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Cell structures in polycrystalline copper undergoing cyclic creep at room temperature
OOOI-6160/85 s3.00 +o.oo Copyright d’ 1985 Pergamon Press I_td
Arco tttrfu//. Vol. 33. NO. 6. PP. 1121-i 127. 1985 Printed in Great Britain. All rights rcwrvcd
CELL STRUCTURES IN POLYCRYSTALLINE COPPER UNDERGOING CYCLIC CREEP AT ROOM TEMPERATURE X. D, CHANDLERY and J. V. BEE’ ‘School of Mechanical Engineering and 2Department of Metaifurgy, University of the Witwatersrand, Jan Smuts Avenue. Johannesburg 2001. South Africa (Received
1 March 1984, in revisedform I2 November 1984)
Abstract-Push-pull cyclic tests were carried out on polycrystalline copper specimens between fixed force limits. When a mean stress was superimposed on the cyclic s&ess. two kinds of cyclic creep were obsentcd, one at low mean stress character&d by relatively symmetrical mechanical hysteresis loops and another at high mean stresses in which hysteresis loops became markedly asymmetric. Examination of the dislocation cell structures provided evidence that such structures change continuously during cycling and deformation proceeds by breakdown of cell walls producing localised areas of high uniform dislocation density from which new cells can form and grow during subsequent cycling before their eventual breakdown. Thus so called steady state cyclic deformation is, in reality, the average effect of a large number of transient defo~ation events. R&m&-Nous avons effect& des essais di dilatation et de compression cycliques SUTdes Cchantillons de cuivre. polycristallins entre des limites de force fix&es. lmsqu’on supwposait unc contrainte moyenne II la contrainte cyclique, nous observ&avons deux types de fluage cyclique: l’un, aux faibles contraintes moyennes, Ctait caractCris6 par des cyl& d’hystir&se m&anique relativement symttriques et l’autre, aux fortes contra&es moyennes, dans lequels les cycles d’hystCr&e devenaient nettemebt a symiitriques. L’observation des structures de c&&s de dislocations montre que ces structures changent continuell~ent au tours des cycles et que la d&formation progmsse par la destruction de parois dc cellules, prod&ant des zones locali& de densi& de dislocations uniforme et forte, B part2 desquelles dc nouvelles cellules peuvent se former et cro&m au coun des cycles ultCrieurs avant leur Cventuelle destruction. La d&formation cyclique dite stationnain est ainsi, en &alit&, l’effet moyen d’un grand nombre d%&ements de diformation transitoires. Zusammeaf~Zyk&che Druck-Zugversuche wurden an polykristallinen Kupferproben zwischen festen Kmftgmnzen du~~~~. Rei iiberiagerung einer mittIeren Spannung fiber dii zyklische Spannung konnten zwei Arten des zjk%chen Kriechens beobachtet werden. Das Kriechen bei kleinen mittieren Spannungen zeichnete sich durch einc vergleichsweise symmetrische mcchanische Hys&Ieife BUS, das Kriechen bci hoher mittlerer Spannuag war gekcnnzeichnet durch dcutlich asymmetrische Hystcrcscschleifen. Di Untersuchung der Zellstruktur wies darauf hin, daB sich solche Strukturen wiihnnd der yklischen Verformung kontinuierlich veriindem. Die Verfonnung IHuftliber das Zusammenbrechen von Zellwiinden, wodurch lokale Bereiche g&hfi%mig hoher Versetzuagsdichtc entstehen. Daraus k&men neue Z&en entstehen und bei da na~fol~en zyklischen Verformung wachsen, his sic wieder ~rnenb~~. Demnach ist dii soeannte station&e xyklischc V~o~~g in Wi~~i~~t ein gemitteiter Effekt iiher tine groBe Anxahl von ineinander iibergehenden Verformungsereignissen.
