Cyclic response and dislocation structures of AISI 316L stainless steel. Part 2: polycrystals fatigued at intermediate strain amplitude

Materials Science and Engineering, A186 (1994) 87-103

87

Cyclic response and dislocation structures of AISI 316L stainless steel. Part 2: polycrystals fatigued at intermediate strain amplitude Y u a n f e n g Li a n d C a m p b e l l L a i r d Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104 (USA) (Received May 3, 1993; in revised form September 10, 1993)

Abstract Polycrystalline AISI 316L stainless steel has been cycled at intermediate strain amplitudes. Cyclic response was analyzed in terms of the cyclic stress-strain curve (CSSC), softening behavior, the friction stress and the back stress. Dislocation structures were determined by transmission electron microscopy (TEM). It was found that cyclic softening behavior occurred and this has a significant influence on the dislocation structures by stimulating the activity of cross slip. The cross slip system becomes the second most important slip system, and causes the development of dislocation wall structure. Compared with the cyclic response of 316L single crystals, which are planar in slip character, polycrystals show a tendency towards wavy slip, despite the low stacking fault energy and high friction stress. It is concluded that grain boundaries, together with dislocation "starvation", have a major influence on the fatigue behavior of polycrystals by increasing the tendency to multi-slip, decreasing the capacity of strain transfer from grain to grain and from band to band, and changing the limit of stress or strain sustainable by a given dislocation structure in the sequence that occurs.

1. Introduction

In part 1 of this series [1], we analyzed the cyclic response of AISI 316L stainless steel single crystals, and reported the CSSC for the steel in monocrystalline form. Cyclic softening was observed at the onset of cycling and this phenomenon was explained in terms of (1) dislocation starvation and (2) the interaction between dislocations and interstitial solute atoms. Dislocation structures were determined by transmission electron microscopy (TEM), and were found to possess a planar slip character. However, in order to understand the overall features of the fatigue properties of this important engineering material, it is necessary to study specimens in polycrystalline form. A considerable literature exists on this topic. For example, Vingsbo et al. [2] performed fatigue tests on an austenitic stainless steel with compositions similar to that of AISI 304 L. The tests were conducted under constant stress control, and the results were analyzed in the form of the SIN curve. Dislocation structures were found in the forms of tangles, elongated loops and dislocation cells. There was a tendency for dislocations to transform from tangles to cell structure, when either the number of cycles or the stress amplitude applied was increased. Recently, similar investigations were also reported by Gerland et al. [3], Zhong et al. [4], and Jin et al. [5] on austenitic stainless steels, but the strain amplitude 0921-5093/94/$7.00 A'37)1 0921-5093(93j09473-V

was controlled. Tendencies similar to those noted above were also observed, i.e. dislocation structures would change in the sequence from planar dislocations, dipoles and multipoles, to dislocation "ladders", walls and cells, when either the number of cycles applied or the applied strain amplitude increased. However, noone seems to have addressed the mechanism of the change in structure specifically for stainless steel, rather they view it as a variant of that which occurs in pure copper under cyclic deformation. Austenitic stainless steel is a material of low stacking fault energy (LSFE), and is widely believed to possess a planar slip character. Kuhlmann-Wilsdorf [6] indicated that the "natural" dislocation structure in LSFE materials, such as austenitic stainless steel, should have the form of a Taylor lattice containing multi-Burgers' vectors, or "carpet" structure, which is different from the structure expected in copper. In part 1, TEM evidence indicated that single crystal stainless steel shows mainly planar slip character when subjected to cyclic deformation [1]. The relationship between these results and those reported for polycrystalline steel noted above is unclear. Vingsbo et al. [2] claimed that: "Cross slip takes place during cyclic loading in the present material also at moderate stress amplitudes, in spite of the very low stacking fault energy." However, without detailed analysis on the cyclic softening behavior, the question as to why cross slip happens, which is important in the © 1994 - Elsevier Sequoia. All rights reserved

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Y. Li, C. Laird

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Behavior of AIS1316L stainless steel

TABLE 1. Chemical composition of the steel (wt.%) C

Mn

P

S

Si

Cr

Ni

Mo

Cu

Co

N

Fe

0.014

1.58

0.033

0.019

0.15

16.43

11.41

2.06

0.38

0.30

0.064

bal.

transformation of dislocation structure, cannot be answered satisfactorily. Cyclic softening, which occurred in the present study, has also been observed by other investigators, when the strain amplitudes were relatively low [3, 4]. This behavior might well be a common feature of the austenitic stainless steels. Therefore, the interactive effect of the cyclic softening behavior and the dislocation structures should also be evaluated. We report fatigue tests on polycrystalline specimens, in an attempt to answer the questions cited above, and to resolve the differences between the dislocation structures reported in polycrystals and those in monocrystals described in part 1 [1].

TABLE 2. Mechanical properties of polycrystalline AISI 316L stainless steel" Hardness

Tensile strength (MPa)

Yield strength (MPa)

Elongation (%)

Area reduction (%)

76 (RB)

540

200

55

65

'~These properties meet the ASTM standard.

2. Specimens and experimental procedures Most of the experimental procedures were given in part 1 [1], therefore only those particular to polycrystals are described here. The material used in this study was commercial AISI 316L stainless steel. Its composition is given in Table 1, and the mechanical properties of the polycrystalline form of the material are given in Table 2. The configuration of the test specimens was similar to that of the single crystals. Before the tests, the specimens were annealed in vacuum at 1050 °C for 1 h, then quenched in water. The typical microstructure of a polycrystal obtained from this annealing is shown in Fig. 1. A uniform distribution of the grains with a size of 100/~m was obtained, together with a high density of annealing twins. Linear stringlets of second phase particles, probably non-metallic inclusions, are seen to be arranged parallel to the longitudinal direction of the material; these were produced during manufacture by drawing. As expected, these particles were very stable and were not affected by heat treatment, even at a temperature as high as 1300 °C. Fatigue tests were conducted under control of the plastic strain, and both constant strain and multi-step tests were run. For most of the constant strain tests, the strain amplitude was chosen as 1 x 10 -3, which lies within the plateau region corresponding to the CSSC of a single crystal (see part 1 [1]). At this strain level, a mixture of planar dislocations and wall structure was expected. The method for preparing TEM samples is similar to that given in part 1, except that thin slices were

Fig. 1. Microstructure of polycrystalline AISI 316L stainless steel after annealing, longitudinal section, 100 ×.

obtained by spark-cutting the polycrystal specimens parallel to the longitudinal direction.

