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Dislocation structures in fatigued polycrystalline copper
Acta metall, mater. Vol. 42, No. 1 I, pp. 3695-3704, 1994
Pergamon
0956-7151(94)E0160-I
Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0956-7151/94 $7.00 + 0.00
DISLOCATION STRUCTURES IN FATIGUED POLYCRYSTALLINE COPPER C. D. LIU, M. N. B A S S I M and D. X. Y O U Laboratory of Physical Metallurgy, Department of Mechanical Engineering, The University of Manitoba, Canada R3T 2N2 (Received 12 July 1993; in revised form 17 March 1994)
Al~tract--The dislocation structures in fatigued polycrystalline copper with small average grain size were investigated over a plastic strain range from 1.5 x l0 5to l0 -2. It was found that the dislocation structures are arranged into three types of configurations, which correspond to the three regions in the cyclic stress-strain curve. Cylindrical loop patch structure are present in region A for low strain amplitudes, similar to those observed previously in coarse grained polycrystals. Moreover, irregular loop patches are also formed in this region for small grains polycrystals rather than in region B at intermediate strain amplitudes for coarse grained polycrystals. In region B, persistent slip band (PSB) structures are formed but with a low volume content compared with the coarse grained polycrystals. In region C, at high plastic strains, the dislocation structures are dominated by dipolar walls. In addition, labyrinth structures are developed in region C instead of region B for coarse grained polycrystals. All the dislocation structures observed are viewed as forms of dipolized structures. A dipolized dislocation arrangement model is proposed to describe the formation process of dislocation structures. It is shown that all the dislocation configurations formed in cycled polycrystalline copper are low energy structures.
1. INTRODUCTION The cyclic behavior of f.c.c, metals was established through work on copper single crystals [1]. The cyclic stress-strain curve consists of three stages centered around a predominant plateau. The dislocation structures which develop in copper single crystals under cyclic deformation were investigated extensively [2-7], and differed for the various regions in the curve. Below the plateau, at low stress and strain amplitudes, the structures consisted of loop patches which were dominated by primary dislocations. In the plateau region, where the saturated resolve shear stress remained at the same value, the dislocation structure was composed of persistent slip bands (PSBs) embedded in veins of loop patches [8]. The PSBs were widely understood to consist of the well know "ladder" structure [9-11] where the strain is much higher than the overall strain applied to the crystal [9]. A two phase model was proposed by Winter [12] and substantiated by Finney and Laird [9] to describe the plateau feature in the cyclic stress-strain curve. It was found that the saturation stress in the region of the plateau was governed by the PSB, despite the variation in PSB content, under a large range of strain. Above the plateau, the dislocations formed cell structures through multiple slip, which gave rise to a higher saturated stress, During the last two decades, cyclic deformation of copper polycrystals was also studied extensively AMM
42/11 H
[13-27]. Early debate as to whether the cyclic stress-strain (C.S.S.) curve for polycrystalline copper contains a plateau now seems to have been resolved. In the course of the previous studies, it is evident that the plateau exists in the C.S.S. curve of coarsegrained (grain size > 100 pm) polycrystalline copper [14, 15, 18, 22] or tested under ramp loading [25], even it is much shorter than the one observed in single crystals. Dislocation configurations in the three regions of the C.S.S. curve of copper polycrystal with large grains display the same features as that in single crystals. Below the plateau, dislocations are arranged into the vein structure which consists of dislocation bundles [28]. In the region of plateau, the PSBs are observed in the bulk of the polycrystals [29]. When plastic strain amplitude is above the plateau, the PSBs gives way to the labyrinth structure [29] and the dipolar walls and the cell structure [14, 29]. However, cyclic deformation and dislocation structures of copper polycrystals with small grain size are less understood. In a recent work by the present authors, comprehensive cyclic tests were performed under constant low strain rate. They revealed the occurrence of a quasi-plateau in the C.S.S. curve of small grained polycrystalline copper [32]. The present investigation examines in detail the evolution of dislocation structures in small grained polycrystalline copper under cyclic loading, compared to that for coarse grained copper and single crystals reported in the literature.
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LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu
2. EXPERIMENTAL The material used in this study was 99.94% purity copper. Cylindrical specimens were machined with a diameter of 6.5 mm and a gauge length of 25 mm. All specimens were annealed in an argon atmosphere for 2 h at 620°C, prestrained to 10% plastic deformation, and then heat-treated for 1 h at 404°C in an argon atmosphere again. This procedure was used in previous studies [30-32], and results in a grain size of 42.5 pm. Fatigue tests was performed under symmetric tension-compression at room temperature using a servohydraulic testing machine. The test procedure was reported earlier [32]. All tested specimens were sliced parallel to the longitudinal axis to obtain transmission electron microscope samples. All samples were cut to 0.5 nun thickness using a diamond wheel. Thin disks were prepared by polishing the slices to 0.2mm thickness. Foils for transmission electron microcopy were thinned by double jet polishing the disks in a 33% nitric acid-67% methanol electrolyte at temperature of 40°C. All foil samples were examined by TEM (JEOL 2000 FX). Fig. 2. Cylindrical shaped dislocation dusters obtained with B=[~33] and g =(0~2) at plastic strain amplitude of 1.2 x 10-5 corresponding to region A of the C.S.S. curve for polycrystalline copper.
3. RESULTS 3.1. Cyclic stress-strain curve
Fatigue tests for polycrystalline copper were performed under various strain amplitudes. It is observed that strain hardening is most pronounced in the early stage of cycling. After a large number of cycles, the strain hardening becomes saturated. It appears that the stress is saturated at almost the same cumulative strain of about 1.00 despite the value of applied strain. This saturation stress, when plotted again the applied plastic strain amplitude, defines the cyclic stress-strain curve. This is shown in Fig. 1. It is noticed that the cyclic strain-stress curve for this small grained polycrystalline copper reveals three regions of cyclic hardening behavior similar to that observed in single crystals and large grained polycrystals. In region A and region C, at low and high plastic 200 .~ .~ ~
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Plastic strain amplitude Aep/2 Fig. I. Cyclic stress-strain curve in fatigued polycrystalline copper,
strain amplitude respectively, the saturated stress increases markedly with increasing A%1/2. While in region B at intermediate plastic strain amplitude, the saturated stress increases slightly and constantly with the increase of A%~/2. 3.2. Dislocation structure 3.2.1. Region A. At low strain amplitude below
1.5 x 10 -5, the dislocation structures in polycrystalline copper produced by cyclic loading reveal three types of features in appearance. Occasionally, in few grains, dislocation clusters are observed as shown in Fig. 2. These dislocation structures are roughly cylindrical in shape and separated by areas which are rather clear of dislocation structures. All dislocation clusters appear to lay on the trace plane of (0~2). In the area of low density dislocations, dislocation "debris" exist. A typical "debris" of dislocation is marked by letter "D". From Fig. 3, it can be seen that the dislocation "debris" appear as two thin lines, which is separated by a distance found to be equal to the width of normal dislocations. These "debris" are dislocation dipoles. Some separated dislocations appear in the rather free dislocation region and are anchored by point defects. A typical example of these dislocations is marked by letter "N", which is a normal edge dislocation or screw dislocation. In addition, it is noticed that each dislocation cluster in the cylindrical loop patch is composed of parallel dislocation dipoles. This means that the dislocation clusters are formed by stacking of dislocation dipoles.
LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu
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This type of dislocation structure is similar to that found in single crystals [21, 33] and coarse grained polycrystals [28] cycled below the plateau. In addition, irregular loop patch structures, which were observed in single crystals, [33] are present in most of the grains of cycled polycrystalline copper in region A. This is shown in Fig. 4(a). It is noticed that no contrast change occurs across the irregular loop patches. This means that the irregular loop patches are fully dipolized dislocation structures. These irregular loop patches terminate into channels which are rather free of dislocations. However, in the channels, dislocation loops are present. The dislocation loops generally form from the jogs after intersection of dislocations coming from different slip systems. Hence, this loop patch structure may be generated from the intersection of dislocations from different slip systems. In some grains, the loop patches become an incomplete cellular structure as shown in Fig. 4(b). This type of loop patches consists of dislocation tangles and networks. In this case, there is a contrast change across the cellular loop patches. This type of loop patch structure may be formed from the interaction of the multiple slip systems. There is few reporting in literature about the occurrence of these irregular and cellular loop patches in region A of polycrystalline copper. They were reported to form at the lower end of the plateau in single crystals [33] and coarse grained polycrystals [29] rather than in region A. 3.2.2. Region B. When the polycrystalline copper with small grain is subjected to cyclic strain in the
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Fig. 4. Loop patch structure formed in polycrystalline copper, fatigued at plastic strain amplitude of 1.2 x 10-s; (a) irregular dislocation loop patches which consist of dislocation loops, electron beam direction is B=[011] and g = (111"), (b) cellular loop patches, electron beam direction is B-[OI1] and g =(111").
Fig. 3. Dislocation clusters stacked by dislocation "debris" of dislocation dipoles, a typical "debris" dislocation dipole in channel marked by "D', electron beam direction is B = [233] and g=(022),
range from 1.5 × 10 5 to 7.5 × 10 4, where saturated stress amplitude increases slightly with the applied strain, a quasi-plateau region is defined (see Fig. 1). In this region, the vein structure is present and remain predominantly similar to what is observed in cycled single crystals [34-37]. A typical vein structure in polycrystalline copper is illustrated in Fig. 5. The vein structure at a strain of 1.14 x 10 4 contains almost
2;
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LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu
Fig. 7. Uncondensed dipolar wall structures produced at plastic strain amplitude of 2.04 × 1 0 - 3 in the region C, electron beam direction is B = [011] and g = (200) Fig. 5. Dislocation vein structure formed in polycrystalline copper at plastic strain amplitude of 1.14 x 10-4 in the quasi-plateau region B, which shows the PSBs structure initiated from the breakdown of loop patches.
is embedded in a vein structure. The PSB structure
observed in this study is similar to that formed in coarse grained polycrystalline copper [25, 29, 38] and half volume of loop patches and half volume of single crystals [9-11]. channel. The content of the loop patches reaches a In the literature, it was reported that the PSB was maximum at this strain. Moreover, the occurrence of a dominant feature in the plateau in coarse grained the persistent slip bands is displayed in this region copper. When plastic strain was 1.13 × 10-4 in the and is shown in Fig. 5. They have been marked by middle of the plateau, almost 10% of the grains PSB. These PSBs just initiate from the breakdown of contained ladder-like PSBs. With increasing plastic loop patches. Well defined PSBs are also observed in strain, the percentage of grains where PSBs were this region as shown in Fig. 6. It reveals that the formed increased significantly. At plastic strain near structure of PSBs consists of a ladder structure which the upper end of the plateau, 60% of the grains in the bulk of polycrystals were occupied entirely by the PSBs [29]. In the present study, the volume fraction of the PSBs in the bulk of small grained polycrystalline copper was measured from optical micrograph samples which are etched by nitric acid. At the lower end of the quasi-plateau, the PSBs cover about 0.3% of the area. At the upper end of the quasi-plateau, the PSBs occupy only about 10% of the bulk area of the polycrystal. Hence, polycrystalline copper with small grain structure has more restriction in the formation of the PSBs than large grain copper. This may explain why the large grained polycrystalline copper has a more flat plateau [18, 22] and the fine grained one exhibits the quasi-plateau in the C.S.S. curve. 3.2.3. Region C. When the applied strain ampli.......... tude is larger than 7.5 x 10-4, the dislocation struck' tures give way smoothly from vein structure to Fig. 6. Optical micrograph of ladder-like PSB structure dipolar wall structure. A typical example of a dipolar formed at plastic strain amplitude of 1.63 x 10-4 in the wall structure at a strain amplitude of 2.04 x 10 -3 is quasi-plateau region B. shown in Fig. 7. Most of the walls have formed on
LIU et al.:
DISLOCATION
STRUCTURES
IN FATIGUED
Cu
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(1 li) plane and are marked by “A”. Some of them have formed on (311) and (135) plane which are marked by “B” and “C” respectively. Because of no change of contrast across the walls, this structure should be dipolar walls. It is worth noticing that these dipolar walls are also separated by channels with rather free dislocations, and that they are not well condensed at this strain amplitude. These walls have a width of about 0.2 pm and occupy almost 30% of the area. The channel structures have a spacing of 0.5 pm and cover 70% of the area. In Fig. 7, it is observed that the walls appear to orient in several directions. Based on the pseudo-polygonalization wall stacking model of Dickson [39-42], this suggest that the wall structures developed from the dislocation glide of multiple slip systems. This multiple slip induced the dipolar wall structures to contain some cell dislocation structures in most of the grains. Meanwhile, labyrinth structure is present at a strain of 2.04 x lo-‘, as shown in Fig. 8. Two types of
Fig. 9. Well-developed labyrinth structure with condensed dipolar walls at plastic strain amplitude of 7.71 x 10m3in the region C.
Fig. 8. Well-developed labyrinth structure at plastic strain amplitude of 2.04 x IO-’ in the region C, electron beam direction
is B = [Ol I] and g = (200).
uncondensed walls have developed in this structure, similar to those observed in single crystals, and therefore a Burgers vector other than that of the primary slip must be represented. However, no loop patch, which may form from the dislocation gliding on a single slip system, has been formed at this strain. Furthermore, there are a lot of “debris”, which appear as loops in the free dislocation channel. This is similar to that observed in loop structures in the quasi-plateau region. This implies that the labyrinth dislocation structure may develop from the same loop stacking mechanism as loop patches do. The dipolar walls in the labyrinth structure have a width of 0.2 pm and are well defined at the beginning of region C. In most of the dipolar walls in the labyrinth, dislocation loops have been included. With increasing strain amplitude, the dipolar walls are still the predominant feature and the labyrinth structures are present till 7.71 x 10e3 strain. It is observed that dipolar walls become more dense and sharper at higher strains as shown in Fig. 9. At applied strain of 1.04 x IO-‘, the dipolar wall structures start to contain some cells with sharp walls, the path in the labyrinth structures is closed and the labyrinth become square shaped cellular structures as shown in Fig. 10. This implies that the third slip system is enhanced during the deformation. Because different contrasts across the walls are observed as shown in Fig. lO(a, b), the dislocation walls becomes tilted walls even though they consists of several dipoles. By comparing the structures in Fig. 10(a) with one in Fig. 7, it can be seen that the
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tilted wall structures at 1.04 x 10 -2 contain almost
4. DISCUSSION
double the number of walls as much as observed in dipolar wall structures at 2.04 x l 0 -3. However, the spacing of free dislocation channels terminated by the walls does not change so much as the number of walls with the increase of applied strain amplitude,
4.1. Characteristics of dislocation structures in small grained copper
Fig. 10. Dipolar wall dislocation structure at strain of 1.06 x l0 -2 in the region C; (a) well-condensed dipolar walls with cell structure, electron beam direction was B = [011] and g = (200); (b) path-closed labyrinth structure, electron beam direction was B ='[01 l] and g = (200).
