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Cyclic-hardening behavior of polycrystalline Cu-16at.%Al alloy
Materials Science and Engineering, A142 ( 1991 ) 1-9
1
Cyclic-hardening behavior of polycrystalline Cu- 16at.%A1 alloy Sun Ig Hong* and Campbell Laird Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104-6272 (U.S.A.)
(Received September 17, 1990; in revised form February 8, 1991 )
Abstract The cyclic-hardening behavior of polycrystalline Cu- 16at.%Al alloy has been investigated with special reference to the back-stress and friction stress behavior and discussed in relation to the behavior of single crystals. The friction stress in the polycrystalline alloy measured by the Cottrell method (42 MPa) at the start of cycling is larger than that predicted (36.7 MPa) from the friction stress of single crystals by using the Taylor factor (3.06). This difference is explained in terms of the difference of initial dislocation densities in the two types of material. The cyclic hardening of this alloy is mainly caused by an increase of back stress. However, unlike alloy single crystals which do not undergo saturation, the back stress in polycrystals gradually saturates with cycles, and such behavior produces overall saturation. This saturation in the peak stresses of polycrystalline Cu-16at.%A1 alloy seems to be caused by the saturation of hardening in the later stages of cyclic deformation, not by the "recovery" of dislocations induced by secondary slip as in copper. The different role of secondary slip in Cu-16at.%Al alloy in comparison to that in copper is discussed.
1. Introduction Studies on the cyclic deformation [1-14] and fracture [13, 15, 16] behavior of planar slip copper alloys, especially those on single crystals [1-5, 11, 13, 15-17], show clearly that the cyclic deformation behavior of planar slip alloys is different from that of wavy slip metals. First of all, the active life of slip bands in Cu-AI single crystals has been found to be very short relative to the fatigue life of this alloy. Irrespective of strain amplitude, in Cu-AI single crystals the gauge length becomes completely filled with slip bands progressively by repeated strain bursts [1-3]. Although the overall deformation becomes rather homogeneous after the gauge length is completely filled with slip bands, the plastic strain is always carried by currently active slip bands in which the deformation subsequently slackens and is taken up again by newly activated and reactivated slip bands [1-3]. Since the localized strain shifts around the gauge length, the terminology "persistent Liiders bands" (PLBs) was introduced to *Present address: Materials Science and Technology Division, Los Alamos National Laboratory, MS K762, Los Alamos, NM 87545, U.S.A. 0921-5093/91/$3.50
describe the slip bands and their behavior in planar slip alloys [2, 10, 11]. Recently Laird et al. [14] observed a similarity of the dislocation structures between monocrystalline and polycrystalline Cu-AI alloy. Since the publication of their work, more results have become available on the cyclic deformation behavior and dislocation structures of single crystals of this alloy [1-5, 15, 16]. In the present paper, more results on the cyclic deformation behavior of the polycrystalline alloy of Cu-16at.% AI are reported in relation to the recent results on the monocrystalline alloy of Cu-16at.%Al. The saturation behavior observed in polycrystalline Cu-16at.%Al alloy is also discussed and compared to that of copper. For more extensive references to previous research on the deformation and fatigue fracture of Cu-AI alloy, see the references cited above.
2. Experimental details Ingots of polycrystalline Cu-AI with 15.3 at.% AI were prepared from 99.99% pure copper and 99.999% aluminum by vacuum casting and subsequent homogenization. Chemical analysis © Elsevier Sequoia/Printed in The Netherlands
showed that the alloy used in this study contained 7.12 wt.% AI plus a trace of zinc and less than 0.02 wt.% Fe. Rods suitable for machining specimens were prepared by repeated swaging. They were annealed at 650 °C for 1 h and furnace cooled. The linear intercept method was used to measure the grain size after material preparation and the mean intercept length was found to be 79 # m (grain size 135 pm). Specimens with a gauge length of 12.7 m m and a diameter of 5 mm, finished by electropolishing, were cyclically deformed in a servohydraulic testing machine under total strain control. Some of these samples were sectioned at 45 ° to the axis, mechanically polished and subsequently thinned by a conventional electropolishing method and observed using a Philips EM 400 electron microscope operated at 120 kV.
Figure 1 shows typical cyclic-hardening curves of polycrystalline Cu-16at.%Al alloys. Contrary to the observation in monocrystalline Cu-AI alloy with the same composition but consistent with the results of polycrystalline alloys previously reported [9, 14], saturation of the peak stress was found to occur. Since no saturation behavior is observed in Cu-16at.%Al single crystals [1-3], this result requires detailed investigation and discussion. In Fig. 2 the saturation peak stresses obtained at the constant total strain amplitudes used in this study are plotted along with the data of Laird et al. [14] obtained in
|
~
-
(1)
2
(2)
where rE is the peak applied stress and rs is the yield stress in each cycle. The basic assumption used for the development of the above equations is that the back stress zB generated in the preceding half-cycle acts in the same direction as the current stress and, at the end of the forward cycle, the back stress reaches its maximum and counteracts the deformation. This assumption is also taken as valid for alloys with low stacking fault energy [3, 5], and eqns. (1) and (2) were used to evaluate the friction stress and back stress in the present study. The friction stress and back stress of polycrystalline Cu-16at.%Al alloy cycled at low
........ I ........ I ........ I ........ I ........ I
r
~c~LU175!150125 ........ I ........ 170
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3.1. Hardening behavior
~200
,t"E Jr ,KS r~-
~'B = - -
3. R e s u l t s
13..
ascending step tests and tests under constant plastic strain amplitudes. To plot the data of this study against the axial plastic strain amplitude, the plastic strain amplitude after saturation of the peak stress was used. No plateau in the cyclic stress-strain curve was observed, consistent with the previous result of Laird et al. [14]. As shown in Figs. 1 and 2, the hardening capacity of the material increases with increase of strain amplitude. A knowledge of the back stress rB and friction stress ,KF acting on the dislocations is helpful for understanding the hardening behavior. Kuhlmann-Wilsdorf and Laird [18] employed the following equations for the evaluation of ~:F and rB (CottreU method [19]):
........
n o3 m
T5
I~J 50
50
tJ') -J
. . . . . . . . i . . . . . . . . I . . . . . . ,I , ....... I . . . . . . . . I 10 102 103 104 105
NUMBER
OF
CYCLES
Fig. 1. Cyclic-hardening curves of C u - A I alloy cycled u n d e r c o n s t a n t strain control. T h e curves are keyed to the points in Fig. 2.
