The reversed asymmetry behaviour (C > T) was found to be associated with the ( 111)(112) viscous slip producing superlattice intrinsic/extrinsic stacking faults (SISF/SESF) in 7' precipitates. At 950:C ( T = C) dislocation climbing over the 7' precipitates becomes the dominant deformation mechanism. Models which can explain the tension-compression asymmetry behaviour were discussed. Copyright tC' 1996 Acta Metallurgica Inc.
1, INTRODUCTION Tension-compression asymmetry of the flow stress as a function of crystallographic orientation has been observed in single crystals of LI, intermetallic compounds [1-3] and of nickel base superalloys containing a high volume fraction of y' phase [4-6] under monotonic loading. Similar to monotonic loading, tension-compression asymmetry of the cyclic hardening or softening (i.e. anisotropic fatigue hardening or softening) has been also observed [7-12]. Lall, Chin and Pope (LCP) [1] modified the model proposed by Takeuchi and K u r a m o t o [13] in which dislocations on {111} slip planes are assumed to become locally pinned by thermally activated cross slip on to {100} planes, and predicted the tension--compression asymmetry in the flow stress of 7' phase single crystals depending on the crystallographic orientation. The modified model, named LCP-model in this paper, assumes that before an a/2[101] superpartial dislocation in the y' phase can cross slip from { ! 11 } to { 100} its core structure must undergo a transformation. Since these a/2[101] superpartial dislocations in the ?' phase are most probably dissociated into two a / 6 ( 1 1 2 ) Shockley partial dislocations on { 111 } planes, any component of the stress tensor which tends to constrict the partial dislocations will promote cross slip and any component which extends them will retard Cross slip.
Based on the study of dislocation core configuration in the LI_, phase [14, 15], Paidar et al. [16] modelled the cross slip process and predicted the orientation dependence of the tension-compression asymmetry in 7' phase single crystals. According to LCP-model [1, 16], the tensile flow stress (T) is greater than the compressive flow stress (C) for orientations near [001], T = C for orientations near the [012]-[113] great circle, but on the [001] side, and C > T for the other regions of orientation in the standard triangle. These predictions have been confirmed by the experimental results [2--4], but the LCP-model can be used only for the deformation conditions, in which the octahedral slip, simultaneously with the pinning of screw dislocations by cross slip, appears to provide a d o m i n a n t deformation mechanism. For example, this theory does not apply at high temperature because the dislocations may climb and thermally activated motion of (110) screw superlattice dislocations on { 100} planes take place [7, 8]. The deformation behaviour of ),' precipitationhardened nickel base superalioys is strongly influenced by temperature, strain rate, volume fraction and particle size of y' and crystallographic orientation, as reviewed by Pope and Ezz [17]. Different deformation mechanisms depending on the loading conditions have been identified in 7' hardened nickel-base superalloys [18-22] and are
3933
J I A O et al.:
3934
TENSION-COMPRESSION
ASYMMETRY
Table 1. Chemical composition of alloy SC 16 (in wt%) Cr
Co
Ti
AI
W
Ta
Mo
Fe
C
Si
S
Ni
15.37
0.05
3.50
3.46
0.09
3.60
2.84
0.30
<0.005
<0,02
0.001
Bal.
summarized as follows. (1) Dislocations overcome the 7' precipitates following the Orowan process. (2) Pairs of a / 2 ( l 1 0 ) dislocations coupled by antiphase boundary (APB) shear the 7' precipitates. (3) Shearing of 7' precipitates by super-Shockley partials leads to superlattice intrinsic or extrinsic stacking faults (SISF or SESF) in 7', (4) Dislocations climb over ";' precipitates. The transition between different deformation mechanisms may cause a change of tension-compression asymmetry behaviour. The purpose of the present investigation was to obtain an improved understanding of the influence of fatigue test condition on the tension-compression asymmetry of single crystal nickel base superalloys. In particular, the effect of strain rate and temperature, which can strongly influence the deformation mechanism on the tension-compression asymmetry of SC16 single crystals, have been examined under cyclic loading. 2. MATERIALS AND EXPERIMENTAL PROCEDURES
The SC16 single crystals used in this study are oriented nearly in the (001) direction (within 10c of
(001)). The chemical composition in weight per cent is given in Table 1. The commercial heat treatment developed for SC16 produces a bimodal distribution of y' precipitates in spheroidal and cuboidal forms having average sizes of 80 nm in diameter and 450 nm in edge length, respectively. The typical morphology of 7' precipitates is shown in Fig. 1. The total volume fraction of the bimodal 7' distribution is about 50%. The single crystals developed a simple unidirectional dendritic structure and also exhibited significant interdendritic porosity. The low cycle fatigue (LCF) tests were performed at a temperature range from 650 to 950°C with a servohydraulic testing machine employing induction heating. The total strain was controlled using an axial extensometer. All tests were fully reversed, R = gin,n/ ~maa= - - 1 , with constant strain rates (~) from 10-: to 10 --~ s -~ imposed on loading and unloading, and a constant strain range (At) of 2.0%. Specimens for transmission electron microscopy (TEM) were prepared from the gauge sections of LCF tested samples sectioned perpendicular to the loading axis (near (001) crystallographic orientation). These specimens were then mechanically thinned to about 0.15 mm and finally jet-electropolished to produce thin areas suitable for examination in TEM. A JEM 4000 FX transmission electron microscope operating at 400 kV was used.
Fig. 1. TEM dark field micrograph showing typical morphology of y" precipitates in the alloy SC16.