INTRODUCITON
When metals are plastically deformed, well defined dislocation sub-structures are formed within grains. Such aggregations may take the form of bundles, walls or all structures and have been observed during monotonic loading [l] and cyclic loading [Z-s]. For cyclic loading, with which the present inv~ti~tion is concerned, different types of sub-structure are formed depending on the plastic strain amplitude (6). For polycrystalline copper it has been suggested that there are four kinds of structure which are, in order of increasing strain amplitude: (I) Formation (II) Formation
of dislocation dipole veins of persistent slip band ladders
(III) Formation of secondary dipole wall or cell structures with cell structures predominating at higher strains (IV) Formation of structures similar to those observed in monotonic loading. Because of the different dislocation densities in wall or vein structures as compared to the material in the intervening spaces, glide in the regions between dislocation aggregates is expected to be relatively easy and such regions would have a lower Row stress than the walls. This had led to a number of “composite model” approaches to describe various aspects of inelastic deformation behaviour. Examples include high temperature transient creep f7j and creep acceleration [8,9] which have been modelled by assuming
1121
1122
CHANDLER and BEE: POLYCRYSTALLlNE
that walls and regions between walls obey different steady state power law creep equations. Studies have also been carried out on the Bauschinger effect [lo] and other aspects of cyclic deformation behaviour using composite models of different degrees of com-
plexity [I l-,14].The basic assumption in such models is that strains are compatible which leads to different stress distributions in walls and intervening regions due to different flow stresses of the different components. For cyclic deformation between fixed strain limits it has been suggested that plastic flow is primarily due to the movement of dislocation loops which are nucleated at cell walls and traverse the intervening spaces [Z].These loops 8re blocked by neigh~u~ng walls and micro-plastic behaviour results. At higher stress levels, however, it is thought that dislocations arriving at a cell wall may nucleate other dislocation loops in neighbouring cells thus effectively rendering the walls transparent to dislocation movement and resulting in macro-plastic flow [14]. The foregoing views envisage dislocation cells 8s being essentialIystatic structures with little change or reorganization occurring once steady state conditions have been achieved. However, some structural changes must be wrpected during transient creep [IS] or settling towards saturation in cyclic deformation. One rn~~~srn suggested for such structurat changes is that cell walls may split, thereby increasing the number of cells and reducing their size [16]. Most work on cyclic plastic behaviour has been carried out between Bxed strain or displacement limits rather than stress or force limits. When metafs 8re cycIed between @ted stress limits, ~~farly if a steady mean stress is superimposed on the cyclic stress, cyclic strain induced creep occurs. Curves of strain accumulation plotted against number of cycles resemble stress-time curves for thermally induced creep in that transient, steady state and tertiary creep 8re observed. A difference is that in cy& creep the creep strains may be relatively large and can approach values close to the elongation at fracture in a conventional tensile test. Although cell structures may be static when the material is cycled between strain limits, it is difficult to envisage from compatibility conside~tions that such large cyclic creep deformations can be accommodated without considerable dislocation sub-structure rearrangement. A phenomenon observed in the cyclic deformation of single crystals which is associated with substructure breakdown is the occurrence of “strain bursts” f17, 181. When f.c.c. or h.c.p, crystals are cycled between slowly increasing force limits, periodic large increases in the strain amplitude occur which fast for a few cycles and then die out. Observation of dislocation sub-structures before and during such strain bursts [18] in copper single crystals indicate that during bursts there is a large increase in the dislocation density and that new ceils are being formed. In addition to single crystals. strain bursts
Cu UNDERGOING
CYCLIC CREEP