-x----25
• ASCENDING STEP TEST [141 O CONSTANT PLASTIC STRAIN { 1 4 ] "~, CONSTANT TOTAL STRAIN, THIS STUDY
i
j j i,,,-I , , ,...d , , ,,,,.,I , ....... ] qO-6 10-5 10-4 10-3 10-2 AXIAL PLASTIC STRAIN AMPLITUDE
Fig. 2. Cyclic s t r e s s - s t r a i n c u r v e of Cu-16at.% AI polycrystailine alloy at low strain amplitudes.
strain (axial plastic strain amplitude 7 x 10-5) and high strain (axial plastic strain amplitude 4.5 x 10 -4) amplitude are plotted in Fig. 3. As shown in this figure, the back stress increases more rapidly than the friction stress, and the friction stress remains constant in the initial stages of cycling as in the case of Cu-AI alloy single crystals [3, 5]. However, unlike the behavior in the alloy single crystals, the back stress gradually saturates with cycles or appears to saturate. The initial friction stress for polycrystalline Cu-AI alloy is 42 MPa.
low strain amplitude (specimen B) in a grain with a single slip orientation. As shown in this figure, one slip system is predominantly activated to form multipoles in the grain. Under the TEM reflection condition of this figure, only one set of the partials of dissociated dislocations is visible. A dislocation pair indicated by arrows shows mirror
3.2. Dislocation structures
The dislocation structures of specimens B and D (see Fig. 1 for corresponding cyclic-hardening curves) were observed by transmission electron microscopy (TEM) in sections cut 45 ° to the specimen axis after saturation was attained. Note that the hardening of specimen D is much higher than that of specimen B (Fig. 2). Figure 4(a) shows the typical dislocation structure found at
~100
I1~11
I
I IItTr
I
,
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I
I Illll
I
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I
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~0 5
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CYCLES
g
120
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~ 60 rr" kO)
20
x ,,H,,I
,,,H,I
10
,,,,.I
10 2
, .....
10:5
CYCLES
I
i111111
10 `4
TO5
ll,~,
10 6
(b)
Fig. 3. Behavior of friction stress rE and back stress ta during cycling (a) at low strain (plastic strain amplitude 7 x 1 0 -5) and (b) at high strain (plastic strain amplitude 4.5 x 10-4).
Fig. 4. Typical dislocation structures observed after cycling to saturation at low strain amplitude in Cu-AI alloy: (a) single-slip grain orientation; (b) multislip grain orientation.
symmetry of the images, indicating that there are visible partials on the opposite sides of the stacking faults; this proves that the dissociated dislocations are in dipolar configuration. Another example of a dislocation structure in a grain of which the zone axis is [1 1 0] is shown in Fig. 4(b). In spite of the duplex slip orientation, dislocations in this figure are also predominantly of one system. However, near grain boundaries, two or three slip systems were often seen to be activated. Typically the spacing between two nearby dislocations in a single glide band was observed to decrease as the dislocations approached the boundary, indicating they were not emitted from the boundary but were piled up against the boundary. Dislocation structures are seen to become more complex at high strain amplitude (specimen D) because of the high primary dislocation density and the strong activity of secondary dislocations, as shown in Fig. 5(a). The imaging condition of Fig. 5(a) is similar to that of Fig. 4(b). This dislocation structure is found to be very similar to those observed in Cu-AI alloy single crystals at high strain amplitude [4]. The effect of increasing the strain amplitude is to decrease the spacing of the dislocation multipolar, planar arrays in alloy single crystals [4]. The dislocation structure produced at high strain amplitude and viewed from a (1 1 1) plane is shown in Fig. 5(b) for polycrystalline specimen D. Note that the dislocations in closely spaced slip planes parallel to the plane of this figure are criss-crossed. No clustered dislocation structures, such as loop patches, ladder structures or cell structures, were observed in these alloy polycrystals. This result is consistent with observations on planar slip alloys in general [1, 4-10, 14]. It has been suggested that the combined effects of the high friction stress and the geometrical repulsion of stacking faults prevent dislocations from clustering in planar slip alloys [20].
3.3. Effect of test interruption Another interesting result in this study is the effect of a test interruption on the shapes of the hysteresis loops. As shown in Fig. 6, after a test interruption lasting 1 h or more, the peak stress is observed to decrease when the test is restarted and the plastic strain increases temporarily, just as observed in Cu-AI alloy single crystals [1, 2]. It was shown by the present investigators that the increase of strain amplitude after an interruption
Fig. 5. Dislocation structures formed in Cu-AI alloy cycled at high strain amplitude (specimen D): (a) closely spaced planar arrays; (b)criss-cross arrays on the dominant slip plane of a single grain.
in Cu-AI alloy single crystals is not connected with recovery during the interruption but by deformation in the undeformed or less deformed
14403
14423cycle
Fig. 6. Shapes of hysteresis loops in Cu-AI polycrystalline specimen, cycled in total strain control, before and after a test interruption. The numbers identify the hysteresis cycles, which bracket the point of interruption.
volume of the crystal when the test is restarted [1, 2]. Since the slip bands active before an interruption could be immobilized by an aging effect of the solute atoms during the interruption in polycrystals just as in single crystals, the same principle appears to apply. It has also been suggested that recovery of planar slip alloys is very difficult at room temperature [20]. Thus caution should be exercised in interpreting recovery-like behavior for planar slip alloys at room temperature. 4. Discussion 4.1. Friction stress and back-stress behavior The hardening behavior of Cu-AI alloy single crystals was found to be divided into low and high strain amplitude regions [2, 3]. It was found in single crystals that hardenability in the high strain amplitude region is higher than that at low strain amplitude [1-3]. It was suggested that massive activity of secondary dislocations at high strain amplitude (defined as the region where the plastic shear strain amplitude is larger than 2 x 10 -3) is responsible for the higher hardenability at high strain amplitude [2] consistent with many T E M observations of the dislocations [4-10]. The axial plastic strain amplitude which marks the transition from the low to high amplitude regions in polycrystalline Cu-AI alloy is approximately 2 x 10-4, as shown in Fig. 2. This transition has nothing to do with the conventional definition of the distinction between high cycle and low cycle fatigue: the point where elastic strain equals plastic strain, which relates to fatigue fracture. The transition here applies only to cyclic hardening and marks the critical strain amplitude where the activity of secondary dislocations becomes significantly stronger. This amplitude measures 2 × 1 0 - 3 in single crystals, and the reduction in polycrystals is attributed to