3. Experimental results 3.1. Multi-step tests

A step ascending test was performed first with specimen P0-11, in order to obtain the CSSC for this testing mode. The total sequence contained ten steps, covering the strain range from i x 10 -4 to 2 x 10 -3. At each step, the specimen was cycled for several thousands of cycles, until saturation was reached (see Fig. 2). The hardening (softening) curves for typical steps are shown in Fig. 2(b). When epl<-1 × 10 -3, the material underwent softening. For the first step, apparently yield point behavior occurred at the beginning of the test. When epl> 10 -3, the softening behavior stopped and cyclic stability was observed. The softening phenom-

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enon was also observed in constant strain tests at strain amplitudes up to 2 x 10- 3 The CSSC obtained from the step test of Fig. 2 is shown in Fig. 3(a). This curve can be viewed as comprising three parts. (1) At the low amplitude end, the saturation stress increases rapidly with increasing strain amplitude. (2) When the strain amplitude reaches about 4 x 10 4, the slope of the CSSC gradually decreases. From 6 x 10 -4 to 2 x 10 -3, the saturation stress varies linearly with applied strain. (3) At the upper end of the CSSC, the slope once again tends to increase. Similarly to the procedure used in part 1, Cottrell's method [7] was employed to analyze the friction stress o~- and back stress a b, which were deduced from the hysteresis loops of the step tests, and the saturated values of these stresses are plotted in Fig. 3(a) along with the peak stresses. It can be seen from these curves (Fig. 3) that the friction stress changed little during the ascending step test, implying that the main source of the inelastic resistance to the dislocation movement did not change within this strain region. On the other hand, the back stress increased with applied plastic strain, behavior which we attribute to the increased elastic interaction between moving dislocations and relatively immobile

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dislocation clusters, as the dislocation density became higher and higher. The ratio of the friction stress to the maximum flow s t r e s s orf/Oma x is plotted in Fig. 3(b) as a function of strain amplitude. When the strain amplitude was increased, the af/Oma~ ratio was observed to decrease gradually, i.e. the back stress became an increasingly important contributor to the cyclic response. The same tendency was observed by Hong and Laird [8] in fatigued Cu-16A1 single crystals in the plastic strain amplitude range 4.3 x 10 4 < 7'p]< 1.4 x 10 3 Another step test was conducted on specimen P012, but in a different way. The specimen was first ramp loaded for 20 000 cycles under stress control using the procedure customarily employed by Neumann and his coworkers. During this period, the applied stress was increased continuously from zero to 200 MPa. After the ramp test, the control mode was switched to strain control, and a step ascending test was performed using 500 cycles in each step. Results are also reported in Figs. 3(a) and 3(b) using open squares. The differences between the two step tests thus reported are seen to be minor, except at the very beginning of the tests, where the flow stress of the ramp loaded specimen was lower than that of the sample cycled without a ramp.

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3.2. Constant strain test Constant strain cycling was performed at a plastic strain amplitude of epl = 1 x 10-3 with four polycrystalline specimens having code numbers P0-4 through P09. The results of these tests are shown in Fig. 4, and the agreement between them is seen to be very good. A stable value of the flow stress, measured to be 210 MPa, was reached at about 2000-3000 cycles. The resolved friction stress and back stress were 120 MPa and 90 MPa respectively. During the test, the ratio of O'f/Omax w a s about 57% without significant change (Fig. 4(b)). It can be seen that the multi-step test and the constant strain test have the same friction stress (Fig. 3(a)), which means the source of the inelastic resistance to moving dislocations was the same for each test. However, the flow stress and back stress were different for these two cases. Generally, the ramp loading and step incremental tests act to improve the strain compatibility between different grains [9]. As a consequence, the percentage of grains deforming with single slip among the whole grain population will increase. However, a constant strain test is expected to produce more multi-slip in the grains [9], which will in turn produce more dislocation pile-ups. It is apparent that the high flow stress for the constant strain test was a direct result of the high back stress.

It was observed that, for some tests, when a specimen was cycled for a longer time, the flow stress and the friction stress would finally tend to increase, indicating that gradually increasing secondary slip and cross slip had produced a noticeable effect of the dislocation interaction on the friction stress. The same tendency was observed by other investigators [10] in fatigued copper single crystals, and this behavior can be viewed as a form of "secondary hardening". The cyclic softening behavior shown in Fig. 4(a) is similar to that observed in the step ascending test; see the softening curve for the first step (10-4) in Fig. 2(b). For the first two or three cycles, the softening rate was very high, which is probably related to the difficulty of generating dislocations in a virgin specimen, in order to carry the applied strain. Afterwards, the softening rate decreases quickly to a low value, and continues to decrease for thousands of cycles.

3.3. Surface morphology Figure 5(a) shows an SEM photograph taken from a polycrystal specimen which was fatigued at a plastic strain amplitude ep~= 5 × 10 -4 for 30 000 cycles. The surface grains are seen to be filled with fine slip lines,

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Fig. 5. (a) Slip lines o n a polycrystal specimen, P0-1, fatigued for 3 0 0 0 0 cycles at ep~=5 × 1 0 -4, S E M . (b) Fatigue extrusions f o r m e d o n polycrystal s p e c i m e n P 0 - 7 after 36 0 0 0 cycles at epl = 1 X 10 -3.