JIAO et al.: TENSION-COMPRESSION ASYMMETRY 1200
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3. RESULTS
3.1. Cyclic deformation behariour Two sets of L C F tests were conducted at a total strain range of 2.0%. For one set the strain rates were varied from 10-: to 10 -~ s-t keeping the temperature at 750:C. For another set the temperatures were changed from 650 to 9 5 0 C while the strain rate was held at 10 -3 s -]. Cyclic hardening/softening curves are given in Fig. 2. The (001) single crystals exhibit an initial cyclic hardening or a cyclic softening within the first cycles of about 10% fatigue lives. At 750°C an initial rapid cyclic hardening is shown under the high strain rates (10--" and 10 -3 s -~) and an initial cyclic softening under the low strain rates (10 -" and 10-~s -~) [see Figs 2(a) and (b)]. At 10-3s -] the material shows an initial cyclic hardening at the low temperatures 650 and 7 5 0 C [see Fig. 2(a)]. Unconventionally, the cyclic curve at 850°C demonstrates an initial softening under tension, but an initial hardening under compression [see Fig. 2(a)]. At 950:C, no initial hardening or softening is shown. Normally the samples reached saturation following the initial cyclic hardening or softening except for the samples fatigued under 10 -2 and 10 -3 s -1 at 750°C which show a cyclic softening in tension and a
continuous cyclic hardening in compression after the initial hardening [see Figs 2(a) and (b)]. This abnormal softening in tension, accompanying the hardening in compression, will have to be studied in future experiments• Aside from the hardening or softening, an important feature of Fig. 2 is that a cyclic tension-compression asymmetry behaviour is present• In order to demonstrate the influence of strain rate and temperature on the tension-compression asymmetry, the ratios of tensile stress to compressive stress in saturation, or the average ratios with error bars using the maximum and minimum values if the hardening or softening curves show no saturation, are plotted against strain rate (see Fig. 3) and temperature (see Fig. 4), respectively. Figure 3 shows that at the high strain rates from 10 -2 to 10 -3 s -j the tensile stress (T) is greater than compressive stress (C), but at low strain rates from 10 -4 to 10-~s -~ C > T asymmetry behaviour is given. Figure 4 indicates that for the strain rate 10-3s -~ the asymmetry behaviour is significantly influenced by
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Temperature (°C) Fig. 4. Ratio' of tensile stress to compressive stresses at fatigue saturation as a function of temperature under = 10 -3 s -I and Ae = 2.0%.
3936
JIAO et al.: TENSION-COMPRESSION ASYMMETRY
Fig. 5. Dislocation substructure developed during fatigue at ~ = 10-: s -~, Ae = 2.0% and T = 750C, corresponding to T > C. (Weak beam: electron beam direction BD~[001] and diffraction vector g = (200), while 4g was at the Bragg condition.)
temperature. The single crystals show T > C at the low temperature 650°C, C > T at the intermediate temperatures 750 and 850°C, and C = T at the high temperature 950°C. 3.2. Dislocation s t r u c t u r e
Representative transmission electron micrographs of dislocation substructures developed during cycling under test conditions corresponding to T > C are presented in Fig. 5. Dislocations are homogeneously distributed in the ), matrix. Superlattice dislocations, a / 2 ( l l 0 ) dislocation pairs coupled by APB, were observed in 7' phase. These superlattice dislocations are normally dissociated either on the octahedral {l l l} planes or on cube {100} planes. To determine the plane of dissociation a tilting experiment was performed. The sample was tilted around [100] and the weak beam images were taken using diffraction vector g = [200] while 4g was at the Bragg condition, as shown in Fig. 6. The dislocation segments in 7' phase imaged under g -- (200) can be classified into two types which are marked A and B, respectively (see Fig. 6). Their Burgers vector (b) has been identified as a/2[10T] using criterion of invisibility of dislocations [23]. Figure 6(a) is the image resulting from beam direction (BD) near [001]. Under this condition each dislocation segment marked with an A illustrates only one image line, which indicates that their dissociation plane is parallel to BD. The dissociation of dislocation segments marked with a B was observed on this micrograph [see double image lines in Fig. 6(a)]. The images of Figs 6(b) and (c) were taken near the [0Tl]
and [011] poles, respectively. The dissociation of segments A is imaged in both micrographs. Comparing the two images, it is found that the dissociation widths for the two crystallographic projection orientations give the same value. This confirms that the dislocation segments A are dissociated on (010). One image line of each dislocation segment marked by a B is shown at BD ~ [0T1] [see Fig. 6(b)] and a large dissociation width is imaged at BD ~ [011] [see Fig. 6(c)]. This indicates that the dislocation segments B are on the (111) plane. According to line vector analysis, the dislocation segments A have screw character with line direction of [10T] lying on the (010) plane, and the dislocation segments B are characterized as mixed segments dissociated on the (111) plane. Figure 7 shows the dislocation substructures in specimens fatigued under test conditions corresponding to C > T. Dislocations are distributed homogeneously in the 7 matrix and superlattice stacking faults in ~,' precipitates lying on different non-parallel { 111 } slip planes were observed. Dislocation pairs in 7' precipitates were very rarely found. Figure 8 shows a superlattice stacking fault which terminates within the ~,,'precipitate and is bounded by two partials, one partial at the 7'/7 interface marked by C and the other within the 7' precipitate marked by D. The fault plane in this case was identified as (111). The Burgers vectors of partials C and D in Fig. 8 were determined using g'h criterion in conjunction with the various rules applied to visibility/invisibility of partial dislocations [23]. As a result, the Burgers vector bc of the partial C is a/6[l~l] (~A), the partial D is a
JIAO et al.:
TENSION-COMPRESSION ASYMMETRY
3937
and dislocation networks at 7/7' interface (see Fig. 9). Superlattice dislocations within 7' precipitates including either octahedral or cube plane dislocation segments were not observed.
superlattice partial having a Burgers vector bd = a~ 31112] (26c). At 950°C (T = C) the deformation microstructure consisted of a non-planar dislocation arrangement
(a)
(b) Fig. 6. (a and b).
3938
JIAO et al.:
TENSION-COMPRESSION ASYMMETRY
(c) Fig. 6. Superlattice dislocation segments dissociated on {001} plane (marked with an A) and on {111} plane (marked with a B) in specimen fatigued at ~ = 10-: s -~. Ae = 2.0% and T = 750~'C. (Weak beam: (a) electron beam direction BD ~ [001], (b) BD ,~ [0"i1], (c) BD ,~ [011] and diffraction vector g = (200). while 4g was at the Bragg condition.)