the presence of grain boundaries. Comparison of the dislocation structures observed at low (Fig. 4(b)) and high (Fig. 5(a)) strain amplitudes shows a difference in the density of secondary dislocations [4]. The similarity of the dislocation structures observed in this study and in other studies on monocrystalline Cu-AI alloy suggests that the same basic dislocation mechanisms as proposed in Cu-AI alloy single crystals could operate at low and high strain amplitudes respectively in Cu-AI polycrystals. As in Cu-Al alloy single crystals, the back stress is found to increase more rapidly than the friction stress in the initial stages of cycling and is associated with the stress fields of dislocation multipoles and pile-ups. Since the morphology of multipoles in planar slip alloys is modified from that found in copper (to form kinked multipoles or cross-gridded multipoles), and because of the high stress concentration of piled-up dislocations, the equality of the back stress and friction stress observed previously for copper [ 18] breaks down for Cu-AI [3, 5]. The flipping stress for kinked and cross-gridded multipoles would be greatly reduced as compared to the flipping stress of the unkinked dipoles found in copper [3, 5]. In this case the zipping-unzipping of a dipole or multipole more appropriately describes the motion of dislocations during cyclic deformation in Cu-AI than the flipping of whole dislocations. This explains also for the polycrystalline alloy (Fig. 3) why the friction stress does not increase with cycles just as in single crystals [3, 5]. For more details on dislocation behavior in Cu-AI alloy, see ref. 3. The back stress of Cu-AI alloy polycrystals, however, seems to have become saturated with increasing cycles, unlike the behavior in Cu-AI alloy single crystals. The presence of grain boundaries could be responsible for the saturation behavior. However, it is also possible that the increase in the back stress becomes so gradual that it is difficult to observe, or fracture intervenes before true saturation is reached. The initial friction stress for Cu-A1 alloy polycrystals is 42 MPa, as shown in Fig. 3, irrespective of strain amplitude. The initial friction stress for Cu-A1 alloy single crystals (associated with the elastic interaction of a dislocation and segregated solute atoms [3]) was found to be 12 MPa [3, 5, 11]. If the friction stress for single crystals is convened to axial stress in polycrystals by using the Taylor factor, the result is 36.7 MPa, yielding a difference of 5.3 MPa ( 1.73 MPa in shear stress)
with respect to the measured value. This difference could be due to the errors in our experiments or the predictive capability of the Taylor model. However, it seems more plausible to explain this difference in terms of the difference of the initial dislocation density in polycrystals, which is usually higher than that of single crystals and could have an effect on friction stress by forest dislocations or jogs. The initial back stress of polycrystals (48-50 MPa), however, is much larger than the initial back stress of single crystals converted by the Taylor factor (8 MPa x 3.06 = 24.5 MPa). This difference cannot be explained by the difference of the initial dislocation density. Randomly distributed dislocations are simply not strong enough as obstacles to cause an appreciable increase of the back stress. It is well known that in h.c.p, metals, where the number of slip systems is limited, the conversion factor is usually larger than the Taylor factor [21-24]. In planar slip alloys the stress concentration at a grain boundary due to piled-up dislocations cannot be relieved easily owing to the difficulty of cross-slip and therefore is used to explain the large conversion factor of the back stress in such alloys. This explanation is further supported by the result that the back stress of Cu-A1 alloy single crystals was observed to reach 30-40 MPa in the high strain amplitude range [3], where pile-ups at Lomer-Cottrell locks were suggested to be responsible for the large back stress. Since the saturated back stress of Cu-AI alloy polycrystals is about 100 MPa at the axial plastic strain amplitude of 4.5 x 10 -4, the conversion factor of the back stress decreases to 2.5-3.3 in the final stages of deformation. It thus seems reasonable to conclude that dislocations piled up at the grain boundaries are responsible for the large back stress in comparison to that of single crystals in the initial stages of deformation. 4.2. Saturation of peak stresses One of the most interesting results in this study is that the peak stress saturates with cycles although no saturation behavior was observed in Cu-A1 alloy single crystals [1-3]. As shown in Fig. 3, the hardening of this alloy is mainly caused by the increase of the back stress and accordingly saturation of peak stress is related to the saturation of the back stress. A possible explanation of the saturation behavior in Cu-Al alloy polycrystals is offered on the basis of the difference of dis-
location behaviors between planar slip alloys and wavy slip metals as follows. It has been suggested that the activation of secondary dislocations promotes rapid annihilation of primary dislocations. An example of this behavior is the saturation of peak stresses associated with the formation of persistent slip bands (PSBs) [25-27] in wavy slip metals. The saturation of peak stresses during fatigue deformation of wavy slip metals, e.g. copper, is maintained by a balance between hardening due to dislocation generation and recovery due to the annihilation of dislocations in the ladder structures. Since no ladder structures have been observed in Cu-16at.%A1 alloy, the saturation behavior cannot be explained in terms of PSBs. One important aspect in planar slip alloys in comparison to wavy slip metals is the difficulty of annihilation of dislocations through difficulty of cross-slip. It is well known that climb and cross-slip of widely dissociated dislocations are very difficult [28]. Furthermore, the geometrical repulsion of closely adjacent stacking faults itself was suggested to prevent dislocations from clustering and therefore from annihilating [20]. No saturation of peak stresses was found to occur in Cu-16at.%A1 single crystals because of the difficulty of annihilating dislocations [1-3]. To explain the saturation behavior observed in polycrystalline Cu-16at.%Al alloy, it has to be assumed that either (1) recovery due to annihilation of dislocations is somehow promoted or (2) hardening due to the generation of dislocations is effectively suppressed by the presence of grain boundaries in the later stages of cyclic deformation. However, no clustered dislocation structures which might lead to easy annihilation were observed near grain boundaries. Although it is possible that piled-up dislocations are induced to cross slip at the grain boundary, cross-slip in planar slip materials is somewhat infrequent and leaves a long and quite localized slip trace once it occurs [2]. Therefore it is unlikely that annihilation of dislocations is promoted by the presence of grain boundaries. Cyclic hardening during fatigue deformation of Cu-16at.%Al single crystals was found to be caused by both the accumulation of planar dislocation arrays on primary slip planes with continually decreasing spacing and the formation of dislocation obstacles such as Lomer-Cottrell locks [2, 3]. Inui et al. [4] also observed that the density of both primary and secondary disloca-
tions increases as the spacing of the activated slip planes decreases with increasing stress level. Primary slip bands could be refined not only by the multiplication of primary dislocations but by the activity of secondary dislocations. In Fig. 7, dislocation mechanisms are illustrated which could multiply activated primary slip bands effectively in both single crystals and polycrystals. In Fig. 7(a) a multipole is shown consisting of groups of dislocations, A and B, of opposite sign. In the initial stage of deformation, where the spacing between two adjacent slip planes is relatively large, dislocations are activated from the primary dislocation source $1 to refine the primary slip bands. As the spacing decreases with cycles, the activation of source $1 is made difficult by the internal stress of the multipole. However, the primary slip band spacing could be refined further by the activation of another source S2. Dislocations gliding from this source could disrupt an otherwise stable multipole and form a stronger multipole with the group of dislocations A-meantime, the spacing between the primary slip bands is reduced from d to d'. The dislocation group B is now free to form a multipole with another group of dislocations. In a polycrystal the refinement of primary slip bands by an outside dislocation source such as Sz could be restrained by the presence of grain boundaries. For example, if the vertical broken line in Fig. 7(a) is taken as a grain boundary, the refinement of the slip bands by source S2 is impossible. In Fig. 7(b) the effect of secondary slip on the refinement of a primary slip band is shown. In this figure the primary slip planes are displaced by the
! AJ.