Dislocation structures in fatigued polycrystalline copper with small grain size display three main different features: the loop patches and the PSBs as well as the dipolar walls including labyrinth structures after the applied strain exceeds 10 -3 which evolve into cell shapes as strain increases. These dislocation structures correspond to the three regions of A, B and C in the stress-strain curve. These three dislocation structures are similar to those observed in coarse grained polycrystals [28, 29] and single crystals [8, 33-37, 43]. It has been pointed out, however, that the small grained polycrystals display some different characteristics in dislocation structures as compared with coarse grained polycrystals and single crystals. In copper monocrystals with oriented single slip, the loop patches are entirely dislocation bundles with a cylindrical shape. In contrast, these cylindrical shaped loop patches exist in only few of the grains in small grained polycrystalline copper. Most of the loop patches are irregular and cellular in shape, which may form from multiple slips. Therefore, the cyclic strain hardening behavior of small grained polycrystals is more like that of single crystals with oriented multislip than single slip which is usually studied. For monocrystals where the PSBs were present, the saturation stress was found to be constant [1]. This behavior was explained by the consistency of the PSB stress. In this plateau region, dislocation structures were observed to be a "two phase" feature where vein coexists with the ladder structure of the PSBs. The volume percentage of the PSBs increased with the increase in applied strain [9, 13, 44] and most of the deformation was localized at the PSBs. For polycrystals with large grain size, because 60% of grains were fully covered by the PSBs at the upper end of the plateau [29], deformation in the plateau were dominated by the localization deformation in the PSBs. Hence, deformation behavior in the intermediate region for coarse grained copper would also be described by the two phase model [9, 12] and the saturation stress in this region should be dominated by the stress in the PSBs. Although the PSBs are also developed in the quasi-plateau region in small grained copper (shown in Fig. 7), they are not the governing structure for the saturation stress, since the PSBs are present in a few grains and only cover a very small volume fraction in this polycrystalline copper. In single crystals, it was found that this plateau could be divided into two regions and that the dislocation structures in these regions displayed two features. At the lower end of the plateau, the dislocations were arranged according to the two-phased model. At strains ranging from 2 × 10 -3 to 10 -2, which were at the upper end of the plateau, the labyrinth structures were frequently observed [8]. Similarly, the labyrinth structures were found in the
LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu upper end of the plateau for coarse grained copper. However, in the quasi-plateau range from 1.5 x 10 -5 to l0 3 for small grained polycrystalline copper, dislocation structures consist entirely of vein and PSBs and no labyrinth structure is observed in this region in the present investigation. Labyrinth structures are found in region C rather than the upper end of the quasi-plateau. It is noticed that the labyrinth structures are restricted within subgrains bounded by a pair of parallel subgrain boundaries and occupies a small volume, In monocrystals, the labyrinth structure coexisted with loop patches and PSB ladder structure, and PSBs were the predominant structure in controlling the cyclic saturation stress. However, in small grained polycrystals, the labyrinth structures coexist with dipolar walls, in which saturation stress is mainly controlled by the stress from the dipolar wall structures. Since the dipolar wall structures have less spacing than the ladder wall in PSBs, higher stress is required to move the dislocations in the channel of the dipolar wall structure than in that of PSBs. Therefore, the increase in the saturation stress is obtained in small grained copper when the labyrinth structure develop with the dipolar walls. 4.2. Dislocation arrangement mechanisms
TEM observations ofcycledpolycrystallinecopper with small grain size reveals three dislocation structures. Besides differencesin their appearance, all three types of dislocation structures have a common feature with dipolized dislocation configurations, no matter how they formed and how much strain hardening they contributed, For loop patch structures produced at low strain amplitudes, it is observed that they are formed by "dipole flipping" as shown in Fig. 3. The dipoles consist of two dislocations with opposite signs, which are attracted with each other. The formation of the dislocation dipoles always reduces the strain energy, In Fig. 3 it is shown that the loop patch was formed from the stacking of the dipoles. This loop patch structure was modelled with Taylor lattice, which consists of dislocations of unlike sign [45-48] as shown in Fig. 11. Kuhlmann-Wilsdorf [47] employed Nabarro's equation to describe the deformation of the loop patches modelled by the Taylor lattice. It was found that theminimum energy configuration sought in an infinitely extended Taylor lattice is s / d f + 2, where s and dfare defined in Fig. 11, that is, the dislocations are arranged as edge dislocations of unlike signs in 45 ° configuration. This low energy aspect of loop patches are in excellent agreement with that of Neumann [48] who performed computer studies of these arrays explicitly with respect to their energy. In addition, Neumann found that the infinite Taylor lattice is inherently unstable and loop patches of finite size are required to adopt certain geometry with the diamond shape,
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It is worth noticing that all dislocation structures in fatigued polycrystalline copper contain rather free dislocation channels, which are terminated by loop patches or ladders in PSBs or walls. A major progress on dislocation mechanisms in cyclic deformation was made by Kuhlmann-Wilsdorf [11, 46, 47] who discussed the various possible configurations involved in fatigue strain carried in PSBs. She suggested that the configuration with continuous screw dislocations which are jogged at the position of the loop walls, is most likely to be responsible for plastic deformation in fatigue. In her model, screw dislocations shuttle in the channel between the dipolar walls and drag edge dislocation dipoles behind themselves, depositing along and in the walls. However, it seems unlikely that the model of the screw dislocation shuttling in the channel and depositing long edge dislocation along the walls does apply in fatigue because it implies reversible strain. If the plastic strain is reversible, then there is no mechanism for fracture. One the other hand, when secondary system is operative, which is required for the formation of the PSBs, or multiple slip systems are enhanced, the screw dislocations may cross-slip, then the strain is indeed irreversible. It is important to emphasize that the TEM observations using neutron irradiation technique show that dislocation loops bowed from the walls, which showed the dislocation structure in the loaded configuration [49, 50]. From Figs 4-10 in the present investigation, it can be also seen that the loop patches, labyrinth walls and dipolar walls are composed of dislocation loops, but not straight dislocation lines. This dislocation configuration makes it possible to emit dislocations from the walls. Based on the TEM observations, the dislocation mechanism in fatigue can be modified as follows. Consider dislocation loop patches consisting of loops with two opposite signs. It may be presumed that, originally, these loop patches have a random distribution of dislocation signs. When the material is subjected to the positive load, dislocations with positive sign in loops would move toward the right,
dt_~e [----] / / S_[ZZ.
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DISLOCATION STRUCTURES IN FATIGUED Cu
(a)
(b)
(¢)
(d) Fig. 12. Idealized dislocation arrangement mechanism in fatigue to produce the dipolized dislocation structure in half of cycle, (a) positive dislocation loops bowed from loop patch meeting negative dislocation loops from the opposite loop patch, (b) formation and sweeping of screw dislocation with opposite signs in the channel, (c) dislocations bowed out of the same side of the loop patch meeting each other, (d) the deposition of the dislocation edge segments with original sign on the opposite loop patches and the dislocation edge segment with reversed sign on its own side, as well as sweeping movement of the dislocation screw segments in the channel.
LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu
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dislocations with negative sign in loops would move toward the left. Thus, dislocations with negative sign located at the fight side of the loop patch and with positive sign located at the left side of the loop patch would not move because they are obstructed by the loop patch they composed, and dislocations with positive sign located at right side of a loop patch and with negative sign located at the left side of the loop patch would be bowed out and expanded as shown in Fig. 12(a). When the latter meet other dislocations with unlike sign from the opposite loop patch, they become two screw dislocation segments with unlike signs and move in opposite direction as shown in Fig. 12(b), until they encounter a screw dislocation of unlike sign with which they annihilate or they sweep out of the grains. When dislocations bowed out of the same side of the loop patch meet each other rather than other dislocations with unlike sign from the opposite loop patch as shown in Fig. 12(c), they expand and strike the adjacent loop patch, depositing their edge segments with their original sign on the opposite loop patch and changing the dislocation sign at the out bound of the opposite loop patch. W i t h t h e expansion of thedislocation loops, unlike sign screw segments from different loops, attract each other and annihilate, leaving a edge dislocation segment with reversed sign to deposit on its own side. Another two screw segments move in opposite direction until they encounter a screw dislocation of unlike sign with which they annihilate or they sweep out of the grains, This is shown in Fig. 12(d). Therefore, after half cycle, the out bound in the fight side of the loop patches would be shielded by edge dislocation segments with negative sign, the out bound in the left side of the loop patches would be shielded by edge dislocation segments with positive sign. For the next half cycle, the load is reversed and the above process is repeated, leading to alternating the dislocation sign in the out bound of the loop patches and some screw dislocation segments sweeping out of the grains. During one cycle, this results in deposition of edge dislocations on loop patch twice but with unlike sign. The edge dislocations with unlike sign must form dislocation loops because of their low strain energy, The repeating deposition of the dislocation loops and the loop patches would cause the loop patches to be Taylor lattice structures and dipolized. This means that all dislocation structures in fatigue are favored to be formed into dipolized structures, Though the dislocation structures have many different appearances like loop patch, vein and dipolar walls, when subjected to different strain amplitude, these structures are formed from a similar
mation in fatigue must be a energy minimization process. It is pointed out that in the above dipolized dislocation structure formation model, the dipolized process included not only edge dislocation segment deposition on the loop patches, but also some screw dislocation segments being swept out of the grains. The screw dislocation segment sweep out the grains results in the formation of intrusions and extrusions. Therefore, this modified model can create irreversible plastic strain causing the nucleation of cracks and the eventual fracture of material.
dislocation deposition mechanism and are dipolized dislocation structure. Difference in appearance is just caused by them being condensed under different conditions, i.e. the dipolar wall structures are condensed more sharper than loop patch structures. Because Taylor lattice structure is a low strain energy configuration, the dipolized dislocation structure for-
Acknowledgement--The authors would like to acknowledge
5. CONCLUSIONS In this investigation, the dislocation structures in fatigued polycrystalline copper with small grain size were studied over an extensive plastic strain range. Based on the observation of these dislocation structures, the following conclusions can be drawn: 1. The dislocation structures produced in fatigued polycrystalline copper with small grain are mainly classified into three types of dislocation structures in the strain range from 1.5× 10 -5 to 10 -2, which correspond to the three regions in the cyclic stress-strain curve. 2. In region A, cylindrical loop patch structure which was observed in single crystals and coarse grained polycrystals is also formed in cyclic saturated polycrystalline copper with small grain size. Moreover, the irregular loop patch and cellular loop patch, that were rarely reported to occur in the coarse grain polycrystals and single crystals, are present in region A of the smaller grained polycrystalline copper. 3. In region B of the small grained polycrystalline copper, the dislocation structure forms veins, PSBs structure are also present in this region but with much lower volume fraction than that found in the coarse grained polycrystals and single crystals reported earlier in literature. 4. In region C, the dislocation structures of the small grained polycrystalline copper are dominated by dipolar walls. In addition, labyrinth structures are formed in this region instead region B as observed in coarse grained polycrystals and single crystals. The dipolar walls become denser and sharper in image as the applied strain increases. At strain close to l0 -2, the dipolar walls become more cell shaped. 5. All the dislocation configurations formed in the fatigued polycrystalline copper are low strain energy structures. A dipolized dislocation arrangement model has been proposed to describe the formation process of dislocation structures such as the loop patches and the dipolar walls. the Natural Science and Engineering Research Council of Canada for support of this investigation. REFERENCES 1. H. Mughrabi, Mater. Sci. Engng 33, 207 (1978). 2. T. Broom and R. K. Ham, Phil. Mag. 7, 95 (1962).
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LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu
3. C. E. Feltner, Phil. Mag. 12, 1229 (1965). 4. C. E. Feltner, Phil. Mag. 14, 1219 (1966). 5. J. R. Hancock and J. C. Grosskreutz, .4cta metall. 17, 77 (1969). 6. S. J. Basinski, Z. S. Basinski and A. Howie, Phil. Mag. 18, 899 (1969). 7. P Lukas and M. Klesnil, Physica status solidi 37, 833 (1970). 8. F. Ackermann, L. P. Kubin, J. Lepinoux and H. Mughrabi, Acta metall. 32, 715 (1984). 9. J. M. Finney and C. Laird, Phil. Mag. 31, 339 (1975). 10. P. J. Woods, Phil. Mag. 28, 155 (1973). 11. D. Kuhlmann-Wilsdorf and C. Laird, Mater. Sci. Engng 27, 137 (1977). 12. A. T. Winter, Phil. Mag. 30, 719 (1974). 13. P. Lukas and M. Klesnil, Mater. Sci. Engng 11, 345 (1973). 14. K. C. Rasmussen and O. B. Pedersen, Acta metall. 28, 1467 (1980). 15. J. C. Figueroa, S. P. Bhat, R. De La Veaux, S. Murzenski and C. Laird, Acta metall. 29, 1667 (1981). 16. H. Mughrabi and R. Wang, Proc. 2nd Ris Int. Syrup. on Metallurgy and Materials Science, (edited by N. Hansen et al.) p. 89. Ris National Laboratory, Roskilde, Denmark (1981). 17. H. Mughrabi and R. Wang, Proc. First Int, Symp. on Defects and Fracture, Tuczno, Poland, (edited by G.C. Sih and H. Zorski), p. 15. Martinus Nijhoff, The Hague (1982). 18. V.-J. Kuokkala, T. Lepisto and P. Kettunen, Scripta metall. 16, 1149 (1982). 19. O. B. Pedersen and K. V. Rasmussen, Acta metall. 30, 57 (1982). 20. J. Polak and M. Klesnil, Mater. Sci. Engng 63, 189 (1984). 21. H. Mullner, B. Weiss, R. Stickler, P. Lukas and L. Kunz, Proc. 2nd Int. Conf. Fatigue and Fatigue Thresholds, University of Birmingham, U.K., Vol. 1 (edited by C. J. Beevers), p. 423. Engineering Materials, Advisory Services (1984). 22. N. Marchand, J. P. Bailon and J. I. Dickson, Proc. 2nd lnt. Syrup., Mont. Gabriel, Canada (edited by G. C. Sih and J. W. Provan) p. 195. Martinus Nijhoff, The Hague (1984). 23. P. Lukas and L. Kunz, Mater. Sci. Engng A 85, 67 (1987). 24. P. Lukas and L. Kunz, Mater. Sci. Engng A 103, 233 (1988).