have also been reported during the cyclic deformation of polycrystalline copper [19,20]. As with single crystals, strain bursts in polycrystals were regarded_as being discontinuous events which occur during a few cycles and die down as deformation proceeds. The object of the present investigation was to carry out cyclic tests on polycrystalline copper specimens between a fixed stress amplitude with various superimposed mean stressesto obtain different degrees of cyclic creep. Dislocation cell structures were then examined to try and determine whether different deformation mechanisms are operating at different creep conditions and to assess whether cell structures are static or dynamic entities. RXPERIMRNTAL The material used was commercial purity copper which ~8s annealed to give 8 grain size of about 250 pm. Button head type specimens having a paraflef -test se&on of 27 x 7.5 mm dia were rna~hin~ from the bar after annealing. Mechanical testing was carried out on an BSH servo-hydraulic machine of 250 kN maximum capacity and strains were measured using a IOmm gauge length clip type strain gauge extensometer. Six specimens were tested betwm cyclic force limits w~ch were adjusts so 8s to give f8irly similar true stress amplitudes after steady state conditions had been reached and after allowing for changes in specimen diameter due to different amounts of cyclic creep in different specimens. Two specimens were tested with zero mean stress, two with a tensile mean stress of 17 MP8 and two with a tensile mean stress of 28 MPa. All specimens were tested at a frequency of 0.01 Hz. For each value of the mean stress, one specimen was unloaded from the tensile phase of the cycle and one from the compressive phase prior to microscope examination. Discs were cut from each specimen transverse to the specimen axis and foils suitable for TEN prepared using standard techniques. The structures were studied using a JEOL 1OOCmicroscope operating at 100kV. MECHANICAL BEHAVIOUR
Figures 1 to 3 show steady state mechanical hysteresis loops for specimens tested at mean stresses of zero, 17 and 28 MPa respectively and true stress amplitudes of 346, 346 and 339 MPa. The plastic strain amplitude from Fig. 1 is 3.38 x lo-’ corresponding to defo~ation regime III [6] in which dislocation wall and cell structures should predominate. In the present tests, strain burst behaviour of the kind reported in Ref. [ 191was not observed. This may be either because such strain burst behaviour only occurs during the first few cycfes before steady state cycling conditions are reached or it may be a toading rate effect, the cycling frequency in the present in-
CHANDLER
200
Stress @Pa)
and BEE: POLYCRYSTALL[N~
Cu UNDERGOING
CYCLIC CREEP
1123
c
150 -
100so0
10
Strain x 1W
-50 -
-100 -150 -
-200
-200 t
t
Fig. 1. Steady state mechanical hysteresis loop for a specimen cycled at a stress amplitude of 346 MPa and zero mean stress.
Fig. 2. Steady state mechanical hysteresis loop for a specimen undergoing type I cyclic creep. Stress amplitude is 346 MPa and mean stress is 17MPa.
vestigation being 0.01 Hz as compared to 0.3-0.5 Hz in Ref. 1191. The mechanicai behaviour of spechnens tested under different mean stress conditions shows some differences. In Fig. 1, the hysteresis loop is symmetrical about the zero stress axis and the specimen is undergoing very little creep (in practice it is difficult to completely suppress cyclic creep when testing between force limits). In Fig. 2, the specimen is undergoing creep at a strain rate of about 0.4 x lop3 per cycle with a plastic strain of 3.4 x lo-’ in the tensile phase of the cycle and 3.0 x 10q3 in compression. Thus, although the true stress amplitude is the same for this specimen as for that shown in Fig, 1, the mechanical behaviour when a mean stress is
applied appears to be stiffer both in tension and compression. The behaviour illustrated in Fig. I has previously been referred to as type I cyclic creep PI]. in this mode of deformation, creep rates are relatively small compared to the plastic strains generated during cycling and the stress strain curves are relatively steep in both phases of the cycle. For testing conditions under which creep rates become very small, hysteresis loops for type I behaviour tend towards symmetry about the mean stress axis. As distinct from Fig. & the specimen in Fig. 3 is undergoing type II cyclic creep. In this mode of behaviour the creep strain per cycle is relatively large with hysteresis loops being markedly assymmetrical and flat topped in the mean stress phase of the cycle.
200
Stress
t 150 -
-50 -
Strain x 1CP
-200 Fig. 3. Mechanical hysteresis loop for specimen undergoing type II cyclic creep. Stress amplitude is 339 MPa and mean stress is 28 MPa.