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Behavior of A1S1316L stainless steel

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and the slip appears single even adjacent to grain boundaries. Thus, for low strain amplitude, the material showed planar slip character similar to that in a single crystal. When the stainless steel was fatigued at epl = 1 x 10-3, the plastic deformation intensified within the grains, and the amount of multi-slip also increased. At high magnification, persistent slip band (PSB) structure could be observed in some of the grains, which is a structure typical of wavy-slip materials. Figure 5(b) shows examples of extrusions formed in the PSBs, which we never observed in single crystals. Although the size of these extrusions is smaller than that observed in copper [9], they undoubtedly provide evidence of strain localization. Note the grain boundary shown in Fig. 5(b). For polycrystal specimens, we consider the grain boundaries to have played an important role in the plastic deformation. Dislocation pile-ups at the grain boundary could change the local stress status. As a result, the probability of cross slip would be increased, despite the low stacking fault energy, and wavy slip behavior would ensue. Therefore, a polycrystal specimen can exhibit wavy slip behavior. Nevertheless, the cross slip would still be more difficult than in copper, and this explains the smaller size of the PSB phenomena. As commented by most investigators who have dealt with the fatigue of copper, the presence of the PSBs marks a state of strain localization which provides preferential sites for crack nucleation [11-13]. The same behavior was observed in the present studies. Microcracks were found to form at the extrusions in polycrystal specimens, and propagate along the slip band. 3.4. Dislocation structures

Figure 6(a) shows an example of the microstructures observed in the TEM foils, in which a stringlet of second phase particles, having various diameters, is observed, similar to those shown in Fig. 1. The alignment of stringlets of second phase particles was found useful for indicating the stress axial direction of the TEM specimens. It was found that in most grains, which had been deformed by single slip, the slip systems were the primary systems with respect to the applied stress direction. Accordingly, in the following paragraphs, the labels of the slip systems, which may appear on the transmission electron micrographs, are referred to the stress direction. Second phase particles might have an influence on the dislocation structures locally, especially when the particles have large diameters. As shown in Fig. 6(b), dislocation tangles were observed to form around such a second phase particle, where primary dislocations have been both blocked (stored) and created as geo-

Fig. 6. (a) Dislocation structure in steel cycled at epl= 1 x 1()-); single slip dominates in the grain; overall features of the dislocation structures are not altered by second phase particles. (b) Dislocation tangles formed around a second phase particle.

metrically necessary dislocations [14, 15]. However, as seen in Fig. 6(a), the second phase particles do not affect the overall dislocation structures. Dislocation walls have developed near both the twin boundary and grain boundary, rather than in the vicinity of second phase particles. For polycrystals fatigued at a strain amplitude of 1 x 10 --~, a variety of types of dislocation structures was observed, such as stacking faults, tangles, dipoles and multipoles, microtwins, walls and ladder structures. However, large portions of the dislocation structures

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Behavior of A1S1316L stainless steel

were found to consist of stacking faults, dislocation tangles and multipoles. These dislocation structures were extended on the primary plane, consistent with the planar slip nature of this material. Even for the wall and ladder structures, the trace of the planar slip could be found by examining the micro-details of the structure. Figure 7(a) shows dislocation structures observed in specimen P0-4, which had been fatigued at ep~= 1 × 10-3 for 50 000 cycles. In this photograph, secondary slip is evident to some extent (arrowed). However, debris from primary slip, such as planar arrays of dislocations and stacking faults, can be found everywhere. Figure 7(b) shows an enlarged image of the center part of Fig 7(a), which indicates that many of the

Fig. 7. (a) Dislocation structure observed in polycrystal P0-4, ept= 1 × 10 -3, mainly primary edge dislocations in planar arrays; there are also "stacking faults". (b) Enlarged image from the center part of (a), showing that the "stacking faults" actually consist of many primary dislocations.

"stacking faults" are not real faults but actually consist of closely packed dislocations. These dislocations lie on the primary slip plane with edge orientation. In one of the slip bands, the primary dislocations are cut along the trace of the cross slip plane, a phenomenon similar to that observed in single crystal specimens [1]. Obviously, such behavior is related to the planar slip nature of materials which have low stacking fault energies. It should be noticed that because of the low stacking fault energy, a perfect dislocation is separated into two partials with a stacking fault between them. When many pairs of partials, with the same Burgers' vector, are closely packed together so as to define a planar defect, an image similar to that of a stacking fault is shown on the photograph. Figure 8(a), which was taken under a weak beam condition, shows that the closely packed dislocations

Fig. 8. (a) Dislocauon dipoles and multipoles revealed under weak beam condition. (b) Planar dislocations packed in the primary slip planes.

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Behavior of AlS1316L stainless steel

consist of dipoles and multipoles of plus and minus dislocations, typical of a low energy dislocation structure. Slip bands containing only one sign of dislocations were also observed; see slip bands B and C in Fig. 8(b). However, these dislocations are separated in distance, due to the absence of a close stress screening effect from oppositely signed dislocations, or due to long range interactions between dislocations of the same sign. Dislocation wall structures were occasionally observed. A typical example is shown in Fig. 9, where planar arrays of dislocations and stacking faults are observed on the left side of the field of view, and poorly formed walls on the right side. Unlike walls in copper, in which the structure forms by breaking down the three-dimensional loop patches, the wall structures in stainless steel are formed from planar arrays of dislocations. In Fig. 9, the dislocation walls seem to develop from a twin boundary where secondary slip can be stimulated [16]; notice the dislocation clusters at A, B, and C. At position D, patches of dislocations seem to be in the act of developing a wall, evidence for which is provided in the magnified images shown in Fig. 10. The three images shown in Fig. 10 were obtained with different diffraction vectors which reveal

93

three intense sets of dislocations combining to make a disorganized wall. A triangular mark is provided to indicate the traces of the primary, cross-slip and conjugate planes. In the photographs shown in Figs. 10(b) and 10(c), which were taken under the [202] and [111] reflections respectively, the dislocations on both the primary and the cross slip planes are invisible. Therefore, they must have the same Burgers' vector, i.e. b=~[i01]. Similarly to the case shown in Fig. 7, stacking fault-like fringes are observed parallel to the traces of the primary slip plane and the cross slip plane, an indication of planar defects on these planes. The residual contrast in both Figs. 10(b) and 10(c) implies that secondary dislocations play an important role in the wall-forming process [17], by helping to cluster the primary dislocations and lowering the energies of all the dislocations in the three systems. Figure l l(a) shows another example of the wallforming process. During cyclic deformation, the dislocation network, which consists of primary and cross systems, shrinks gradually. Notice the residual contrast of dislocation debris on the primary plane and the cross slip plane, arrowed, in the upper right corner of the photograph. These stacking fault-like fringes indi-

Fig. 9. Dislocation structures observed in polycrystallinesteel, showingplanar dislocations in process of developinginto wall structure.