i
.L
±
i
Al .i'd/T
S, B
T
T
T
T
T T T
S~,
T
I
(a)
/ A ± B
± T
± T
± ± / ; ~_____ A , A I J.t ±. T T
T
T
T
T
± 8~
(b) Fig. 7. Refinement in the spacing of primary dislocation arrays (multipoles) in Cu-AI alloy by various mechanisms: (a) multisource operation; (b) activation of secondary slip.
secondary slip activated by the internal stress of the primary dislocations. In this case a multipolar group of dislocations B and/~ could be produced by glide into the slip bands as indicated by arrows and so form a stronger multipole. Freed dislocation groups A and B' could in turn form multipoles with other groups of dislocations. Since the propagation of the secondary slip activated by the internal stress of primary dislocations is restrained by the presence of grain boundaries, the volume of primary slip bands which is affected by the mechanism described in Fig. 7(b) is suggested to decrease. The typical length of a secondary slip system was observed to be 30/~m or longer [4, 29] in Cu-A1 single crystals, which is of the same order as the linear intercept measure of the grains if twin boundaries are included in the intercept count. Therefore the refinement of primary slip band spacing which is necessary for continuous cyclic hardening [1-4] is restrained in the later stages of deformation in polycrystalline Cu-AI alloy and saturation occurs. It should be noted here that secondary slip activated by the internal stress of primary dislocations has been suggested to promote the gradual annihilation of dislocations in copper [18, 30]. A model similar to that used in Fig. 7(b) has been used, for example, to explain the formation of PSBs in copper. The reason why secondary slip activated by the internal stress causes hardening in planar slip alloys and softening in wavy slip metals can be explained by the different dislocation behaviors between the two materials. If annihilation was to occur in Cu-AI, for example, it would be necessary to displace dislocations in B and ~ (Fig. 7(b)) into precise alignment (displacement of d / c o s ( 9 0 - a ) ) by secondary slip. Then groups B and A~, having opposite signs, could annihilate by glide. For all other displacements they could not be annihilated. Such precise alignment is not necessary for annihilation in copper. Approximate alignment only is necessary, because the opposing dislocations could then find each other by cross-slip. Therefore it is much more likely that activity of secondary slip causes hardening in planar slip alloys. In summary, the saturation of peak stresses in polycrystalline Cu-AI alloy is not caused by the recovery of dislocations induced by secondary slip but by the retardation of hardening. Unlike monocrystalline Cu-A1 alloy, the refinement of the spacing of the activated primary slip planes becomes restrained owing to the presence of
grain boundaries. It would be interesting to investigate whether or not secondary hardening would develop with continuous cycling, as observed in copper when the life is extended by cycling under an inert environment [31], or whether true saturation would occur. Further work is required to answer these questions for planar slip alloys.
tests on polycrystals carried out in total strain control, just as in the monocrystalline alloy. This increase of plastic deformation after an interruption in Cu-AI alloy is suggested to be connected with strain burst behavior, not with recovery during the interruption.
5. Conclusions
Acknowledgments
Studies on the cyclic-hardening behaviors of polycrystalline Cu-16at.%Al alloy in comparison to the behaviors of the monocrystalline alloy lead to the following conclusions. (1) The dislocation structures of cyclically deformed polycrystalline Cu-16at.% Al alloy are quite similar to those of monocrystalline Cu-Al alloy. (2) Contrary to the observation in monocrystalline Cu-A1 alloy with the same composition, saturation of the peak stress was found to occur. The saturation of peak stresses in polycrystalline Cu-16at.% Al alloy seems to be caused by the difficulty of refinement of primary slip bands in the later stages of cyclic deformation, not by the recovery of dislocations induced by secondary slip as in copper. (3) The initial friction stress in the polycrystalline alloy (42 MPa) is larger than that (36.7 MPa) converted from the friction stress of single crystals by using the Taylor factor (3.06). The difference is explained in terms of the difference of initial dislocation densities in mono- and polycrystalline material. (4) The cyclic hardening of this alloy is mainly caused by an increase of back stress. However, unlike the behavior in the alloy single crystals, the back stress in polycrystals gradually saturates with cycles. (5) Because of the planar distribution of dislocations and wider spacing between activated primary slip planes in Cu-AI alloy, the spacing of activated primary slip bands can be refined by the activity of secondary slip. In copper, because of the much more tangled and closely packed nature of the dislocations in the loop patch structures, the primary slip bands cannot be refined. Instead, gradual annihilation of primary dislocations is induced if primary dislocations, displaced by the secondary slip, are faced with oppositely signed primary dislocations. (6) The plastic strain amplitude was found to increase temporarily after an interruption for
Grateful acknowledgment is offered for support of this work by the Laboratory for Research on the Structure of Matter in the University of Pennsylvania under NSF grant No. DMR8819885. We also thank our colleagues in the fatigue group for valuable discussions and A. L. Radin and D. Ricketts-Foot for their generous help.
References 1 S. I. Hong and C. Laird, Mater. Sci. Eng. A, 124 (1990) 159. 2 S. I. Hong and C. Laird, Mater. Sci. Eng. A, 128 (1990) 55. 3 S. I. Hong and C. Laird, Mater. Sci. Eng. A, 128 (1990) 155. 4 H~ Inui, S. I. Hong and C. Laird, Acta Metall. Mater., 38 (1990) 2261. 5 S.I. Hong and C. Laird, Acta Metall. Mater., in the press. 6 P. Lukas and M. Klesnil, Phys. Status Solidi, 37 (1970) 833. 7 P. Lukas and M. Klesnil, Phys. Status Solidi A, 5 ( 1971 ) 247. 8 T.H. Youseff, Phys. Status Solidi A, 3(1970) 801. 9 C.E. Feltner and C. Laird, Acta Metall., 15 (1967) 1633. 10 L. Buchinger, A. S. Cheng, S. Stanzl and C. Laird, Mater Sci. Eng., 80(1986) 155. 11 B. D. Yan, A. S. Cheng, L. Buchinger, S. Stanzl and C. Laird, Mater Sci. Eng., 80(1986) 129. 12 P. Luk~is and M. Klesnil, in O. F. Devereux, A. J. McEvily and R. W. Staehle (eds.), Corrosion Fatigue, NACE-2, Houston, TX, 1972, p. 115. 13 D. H. Avery and W. A. Backofen, in D. C. Drucker and J. J. Gilman (eds.), Fracture of Solids, Interscience, New York, 1962, p. 335. 14 C. Laird, S. Stanzl, R. De La Veaux and L. Buchinger, Mater. Sci. Eng., 80(1986) 143. 15 S. I. Hong and C. Laird, Fatigue Fract. Eng. Mater. Struct., 14(1991) 143. 16 S.I. Hong and C. Laird, Met. Trans. A, 22 (1991) 415. relation to crystallographic slip systems, to be published. 17 Z. Wang and H. Margolin, Acta Metall., 34 (1986) 721. 18 D. Kuhlmann-Wilsdorf and C. Laird, Mater. Sci. Eng., 27 (1977) 137. 19 A. H. Cottrell, Dislocations and Plastic Flow in Crystals, Oxford University Press, Oxford, 1953. 20 S.I. Hong and C. Laird, Acta Metall., 38 (1990) 1581.