1124
CHANDLER
and BEE:
POLYCRYSTALLINE
Fig. 4. Dislocation cell structure from a specimen undergoing type I cyclic creep. Typical structures are (A) areas of wall breakdown, (B) small cells indicating recovery, (C), elongated cells and (D) wails terminating within cells.
Cu UNDERGOING
CYCLIC CREEP
Fig. 6. Areas of distributed dislocations which are not surrounded by well defined walls. These are probably due to wall breakdown caused by local strain bursts.
type I cyclic creep unloaded from the tensile phase of the c$zle. These are (as labelled in Fig. 4): All specimens possessed similar dislocation substructures with the exception of a particular structure only observed in one of the specimens undergoing type II creep. Essentially the structures were similar to those described in Refs [18] and [20] and all specimens posses& features which were described as being typical of those present before, during and after
a strain burst. In the present inv~tigation, microstructural observations were made after steady state cycling conditions had been achieved. It is thus likely that the kind of strain bursts which produce noticeable changes in the stress-strain behaviour over several cycles and in which particular structural features appear to dominate before, during and following a strain burst are associated with settling towards a steady state, either at the commencement of cycling, or following load changes. The principal structu!af features are shown in Fig. 4 which was obtained from the specimen undergoing
Fig. 5. Cells showing locally continuous distributions of dislocations. At the bottom. the distributed dislocations may be an obliquety sectioned wall since they are surrounded by a well detmcd wall structure.
(A) Localised areas with fairly uniform dislocation density and poorly defined wall stnlctures. (B) Small cell sects forming within regions such as A. (C) Large relatively dislocation free cells enclosed by well defined walls. Such cells are
fixquently elongated. which terminate within cells.
(D) Wall structures
Figures 5 and 6 show more detailed views of areas with relatively uniform dislocation densities. Such structures may be interpreted as being either cell walls which have been sectioned obliquely or as structures produced by cell wall disruption, i.e. isolated strain bursts. Considering the former inte~retation, it may be expected that walls more or less perpendicular to the plane,of the foil as well as the obliquely sectioned wall would be visible and that the uniform dislocation density would be outlined by relatively well defined structures. This may well be the case for the cell at the bottom of Fig. 5. However, the latter interpretation, that of a localised strain burst, is more likely where there are no well defined surrounding walls such as regions A in Fig. 4, structures at the right and left of Fig. 5 and in Fig. 6. In areas where cell breakdown has occurred producing avalanche dislocations, recovery processes resulting in the formation of new cells are likely to take place over a number of cycles. Structural features such as that labelled B in Fig. 4 are probably nuctei for new cell development. A particular structure which may be associated with recovery is that shown in Fig. 7 which was only observed in the specimen undergoing type II cyclic creep unloaded from the tensile phase of the cycle. Cells are of variable size and irregularly shaped as compared to the more usual structures shown in Figs 4, 5, 6 and
CHANDLER
and BEE:
POLYCRYSTALLINE
Fig. 7. Irregular size and shape cells which were only observed in tt? specimen undergoing type II cyclic creep. Such structures are probably associatedwith recovery in
Cu UNDERGOING
CYCLIC
CREEP
1125
(a)
areas where there has been widespread cell wail breakdown.
8. Under the relatively high stresses at which type II behaviour occurs it is possible that strain bursts are
not as localised as &i type I deformation and that large numbers of neighbouring cells break down. Structures such as that in Fig. 7 possibly arise from the recovery of widespread regions of avalanche dislocations. It is probable that type I and II behaviour differ due to the localised nature of strain bursts in the former and widespread strain bursts in the latter case. Elongated cells (C in Fig. 4) are characteristic features of dislocation sub-structures in cycled metals. Such structures often consist of dense long walls with thinner traversing walls dividing them into cells as,shown in Fig. 4 and the left of Fig. 8. In copper, it has been shown that the long walls tend to lie along the primary (111) and conjugate (trl) slip systems 118,201.The. micrograph in Fig. 9(a) indicates that cell elongation occurs by the absorption of dislocations from traversing walls into long walls and the structure of Fig. 9(a) seems to have formed from a set of equiaxed, mainly hexagonal cells as illustrated
Fig. 9. (a) Elongatedcells showing arts’ of cell walls which probably traversed them and divided the structure into equiaxed polygonal cells as illustrated in (b).