25. Z. Wang and C. Laird, Mater. Sci. Engng A 100, 57 (1988). 26. L. Llanes and C. Laird, Mater. Sci. Engng ;4 128, L9 (1990). 27. O. B. Pedersen, Acta metall 38, 1221 (1992). 28. K. Obrtlik, J. Polak and J. Komurka, Scripta metall. 28, 495 (1993). 29. A. T. Winter, O. B. Pedersen and K. V. Rasmussen, Actametall. 29, 735 (1981). 30. C. D. Liu and M. N. Bassim, Metall. Trans. A 24, 361 (1993). 31. M. N. Bassim and C. D. Liu, Mater. Sci. EngngA 164, 170 (1993). 32. C. D. Liu, D. X. You and M. N. Bassim, Acta metall. mater. 42, 1631 (1994). 33. B. D. Yan, A Hunsche, P. Neumann and C. Laird, Mater. Sci. Engng 79, 9 (1986). 34. N. Y. Jin, Phil. Mag. A 48, L33 (1983). 35. N. Y. Jin and A. T. Winter, Acta metall. 32, 989 (1984). 36. N . Y . JinandA. T. Winter, Actametall. 32,1173 (1984). 37. L. Buchinger, S. Stanzl and C. Laird, Phil. Mag. A 50, 275 (1984). 38. L. Llanes and C. Laird, Mater. Sci, Engng A 161, 1 (1993). 39. J. L. Dickson, Hong Bande and G. L'Esperance, Mater. Sci. Engng A 101, 75 (1988). 40. G. L'Esperance, J. B. Vogt and J. I. Dickson, Mater. Sci. Engng 79, 141 (1986). 41. J. I. Dickson, J. Boutin and G. L'Esperance, Acta metall. 34, 1505 (1986). 42. J. I. Dickson, L. Handfield and G. L'Esperance, 81, 477 (1986). 43. C. Laird, P. Charsley and H. Mughrabi, Mater. Sci. Engng 81, 433 (1986). 44. H. Mughrabi, Mater. Sci. Engng A 33, 207 (1978). 45. D. Kuhlmann-WilsdorfandC. Laird, Mater. Sci. Engng 37, 111 (1979). 46. D. Kuhlmann-Wilsdorf, Mater. Sci. Engng 39, 127 (1979). 47. D. Kuhlmann-Wilsdorf and C. Laird, Mater. Sci. Engng 39, 231 (1979). 48. P. Neumann, Mater. Sci. Engng 81, 465 (1986). 49. J. C. Grosskreutz and H. Mughrabi, in Constitutive Equations in Plasticity (edited by A. S. Argon), p. 251. MIT Press, Cambridge (1975). 50. H. Mughrabi, F. Ackermann and K. Herz, in Fatigue Mechanisms (edited by J. T. Fong), ASTM, STP 675, p. 69 (1979).
Pergamon
0956-7151(94)E0160-I
Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0956-7151/94 $7.00 + 0.00
DISLOCATION STRUCTURES IN FATIGUED POLYCRYSTALLINE COPPER C. D. LIU, M. N. B A S S I M and D. X. Y O U Laboratory of Physical Metallurgy, Department of Mechanical Engineering, The University of Manitoba, Canada R3T 2N2 (Received 12 July 1993; in revised form 17 March 1994)
Al~tract--The dislocation structures in fatigued polycrystalline copper with small average grain size were investigated over a plastic strain range from 1.5 x l0 5to l0 -2. It was found that the dislocation structures are arranged into three types of configurations, which correspond to the three regions in the cyclic stress-strain curve. Cylindrical loop patch structure are present in region A for low strain amplitudes, similar to those observed previously in coarse grained polycrystals. Moreover, irregular loop patches are also formed in this region for small grains polycrystals rather than in region B at intermediate strain amplitudes for coarse grained polycrystals. In region B, persistent slip band (PSB) structures are formed but with a low volume content compared with the coarse grained polycrystals. In region C, at high plastic strains, the dislocation structures are dominated by dipolar walls. In addition, labyrinth structures are developed in region C instead of region B for coarse grained polycrystals. All the dislocation structures observed are viewed as forms of dipolized structures. A dipolized dislocation arrangement model is proposed to describe the formation process of dislocation structures. It is shown that all the dislocation configurations formed in cycled polycrystalline copper are low energy structures.
1. INTRODUCTION The cyclic behavior of f.c.c, metals was established through work on copper single crystals [1]. The cyclic stress-strain curve consists of three stages centered around a predominant plateau. The dislocation structures which develop in copper single crystals under cyclic deformation were investigated extensively [2-7], and differed for the various regions in the curve. Below the plateau, at low stress and strain amplitudes, the structures consisted of loop patches which were dominated by primary dislocations. In the plateau region, where the saturated resolve shear stress remained at the same value, the dislocation structure was composed of persistent slip bands (PSBs) embedded in veins of loop patches [8]. The PSBs were widely understood to consist of the well know "ladder" structure [9-11] where the strain is much higher than the overall strain applied to the crystal [9]. A two phase model was proposed by Winter [12] and substantiated by Finney and Laird [9] to describe the plateau feature in the cyclic stress-strain curve. It was found that the saturation stress in the region of the plateau was governed by the PSB, despite the variation in PSB content, under a large range of strain. Above the plateau, the dislocations formed cell structures through multiple slip, which gave rise to a higher saturated stress, During the last two decades, cyclic deformation of copper polycrystals was also studied extensively AMM
42/11 H
[13-27]. Early debate as to whether the cyclic stress-strain (C.S.S.) curve for polycrystalline copper contains a plateau now seems to have been resolved. In the course of the previous studies, it is evident that the plateau exists in the C.S.S. curve of coarsegrained (grain size > 100 pm) polycrystalline copper [14, 15, 18, 22] or tested under ramp loading [25], even it is much shorter than the one observed in single crystals. Dislocation configurations in the three regions of the C.S.S. curve of copper polycrystal with large grains display the same features as that in single crystals. Below the plateau, dislocations are arranged into the vein structure which consists of dislocation bundles [28]. In the region of plateau, the PSBs are observed in the bulk of the polycrystals [29]. When plastic strain amplitude is above the plateau, the PSBs gives way to the labyrinth structure [29] and the dipolar walls and the cell structure [14, 29]. However, cyclic deformation and dislocation structures of copper polycrystals with small grain size are less understood. In a recent work by the present authors, comprehensive cyclic tests were performed under constant low strain rate. They revealed the occurrence of a quasi-plateau in the C.S.S. curve of small grained polycrystalline copper [32]. The present investigation examines in detail the evolution of dislocation structures in small grained polycrystalline copper under cyclic loading, compared to that for coarse grained copper and single crystals reported in the literature.
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LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu
2. EXPERIMENTAL The material used in this study was 99.94% purity copper. Cylindrical specimens were machined with a diameter of 6.5 mm and a gauge length of 25 mm. All specimens were annealed in an argon atmosphere for 2 h at 620°C, prestrained to 10% plastic deformation, and then heat-treated for 1 h at 404°C in an argon atmosphere again. This procedure was used in previous studies [30-32], and results in a grain size of 42.5 pm. Fatigue tests was performed under symmetric tension-compression at room temperature using a servohydraulic testing machine. The test procedure was reported earlier [32]. All tested specimens were sliced parallel to the longitudinal axis to obtain transmission electron microscope samples. All samples were cut to 0.5 nun thickness using a diamond wheel. Thin disks were prepared by polishing the slices to 0.2mm thickness. Foils for transmission electron microcopy were thinned by double jet polishing the disks in a 33% nitric acid-67% methanol electrolyte at temperature of 40°C. All foil samples were examined by TEM (JEOL 2000 FX). Fig. 2. Cylindrical shaped dislocation dusters obtained with B=[~33] and g =(0~2) at plastic strain amplitude of 1.2 x 10-5 corresponding to region A of the C.S.S. curve for polycrystalline copper.