4. DISCUSSION The experimental results document that tensioncompression asymmetry of cyclic deformation exists during fatigue. At high strain rates and low temperatures the tensile stress is greater than compressive stress. This result agrees with the observations in (001) single crystals of other nickel base superalloys [9, 11] and of ";' phase alloys [7, 10, 12], and can been explained by the LCP-model [1, 16]. This model assumes that an a / 2 ( l 1 0 ) screw dislocation is initially dissociated into two Shockley partials on the octahedral plane a n d must be constricted before it can cross slip on to a cube plane. For (001) single crystals, tensile stress tends to constrict the Shockley partials [1, 4]. Cube cross slip is promoted and the dislocation segments on the octahedral plane are locally pinned by the segments on the cube plane. In compression the Shockley partial would be extended. In this case, cube cross slip is inhibited and the pinning effect should decrease. That is, the tensile stress should be greater than the compressive stress. The TEM investigation shows superlattice dislocations within ),' phase containing segments either on cube planes or on octahedral planes (see Fig. 6). This observation indicates that y' precipitates are sheared by dislocation pairs. As soon as the dislocation pair enters an ordered 7' precipitate, cube slip becomes a viable slip mode due
to low APB energy on a cube plane. If sufficient thermal activation is available, segments of the leading dislocation may cross slip to the cube plane to form sessile obstacles. In this case, the LCP-model can be used to explain the tension--compression asymmetry of T > C. Under the low strain rates from 10 -4 to 10 -~ s -~ at 750°C or under 10-3s -~ at 850°C the (001) SCl6 single crystals show the tension-compression asymmetry of T < C which is reversed in comparison to that at high strain rates and low temperatures and doesn't agree with the LCP-model. In specimens showing T < C, superlattice intrinsic/extrinsic stacking faults within ~' precipitates were observed. instead of a/2(110) dislocation pairs corresponding to T > C. This indicates that the y' precipitates were sheared by a/3(112) superlattice Shockley partials. which can take place under lower applied stress compared to ~,' shearing by a / 2 ( l 1 0 ) dislocation pairs [21,24]. Different models producing the stacking faults in ),' precipitates proposed in Refs [24-30] are summarized as follows. Model 1: Kear et al. [25, 26] proposed that the superlattice stacking fault could be formed by the glide of an a / 2 ( 1 1 2 ) (3Bt$) dislocation which could separate into an a/3(112) (2B6) dislocation which enters the ),' phase and produces the superlattice stacking fault and an a/6(112) (B~) Shockley
JIAO et al.: TENSION-COMPRESSION ASYMMETRY partial lying at the 7/7' interface. The a/2
3939
the ~/7" interface have a angle of 120 = between each other. This type of dislocation configuration was observed in Refs [21, 27-29], but it is difficult to distinguish between the models 2 and 3 experimentally. Our TEM analysis showed that the Burgers vectors of the partial dislocations associated with a stacking fault in the 7' phase (see Fig. 8) are of a/6(121) and a/3
Fig. 7. Dislocation substructure developed during fatigue at £ = 10-3 s-< Ae = 2.0% and T = 850°C, corresponding to T < C. (Weak beam: electron beam direction BD ~ [001] and diffraction vector g = (200), while 4g was at the Bragg condition.)
3940
JIAO et al.:
TENSION-COMPRESSION ASYMMETRY
Fig. 8. Representative micrographs used for the analysis of Burgers vectors of partial dislocations (marked with C and D) bounding stacking faults in 7' precipitates in the specimen fatigued at ~ = 10-5 s-', A~ = 2.0% and T = 750~C. (Bright field: (a) electron beam direction BD ~ [101] and diffraction vector g = (020) (C and D are visible) and (b) g = (0'~0) (C and D are invisible), while deviation parameter w (~.s) > 0.7.) dislocation loop 3A must occur at the interface inside the APB area in order to develop the super-Shockley partial 23C which is required for the formation of SISF [see Fig. ll(c)]. The 26C shears through the 7' precipitates, and the 3C is left at the 7/7' interface [see Fig. l l(d)]. The area of complex stacking fault in compression tending to extend the two partials B6 and 6C should be larger than that in tension tending to constrict the two partials. Therefore, a higher
applied stress under compression than that under tension is required because of the very high energy of complex stacking fault [! 7]. The above analysis points out that the tensile stress is more effective on driving {111}(112) slip than the compressive stress, if the stacking faults are formed following model 2 or 3, which is experimentally evidenced in this study (see Fig. 8). This may be the reason for T < C at low strain rates.
JIAO et al.:
TENSION-COMPRESSION ASYMMETRY
3941
Fig. 9. Dislocation substructure developed during fatigue at ~ = 10-9 s-L Ae = 2.0% and T = 950 C. (Bright field: electron beam direction BD ~ [001] and diffraction vector g = (200).)
lower stress level compared to shearing by dislocation pairs. The deformation mechanisms under L C F loading in this work show the same temperature and strain rate dependence as those under monotonic loading [21]. Non-planar dislocation arrangements which resulted from dislocation climb were observed at 9 5 0 C (see Fig. 9). In this case the dislocations can climb over the 7' precipitates. The climb process can take place only under strong thermal activation. Therefore, no tension-compression asymmetry was present at this temperature.
The results of tensile and creep tests on SC16 single crystals [32] and the IN 738 polycrystals [21, 22] (which is chemically similar to the alloy SCI6) show that active deformation mechanisms were strongly dependent on the temperature and the strain rate. Superlattice stacking faults in 7' phase have been observed on deformation at 750 C under the strain rates from 10-4 to 10 -~ s -] and at 850~C under the strain rates from 10-= to 10 -7 S- t , but at 750:C under the high strain rates from 10 --~ to 10 -3 s -~ 7' shearing by dislocation pairs took place [21]. The nucleation of the stacking faults appears to be a time and temperature dependent process [21]. If the thermal activation is sufficient to form the stacking fault in 7' phase, the shearing process by the formation of the stacking fault can occur, which corresponds to a
5. CONCLUSIONS At 7 5 0 C under 10 --~ and 10-3s -' and at 65@'C under 10-~s -~, the S C I 6 single crystals with (001)
Glide motion
Dislocation line vector SF --.. "
(a)
""
(b)
6C
~
B6
(c)
Fig. 10. Schematic representations of SISF formation following model 2.