in Fig. 9(b). The process of cell elongation probably occupies a number of cycles during which the structures are relatively stable until local stresses reach a value such that a strain burst is precipitated. A further possible mechanism for cell growth or division is the contraction or extension of walls which terminate within cells, e.g. D in Fig. 4. Many terrninating walls are probably formed follo~ng absorbtion of cross walls into more stable walls as indicated with an arrow at the top left of Fig. 4. Cell walescence by wall contraction also appears to be occurring at the top of Fig. 8 (arrowed) where there seems to have been a junction between four walb. IX&cation loops have formed at the wall ends and it is likely that glide of these across cells could result in dissipation of parts of the walls. DISCUSSION
Fig. 8. Elongated cells with, at the left, less dense all walls spanning dense continuous walls.
Even under so called steady state or saturation conditions, it appears that cyclic defo~ation is not homogeneous but invoIves spatially localised strain bursts producing regions of relatively uniform dislocation density from which new cells form. The new cells grow during succeeding cycles, often by elon-
I126
CHANDLER
and BEE:
~LYCRYSTALLINE
gation, until they in their turn suffer strain bursts. This mechanism is able to account for the large strains that may be accumulated under cyclic creep conditions in a more satisfactory way than by considering dislocation sub-structures to be essentially static. Thus the apparently steady state condition is, in fact, the average effect of a large number of transient deformation events. The effect of strain bursts is to cause localised deformations which would relieve the local stress. Stress relief in one area would cause stress increases elsewhere in the material and, depending on c&l orientation and stress magnitude cause other strain bursts to occur. In a single crystal where slip planes have the same orientation with respect to the applied stress, strain bursts should propagate through a large region of the crystal giving the observed large increase in the overall strain [ 17,181, Slip line formation is associated with strain bursts in single crystals of copper [18]. In polycrystals during initial stages of cycling before well defined cell structures have been established, strain bursts may be expected to propagate through a large proportion of a suitably orientated grain and this, over a number of grains, probably gives rise to the less pronoun gross strain burst behaviour observed f19]. However, once cell structures have been fully established, there is probably suiTGent misorientation between cells within an individual grain to prevent strain bursts from extending over more than a few cells (in type I creep) so that noticeable changes in the hysteresis behaviour as cycling proceeds are not observed. Previous work [21]‘indicates that onset of type II cyclic crep as in Fig. 3 does not depend on the stress amplitude but orxurs when the maximum stress reaches a&ticaI value which is close to the ultimate tensile strength of the mate&i. As indicated above, it is likeIy that widespread rather than IocaIisedstrain bursts occur in this mode of deformation and therefore that cell misorientations are not large enough to lo&se. burst behaviour once a critical stress is reached. Type II behaviour can possibly be considered to be strain burst behaviour similar to that described in Ref. [19] which does not die out after a few cycles but continues at the same rate in succeeding cycles. If, during steady state cycling, the force is heId constant at some point during the cycle, creep continues to occur. At low tem~ratur~ (such that steady state thermally activated creep is insignifi~nt) such cr&p practically ceases within a few hours. it is likely that most of this deformation arises from recovery and cell growth and the structure tends to an equilibrium configuration. The material softens during such creep deformation which can be shown by unloading from the hold point and continuing cycling at the same rate as before. The initial stress-strain behaviour is much softer than the steady state curve and the material hardens during the next few cycles to the previous steady state condition. If