N. Hansen, Metall. Trans. A, 16(1985) 2167. K. Okazaki and H. Conrad, Acta Meiall., 21 (1973) 1117. S.I. Hong, Mater Sci. Eng., 76 (1985) 77. S. I. Hong, W. S. Ryu and C. S. Rim, J. Nucl. Mater., 120 (1984) 1. 25 C. Laird, in E R. N. Nabarro (ed.), Dislocations in Solids, Vol. 6, North-Holland, Amsterdam, 1983, p. 57. 26 E Neumann, in R. W. Cahn and P. Haasen (eds.), Physical Metallurgy, Elsevier, Amsterdam, 1983, p. 1554. 21 22 23 24
27 U. Essmann, U. G6sele and H. Mughrabi, PhiL Mag. A, 44(1981)405. 28 J. P. Hirth and J. Lothe, Theory of Dislocations, McGrawHill, New York, 1968, p. 531. 29 H. Fujita and S. Kimura, J. Phys. Soc. Jpn., 52(1983) 157. 30 D. Kuhlmann-Wilsdorf and C. Laird, Mater. Sci. Eng., 46 (1980) 209. 31 R. Wang and H. Mughrabi, Mater. Sci. Eng., 63 (1984) 147.
1
Cyclic-hardening behavior of polycrystalline Cu- 16at.%A1 alloy Sun Ig Hong* and Campbell Laird Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104-6272 (U.S.A.)
(Received September 17, 1990; in revised form February 8, 1991 )
Abstract The cyclic-hardening behavior of polycrystalline Cu- 16at.%Al alloy has been investigated with special reference to the back-stress and friction stress behavior and discussed in relation to the behavior of single crystals. The friction stress in the polycrystalline alloy measured by the Cottrell method (42 MPa) at the start of cycling is larger than that predicted (36.7 MPa) from the friction stress of single crystals by using the Taylor factor (3.06). This difference is explained in terms of the difference of initial dislocation densities in the two types of material. The cyclic hardening of this alloy is mainly caused by an increase of back stress. However, unlike alloy single crystals which do not undergo saturation, the back stress in polycrystals gradually saturates with cycles, and such behavior produces overall saturation. This saturation in the peak stresses of polycrystalline Cu-16at.%A1 alloy seems to be caused by the saturation of hardening in the later stages of cyclic deformation, not by the "recovery" of dislocations induced by secondary slip as in copper. The different role of secondary slip in Cu-16at.%Al alloy in comparison to that in copper is discussed.
1. Introduction Studies on the cyclic deformation [1-14] and fracture [13, 15, 16] behavior of planar slip copper alloys, especially those on single crystals [1-5, 11, 13, 15-17], show clearly that the cyclic deformation behavior of planar slip alloys is different from that of wavy slip metals. First of all, the active life of slip bands in Cu-AI single crystals has been found to be very short relative to the fatigue life of this alloy. Irrespective of strain amplitude, in Cu-AI single crystals the gauge length becomes completely filled with slip bands progressively by repeated strain bursts [1-3]. Although the overall deformation becomes rather homogeneous after the gauge length is completely filled with slip bands, the plastic strain is always carried by currently active slip bands in which the deformation subsequently slackens and is taken up again by newly activated and reactivated slip bands [1-3]. Since the localized strain shifts around the gauge length, the terminology "persistent Liiders bands" (PLBs) was introduced to *Present address: Materials Science and Technology Division, Los Alamos National Laboratory, MS K762, Los Alamos, NM 87545, U.S.A. 0921-5093/91/$3.50
describe the slip bands and their behavior in planar slip alloys [2, 10, 11]. Recently Laird et al. [14] observed a similarity of the dislocation structures between monocrystalline and polycrystalline Cu-AI alloy. Since the publication of their work, more results have become available on the cyclic deformation behavior and dislocation structures of single crystals of this alloy [1-5, 15, 16]. In the present paper, more results on the cyclic deformation behavior of the polycrystalline alloy of Cu-16at.% AI are reported in relation to the recent results on the monocrystalline alloy of Cu-16at.%Al. The saturation behavior observed in polycrystalline Cu-16at.%Al alloy is also discussed and compared to that of copper. For more extensive references to previous research on the deformation and fatigue fracture of Cu-AI alloy, see the references cited above.
2. Experimental details Ingots of polycrystalline Cu-AI with 15.3 at.% AI were prepared from 99.99% pure copper and 99.999% aluminum by vacuum casting and subsequent homogenization. Chemical analysis © Elsevier Sequoia/Printed in The Netherlands
showed that the alloy used in this study contained 7.12 wt.% AI plus a trace of zinc and less than 0.02 wt.% Fe. Rods suitable for machining specimens were prepared by repeated swaging. They were annealed at 650 °C for 1 h and furnace cooled. The linear intercept method was used to measure the grain size after material preparation and the mean intercept length was found to be 79 # m (grain size 135 pm). Specimens with a gauge length of 12.7 m m and a diameter of 5 mm, finished by electropolishing, were cyclically deformed in a servohydraulic testing machine under total strain control. Some of these samples were sectioned at 45 ° to the axis, mechanically polished and subsequently thinned by a conventional electropolishing method and observed using a Philips EM 400 electron microscope operated at 120 kV.
Figure 1 shows typical cyclic-hardening curves of polycrystalline Cu-16at.%Al alloys. Contrary to the observation in monocrystalline Cu-AI alloy with the same composition but consistent with the results of polycrystalline alloys previously reported [9, 14], saturation of the peak stress was found to occur. Since no saturation behavior is observed in Cu-16at.%Al single crystals [1-3], this result requires detailed investigation and discussion. In Fig. 2 the saturation peak stresses obtained at the constant total strain amplitudes used in this study are plotted along with the data of Laird et al. [14] obtained in
|
~
-
(1)
2
(2)
where rE is the peak applied stress and rs is the yield stress in each cycle. The basic assumption used for the development of the above equations is that the back stress zB generated in the preceding half-cycle acts in the same direction as the current stress and, at the end of the forward cycle, the back stress reaches its maximum and counteracts the deformation. This assumption is also taken as valid for alloys with low stacking fault energy [3, 5], and eqns. (1) and (2) were used to evaluate the friction stress and back stress in the present study. The friction stress and back stress of polycrystalline Cu-16at.%Al alloy cycled at low
........ I ........ I ........ I ........ I ........ I
r
~c~LU175!150125 ........ I ........ 170
I
i-m _J
-
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3.1. Hardening behavior
~200
,t"E Jr ,KS r~-
~'B = - -
3. R e s u l t s
13..
ascending step tests and tests under constant plastic strain amplitudes. To plot the data of this study against the axial plastic strain amplitude, the plastic strain amplitude after saturation of the peak stress was used. No plateau in the cyclic stress-strain curve was observed, consistent with the previous result of Laird et al. [14]. As shown in Figs. 1 and 2, the hardening capacity of the material increases with increase of strain amplitude. A knowledge of the back stress rB and friction stress ,KF acting on the dislocations is helpful for understanding the hardening behavior. Kuhlmann-Wilsdorf and Laird [18] employed the following equations for the evaluation of ~:F and rB (CottreU method [19]):
........
n o3 m
T5
I~J 50
50
tJ') -J
. . . . . . . . i . . . . . . . . I . . . . . . ,I , ....... I . . . . . . . . I 10 102 103 104 105
NUMBER
OF
CYCLES
Fig. 1. Cyclic-hardening curves of C u - A I alloy cycled u n d e r c o n s t a n t strain control. T h e curves are keyed to the points in Fig. 2.