SISF/ SESF
3942
JIAO et al.: TENSION-COMPRESSION ASYMMETRY
i' Dislocation line vector
SF
CSF
SISF/SESF
APB
Glide motion J ,4"
I
/ I
~A (
(a)
(b)
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(c)
(d)
Fig. 11. Schematic representations of S1SF formation following model 3. o r i e n t a t i o n show that the tensile stress (T) is higher t h a n the compressive stress ( C ) during fatigue testing, which c o r r e s p o n d s to the 7' shearing m e c h a n i s m by pairs of a/2<110> dislocations coupled by APB. A t 750~C u n d e r 10 -4 and 10 -~s -~ a n d at 850°C u n d e r 10 -3 s - I the cyclic t e n s i o n - c o m p r e s s i o n asymmetry of T < C was observed. It is f o u n d that this a s y m m e t r y b e h a v i o u r is associated with the (111)< 112> viscous slip p r o d u c i n g superlattice intrinsic/extrinsic stacking faults in 7' precipitates. Two possible models based o n the m e c h a n i s m s o f stacking fault f o r m a t i o n a n d observed dislocation configurations have been p r o p o s e d to explain the T < C asymmetry behaviour. A t 9 5 f f C u n d e r 10 -3 s -~. dislocation climbing over the 7' precipitates becomes the dominant d e f o r m a t i o n mechanism. In this case, no t e n s i o n compression asymmetry was observed. Acknowledgements--This work was supported by the Deutsche Forschungsgemeinschaft (SFB 339). The authors would like to thank Dr H. Klingelh6ffer for his helpful discussion and Mr W. Wedell. Mrs H. Rooch and Mr W. Gesatzke for their technical assistance.
REFERENCES 1. C. Lall, S. Chin and D. P. Pope, Metall. Trans. 10A, 1323 (1979). 2. S. S. Ezz, D. P. Pope and V. Paidar, Acta metall. 30, 921 (1982). 3. Y. Umakoshi, D. P. Pope and V. Vitek, Acta metall. 32, 449 (1984). 4. D. M. Shah and D. N. Duhl, Superallovs 1984 (edited by M. Gell et al.), p. 105. AIME, Warrendale, PA (1984). 5. F. E. Heredia and D. P. Pope. ,4cta metall. 34, 279 (1986). 6. R. V. Miner. T. P. Gabb, J. Gayda and K. J. Hemker, Metall. Trans. 17A, 507 (1986). 7. N. R. Bonda, D. P. Pope and C. Laird, Aeta metall. 35, 2371 (1987).
8. N. R. Bonda, D. P. Pope and C. Laird, Acta metall. 35, 2385 (1987). 9. W. W. Milligan, N. Jayaraman and R. C. Bill, Mater. Sci. Engng 82, 127 (1986). 10. S. S. Ezz and D. P. Pope. Scripta metall. 19, 741 (1985). 11. T. P. Gabb, J. Gayda and R. V. Miner, Metall. Trans. 17A, 497 (1986). 12. L. M. Hsiung and N. S. Stoloff, Acta metall, mater. 40, 2993 (1992). 13. S. Takeuchi and E. Kuramoto, Acta metall. 21, 415 (1973). 14. M. Yamaguchi, V. Paidar, D. P, Pope and V. Vitek, Phil. Mag. 45, 867 (1982). 15. V. Paidar, M. Yamaguchi, D. P. Pope and V. Vitek, Phil. Mag. 45, 883 (1982). 16. V. Paidar, D. P. Pope and V. Vitek, Acta metall. 32, 435 (1984). 17. D. P. Pope and S. S. Ezz, Int. Met. Rez'. 29, 136 (1984). 18. G. R. Leverant, M. Gell and S. W. Hopkins, Mater. Sci. Engng 8, 125 (1971). 19. R. A. Stevens and P. E. J. Flewitt, Acta metall. 29, 867 (1981). 20. P. J. Henderson and M. McLean, Aeta metall. 30, 1121 (1982). 21. D. Mukherji, F. Jiao, W. Chen and R. P. Wahi, Acta metall, mater. 39, 1515 (1991). 22. D. Bettge, W. ()sterle and J. Ziebs, Z. Metallk. 86, 190 (1995). 23. J. W. Edington, Practical Electron Microscopy in Material Science, Vol. 3. Macmillan, London (1975). 24. B. H. Kear, A. F. Giamei, J. M. Silcock and R. K. Ham, Scripta metall. 2, 287 (1968). 25. B. H. Kear, A. F. Giamei, G. R. Leverant and J. M. Oblak, Scripta metall. 3, 123 (1969). 26. B. H. Kear, A. F. Giamei, G. R. Leverant and J. M. Oblak, Scripta metall. 3, 455 (1969). 27. M. Condat and B. D+camps, Scripta metall. 21, 607 (1987). 28. A. J. Huis in't Veld, G. Boom, P. M. Bronsveld and J. Th. M. De Hossen, Scripta metall. 19, 1123 (1985). 29. P. Caron, T. Kahn and P. Veyssi+re, Phil. Mag. 57A, 859 (1988). 30. P. Veyssi6re, J. Douin and P. Beauchamp, Phil. Mag. 51A, 469 (1985). 31. B. H. Kear, J. M. Oblak and A. F. Giamei, Metall. Trans. I, 2477 (1970). 32. D. Bettge, W. Osterle and J. Ziebs, to be published.