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Behavior of AIS1316L stainless steel

primary 1 pm Fig._10. Enlarged image of patches of dislocations shown in Fig. 9, position D. Images were formed by using different reflections: (at [111]; (b)[202]; (c)[111].

cate the existence of point defects and small dislocation loops, left behind after the dislocations on these planes glided into the embryonic wall and underwent clustering and annihilation. Figure ll(b) shows details of a dislocation wall, observed in the same grain as that in Fig. 9. Apparently, it consists of primary dislocations on both the primary plane and the cross slip plane. The dislocation wall structure observed in this photograph is much different from that observed in copper, which is believed to consist mainly of primary dislocations on the primary slip plane [18-20]. Grain boundaries are expected to be important in the deformation behavior of polycrystals. However, under the plastic strain used in the present study, single slip was observed in most grains, usually the primary slip system referred to the direction of the applied stress. Occasionally, multi-slip was observed. Figure 12 shows a grain in which at least four slip systems were active. These systems appear to have been equally deformed, even from the very beginning of the cycling, because no stacking faults or closely packed multipoles were found. Another feature of this structure is that dislocation walls were not observed in grains where

multi-slip occurred. This behavior indicates that, in stainless steel, wall-like structure is related to dislocation processes involving a single Burgers' vector. However, the multi-slip structure seen in Fig. 12 is similar to that observed in both monocrystalline and polycrystalline Cu-16A1 specimens, typical of planar slip material [8, 21, 22]. Dislocations were confined to their own slip planes, and the interactions between dislocations of different slip systems produced localized networks in which Lomer-Cottrell locks formed as barriers to the dislocation movement. We consider that further deformation, by increasing either the number of cycles or the strain amplitude, is accommodated by decreasing the distances between slip planes containing planar arrays. As a result, denser dislocation networks are gradually developed, as shown in Fig. 12(b). These appear similar to "carpet" structure [6]. Surface observations such as that shown in Fig. 5(b) indicated that strain localization also occurred in stainless steel, as shown in Figs. 13(a) and 13(b). The two foils illustrated were taken from grains lying in the specimen surface. Apparently, the dislocations in the strain localized bands are mainly planar arrays of

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Fig. 11. (a) Dislocation patches in the wall structure comprising dislocation networks; note the residual contrast of the slip planes in the upper right comer, arrowed. (b) Typical structure observed in dislocation walls; the dislocation density on the cross slip plane is quite high.

primary dislocations. The distance between the indicated slip bands measured about 3 ~m, very close to the distance between the extruded bands shown in Fig. 5. Within each band, there are two to four active slip planes, and the width of the band is about 0.4/~m, much narrower than those observed in copper (about

Fig. 12. (a) Multi-slip observed in some grains; this structure is similar to that observed in Cu-16AI alloy. (b) Dense dislocation network produced by multi-slip, similar to "carpet" structure.

1/~m) [23]. Because strain localized slip bands were not observed in single crystal specimens, we believe that the strain localization shown in Fig. 13 is a grain boundary effect. Strain compatibility at a grain boundary will affect the strain distribution inside the grain. As shown in Fig. 13(b), both strain localized bands and uniformly distributed slip planes were observed in different parts of the same grain. A grain boundary is

visible in the top left of Fig. 13(b). This boundary was observed to terminate (in a rightward direction) at a triple point, aligned with respect to the slip bands so as to separate the regions of localized slip and more uniform slip. We believe that different compatibility conditions, with the upper grain neighbor and with the right neighbor, produced these differences in the slip behavior.

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Behavior of AIS1316L stainless steel

Because of the strain inhomogeneity shown in Fig. 13(b), it can be expected that the stress status near the grain boundary region would be complicated, which can in turn create secondary dislocations, interactions with the primary slip, and pile-ups, although the last

Fig. 13. (a) Evidence of strain localization (or PLB structure) in a surface grain, mainly consisting of planar arrays. (b) Inhomogeneous structure in a surface grain; part of it shows strain localizatlon.

might be short-lived in cyclic deformation. However, the near-boundary stress state has only a minor effect on the dislocation structures in the center of the grain, probably owing to surface relaxation, because a surface grain is involved here. Figure 14 shows an example of strain localization observed in a grain inside the specimen, where the planar slip character is also apparent. Four heavily deformed slip bands were observed to penetrate the grain from a neighboring grain without interruption. Within these bands, the dislocation density is very high. The content of secondary dislocations is also significant. Near the grain boundary, dense dislocation pileups and tangles indicate the complicated stress status required by strain compatibility. These dislocations extend towards the interior of the grain, and react with both dislocations in the localized slip bands and with adjacent slip bands. This multi-slip produces Lomer-Cottrell locks, and dislocation nodes, as shown in Fig. 14. Comparison of the dislocation structures shown in Figs. 13 and 14, and comparison with persistent L/iders' band (PLB) structure in Cu-A1 alloy [22], suggests that strain localization in stainless steel is produced by planar slip dislocations, unlike those in copper, where PSB "ladder" structure is the main indicator of strain localization. Dislocation ladder-like structure was also observed in a polycrystal specimen, P0-7, as shown in Fig. 15. However, the chance of finding ladder structure is judged to be very low. Of the 4 0 - 6 0 foils we have examined, only three were found to contain "ladder"like structures. Since there are generally more than ten

Fig. 14. Strain localization observed in an interior grain; dense slip bands similar to PLBs in Cu-16A1 alloy.