-x----25
• ASCENDING STEP TEST [141 O CONSTANT PLASTIC STRAIN { 1 4 ] "~, CONSTANT TOTAL STRAIN, THIS STUDY
i
j j i,,,-I , , ,...d , , ,,,,.,I , ....... ] qO-6 10-5 10-4 10-3 10-2 AXIAL PLASTIC STRAIN AMPLITUDE
Fig. 2. Cyclic s t r e s s - s t r a i n c u r v e of Cu-16at.% AI polycrystailine alloy at low strain amplitudes.
strain (axial plastic strain amplitude 7 x 10-5) and high strain (axial plastic strain amplitude 4.5 x 10 -4) amplitude are plotted in Fig. 3. As shown in this figure, the back stress increases more rapidly than the friction stress, and the friction stress remains constant in the initial stages of cycling as in the case of Cu-AI alloy single crystals [3, 5]. However, unlike the behavior in the alloy single crystals, the back stress gradually saturates with cycles or appears to saturate. The initial friction stress for polycrystalline Cu-AI alloy is 42 MPa.
low strain amplitude (specimen B) in a grain with a single slip orientation. As shown in this figure, one slip system is predominantly activated to form multipoles in the grain. Under the TEM reflection condition of this figure, only one set of the partials of dissociated dislocations is visible. A dislocation pair indicated by arrows shows mirror
3.2. Dislocation structures
The dislocation structures of specimens B and D (see Fig. 1 for corresponding cyclic-hardening curves) were observed by transmission electron microscopy (TEM) in sections cut 45 ° to the specimen axis after saturation was attained. Note that the hardening of specimen D is much higher than that of specimen B (Fig. 2). Figure 4(a) shows the typical dislocation structure found at
~100
I1~11
I
I IItTr
I
,
llr,r
I
I Illll
I
I II,tr
I
I
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< 6O
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if)
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~ 20 10
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~0 5
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CYCLES
g
120
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(a)
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~ 60 rr" kO)
20
x ,,H,,I
,,,H,I
10
,,,,.I
10 2
, .....
10:5
CYCLES
I
i111111
10 `4
TO5
ll,~,
10 6
(b)
Fig. 3. Behavior of friction stress rE and back stress ta during cycling (a) at low strain (plastic strain amplitude 7 x 1 0 -5) and (b) at high strain (plastic strain amplitude 4.5 x 10-4).
Fig. 4. Typical dislocation structures observed after cycling to saturation at low strain amplitude in Cu-AI alloy: (a) single-slip grain orientation; (b) multislip grain orientation.
symmetry of the images, indicating that there are visible partials on the opposite sides of the stacking faults; this proves that the dissociated dislocations are in dipolar configuration. Another example of a dislocation structure in a grain of which the zone axis is [1 1 0] is shown in Fig. 4(b). In spite of the duplex slip orientation, dislocations in this figure are also predominantly of one system. However, near grain boundaries, two or three slip systems were often seen to be activated. Typically the spacing between two nearby dislocations in a single glide band was observed to decrease as the dislocations approached the boundary, indicating they were not emitted from the boundary but were piled up against the boundary. Dislocation structures are seen to become more complex at high strain amplitude (specimen D) because of the high primary dislocation density and the strong activity of secondary dislocations, as shown in Fig. 5(a). The imaging condition of Fig. 5(a) is similar to that of Fig. 4(b). This dislocation structure is found to be very similar to those observed in Cu-AI alloy single crystals at high strain amplitude [4]. The effect of increasing the strain amplitude is to decrease the spacing of the dislocation multipolar, planar arrays in alloy single crystals [4]. The dislocation structure produced at high strain amplitude and viewed from a (1 1 1) plane is shown in Fig. 5(b) for polycrystalline specimen D. Note that the dislocations in closely spaced slip planes parallel to the plane of this figure are criss-crossed. No clustered dislocation structures, such as loop patches, ladder structures or cell structures, were observed in these alloy polycrystals. This result is consistent with observations on planar slip alloys in general [1, 4-10, 14]. It has been suggested that the combined effects of the high friction stress and the geometrical repulsion of stacking faults prevent dislocations from clustering in planar slip alloys [20].
3.3. Effect of test interruption Another interesting result in this study is the effect of a test interruption on the shapes of the hysteresis loops. As shown in Fig. 6, after a test interruption lasting 1 h or more, the peak stress is observed to decrease when the test is restarted and the plastic strain increases temporarily, just as observed in Cu-AI alloy single crystals [1, 2]. It was shown by the present investigators that the increase of strain amplitude after an interruption
Fig. 5. Dislocation structures formed in Cu-AI alloy cycled at high strain amplitude (specimen D): (a) closely spaced planar arrays; (b)criss-cross arrays on the dominant slip plane of a single grain.
in Cu-AI alloy single crystals is not connected with recovery during the interruption but by deformation in the undeformed or less deformed
14403
14423cycle
Fig. 6. Shapes of hysteresis loops in Cu-AI polycrystalline specimen, cycled in total strain control, before and after a test interruption. The numbers identify the hysteresis cycles, which bracket the point of interruption.