~
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Copyright ! 1996Acta MetallurgicaInc. Published b.~ ElsevierScience Lid Printed in Great Britain. All rights reserved 1359-6454'96$15.00 + 0.00
TENSION-COMPRESSION ASYMMETRY OF THE (001) SINGLE CRYSTAL NICKEL BASE SUPERALLOY SC16 UNDER CYCLIC LOADING AT ELEVATED TEMPERATURES F. JIAO, D. BETTGE, W. OSTERLE and J. ZIEBS Bundesanstalt ffir Materialforschung und -priifung. Laboratorium V.13-Elektronenmikroskopie, 12205 Berlin, Germany (Received 25 October 1995: in revised form 24 Janua o" 1996)
Abstract--Fully reversed low cycle fatigue tests were conducted on (001) oriented single crystals of the nickel base superalloy SC16 at a constant total strain range of 2.0%. The strain rates were varied from l0 -2 to 10-5 s -t at 750:C and the temperatures were changed from 650 to 950:C under the strain rate 10-~ s ~. During cycling under the high strain rates 10 z and 10-3 s ~at 750C or under the strain rate l0 -3 s -~ at 650°C, the SC16 single crystals show that the tensile stress (T) is higher than the compressive stress (C). During cycling under the low strain rates l0 -4 and l0 -5 s -~ at 750 C or under the strain rate 10 3 s-~ at 850°C, the cyclic tension-compression asymmetry of C > Twas observed. At 950:C under the strain rate 10-~s -~, no tension-compression asymmetry (T = C) was present during fatigue testing. The deformation mechanism corresponding to T > C determined by transmission electron microscopy (TEM) is that the 7' precipitates are sheared by pairs of a/2(110) matrix dislocations coupled by antiphase boundaries (APB) within 7' phase. The reversed asymmetry behaviour (C > T) was found to be associated with the ( 111)(112) viscous slip producing superlattice intrinsic/extrinsic stacking faults (SISF/SESF) in 7' precipitates. At 950:C ( T = C) dislocation climbing over the 7' precipitates becomes the dominant deformation mechanism. Models which can explain the tension-compression asymmetry behaviour were discussed. Copyright tC' 1996 Acta Metallurgica Inc.
1, INTRODUCTION Tension-compression asymmetry of the flow stress as a function of crystallographic orientation has been observed in single crystals of LI, intermetallic compounds [1-3] and of nickel base superalloys containing a high volume fraction of y' phase [4-6] under monotonic loading. Similar to monotonic loading, tension-compression asymmetry of the cyclic hardening or softening (i.e. anisotropic fatigue hardening or softening) has been also observed [7-12]. Lall, Chin and Pope (LCP) [1] modified the model proposed by Takeuchi and K u r a m o t o [13] in which dislocations on {111} slip planes are assumed to become locally pinned by thermally activated cross slip on to {100} planes, and predicted the tension--compression asymmetry in the flow stress of 7' phase single crystals depending on the crystallographic orientation. The modified model, named LCP-model in this paper, assumes that before an a/2[101] superpartial dislocation in the y' phase can cross slip from { ! 11 } to { 100} its core structure must undergo a transformation. Since these a/2[101] superpartial dislocations in the ?' phase are most probably dissociated into two a / 6 ( 1 1 2 ) Shockley partial dislocations on { 111 } planes, any component of the stress tensor which tends to constrict the partial dislocations will promote cross slip and any component which extends them will retard Cross slip.
Based on the study of dislocation core configuration in the LI_, phase [14, 15], Paidar et al. [16] modelled the cross slip process and predicted the orientation dependence of the tension-compression asymmetry in 7' phase single crystals. According to LCP-model [1, 16], the tensile flow stress (T) is greater than the compressive flow stress (C) for orientations near [001], T = C for orientations near the [012]-[113] great circle, but on the [001] side, and C > T for the other regions of orientation in the standard triangle. These predictions have been confirmed by the experimental results [2--4], but the LCP-model can be used only for the deformation conditions, in which the octahedral slip, simultaneously with the pinning of screw dislocations by cross slip, appears to provide a d o m i n a n t deformation mechanism. For example, this theory does not apply at high temperature because the dislocations may climb and thermally activated motion of (110) screw superlattice dislocations on { 100} planes take place [7, 8]. The deformation behaviour of ),' precipitationhardened nickel base superalioys is strongly influenced by temperature, strain rate, volume fraction and particle size of y' and crystallographic orientation, as reviewed by Pope and Ezz [17]. Different deformation mechanisms depending on the loading conditions have been identified in 7' hardened nickel-base superalloys [18-22] and are
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TENSION-COMPRESSION
ASYMMETRY
Table 1. Chemical composition of alloy SC 16 (in wt%) Cr
Co
Ti
AI
W
Ta
Mo
Fe
C
Si
S
Ni
15.37
0.05
3.50
3.46
0.09
3.60
2.84
0.30
<0.005
<0,02
0.001
Bal.
summarized as follows. (1) Dislocations overcome the 7' precipitates following the Orowan process. (2) Pairs of a / 2 ( l 1 0 ) dislocations coupled by antiphase boundary (APB) shear the 7' precipitates. (3) Shearing of 7' precipitates by super-Shockley partials leads to superlattice intrinsic or extrinsic stacking faults (SISF or SESF) in 7', (4) Dislocations climb over ";' precipitates. The transition between different deformation mechanisms may cause a change of tension-compression asymmetry behaviour. The purpose of the present investigation was to obtain an improved understanding of the influence of fatigue test condition on the tension-compression asymmetry of single crystal nickel base superalloys. In particular, the effect of strain rate and temperature, which can strongly influence the deformation mechanism on the tension-compression asymmetry of SC16 single crystals, have been examined under cyclic loading. 2. MATERIALS AND EXPERIMENTAL PROCEDURES
The SC16 single crystals used in this study are oriented nearly in the (001) direction (within 10c of
(001)). The chemical composition in weight per cent is given in Table 1. The commercial heat treatment developed for SC16 produces a bimodal distribution of y' precipitates in spheroidal and cuboidal forms having average sizes of 80 nm in diameter and 450 nm in edge length, respectively. The typical morphology of 7' precipitates is shown in Fig. 1. The total volume fraction of the bimodal 7' distribution is about 50%. The single crystals developed a simple unidirectional dendritic structure and also exhibited significant interdendritic porosity. The low cycle fatigue (LCF) tests were performed at a temperature range from 650 to 950°C with a servohydraulic testing machine employing induction heating. The total strain was controlled using an axial extensometer. All tests were fully reversed, R = gin,n/ ~maa= - - 1 , with constant strain rates (~) from 10-: to 10 --~ s -~ imposed on loading and unloading, and a constant strain range (At) of 2.0%. Specimens for transmission electron microscopy (TEM) were prepared from the gauge sections of LCF tested samples sectioned perpendicular to the loading axis (near (001) crystallographic orientation). These specimens were then mechanically thinned to about 0.15 mm and finally jet-electropolished to produce thin areas suitable for examination in TEM. A JEM 4000 FX transmission electron microscope operating at 400 kV was used.