Cu UNDERGOING CYCLIC CREEP
the material is cycled sufficiently slowly, a quasi equilibrium hysteresis loop is formed which may be expected since strain bursts followed by cell formation and growth could occur over a time interval in which there is little increase in load, tending to form a low energy structure. This, therefore, provides some physical justification for describing cyclic deformation in terms of “overstress” theories of viscoplasticity [22-241. In such theories the strain rate is
considered to be not only a function of stress as is the casezwith most plastic flow theories ‘but aIso is a function of the difference in stress (overstress) between the actual stress-strain point and the corresponding strain point on an “equilibrium” stress strain curve. In terms of the microstructural events described above, strain burst behaviour is expected to give rise to the dependence of strain rate on the actual stress and softening processes i.e. cell nucleation and growth would lead to the strain rate being a function of the overstress. CONCLUSIONS
Ex~nation of dislocation sub-structure in polycrystalline copper specimens undergoing differing degrees of cycfic creep deformation under steady state cyclic conditions indicates that cell structures arc not static: Deformation occurs by a process involving localised cell wall breakdown (strain bursts) producing regions of relatively uniform dislocation density (dislocation avalanches). This is similar to that observed in single crystals and in polycrystals during the initial stages of cycling. However, under steady state conditions, the strain bursts are small and isolated and do not produce the fluctuations in hysteresis behaviour seen in single crystals and during settling to steady state conditions. New cells nucleate within dislocation avalanches and grow, mostly by c&I elongation until orientation and local stress conditions render them unstable and they stier strain bursts. These events occur simultaneously in different parts of the specimen tid not co-operatively as in single crystals thus giving an apparently steady state hysteresis loop which is an averaged effect of many transient deformation events. Acknowl~dgetnents-The authors would like to thank the Barlow Rand Group, the C.S.I.R. and the Senate Research Committee of the University of the Witwate~nd for financial assistance.
REFERENCES 1. H. Mughrabi, in Constitutive Relations in Plasticity (edited by A. S. Argon), p. 199. MIT Press, Cambridge, MA (1975). 2. C. E. Feltner and C. Laird, Acta metall. 15, 1633 (1967). 3. J. C. Grosskreutz and H. Mughrabi, in Cons/itutiue Relations in Plasticity (edited by A. S. Argon), p. 251. MIT Press. Gunbridge, MA (1975). 4. A. T. Winter, &-ICImetall. 28, 963 (1980).
CHANDLER
and BEE:
POLY~RYSTALLlNE
5, K. V. Rasmussen and 0. 13. Pederscn. Aeru twtufl. Lx, 1467 (1980). 6. H. Mughrabi and R. Wang, in froc. Second Ri.w It~i. S,vmp. on Mercdlurgy ottci hfulcriuis Scietrcc. Rise. 1980 (cditcd by N. Hansen. A. Horsewell, T. Letfers and H. Lilholt). p. X7. Riser National Laboratory, Roskilde (1981). 7. W. Blum. Scr#ru ntrrt~ll. 16, I353 (1982). 8. T. Mura, H. Shirai and M. Meshii, Mater. .Sci. .!%grzg 17, 221 (1975). 9. M. Meshii, M. Ueki and H. D. Chion. in Proc.,fifib fnr. C~I$ on Strengrh qf Metals and Aiioys, Aachen, 1979 (edited by P. Haasen, V. Gerold and G. Koston), Vol. I, p. 245. Pergamon Press, Oxford (1979). 10. 0. B. Pedersen, L. M. Brown and W. M. Stobbs, Acta mefall. 29, 1843 (1981). II. C. Holste and H. J. Burmeister, Physica stafus solidi A57, 269 (I 980). 12. H. J. Burrneister and C. Holste, Physica status solidi A64 61 I (1981).