volume of the crystal when the test is restarted [1, 2]. Since the slip bands active before an interruption could be immobilized by an aging effect of the solute atoms during the interruption in polycrystals just as in single crystals, the same principle appears to apply. It has also been suggested that recovery of planar slip alloys is very difficult at room temperature [20]. Thus caution should be exercised in interpreting recovery-like behavior for planar slip alloys at room temperature. 4. Discussion 4.1. Friction stress and back-stress behavior The hardening behavior of Cu-AI alloy single crystals was found to be divided into low and high strain amplitude regions [2, 3]. It was found in single crystals that hardenability in the high strain amplitude region is higher than that at low strain amplitude [1-3]. It was suggested that massive activity of secondary dislocations at high strain amplitude (defined as the region where the plastic shear strain amplitude is larger than 2 x 10 -3) is responsible for the higher hardenability at high strain amplitude [2] consistent with many T E M observations of the dislocations [4-10]. The axial plastic strain amplitude which marks the transition from the low to high amplitude regions in polycrystalline Cu-AI alloy is approximately 2 x 10-4, as shown in Fig. 2. This transition has nothing to do with the conventional definition of the distinction between high cycle and low cycle fatigue: the point where elastic strain equals plastic strain, which relates to fatigue fracture. The transition here applies only to cyclic hardening and marks the critical strain amplitude where the activity of secondary dislocations becomes significantly stronger. This amplitude measures 2 × 1 0 - 3 in single crystals, and the reduction in polycrystals is attributed to
the presence of grain boundaries. Comparison of the dislocation structures observed at low (Fig. 4(b)) and high (Fig. 5(a)) strain amplitudes shows a difference in the density of secondary dislocations [4]. The similarity of the dislocation structures observed in this study and in other studies on monocrystalline Cu-AI alloy suggests that the same basic dislocation mechanisms as proposed in Cu-AI alloy single crystals could operate at low and high strain amplitudes respectively in Cu-AI polycrystals. As in Cu-Al alloy single crystals, the back stress is found to increase more rapidly than the friction stress in the initial stages of cycling and is associated with the stress fields of dislocation multipoles and pile-ups. Since the morphology of multipoles in planar slip alloys is modified from that found in copper (to form kinked multipoles or cross-gridded multipoles), and because of the high stress concentration of piled-up dislocations, the equality of the back stress and friction stress observed previously for copper [ 18] breaks down for Cu-AI [3, 5]. The flipping stress for kinked and cross-gridded multipoles would be greatly reduced as compared to the flipping stress of the unkinked dipoles found in copper [3, 5]. In this case the zipping-unzipping of a dipole or multipole more appropriately describes the motion of dislocations during cyclic deformation in Cu-AI than the flipping of whole dislocations. This explains also for the polycrystalline alloy (Fig. 3) why the friction stress does not increase with cycles just as in single crystals [3, 5]. For more details on dislocation behavior in Cu-AI alloy, see ref. 3. The back stress of Cu-AI alloy polycrystals, however, seems to have become saturated with increasing cycles, unlike the behavior in Cu-AI alloy single crystals. The presence of grain boundaries could be responsible for the saturation behavior. However, it is also possible that the increase in the back stress becomes so gradual that it is difficult to observe, or fracture intervenes before true saturation is reached. The initial friction stress for Cu-A1 alloy polycrystals is 42 MPa, as shown in Fig. 3, irrespective of strain amplitude. The initial friction stress for Cu-A1 alloy single crystals (associated with the elastic interaction of a dislocation and segregated solute atoms [3]) was found to be 12 MPa [3, 5, 11]. If the friction stress for single crystals is convened to axial stress in polycrystals by using the Taylor factor, the result is 36.7 MPa, yielding a difference of 5.3 MPa ( 1.73 MPa in shear stress)
with respect to the measured value. This difference could be due to the errors in our experiments or the predictive capability of the Taylor model. However, it seems more plausible to explain this difference in terms of the difference of the initial dislocation density in polycrystals, which is usually higher than that of single crystals and could have an effect on friction stress by forest dislocations or jogs. The initial back stress of polycrystals (48-50 MPa), however, is much larger than the initial back stress of single crystals converted by the Taylor factor (8 MPa x 3.06 = 24.5 MPa). This difference cannot be explained by the difference of the initial dislocation density. Randomly distributed dislocations are simply not strong enough as obstacles to cause an appreciable increase of the back stress. It is well known that in h.c.p, metals, where the number of slip systems is limited, the conversion factor is usually larger than the Taylor factor [21-24]. In planar slip alloys the stress concentration at a grain boundary due to piled-up dislocations cannot be relieved easily owing to the difficulty of cross-slip and therefore is used to explain the large conversion factor of the back stress in such alloys. This explanation is further supported by the result that the back stress of Cu-A1 alloy single crystals was observed to reach 30-40 MPa in the high strain amplitude range [3], where pile-ups at Lomer-Cottrell locks were suggested to be responsible for the large back stress. Since the saturated back stress of Cu-AI alloy polycrystals is about 100 MPa at the axial plastic strain amplitude of 4.5 x 10 -4, the conversion factor of the back stress decreases to 2.5-3.3 in the final stages of deformation. It thus seems reasonable to conclude that dislocations piled up at the grain boundaries are responsible for the large back stress in comparison to that of single crystals in the initial stages of deformation. 4.2. Saturation of peak stresses One of the most interesting results in this study is that the peak stress saturates with cycles although no saturation behavior was observed in Cu-A1 alloy single crystals [1-3]. As shown in Fig. 3, the hardening of this alloy is mainly caused by the increase of the back stress and accordingly saturation of peak stress is related to the saturation of the back stress. A possible explanation of the saturation behavior in Cu-Al alloy polycrystals is offered on the basis of the difference of dis-
location behaviors between planar slip alloys and wavy slip metals as follows. It has been suggested that the activation of secondary dislocations promotes rapid annihilation of primary dislocations. An example of this behavior is the saturation of peak stresses associated with the formation of persistent slip bands (PSBs) [25-27] in wavy slip metals. The saturation of peak stresses during fatigue deformation of wavy slip metals, e.g. copper, is maintained by a balance between hardening due to dislocation generation and recovery due to the annihilation of dislocations in the ladder structures. Since no ladder structures have been observed in Cu-16at.%A1 alloy, the saturation behavior cannot be explained in terms of PSBs. One important aspect in planar slip alloys in comparison to wavy slip metals is the difficulty of annihilation of dislocations through difficulty of cross-slip. It is well known that climb and cross-slip of widely dissociated dislocations are very difficult [28]. Furthermore, the geometrical repulsion of closely adjacent stacking faults itself was suggested to prevent dislocations from clustering and therefore from annihilating [20]. No saturation of peak stresses was found to occur in Cu-16at.%A1 single crystals because of the difficulty of annihilating dislocations [1-3]. To explain the saturation behavior observed in polycrystalline Cu-16at.%Al alloy, it has to be assumed that either (1) recovery due to annihilation of dislocations is somehow promoted or (2) hardening due to the generation of dislocations is effectively suppressed by the presence of grain boundaries in the later stages of cyclic deformation. However, no clustered dislocation structures which might lead to easy annihilation were observed near grain boundaries. Although it is possible that piled-up dislocations are induced to cross slip at the grain boundary, cross-slip in planar slip materials is somewhat infrequent and leaves a long and quite localized slip trace once it occurs [2]. Therefore it is unlikely that annihilation of dislocations is promoted by the presence of grain boundaries. Cyclic hardening during fatigue deformation of Cu-16at.%Al single crystals was found to be caused by both the accumulation of planar dislocation arrays on primary slip planes with continually decreasing spacing and the formation of dislocation obstacles such as Lomer-Cottrell locks [2, 3]. Inui et al. [4] also observed that the density of both primary and secondary disloca-
tions increases as the spacing of the activated slip planes decreases with increasing stress level. Primary slip bands could be refined not only by the multiplication of primary dislocations but by the activity of secondary dislocations. In Fig. 7, dislocation mechanisms are illustrated which could multiply activated primary slip bands effectively in both single crystals and polycrystals. In Fig. 7(a) a multipole is shown consisting of groups of dislocations, A and B, of opposite sign. In the initial stage of deformation, where the spacing between two adjacent slip planes is relatively large, dislocations are activated from the primary dislocation source $1 to refine the primary slip bands. As the spacing decreases with cycles, the activation of source $1 is made difficult by the internal stress of the multipole. However, the primary slip band spacing could be refined further by the activation of another source S2. Dislocations gliding from this source could disrupt an otherwise stable multipole and form a stronger multipole with the group of dislocations A-meantime, the spacing between the primary slip bands is reduced from d to d'. The dislocation group B is now free to form a multipole with another group of dislocations. In a polycrystal the refinement of primary slip bands by an outside dislocation source such as Sz could be restrained by the presence of grain boundaries. For example, if the vertical broken line in Fig. 7(a) is taken as a grain boundary, the refinement of the slip bands by source S2 is impossible. In Fig. 7(b) the effect of secondary slip on the refinement of a primary slip band is shown. In this figure the primary slip planes are displaced by the
! AJ.