Fig. 1. TEM dark field micrograph showing typical morphology of y" precipitates in the alloy SC16.
JIAO et al.: TENSION-COMPRESSION ASYMMETRY 1200
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3. RESULTS
3.1. Cyclic deformation behariour Two sets of L C F tests were conducted at a total strain range of 2.0%. For one set the strain rates were varied from 10-: to 10 -~ s-t keeping the temperature at 750:C. For another set the temperatures were changed from 650 to 9 5 0 C while the strain rate was held at 10 -3 s -]. Cyclic hardening/softening curves are given in Fig. 2. The (001) single crystals exhibit an initial cyclic hardening or a cyclic softening within the first cycles of about 10% fatigue lives. At 750°C an initial rapid cyclic hardening is shown under the high strain rates (10--" and 10 -3 s -~) and an initial cyclic softening under the low strain rates (10 -" and 10-~s -~) [see Figs 2(a) and (b)]. At 10-3s -] the material shows an initial cyclic hardening at the low temperatures 650 and 7 5 0 C [see Fig. 2(a)]. Unconventionally, the cyclic curve at 850°C demonstrates an initial softening under tension, but an initial hardening under compression [see Fig. 2(a)]. At 950:C, no initial hardening or softening is shown. Normally the samples reached saturation following the initial cyclic hardening or softening except for the samples fatigued under 10 -2 and 10 -3 s -1 at 750°C which show a cyclic softening in tension and a
continuous cyclic hardening in compression after the initial hardening [see Figs 2(a) and (b)]. This abnormal softening in tension, accompanying the hardening in compression, will have to be studied in future experiments• Aside from the hardening or softening, an important feature of Fig. 2 is that a cyclic tension-compression asymmetry behaviour is present• In order to demonstrate the influence of strain rate and temperature on the tension-compression asymmetry, the ratios of tensile stress to compressive stress in saturation, or the average ratios with error bars using the maximum and minimum values if the hardening or softening curves show no saturation, are plotted against strain rate (see Fig. 3) and temperature (see Fig. 4), respectively. Figure 3 shows that at the high strain rates from 10 -2 to 10 -3 s -j the tensile stress (T) is greater than compressive stress (C), but at low strain rates from 10 -4 to 10-~s -~ C > T asymmetry behaviour is given. Figure 4 indicates that for the strain rate 10-3s -~ the asymmetry behaviour is significantly influenced by
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Temperature (°C) Fig. 4. Ratio' of tensile stress to compressive stresses at fatigue saturation as a function of temperature under = 10 -3 s -I and Ae = 2.0%.
3936
JIAO et al.: TENSION-COMPRESSION ASYMMETRY
Fig. 5. Dislocation substructure developed during fatigue at ~ = 10-: s -~, Ae = 2.0% and T = 750C, corresponding to T > C. (Weak beam: electron beam direction BD~[001] and diffraction vector g = (200), while 4g was at the Bragg condition.)
temperature. The single crystals show T > C at the low temperature 650°C, C > T at the intermediate temperatures 750 and 850°C, and C = T at the high temperature 950°C. 3.2. Dislocation s t r u c t u r e
Representative transmission electron micrographs of dislocation substructures developed during cycling under test conditions corresponding to T > C are presented in Fig. 5. Dislocations are homogeneously distributed in the ), matrix. Superlattice dislocations, a / 2 ( l l 0 ) dislocation pairs coupled by APB, were observed in 7' phase. These superlattice dislocations are normally dissociated either on the octahedral {l l l} planes or on cube {100} planes. To determine the plane of dissociation a tilting experiment was performed. The sample was tilted around [100] and the weak beam images were taken using diffraction vector g = [200] while 4g was at the Bragg condition, as shown in Fig. 6. The dislocation segments in 7' phase imaged under g -- (200) can be classified into two types which are marked A and B, respectively (see Fig. 6). Their Burgers vector (b) has been identified as a/2[10T] using criterion of invisibility of dislocations [23]. Figure 6(a) is the image resulting from beam direction (BD) near [001]. Under this condition each dislocation segment marked with an A illustrates only one image line, which indicates that their dissociation plane is parallel to BD. The dissociation of dislocation segments marked with a B was observed on this micrograph [see double image lines in Fig. 6(a)]. The images of Figs 6(b) and (c) were taken near the [0Tl]
and [011] poles, respectively. The dissociation of segments A is imaged in both micrographs. Comparing the two images, it is found that the dissociation widths for the two crystallographic projection orientations give the same value. This confirms that the dislocation segments A are dissociated on (010). One image line of each dislocation segment marked by a B is shown at BD ~ [0T1] [see Fig. 6(b)] and a large dissociation width is imaged at BD ~ [011] [see Fig. 6(c)]. This indicates that the dislocation segments B are on the (111) plane. According to line vector analysis, the dislocation segments A have screw character with line direction of [10T] lying on the (010) plane, and the dislocation segments B are characterized as mixed segments dissociated on the (111) plane. Figure 7 shows the dislocation substructures in specimens fatigued under test conditions corresponding to C > T. Dislocations are distributed homogeneously in the 7 matrix and superlattice stacking faults in ~,' precipitates lying on different non-parallel { 111 } slip planes were observed. Dislocation pairs in 7' precipitates were very rarely found. Figure 8 shows a superlattice stacking fault which terminates within the ~,,'precipitate and is bounded by two partials, one partial at the 7'/7 interface marked by C and the other within the 7' precipitate marked by D. The fault plane in this case was identified as (111). The Burgers vectors of partials C and D in Fig. 8 were determined using g'h criterion in conjunction with the various rules applied to visibility/invisibility of partial dislocations [23]. As a result, the Burgers vector bc of the partial C is a/6[l~l] (~A), the partial D is a
JIAO et al.:
TENSION-COMPRESSION ASYMMETRY
3937
and dislocation networks at 7/7' interface (see Fig. 9). Superlattice dislocations within 7' precipitates including either octahedral or cube plane dislocation segments were not observed.
superlattice partial having a Burgers vector bd = a~ 31112] (26c). At 950°C (T = C) the deformation microstructure consisted of a non-planar dislocation arrangement
(a)
(b) Fig. 6. (a and b).