3. RESULTS 3.1. Cyclic stress-strain curve
Fatigue tests for polycrystalline copper were performed under various strain amplitudes. It is observed that strain hardening is most pronounced in the early stage of cycling. After a large number of cycles, the strain hardening becomes saturated. It appears that the stress is saturated at almost the same cumulative strain of about 1.00 despite the value of applied strain. This saturation stress, when plotted again the applied plastic strain amplitude, defines the cyclic stress-strain curve. This is shown in Fig. 1. It is noticed that the cyclic strain-stress curve for this small grained polycrystalline copper reveals three regions of cyclic hardening behavior similar to that observed in single crystals and large grained polycrystals. In region A and region C, at low and high plastic 200 .~ .~ ~
180 - (a)
14o
~ ~ ~ ~ •~
B, /
160
120
100 --
80 60 40 ~ . 20 0 -
i i I/a ~'l
A I
Ii¢r.~.~-~ul--'~lJ
-
10-7
c . :
aJ
~
~
I
,
I
I
[
I
I
10-6
10-5
10-4
10-3
10-2
Plastic strain amplitude Aep/2 Fig. I. Cyclic stress-strain curve in fatigued polycrystalline copper,
strain amplitude respectively, the saturated stress increases markedly with increasing A%1/2. While in region B at intermediate plastic strain amplitude, the saturated stress increases slightly and constantly with the increase of A%~/2. 3.2. Dislocation structure 3.2.1. Region A. At low strain amplitude below
1.5 x 10 -5, the dislocation structures in polycrystalline copper produced by cyclic loading reveal three types of features in appearance. Occasionally, in few grains, dislocation clusters are observed as shown in Fig. 2. These dislocation structures are roughly cylindrical in shape and separated by areas which are rather clear of dislocation structures. All dislocation clusters appear to lay on the trace plane of (0~2). In the area of low density dislocations, dislocation "debris" exist. A typical "debris" of dislocation is marked by letter "D". From Fig. 3, it can be seen that the dislocation "debris" appear as two thin lines, which is separated by a distance found to be equal to the width of normal dislocations. These "debris" are dislocation dipoles. Some separated dislocations appear in the rather free dislocation region and are anchored by point defects. A typical example of these dislocations is marked by letter "N", which is a normal edge dislocation or screw dislocation. In addition, it is noticed that each dislocation cluster in the cylindrical loop patch is composed of parallel dislocation dipoles. This means that the dislocation clusters are formed by stacking of dislocation dipoles.
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This type of dislocation structure is similar to that found in single crystals [21, 33] and coarse grained polycrystals [28] cycled below the plateau. In addition, irregular loop patch structures, which were observed in single crystals, [33] are present in most of the grains of cycled polycrystalline copper in region A. This is shown in Fig. 4(a). It is noticed that no contrast change occurs across the irregular loop patches. This means that the irregular loop patches are fully dipolized dislocation structures. These irregular loop patches terminate into channels which are rather free of dislocations. However, in the channels, dislocation loops are present. The dislocation loops generally form from the jogs after intersection of dislocations coming from different slip systems. Hence, this loop patch structure may be generated from the intersection of dislocations from different slip systems. In some grains, the loop patches become an incomplete cellular structure as shown in Fig. 4(b). This type of loop patches consists of dislocation tangles and networks. In this case, there is a contrast change across the cellular loop patches. This type of loop patch structure may be formed from the interaction of the multiple slip systems. There is few reporting in literature about the occurrence of these irregular and cellular loop patches in region A of polycrystalline copper. They were reported to form at the lower end of the plateau in single crystals [33] and coarse grained polycrystals [29] rather than in region A. 3.2.2. Region B. When the polycrystalline copper with small grain is subjected to cyclic strain in the
o•
"r . ~ ~.-., t :-:~t~ : , ~ i : , : ~ ~;~ ~ ~ ~ ~,,)~:'r" ~- :~,: ~,~. .. ~ . . . . . . ...... '~ ;~' ~ ' ~
Fig. 4. Loop patch structure formed in polycrystalline copper, fatigued at plastic strain amplitude of 1.2 x 10-s; (a) irregular dislocation loop patches which consist of dislocation loops, electron beam direction is B=[011] and g = (111"), (b) cellular loop patches, electron beam direction is B-[OI1] and g =(111").
Fig. 3. Dislocation clusters stacked by dislocation "debris" of dislocation dipoles, a typical "debris" dislocation dipole in channel marked by "D', electron beam direction is B = [233] and g=(022),
range from 1.5 × 10 5 to 7.5 × 10 4, where saturated stress amplitude increases slightly with the applied strain, a quasi-plateau region is defined (see Fig. 1). In this region, the vein structure is present and remain predominantly similar to what is observed in cycled single crystals [34-37]. A typical vein structure in polycrystalline copper is illustrated in Fig. 5. The vein structure at a strain of 1.14 x 10 4 contains almost
2;
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LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu
Fig. 7. Uncondensed dipolar wall structures produced at plastic strain amplitude of 2.04 × 1 0 - 3 in the region C, electron beam direction is B = [011] and g = (200) Fig. 5. Dislocation vein structure formed in polycrystalline copper at plastic strain amplitude of 1.14 x 10-4 in the quasi-plateau region B, which shows the PSBs structure initiated from the breakdown of loop patches.
is embedded in a vein structure. The PSB structure
observed in this study is similar to that formed in coarse grained polycrystalline copper [25, 29, 38] and half volume of loop patches and half volume of single crystals [9-11]. channel. The content of the loop patches reaches a In the literature, it was reported that the PSB was maximum at this strain. Moreover, the occurrence of a dominant feature in the plateau in coarse grained the persistent slip bands is displayed in this region copper. When plastic strain was 1.13 × 10-4 in the and is shown in Fig. 5. They have been marked by middle of the plateau, almost 10% of the grains PSB. These PSBs just initiate from the breakdown of contained ladder-like PSBs. With increasing plastic loop patches. Well defined PSBs are also observed in strain, the percentage of grains where PSBs were this region as shown in Fig. 6. It reveals that the formed increased significantly. At plastic strain near structure of PSBs consists of a ladder structure which the upper end of the plateau, 60% of the grains in the bulk of polycrystals were occupied entirely by the PSBs [29]. In the present study, the volume fraction of the PSBs in the bulk of small grained polycrystalline copper was measured from optical micrograph samples which are etched by nitric acid. At the lower end of the quasi-plateau, the PSBs cover about 0.3% of the area. At the upper end of the quasi-plateau, the PSBs occupy only about 10% of the bulk area of the polycrystal. Hence, polycrystalline copper with small grain structure has more restriction in the formation of the PSBs than large grain copper. This may explain why the large grained polycrystalline copper has a more flat plateau [18, 22] and the fine grained one exhibits the quasi-plateau in the C.S.S. curve. 3.2.3. Region C. When the applied strain ampli.......... tude is larger than 7.5 x 10-4, the dislocation struck' tures give way smoothly from vein structure to Fig. 6. Optical micrograph of ladder-like PSB structure dipolar wall structure. A typical example of a dipolar formed at plastic strain amplitude of 1.63 x 10-4 in the wall structure at a strain amplitude of 2.04 x 10 -3 is quasi-plateau region B. shown in Fig. 7. Most of the walls have formed on
LIU et al.:
DISLOCATION
STRUCTURES
IN FATIGUED
Cu
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(1 li) plane and are marked by “A”. Some of them have formed on (311) and (135) plane which are marked by “B” and “C” respectively. Because of no change of contrast across the walls, this structure should be dipolar walls. It is worth noticing that these dipolar walls are also separated by channels with rather free dislocations, and that they are not well condensed at this strain amplitude. These walls have a width of about 0.2 pm and occupy almost 30% of the area. The channel structures have a spacing of 0.5 pm and cover 70% of the area. In Fig. 7, it is observed that the walls appear to orient in several directions. Based on the pseudo-polygonalization wall stacking model of Dickson [39-42], this suggest that the wall structures developed from the dislocation glide of multiple slip systems. This multiple slip induced the dipolar wall structures to contain some cell dislocation structures in most of the grains. Meanwhile, labyrinth structure is present at a strain of 2.04 x lo-‘, as shown in Fig. 8. Two types of
Fig. 9. Well-developed labyrinth structure with condensed dipolar walls at plastic strain amplitude of 7.71 x 10m3in the region C.