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Behavior of A1S1316L stainless steel

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in TEM studies, "PSB" is often used in reference to the characteristic "ladder" structure typically observed in fatigued copper. Since typical PSB structure, exactly like that in copper, has not been observed in the present study, we prefer to use the term PLB to describe the dislocation structure associated with strain localization. The connection between the morphology of slip bands observed on the surface by SEM and that of slip bands observed in the bulk by TEM is not straightforward. Since the spacing and width of the extrusions shown on the surface (illustrated typically by Fig. 5(b)) correspond to those of the slip bands observed by TEM, we believe that the surface extrusions are in fact closely related to PLBs, rather than to PSBs. However, this conclusion does not completely exclude the possibility that PSB ladder structure could be found in the surface layers of stainless steel. Further TEM investigation is needed.

4. Discussion

4.1. Cyclic softening phenomenon Fig. 15. "Ladder"-like dislocation structure found to develop near a grain boundary region in stainless steel.

grains in each foil which are thin enough to be viewable, the chance of finding a "ladder" is less than 1%. Even for the ladder structure, the planar slip character can be observed both in the ladder wall (arrowed in Fig. 15) and in the matrix from which the ladder structure has developed (arrowed in Fig. 15). Furthermore, the "ladder"-like structure shown in Fig. 15 covers only one third of the grain, and the rest of the grain (on the right side of the photograph) contains only planar dislocations similar to those shown in Figs. 6 and 9. This feature is different from the PSBs found in copper polycrystals, in which the PSB ladders can often penetrate the whole grain [24]. Compared with those in Figs. 6 and 9, the "ladder rungs" shown in Fig. 15 can be considered as dislocation walls similar to those shown in the other two photographs. The "'matrix" structures between two adjacent "ladders", are attributed to the strain inhomogeneity near the grain boundary. Therefore, we believe that the "ladder"-Iike structure in Fig. 15 is a phenomenon produced by local stress concentration, rather than a sign of strain localization. After all, the ladders are quite wide in Fig. 15. It should be clarified that, in Fig. 5(b), we used the term "PSB" to describe the surface morphologies of regions of localized slip, including extrusions, which look similar to those of PSBs in copper. This terminology agrees with the original definition of PSBs, i.e. "persistent" and "strain localized" slip bands. However,

In part 1 [1], we reported that cyclic softening was observed in single crystal stainless steel. We also analyzed why cyclic softening occurred in a well annealed crystal, and attributed this phenomenon to the following three factors: dislocation starvation, interstitial solute atoms, and the transition of dislocation structures. In a polycrystal specimen, cyclic softening also occurred. For example, in Fig. 2(b)(the first step in a step ascending test), a rapid decrease in flow stress occurs in a virgin specimen cycled at low plastic strain amplitude 1 x 10 -4. The stress drop due to the softening is about 30 MPa. For a constant strain test at a plastic strain amplitude 1 x 10 3, the stress drop can be as high as 60 MPa (see Fig. 4(a)). Just as we concluded in part 1, we believe that the cyclic softening, for polycrystal specimens fatigued in the present range of strain amplitudes, is caused mainly by dislocation starvation. This conclusion can be justified by comparing the softening curves of a constant strain test (Fig. 4(a), ep~= ] x 10 3) with that in an ascending step test at ~p~= I x 10 -~(Fig. 2(b)). In a step ascending test, the cyclic softening behavior can be observed in several steps (Fig. 2(b)). After saturation at a given strain amplitude, the specimen contains a certain population of dislocations. However, this population is not enough to carry the plastic strain at the next higher step. As a result, more dislocations are generated when the strain amplitude is increased and this multiplication causes softening to occur again (see the softening curves at 2 x 10 4 and 4 x 10 -4 in Fig. 2(b)). However, as the strain amplitude is increased

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Behavior of AISl 316L stainless steel

from step to step, the softening rate will decrease continuously, because more and more dislocations are available for carrying the strain. That explains why the initial flow stress of the constant strain test (lack of dislocations) is much higher than the flow stress for the corresponding amplitude of the step test (a large number of dislocations is available). Unlike the experimental results obtained in pure copper (high stacking fault energy material) and in Cu-16AI (a typical low stacking fault energy material), in which cyclic hardening was observed, cyclic softening seems to be a common feature for the austenitic stainless steels, especially when the strain amplitude is low [3, 4]. Cyclic softening in stainless steel has been previously explained [3] as being caused by dislocation transformation from matrix stucture to PSBs or wall structure, similar to the overshooting phenomenon observed in copper [25, 26]. However, this explanation cannot explain why softening occurs at the very beginning of cycling when the strain amplitude is low, and why the drop in flow stress is so large, about 23% for a polycrystal cycled at 1 × 10-3. The major factors which would affect the hardening behavior of the specimen at room temperature include (1) the ease of operating dislocation sources, (2) the dislocation density in the specimen, and (3) the solute content. In general, for a virgin annealed specimen, which has no difficulty in generating dislocations, cyclic hardening by dislocation accumulation ("statistical" dislocations) will be the main feature during the initial cycling, until possible transformations in dislocation structure subsequently occur when the dislocation density is high enough. That is why "overshooting" occurs in copper only after hundreds of cycles. If solute atoms are present and exert an effect on the hardening behavior, they can be expected to be more potent when a certain amount of dislocations (less than that required for structure transformation) has been generated, especially for polycrystalline specimens. Therefore, the initial, rapid decrease in flow stress observed for stainless steel must be caused by the difficulty in generating dislocations, which we term "dislocation starvation". In some sense, this phenomenon is similar to the yield-drop produced in some metals by monotonic loading. If the strain amplitude is so high that a large density of dislocations must be created to accommodate the applied strain, then interactions between these dislocations, during subsequent cycling, will harden the specimen and overshadow the possible effects caused by dislocation source problems and by solute atoms. Such dislocation hardening explains why cyclic hardening occurs at high strain amplitudes, because enough dislocations have been generated in the first cycle.