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TENSION-COMPRESSION ASYMMETRY
(c) Fig. 6. Superlattice dislocation segments dissociated on {001} plane (marked with an A) and on {111} plane (marked with a B) in specimen fatigued at ~ = 10-: s -~. Ae = 2.0% and T = 750~'C. (Weak beam: (a) electron beam direction BD ~ [001], (b) BD ,~ [0"i1], (c) BD ,~ [011] and diffraction vector g = (200). while 4g was at the Bragg condition.)
4. DISCUSSION The experimental results document that tensioncompression asymmetry of cyclic deformation exists during fatigue. At high strain rates and low temperatures the tensile stress is greater than compressive stress. This result agrees with the observations in (001) single crystals of other nickel base superalloys [9, 11] and of ";' phase alloys [7, 10, 12], and can been explained by the LCP-model [1, 16]. This model assumes that an a / 2 ( l 1 0 ) screw dislocation is initially dissociated into two Shockley partials on the octahedral plane a n d must be constricted before it can cross slip on to a cube plane. For (001) single crystals, tensile stress tends to constrict the Shockley partials [1, 4]. Cube cross slip is promoted and the dislocation segments on the octahedral plane are locally pinned by the segments on the cube plane. In compression the Shockley partial would be extended. In this case, cube cross slip is inhibited and the pinning effect should decrease. That is, the tensile stress should be greater than the compressive stress. The TEM investigation shows superlattice dislocations within ),' phase containing segments either on cube planes or on octahedral planes (see Fig. 6). This observation indicates that y' precipitates are sheared by dislocation pairs. As soon as the dislocation pair enters an ordered 7' precipitate, cube slip becomes a viable slip mode due
to low APB energy on a cube plane. If sufficient thermal activation is available, segments of the leading dislocation may cross slip to the cube plane to form sessile obstacles. In this case, the LCP-model can be used to explain the tension--compression asymmetry of T > C. Under the low strain rates from 10 -4 to 10 -~ s -~ at 750°C or under 10-3s -~ at 850°C the (001) SCl6 single crystals show the tension-compression asymmetry of T < C which is reversed in comparison to that at high strain rates and low temperatures and doesn't agree with the LCP-model. In specimens showing T < C, superlattice intrinsic/extrinsic stacking faults within ~' precipitates were observed. instead of a/2(110) dislocation pairs corresponding to T > C. This indicates that the y' precipitates were sheared by a/3(112) superlattice Shockley partials. which can take place under lower applied stress compared to ~,' shearing by a / 2 ( l 1 0 ) dislocation pairs [21,24]. Different models producing the stacking faults in ),' precipitates proposed in Refs [24-30] are summarized as follows. Model 1: Kear et al. [25, 26] proposed that the superlattice stacking fault could be formed by the glide of an a / 2 ( 1 1 2 ) (3Bt$) dislocation which could separate into an a/3(112) (2B6) dislocation which enters the ),' phase and produces the superlattice stacking fault and an a/6(112) (B~) Shockley
JIAO et al.: TENSION-COMPRESSION ASYMMETRY partial lying at the 7/7' interface. The a/2
3939
the ~/7" interface have a angle of 120 = between each other. This type of dislocation configuration was observed in Refs [21, 27-29], but it is difficult to distinguish between the models 2 and 3 experimentally. Our TEM analysis showed that the Burgers vectors of the partial dislocations associated with a stacking fault in the 7' phase (see Fig. 8) are of a/6(121) and a/3
Fig. 7. Dislocation substructure developed during fatigue at £ = 10-3 s-< Ae = 2.0% and T = 850°C, corresponding to T < C. (Weak beam: electron beam direction BD ~ [001] and diffraction vector g = (200), while 4g was at the Bragg condition.)
3940
JIAO et al.:
TENSION-COMPRESSION ASYMMETRY
Fig. 8. Representative micrographs used for the analysis of Burgers vectors of partial dislocations (marked with C and D) bounding stacking faults in 7' precipitates in the specimen fatigued at ~ = 10-5 s-', A~ = 2.0% and T = 750~C. (Bright field: (a) electron beam direction BD ~ [101] and diffraction vector g = (020) (C and D are visible) and (b) g = (0'~0) (C and D are invisible), while deviation parameter w (~.s) > 0.7.) dislocation loop 3A must occur at the interface inside the APB area in order to develop the super-Shockley partial 23C which is required for the formation of SISF [see Fig. ll(c)]. The 26C shears through the 7' precipitates, and the 3C is left at the 7/7' interface [see Fig. l l(d)]. The area of complex stacking fault in compression tending to extend the two partials B6 and 6C should be larger than that in tension tending to constrict the two partials. Therefore, a higher
applied stress under compression than that under tension is required because of the very high energy of complex stacking fault [! 7]. The above analysis points out that the tensile stress is more effective on driving {111}(112) slip than the compressive stress, if the stacking faults are formed following model 2 or 3, which is experimentally evidenced in this study (see Fig. 8). This may be the reason for T < C at low strain rates.
JIAO et al.:
TENSION-COMPRESSION ASYMMETRY
3941
Fig. 9. Dislocation substructure developed during fatigue at ~ = 10-9 s-L Ae = 2.0% and T = 950 C. (Bright field: electron beam direction BD ~ [001] and diffraction vector g = (200).)
lower stress level compared to shearing by dislocation pairs. The deformation mechanisms under L C F loading in this work show the same temperature and strain rate dependence as those under monotonic loading [21]. Non-planar dislocation arrangements which resulted from dislocation climb were observed at 9 5 0 C (see Fig. 9). In this case the dislocations can climb over the 7' precipitates. The climb process can take place only under strong thermal activation. Therefore, no tension-compression asymmetry was present at this temperature.