Fig. 8. Well-developed labyrinth structure at plastic strain amplitude of 2.04 x IO-’ in the region C, electron beam direction
is B = [Ol I] and g = (200).
uncondensed walls have developed in this structure, similar to those observed in single crystals, and therefore a Burgers vector other than that of the primary slip must be represented. However, no loop patch, which may form from the dislocation gliding on a single slip system, has been formed at this strain. Furthermore, there are a lot of “debris”, which appear as loops in the free dislocation channel. This is similar to that observed in loop structures in the quasi-plateau region. This implies that the labyrinth dislocation structure may develop from the same loop stacking mechanism as loop patches do. The dipolar walls in the labyrinth structure have a width of 0.2 pm and are well defined at the beginning of region C. In most of the dipolar walls in the labyrinth, dislocation loops have been included. With increasing strain amplitude, the dipolar walls are still the predominant feature and the labyrinth structures are present till 7.71 x 10e3 strain. It is observed that dipolar walls become more dense and sharper at higher strains as shown in Fig. 9. At applied strain of 1.04 x IO-‘, the dipolar wall structures start to contain some cells with sharp walls, the path in the labyrinth structures is closed and the labyrinth become square shaped cellular structures as shown in Fig. 10. This implies that the third slip system is enhanced during the deformation. Because different contrasts across the walls are observed as shown in Fig. lO(a, b), the dislocation walls becomes tilted walls even though they consists of several dipoles. By comparing the structures in Fig. 10(a) with one in Fig. 7, it can be seen that the
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LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu
tilted wall structures at 1.04 x 10 -2 contain almost
4. DISCUSSION
double the number of walls as much as observed in dipolar wall structures at 2.04 x l 0 -3. However, the spacing of free dislocation channels terminated by the walls does not change so much as the number of walls with the increase of applied strain amplitude,
4.1. Characteristics of dislocation structures in small grained copper
Fig. 10. Dipolar wall dislocation structure at strain of 1.06 x l0 -2 in the region C; (a) well-condensed dipolar walls with cell structure, electron beam direction was B = [011] and g = (200); (b) path-closed labyrinth structure, electron beam direction was B ='[01 l] and g = (200).
Dislocation structures in fatigued polycrystalline copper with small grain size display three main different features: the loop patches and the PSBs as well as the dipolar walls including labyrinth structures after the applied strain exceeds 10 -3 which evolve into cell shapes as strain increases. These dislocation structures correspond to the three regions of A, B and C in the stress-strain curve. These three dislocation structures are similar to those observed in coarse grained polycrystals [28, 29] and single crystals [8, 33-37, 43]. It has been pointed out, however, that the small grained polycrystals display some different characteristics in dislocation structures as compared with coarse grained polycrystals and single crystals. In copper monocrystals with oriented single slip, the loop patches are entirely dislocation bundles with a cylindrical shape. In contrast, these cylindrical shaped loop patches exist in only few of the grains in small grained polycrystalline copper. Most of the loop patches are irregular and cellular in shape, which may form from multiple slips. Therefore, the cyclic strain hardening behavior of small grained polycrystals is more like that of single crystals with oriented multislip than single slip which is usually studied. For monocrystals where the PSBs were present, the saturation stress was found to be constant [1]. This behavior was explained by the consistency of the PSB stress. In this plateau region, dislocation structures were observed to be a "two phase" feature where vein coexists with the ladder structure of the PSBs. The volume percentage of the PSBs increased with the increase in applied strain [9, 13, 44] and most of the deformation was localized at the PSBs. For polycrystals with large grain size, because 60% of grains were fully covered by the PSBs at the upper end of the plateau [29], deformation in the plateau were dominated by the localization deformation in the PSBs. Hence, deformation behavior in the intermediate region for coarse grained copper would also be described by the two phase model [9, 12] and the saturation stress in this region should be dominated by the stress in the PSBs. Although the PSBs are also developed in the quasi-plateau region in small grained copper (shown in Fig. 7), they are not the governing structure for the saturation stress, since the PSBs are present in a few grains and only cover a very small volume fraction in this polycrystalline copper. In single crystals, it was found that this plateau could be divided into two regions and that the dislocation structures in these regions displayed two features. At the lower end of the plateau, the dislocations were arranged according to the two-phased model. At strains ranging from 2 × 10 -3 to 10 -2, which were at the upper end of the plateau, the labyrinth structures were frequently observed [8]. Similarly, the labyrinth structures were found in the
LIU et al.: DISLOCATION STRUCTURES IN FATIGUED Cu upper end of the plateau for coarse grained copper. However, in the quasi-plateau range from 1.5 x 10 -5 to l0 3 for small grained polycrystalline copper, dislocation structures consist entirely of vein and PSBs and no labyrinth structure is observed in this region in the present investigation. Labyrinth structures are found in region C rather than the upper end of the quasi-plateau. It is noticed that the labyrinth structures are restricted within subgrains bounded by a pair of parallel subgrain boundaries and occupies a small volume, In monocrystals, the labyrinth structure coexisted with loop patches and PSB ladder structure, and PSBs were the predominant structure in controlling the cyclic saturation stress. However, in small grained polycrystals, the labyrinth structures coexist with dipolar walls, in which saturation stress is mainly controlled by the stress from the dipolar wall structures. Since the dipolar wall structures have less spacing than the ladder wall in PSBs, higher stress is required to move the dislocations in the channel of the dipolar wall structure than in that of PSBs. Therefore, the increase in the saturation stress is obtained in small grained copper when the labyrinth structure develop with the dipolar walls. 4.2. Dislocation arrangement mechanisms
TEM observations ofcycledpolycrystallinecopper with small grain size reveals three dislocation structures. Besides differencesin their appearance, all three types of dislocation structures have a common feature with dipolized dislocation configurations, no matter how they formed and how much strain hardening they contributed, For loop patch structures produced at low strain amplitudes, it is observed that they are formed by "dipole flipping" as shown in Fig. 3. The dipoles consist of two dislocations with opposite signs, which are attracted with each other. The formation of the dislocation dipoles always reduces the strain energy, In Fig. 3 it is shown that the loop patch was formed from the stacking of the dipoles. This loop patch structure was modelled with Taylor lattice, which consists of dislocations of unlike sign [45-48] as shown in Fig. 11. Kuhlmann-Wilsdorf [47] employed Nabarro's equation to describe the deformation of the loop patches modelled by the Taylor lattice. It was found that theminimum energy configuration sought in an infinitely extended Taylor lattice is s / d f + 2, where s and dfare defined in Fig. 11, that is, the dislocations are arranged as edge dislocations of unlike signs in 45 ° configuration. This low energy aspect of loop patches are in excellent agreement with that of Neumann [48] who performed computer studies of these arrays explicitly with respect to their energy. In addition, Neumann found that the infinite Taylor lattice is inherently unstable and loop patches of finite size are required to adopt certain geometry with the diamond shape,
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It is worth noticing that all dislocation structures in fatigued polycrystalline copper contain rather free dislocation channels, which are terminated by loop patches or ladders in PSBs or walls. A major progress on dislocation mechanisms in cyclic deformation was made by Kuhlmann-Wilsdorf [11, 46, 47] who discussed the various possible configurations involved in fatigue strain carried in PSBs. She suggested that the configuration with continuous screw dislocations which are jogged at the position of the loop walls, is most likely to be responsible for plastic deformation in fatigue. In her model, screw dislocations shuttle in the channel between the dipolar walls and drag edge dislocation dipoles behind themselves, depositing along and in the walls. However, it seems unlikely that the model of the screw dislocation shuttling in the channel and depositing long edge dislocation along the walls does apply in fatigue because it implies reversible strain. If the plastic strain is reversible, then there is no mechanism for fracture. One the other hand, when secondary system is operative, which is required for the formation of the PSBs, or multiple slip systems are enhanced, the screw dislocations may cross-slip, then the strain is indeed irreversible. It is important to emphasize that the TEM observations using neutron irradiation technique show that dislocation loops bowed from the walls, which showed the dislocation structure in the loaded configuration [49, 50]. From Figs 4-10 in the present investigation, it can be also seen that the loop patches, labyrinth walls and dipolar walls are composed of dislocation loops, but not straight dislocation lines. This dislocation configuration makes it possible to emit dislocations from the walls. Based on the TEM observations, the dislocation mechanism in fatigue can be modified as follows. Consider dislocation loop patches consisting of loops with two opposite signs. It may be presumed that, originally, these loop patches have a random distribution of dislocation signs. When the material is subjected to the positive load, dislocations with positive sign in loops would move toward the right,
dt_~e [----] / / S_[ZZ.