For polycrystals cycled at 1 x 10 -3, about 80% of the grains were observed to be deformed in single slip, as shown in Figs. 6 and 7. The content of secondary dislocations was very low, however, and most of them were located near grain boundaries. This behavior, we believe, results from dislocation starvation. When a grain is deformed, one slip system within this grain is preferentially activated, probably because it has an appropriate orientation or suitable stress status. Then, this system becomes cyclically softened, which means the stress required to move dislocations in the system is much lower than that to operate other systems. As a consequence, other slip systems are inhibited from operating, unless the stress status changes later. For the same reason, we believe, the grains with multi-slip (Fig. 12) must have deformed by multi-slip from the very beginning of cycling, which means the stress fields around those grains provided nearly equal opportunity for multi-systems to activate and multiply their dislocation sources. Finally, a uniform dislocation network is developed. Apparently, this explanation is suitable only to the strain amplitude at which the saturated stress is lower than the yield stress, such as the majority of amplitudes used in the present study. For high strain tests, cyclic hardening has been typically observed, and secondary slip operates significantly, which explains the prior observations of more regular dislocation walls and cell structure [3, 4]. 4.2. Cross slip behavior

Another phenomenon, which is closely related to that of cyclic softening, is the cross slip behavior. Stainless steel is a low stacking fault material; this is responsible for the observed planar slip character, especially in single crystals. Nevertheless, considerable amounts of cross slip were observed in both single crystals and polycrystals, when subjected to cyclic deformation, consistent with reports of cross slip in other planar slip metals [27]. For all the TEM foils we examined in polycrystalline specimens, dislocation walls were exclusively observed in the grains which were previously deformed by single slip (see Figs. 6 and 9). When the walls are formed or in the process of developing, there are mainly two systems in operation, the primary and the cross slip, with a Burgers' vector common to both (Fig. 10). The dislocations in the cross slip system are also in edge orientation, with density comparable with that in the primary plane. The question as to why the cross slip system and not another system participates in the wall forming process can only be answered, we believe, on the basis of cyclic softening (or dislocation starvation). When the primary system is hardened to such a level that another system is required to operate, the system

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99

Behavior of AIS1316L stainless steel

with lowest stress necessary to activate its dislocation sources will come into action. Obviously, the primary dislocations make sources available to the cross slip system, and the stress for cross slip is much lower, by about 60 MPa for ep~= 1 x 10 3, than that for creating dislocations in other systems. This behavior, in some sense, is similar to the latent hardening phenomenon found in single crystal copper [28], by which the deformation in one slip system changes the hardening behaviors of other slip systems. In stainless steel, the provision of dislocation sources easily to a second system can only happen between two slip systems which share the same Burgers' vector. In part 1, we mentioned that the relative ease of cross slip is the main reason for the observed difference in dislocation structures between stainless steel and Cu-16A1 single crystals, i.e. the massive annihilation of dislocations in the dislocation-sparse channels produces the dislocation clusters in stainless steel. In polycrystals, the cross slip effect is even larger, which finally creates wall structure. This process can be described as follows. First, consider that most of the grains in a polycrystal are deformed by single slip, in which primary edge dislocations are closely packed into planar arrays, such as the slip bands a, b, and c in Fig. 8. With continuing deformation, the stress in these slip bands increases due to the increase in dislocation density, especially in slip bands b and c, where stress screening from dslocations of opposite sign is absent. Then new slip bands in the primary system are created mainly by a cross slip mechanism, owing to starvation of dislocation sources. For those grains which still remain in single slip, this mechanism of primary multiplication is similar to that which occurs in a single crystal. However, owing to the grain boundary effect, there is a portion of grains in which the stress for carrying the applied strain in the cross slip plane is less than that for creating new slip bands in the primary plane. Furthermore, dislocation sources for operating the cross slip system are readily available. Therefore, the cross slip system becomes the second most important slip system in the grain. Because of the pull-push loading mode, the dislocations in the cross slip system also form in edge orientation. Since the dislocation density in the cross slip system increases with cyclic deformation, a two-dimensional dislocation network is gradually developed, as shown in Fig. 1 l(a). When the dislocation density in the cross slip plane is saturated, further deformation is enforced by creating new slip bands in the primary planes, and by developing channels. In Fig. 9, the distance between the primary slip planes in the walls (see blocks D and E in Fig. 9) has been decreased to one half or one third of that shown on the left side of the photograph, where

the dislocations are closely packed in primary planes without cross slip. Figure 16 shows schematically how the inter-band distances can be reduced by dislocations fed back from the cross slip plane to the primary planes. In this figure, the solid horizontal lines represent active slip bands in the primary system, while the broken horizontal lines indicate the newly developed slip bands in the primary system. The angled line represents the trace of an active cross slip band from which dislocations are cross-slipping back onto the primary system and triggering the development of new slip bands. In Fig. 16(a), the dislocations on the adjacent primary slip bands have the same sign. In order to balance the elastic stress, a slip band is produced by feeding back an oppositely signed dislocation from the cross slip band, and the interband distance is decreased by one half. In Fig. 16(b), the dislocations on the adjacent primary slip bands have opposite signs; consequently, two slip bands have to be introduced when the interband distance is decreased so as to balance the dislocation signs. In this case, the distance is reduced by one third. For the same reason, the interband distances in Figs. 16(c) and 16(d) are reduced by one half and one third respectively, depending on the signs of the dipoles on the adjacent primary slip bands. However, the capacity of the edge dislocation arrays, in both slip systems, for carrying the applied strain is limited since the slip distances are short, and the density of edge dislocations on both systems will soon be saturated. Ultimately, dislocationfree channels are developed, in which the strain can be carried more effectively by screw dislocations gliding over longer distances.