The results of tensile and creep tests on SC16 single crystals [32] and the IN 738 polycrystals [21, 22] (which is chemically similar to the alloy SCI6) show that active deformation mechanisms were strongly dependent on the temperature and the strain rate. Superlattice stacking faults in 7' phase have been observed on deformation at 750 C under the strain rates from 10-4 to 10 -~ s -] and at 850~C under the strain rates from 10-= to 10 -7 S- t , but at 750:C under the high strain rates from 10 --~ to 10 -3 s -~ 7' shearing by dislocation pairs took place [21]. The nucleation of the stacking faults appears to be a time and temperature dependent process [21]. If the thermal activation is sufficient to form the stacking fault in 7' phase, the shearing process by the formation of the stacking fault can occur, which corresponds to a
5. CONCLUSIONS At 7 5 0 C under 10 --~ and 10-3s -' and at 65@'C under 10-~s -~, the S C I 6 single crystals with (001)
Glide motion
Dislocation line vector SF --.. "
(a)
""
(b)
6C
~
B6
(c)
Fig. 10. Schematic representations of SISF formation following model 2.
SISF/ SESF
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JIAO et al.: TENSION-COMPRESSION ASYMMETRY
i' Dislocation line vector
SF
CSF
SISF/SESF
APB
Glide motion J ,4"
I
/ I
~A (
(a)
(b)
(SA i~ 25C
(c)
(d)
Fig. 11. Schematic representations of S1SF formation following model 3. o r i e n t a t i o n show that the tensile stress (T) is higher t h a n the compressive stress ( C ) during fatigue testing, which c o r r e s p o n d s to the 7' shearing m e c h a n i s m by pairs of a/2<110> dislocations coupled by APB. A t 750~C u n d e r 10 -4 and 10 -~s -~ a n d at 850°C u n d e r 10 -3 s - I the cyclic t e n s i o n - c o m p r e s s i o n asymmetry of T < C was observed. It is f o u n d that this a s y m m e t r y b e h a v i o u r is associated with the (111)< 112> viscous slip p r o d u c i n g superlattice intrinsic/extrinsic stacking faults in 7' precipitates. Two possible models based o n the m e c h a n i s m s o f stacking fault f o r m a t i o n a n d observed dislocation configurations have been p r o p o s e d to explain the T < C asymmetry behaviour. A t 9 5 f f C u n d e r 10 -3 s -~. dislocation climbing over the 7' precipitates becomes the dominant d e f o r m a t i o n mechanism. In this case, no t e n s i o n compression asymmetry was observed. Acknowledgements--This work was supported by the Deutsche Forschungsgemeinschaft (SFB 339). The authors would like to thank Dr H. Klingelh6ffer for his helpful discussion and Mr W. Wedell. Mrs H. Rooch and Mr W. Gesatzke for their technical assistance.
REFERENCES 1. C. Lall, S. Chin and D. P. Pope, Metall. Trans. 10A, 1323 (1979). 2. S. S. Ezz, D. P. Pope and V. Paidar, Acta metall. 30, 921 (1982). 3. Y. Umakoshi, D. P. Pope and V. Vitek, Acta metall. 32, 449 (1984). 4. D. M. Shah and D. N. Duhl, Superallovs 1984 (edited by M. Gell et al.), p. 105. AIME, Warrendale, PA (1984). 5. F. E. Heredia and D. P. Pope. ,4cta metall. 34, 279 (1986). 6. R. V. Miner. T. P. Gabb, J. Gayda and K. J. Hemker, Metall. Trans. 17A, 507 (1986). 7. N. R. Bonda, D. P. Pope and C. Laird, Aeta metall. 35, 2371 (1987).
8. N. R. Bonda, D. P. Pope and C. Laird, Acta metall. 35, 2385 (1987). 9. W. W. Milligan, N. Jayaraman and R. C. Bill, Mater. Sci. Engng 82, 127 (1986). 10. S. S. Ezz and D. P. Pope. Scripta metall. 19, 741 (1985). 11. T. P. Gabb, J. Gayda and R. V. Miner, Metall. Trans. 17A, 497 (1986). 12. L. M. Hsiung and N. S. Stoloff, Acta metall, mater. 40, 2993 (1992). 13. S. Takeuchi and E. Kuramoto, Acta metall. 21, 415 (1973). 14. M. Yamaguchi, V. Paidar, D. P, Pope and V. Vitek, Phil. Mag. 45, 867 (1982). 15. V. Paidar, M. Yamaguchi, D. P. Pope and V. Vitek, Phil. Mag. 45, 883 (1982). 16. V. Paidar, D. P. Pope and V. Vitek, Acta metall. 32, 435 (1984). 17. D. P. Pope and S. S. Ezz, Int. Met. Rez'. 29, 136 (1984). 18. G. R. Leverant, M. Gell and S. W. Hopkins, Mater. Sci. Engng 8, 125 (1971). 19. R. A. Stevens and P. E. J. Flewitt, Acta metall. 29, 867 (1981). 20. P. J. Henderson and M. McLean, Aeta metall. 30, 1121 (1982). 21. D. Mukherji, F. Jiao, W. Chen and R. P. Wahi, Acta metall, mater. 39, 1515 (1991). 22. D. Bettge, W. ()sterle and J. Ziebs, Z. Metallk. 86, 190 (1995). 23. J. W. Edington, Practical Electron Microscopy in Material Science, Vol. 3. Macmillan, London (1975). 24. B. H. Kear, A. F. Giamei, J. M. Silcock and R. K. Ham, Scripta metall. 2, 287 (1968). 25. B. H. Kear, A. F. Giamei, G. R. Leverant and J. M. Oblak, Scripta metall. 3, 123 (1969). 26. B. H. Kear, A. F. Giamei, G. R. Leverant and J. M. Oblak, Scripta metall. 3, 455 (1969). 27. M. Condat and B. D+camps, Scripta metall. 21, 607 (1987). 28. A. J. Huis in't Veld, G. Boom, P. M. Bronsveld and J. Th. M. De Hossen, Scripta metall. 19, 1123 (1985). 29. P. Caron, T. Kahn and P. Veyssi+re, Phil. Mag. 57A, 859 (1988). 30. P. Veyssi6re, J. Douin and P. Beauchamp, Phil. Mag. 51A, 469 (1985). 31. B. H. Kear, J. M. Oblak and A. F. Giamei, Metall. Trans. I, 2477 (1970). 32. D. Bettge, W. Osterle and J. Ziebs, to be published.