i
.L
±
i
Al .i'd/T
S, B
T
T
T
T
T T T
S~,
T
I
(a)
/ A ± B
± T
± T
± ± / ; ~_____ A , A I J.t ±. T T
T
T
T
T
± 8~
(b) Fig. 7. Refinement in the spacing of primary dislocation arrays (multipoles) in Cu-AI alloy by various mechanisms: (a) multisource operation; (b) activation of secondary slip.
secondary slip activated by the internal stress of the primary dislocations. In this case a multipolar group of dislocations B and/~ could be produced by glide into the slip bands as indicated by arrows and so form a stronger multipole. Freed dislocation groups A and B' could in turn form multipoles with other groups of dislocations. Since the propagation of the secondary slip activated by the internal stress of primary dislocations is restrained by the presence of grain boundaries, the volume of primary slip bands which is affected by the mechanism described in Fig. 7(b) is suggested to decrease. The typical length of a secondary slip system was observed to be 30/~m or longer [4, 29] in Cu-A1 single crystals, which is of the same order as the linear intercept measure of the grains if twin boundaries are included in the intercept count. Therefore the refinement of primary slip band spacing which is necessary for continuous cyclic hardening [1-4] is restrained in the later stages of deformation in polycrystalline Cu-AI alloy and saturation occurs. It should be noted here that secondary slip activated by the internal stress of primary dislocations has been suggested to promote the gradual annihilation of dislocations in copper [18, 30]. A model similar to that used in Fig. 7(b) has been used, for example, to explain the formation of PSBs in copper. The reason why secondary slip activated by the internal stress causes hardening in planar slip alloys and softening in wavy slip metals can be explained by the different dislocation behaviors between the two materials. If annihilation was to occur in Cu-AI, for example, it would be necessary to displace dislocations in B and ~ (Fig. 7(b)) into precise alignment (displacement of d / c o s ( 9 0 - a ) ) by secondary slip. Then groups B and A~, having opposite signs, could annihilate by glide. For all other displacements they could not be annihilated. Such precise alignment is not necessary for annihilation in copper. Approximate alignment only is necessary, because the opposing dislocations could then find each other by cross-slip. Therefore it is much more likely that activity of secondary slip causes hardening in planar slip alloys. In summary, the saturation of peak stresses in polycrystalline Cu-AI alloy is not caused by the recovery of dislocations induced by secondary slip but by the retardation of hardening. Unlike monocrystalline Cu-A1 alloy, the refinement of the spacing of the activated primary slip planes becomes restrained owing to the presence of
grain boundaries. It would be interesting to investigate whether or not secondary hardening would develop with continuous cycling, as observed in copper when the life is extended by cycling under an inert environment [31], or whether true saturation would occur. Further work is required to answer these questions for planar slip alloys.
tests on polycrystals carried out in total strain control, just as in the monocrystalline alloy. This increase of plastic deformation after an interruption in Cu-AI alloy is suggested to be connected with strain burst behavior, not with recovery during the interruption.
5. Conclusions
Acknowledgments
Studies on the cyclic-hardening behaviors of polycrystalline Cu-16at.%Al alloy in comparison to the behaviors of the monocrystalline alloy lead to the following conclusions. (1) The dislocation structures of cyclically deformed polycrystalline Cu-16at.% Al alloy are quite similar to those of monocrystalline Cu-Al alloy. (2) Contrary to the observation in monocrystalline Cu-A1 alloy with the same composition, saturation of the peak stress was found to occur. The saturation of peak stresses in polycrystalline Cu-16at.% Al alloy seems to be caused by the difficulty of refinement of primary slip bands in the later stages of cyclic deformation, not by the recovery of dislocations induced by secondary slip as in copper. (3) The initial friction stress in the polycrystalline alloy (42 MPa) is larger than that (36.7 MPa) converted from the friction stress of single crystals by using the Taylor factor (3.06). The difference is explained in terms of the difference of initial dislocation densities in mono- and polycrystalline material. (4) The cyclic hardening of this alloy is mainly caused by an increase of back stress. However, unlike the behavior in the alloy single crystals, the back stress in polycrystals gradually saturates with cycles. (5) Because of the planar distribution of dislocations and wider spacing between activated primary slip planes in Cu-AI alloy, the spacing of activated primary slip bands can be refined by the activity of secondary slip. In copper, because of the much more tangled and closely packed nature of the dislocations in the loop patch structures, the primary slip bands cannot be refined. Instead, gradual annihilation of primary dislocations is induced if primary dislocations, displaced by the secondary slip, are faced with oppositely signed primary dislocations. (6) The plastic strain amplitude was found to increase temporarily after an interruption for
Grateful acknowledgment is offered for support of this work by the Laboratory for Research on the Structure of Matter in the University of Pennsylvania under NSF grant No. DMR8819885. We also thank our colleagues in the fatigue group for valuable discussions and A. L. Radin and D. Ricketts-Foot for their generous help.
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27 U. Essmann, U. G6sele and H. Mughrabi, PhiL Mag. A, 44(1981)405. 28 J. P. Hirth and J. Lothe, Theory of Dislocations, McGrawHill, New York, 1968, p. 531. 29 H. Fujita and S. Kimura, J. Phys. Soc. Jpn., 52(1983) 157. 30 D. Kuhlmann-Wilsdorf and C. Laird, Mater. Sci. Eng., 46 (1980) 209. 31 R. Wang and H. Mughrabi, Mater. Sci. Eng., 63 (1984) 147.