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Behavior of AISI 316L stainless steel

Depending on the local stress status, the channels can be developed either before (see position E in Fig. 9) or after (Fig. 1 l(a)) the deformation in the cross slip planes has been intensified. Therefore, the dislocation structure in Fig. 9, especially at position E, represents a critical moment in which the values of the stresses required for producing competing processes are very close. These processes are: (1) creating new slip bands in the primary system; (2) stimulating activity in the cross slip system; and (3) producing walls and channels. The role of secondary dislocations is critical to the wall forming process. Because they have the same Burgers' vector, the edge dislocations in both the primary plane and the cross slip plane may move relatively independently. Therefore, secondary dislocations are necessary to stabilize the wall structure, by interaction with the primary dislocations. Compare the shape of the dislocation patches shown in Fig. 10 with the trace of the conjugate plane, and an alignment tendency can be noted. We concluded that secondary dislocations (probably conjugate dislocations) are helping the patches to cluster, or preventing them from spreading out, or both. The interaction of primary and conjugate dislocations would produce a local twist force that favors the primary dislocations adopting a screw orientation. The screw dislocations then move back and forth between primary and cross slip planes to clear out the channels by dislocation annihilation. However, if the density of secondary dislocations is comparable with that of primary dislocations (for example, because the grain was in a multi-slip condition at the start of cycling), then a uniform dislocation network of interacting arrays will form, instead of wallchannel structure (see Fig. 12). In such a case, cross slip is not needed to overcome dislocation starvation and the activity of cross slip is suppressed. However, a distinct example of wall-channel structure has not been observed in single crystals. Therefore, the observed difference between the planar slip character of single crystals and the more wavy character of polycrystals is attributed to the grain boundary effect. 4.3. Grain boundary effects

While we have reported here certain similarities between the cyclic responses of single crystals and polycrystals, for example the cyclic softening phenomenon, the planar slip character of the dislocations and slip bands cracking, differences between them are also observed, which are summarized in Table 3. We believe that all these differences are related to grain boundary effects, which emphasize the following: (1) an enhanced tendency to multi-slip; (2) a decreased tendency to transfer strain between slip lines and between grains; and (3) a variation in the stress-strain limits sustainable

TABLE 3. Differencesin the cyclicresponse of AISI 316L stainless steel singlecrystalsand polycrystals Singlecrystals

Polycrystals

Cyclic CSS curve Shows plateau Withoutplateau response Softeningrate Moderate High Friction stress Back stress much Back stress close and back stress lower than to friction stress friction stress Micro- Crossslip Observed in The second structure prolonged test mostimportant slip system Slip character Mainlyplanar Mixtureof wavy slip and planar slips Dislocation Planar arrays Planar arrays structure and walls Strain Not observed Observed localization by certain types of dislocation structure. These factors are now discussed. (1) Multi-slip is often observed in polycrystal specimens, partly owing to the fact that individual grains can have different orientations with respect to the applied stress. Those grains with a hard orientation are most likely to be deformed by multi-slip. Another source, maybe the most important source, of multi-slip comes from the requirement of strain compatibility between different grains, which are traditionally regarded as needing at least five slip systems. Therefore, even a grain with an orientation soft to the applied stress may be deformed by multi-slip. It has been demonstrated that single crystal copper has a high hardening rate and a high saturation stress, if it is deformed by multi-slip [29]. A similar tendency was also observed in single crystal stainless steel, by the present authors [1]. Therefore, it is difficult for a polycrystal to show a CSS curve with the plateau region sometimes expected of single crystals, because the tendency to multi-slip will be intensified by an increase in strain amplitude. It should be pointed out that, owing to the cyclic softening effect observed in the present study, single slip was observed in most grains (about 80% of them), similar to the results obtained by other investigators at low strain amplitude [3, 5]. However, the tendency towards multi-slip still exists, which produces the stress status favoring the formation of wall-channel structures in polycrystals. (2) For a single crystal under fatigue, the amount of plastic strain carried by an individual slip plane or slip band changes often, especially during the hardening stage. For example, strain localization occurs in copper single crystals during both rapid hardening and saturation, i.e. plastic strain is transferred from one part of the matrix to another and then from the matrix to the

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Behavior of AIS1316L stainless steel

developing PSBs. On the other hand, strain spreads out differently in Cu-16A1, i.e. plastic strain is transferred from one slip band to another. For polycrystals, this strain-transfer is not so easy, because of the compatibility requirement. During cycling, the intragranular strain-transfer which is favored by one particular grain may not be favored by other neighboring grains. Thus, such transfer will be delayed or cancelled. Because of such effects, the fatigue properties of polycrystal and monocrystals should show some differences. For planar slip material, the polycrystal specimen will show some wavy slip features; since the plastic strain cannot effectively spread out, it becomes localized, as shown in Figs. 13 and 14. On the other hand, some limited tendency to planar-like behavior should be observed even in polycrystalline copper, because strain localization is limited by the grain boundary effect. For example, it has been observed by other investigators [24] that PSB ladders are often found as narrow slabs in polycrystals, where the loop patches (matrix structure) occupy the greatest area of the photograph. They also reported that, even at fairly high strain amplitudes, grains showing nothing but matrix structure are easy to find [24]. In polycrystals, strain transfer also occurs between grains, in order to maintain strain continuity. Such strain transfer between grains requires a higher stress than driving dislocations within the grains, which causes the differences in softening rate and flow stress between a polycrystal and a single crystal. Figure 17 shows the softening curves for both a single crystal and a polycrystal cycled under the same plastic strain amplitude. In the figure, the stress value of the single crystal curve has been multiplied by the Taylor factor, 3.06, the standard f.c.c, parameter used by investigators who have attempted to correlate the flow stresses of single crystals and polycrystals [9]. Also included in Fig. 17 are the curves for the friction stresses and back stresses for both forms of crystal. Figure 17 shows the saturated stress is higher for the polyerystal than for the single crystal. Analysis of the friction stress and back stress indicates that the observed difference is mainly due to the back stress component (Fig. 17), which indicates the effect of dislocation pile-ups at grain boundaries. However, the big difference between the single crystal and the polycrystal is the softening rate, which is higher in the polycrystal than in the single crystal, as evidenced in Fig. 17. The friction stress is controlled by the short range resistance to dislocation movement [20, 30], which may be influenced by both interstitial and substitutional solutes. This stress should remain stable after saturation has been reached. However, during the initial hardening (or softening) stage or during second dry hardening, it can vary with the applied number of