/
/ / T J Z
/
/ T
/
/ V
/
/ "r
/
T /
T T T T T T T T T /
/ T
/
/ T
/
/ T
/
.1. / T
/
T /
/ T
/
/ T
/
.L T
/
T /
T T T T T T T T T Fig. 11. A Taylor lattice model with dislocations arranged with unlike sign of the loop patch structure.
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LIU et al.:
DISLOCATION STRUCTURES IN FATIGUED Cu
(a)
(b)
(¢)
(d) Fig. 12. Idealized dislocation arrangement mechanism in fatigue to produce the dipolized dislocation structure in half of cycle, (a) positive dislocation loops bowed from loop patch meeting negative dislocation loops from the opposite loop patch, (b) formation and sweeping of screw dislocation with opposite signs in the channel, (c) dislocations bowed out of the same side of the loop patch meeting each other, (d) the deposition of the dislocation edge segments with original sign on the opposite loop patches and the dislocation edge segment with reversed sign on its own side, as well as sweeping movement of the dislocation screw segments in the channel.
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dislocations with negative sign in loops would move toward the left. Thus, dislocations with negative sign located at the fight side of the loop patch and with positive sign located at the left side of the loop patch would not move because they are obstructed by the loop patch they composed, and dislocations with positive sign located at right side of a loop patch and with negative sign located at the left side of the loop patch would be bowed out and expanded as shown in Fig. 12(a). When the latter meet other dislocations with unlike sign from the opposite loop patch, they become two screw dislocation segments with unlike signs and move in opposite direction as shown in Fig. 12(b), until they encounter a screw dislocation of unlike sign with which they annihilate or they sweep out of the grains. When dislocations bowed out of the same side of the loop patch meet each other rather than other dislocations with unlike sign from the opposite loop patch as shown in Fig. 12(c), they expand and strike the adjacent loop patch, depositing their edge segments with their original sign on the opposite loop patch and changing the dislocation sign at the out bound of the opposite loop patch. W i t h t h e expansion of thedislocation loops, unlike sign screw segments from different loops, attract each other and annihilate, leaving a edge dislocation segment with reversed sign to deposit on its own side. Another two screw segments move in opposite direction until they encounter a screw dislocation of unlike sign with which they annihilate or they sweep out of the grains, This is shown in Fig. 12(d). Therefore, after half cycle, the out bound in the fight side of the loop patches would be shielded by edge dislocation segments with negative sign, the out bound in the left side of the loop patches would be shielded by edge dislocation segments with positive sign. For the next half cycle, the load is reversed and the above process is repeated, leading to alternating the dislocation sign in the out bound of the loop patches and some screw dislocation segments sweeping out of the grains. During one cycle, this results in deposition of edge dislocations on loop patch twice but with unlike sign. The edge dislocations with unlike sign must form dislocation loops because of their low strain energy, The repeating deposition of the dislocation loops and the loop patches would cause the loop patches to be Taylor lattice structures and dipolized. This means that all dislocation structures in fatigue are favored to be formed into dipolized structures, Though the dislocation structures have many different appearances like loop patch, vein and dipolar walls, when subjected to different strain amplitude, these structures are formed from a similar
mation in fatigue must be a energy minimization process. It is pointed out that in the above dipolized dislocation structure formation model, the dipolized process included not only edge dislocation segment deposition on the loop patches, but also some screw dislocation segments being swept out of the grains. The screw dislocation segment sweep out the grains results in the formation of intrusions and extrusions. Therefore, this modified model can create irreversible plastic strain causing the nucleation of cracks and the eventual fracture of material.
dislocation deposition mechanism and are dipolized dislocation structure. Difference in appearance is just caused by them being condensed under different conditions, i.e. the dipolar wall structures are condensed more sharper than loop patch structures. Because Taylor lattice structure is a low strain energy configuration, the dipolized dislocation structure for-
Acknowledgement--The authors would like to acknowledge
5. CONCLUSIONS In this investigation, the dislocation structures in fatigued polycrystalline copper with small grain size were studied over an extensive plastic strain range. Based on the observation of these dislocation structures, the following conclusions can be drawn: 1. The dislocation structures produced in fatigued polycrystalline copper with small grain are mainly classified into three types of dislocation structures in the strain range from 1.5× 10 -5 to 10 -2, which correspond to the three regions in the cyclic stress-strain curve. 2. In region A, cylindrical loop patch structure which was observed in single crystals and coarse grained polycrystals is also formed in cyclic saturated polycrystalline copper with small grain size. Moreover, the irregular loop patch and cellular loop patch, that were rarely reported to occur in the coarse grain polycrystals and single crystals, are present in region A of the smaller grained polycrystalline copper. 3. In region B of the small grained polycrystalline copper, the dislocation structure forms veins, PSBs structure are also present in this region but with much lower volume fraction than that found in the coarse grained polycrystals and single crystals reported earlier in literature. 4. In region C, the dislocation structures of the small grained polycrystalline copper are dominated by dipolar walls. In addition, labyrinth structures are formed in this region instead region B as observed in coarse grained polycrystals and single crystals. The dipolar walls become denser and sharper in image as the applied strain increases. At strain close to l0 -2, the dipolar walls become more cell shaped. 5. All the dislocation configurations formed in the fatigued polycrystalline copper are low strain energy structures. A dipolized dislocation arrangement model has been proposed to describe the formation process of dislocation structures such as the loop patches and the dipolar walls. the Natural Science and Engineering Research Council of Canada for support of this investigation. REFERENCES 1. H. Mughrabi, Mater. Sci. Engng 33, 207 (1978). 2. T. Broom and R. K. Ham, Phil. Mag. 7, 95 (1962).
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