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cycles. In stainless steel, dislocation starvation can be considered to derive from short range obstacles. Figure 17 shows that the big difference in the softening rate between the single crystal and polycrystal is mainly due to the friction stresses, which implies that it is more difficult to generate enough dislocations in a polycrystal than in a single crystal, in order to carry the applied strain in a virgin specimen. It is apparent that, in order to carry the applied strain, dislocations must be generated in most, if not all, of the grains in a polycrystal. A high yield stress followed by, after a number of cycles, a large drop in flow stress produces a high softening rate for polycrystals. Therefore, this behavior can be attributed to the combined action of dislocation starvation and grain boundary effect. (3) Grain boundaries can also affect the magnitude of stress or strain that a particular kind of dislocation structure can withstand. It has been observed in single crystal copper that the stress level at which the dislocation structure transforms from loop patches to PSBs is affected by the experimental conditions [25, 31]. Such behavior can also occur in polycrystals, probably even in a major way. As mentioned previously, inter-band strain transfer in polycrystals can be delayed or even stopped by the grain boundaries. Accordingly, for polycrystalline copper, the transition of the dislocation structure from loop patches to ladders is also delayed or stopped. Therefore, the flow stress in such loop patches must be higher than the stress in the loop patches of a single crystal specimen. For stainless steel polycrystals, the slip bands would have a tendency to spread out as the cycling continues, but strain localization is actually observed. Therefore,

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the internal stress of polycrystals is higher than that of single crystals, which may be one of the reasons why wall and "ladder-like" structures are easy to form in polycrystals. For those grains in which cross slip is not favored, the internal stress on the primary dislocations could be even higher. This interpretation is supported by TEM observations: for example, in Fig. 7, the dislocations are so closely packed in the primary planes that they look like a perfect "stacking fault". In single crystals, such a "stacking fault" is hardly observed.

4.4. Planar slipvs, wavy slip

In the present study, the fatigue behavior of the polycrystal exhibits both planar slip and wavy slip character. On the one hand, single slip was observed in most grains, in which planar arrays of dislocations dominate. On the other hand, the presence of dislocation walls indicates a tendency to wavy slip. In agreement with other investigators [2-5], the strain amplitude adopted in the present study represents the transition point at which dislocation structures change from low strain types to high strain types. However, it should be emphasized that planar slip still is the main feature of the cyclic deformation here. As discussed above, the "ladder"-like structure shown in Fig. 15 and the wall structure in Fig. 9 do not represent strain localization. On the contrary, strain localization occurred in the slip bands where planar dislocations were the main vehicles to carry the applied strain (Figs. 13 and 14). This structure is similar to that of the PLBs observed in Cu-16AI alloy [21, 22, 32] rather than that of PSBs in copper. The wall structures shown in Figs. 9 and 11 indicate another difference between the fatigue properties of copper and those of stainless steel. For the latter, the walls consist of a dislocation network which is rarely observed in copper. Kuhlmann-Wilsdorf reasoned, without actually making an experimental determination of dislocations, that the relationship between the dislocations in a network is in cross slip relation [6]. In Fig. 10, we have demonstrated that the dislocations on both the primary slip plane and the cross slip plane do have the same Burgers' vector or, in other words, another slip system has been activated to participate in the wall forming process. In copper, the applied strain is mainly carried by dislocations in the primary planes, while the cross slip plane acts as a bridge to transfer the dislocations from one primary plane to another. However, in stainless steel the cross slip system itself contributes significantly to the applied strain. Considering the importance of the dislocations, which lie on the cross slip planes, in the wall-forming process, we term the wall structure in stainless steel a "one Burgers' vector construction".

The reason for this behavior is a result of the low stacking fault energy (SFE). The SFE of stainless steel (about 20 ergs cm -2) is lower than that of copper (about 50 ergs cm-2), and somewhat higher than that of Cu-16AI alloy (2-4 ergs cm-2). This low SFE would have made cross slip difficult in stainless steel. However, dislocation starvation, as discussed above, has caused cross slip to be easier than expected simply because the stress is forced to be higher. After enough dislocations have been generated in the cross slip planes, the effect of the low SFE becomes important, because it casts the cross slip planes as the second most important slip system, until dislocation channels form. Therefore, even the wall structure still shows planar slip character.

5. Conclusions

A study of cyclic deformation in polycrystalline AISI 316L stainless steel has led to the following conclusions. (1) The cyclic stress strain curve obtained by cycling polycrystalline steel does not contain a plateau, unlike that for single crystals; this behavior is attributed to the continuous increase in back stress when the applied plastic strain is increased. (2) Cyclic softening occurs significantly in polycrystals, mainly owing to dislocation starvation, and partly owing to the interstitial solute effect and the transformation in dislocation structures. (3) The cyclic softening phenomenon has a major effect on the cyclic response of the steel by stimulating cross slip activity, which promotes the cross slip system to the second most important slip system. (4) Similarities between the cyclic responses of single crystals and polycrystals include: (1) cyclic softening behavior; (2) slip band cracking; and (3) planar slip character of the dislocations. These similarities are attributed to the intrinsic nature of the low SFE of the material. (5) Major differences between the experimental results of single crystals and polycrystals include: (i) a tendency towards wavy slip in polycrystals; (ii) dislocation wall structure formed in polycrystals; and (iii) strain localization, in the form of PLBs, observed in polycrystals. These differences are caused by the grain boundary effect. (6) Grain boundaries can affect the fatigue behavior of polycrystals in three ways: (i) increasing the tendency to multi-slip; (ii) decreasing the capability of strain transfer for both inter-band and inter-grain; and (iii) changing the stress or strain limit which a certain type of dislocation structure can sustain.

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Behavior of AlSl 316L stainless steel

(7) T h e fatigue behavior of stainless steel is different f r o m that of both typical wavy slip materials, such as copper, and typical planar slip materials, such as C u - 1 6 A I alloy. This behavior is closely related to the activity of cross slip of the steel, which is m o r e difficult than that in c o p p e r and easier than that in C u - 1 6 A I alloy.

Acknowledgments This work was s u p p o r t e d by the National Science Foundation under G r a n t D M R 9 0 - 1 4 3 8 1 , by the L a b o r a t o r y for Research on the Structure of Matter under G r a n t D M R 9 1 - 2 0 6 6 8 through help with facilities, and by the University of Pennsylvania. We are grateful for this support. We also acknowledge many stimulating discussions with the fatigue group at the University of Pennsylvania.

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