Cu UNDERGOING
CYCLIC
CREEP
It27
13. 0. B. Pcdcrscn atId A. T. Winter, Acra metal/. 30, 71 I (1982). 14. H. Mughrabi, Acw meral/. 31, 1367 (1983). 15. W. D. Nix and B. Ischncr. in Proc.JTfih Int. CO& on /he Sfwrr,~fh r!/‘ Mc/u/.v cud A//o,ws. Aachen, 1979 (edited by P. Haasen. V. Gerold and G. Kostorz), Vol. 3, p. 1503. Pergamon Press. Oxford (1980). and R. 0. Scattergood, 16. U. F. Kocks. T. &Wgdw Scripla /71alcrN. 14, 449 (I 980). 17. P. Neumann, Z. Me/o//k. 58. 780 (1967). 18. F. Lorenzo and C. Laird, Acla mefall. 32, 671 (1984). 19. F. Lorenzo and C. Laird. Muler. Sci. Enpzg 52, I87 (1982). 20. F. Lorenzo and C. Laird, Acta me&i. 32, 681 (1984). 21. H. D. Chandler. Acta ~zer~~li.32, 1253 (1984). 22. M. A. Eisenberg, C. W. Lee and A. Phillips. In<. J. Solids Strut’f. 13, 1239 (1977). 27, 363 (1979). 23. E. Krempl. J. &tech. P!J~s. Solids 24. D. Kujawski, V. Kallianpur and E. Krempl, J. Me& fhys. Solids 28, 129 (1980).
Arco tttrfu//. Vol. 33. NO. 6. PP. 1121-i 127. 1985 Printed in Great Britain. All rights rcwrvcd
CELL STRUCTURES IN POLYCRYSTALLINE COPPER UNDERGOING CYCLIC CREEP AT ROOM TEMPERATURE X. D, CHANDLERY and J. V. BEE’ ‘School of Mechanical Engineering and 2Department of Metaifurgy, University of the Witwatersrand, Jan Smuts Avenue. Johannesburg 2001. South Africa (Received
1 March 1984, in revisedform I2 November 1984)
Abstract-Push-pull cyclic tests were carried out on polycrystalline copper specimens between fixed force limits. When a mean stress was superimposed on the cyclic s&ess. two kinds of cyclic creep were obsentcd, one at low mean stress character&d by relatively symmetrical mechanical hysteresis loops and another at high mean stresses in which hysteresis loops became markedly asymmetric. Examination of the dislocation cell structures provided evidence that such structures change continuously during cycling and deformation proceeds by breakdown of cell walls producing localised areas of high uniform dislocation density from which new cells can form and grow during subsequent cycling before their eventual breakdown. Thus so called steady state cyclic deformation is, in reality, the average effect of a large number of transient defo~ation events. R&m&-Nous avons effect& des essais di dilatation et de compression cycliques SUTdes Cchantillons de cuivre. polycristallins entre des limites de force fix&es. lmsqu’on supwposait unc contrainte moyenne II la contrainte cyclique, nous observ&avons deux types de fluage cyclique: l’un, aux faibles contraintes moyennes, Ctait caractCris6 par des cyl& d’hystir&se m&anique relativement symttriques et l’autre, aux fortes contra&es moyennes, dans lequels les cycles d’hystCr&e devenaient nettemebt a symiitriques. L’observation des structures de c&&s de dislocations montre que ces structures changent continuell~ent au tours des cycles et que la d&formation progmsse par la destruction de parois dc cellules, prod&ant des zones locali& de densi& de dislocations uniforme et forte, B part2 desquelles dc nouvelles cellules peuvent se former et cro&m au coun des cycles ultCrieurs avant leur Cventuelle destruction. La d&formation cyclique dite stationnain est ainsi, en &alit&, l’effet moyen d’un grand nombre d%&ements de diformation transitoires. Zusammeaf~Zyk&che Druck-Zugversuche wurden an polykristallinen Kupferproben zwischen festen Kmftgmnzen du~~~~. Rei iiberiagerung einer mittIeren Spannung fiber dii zyklische Spannung konnten zwei Arten des zjk%chen Kriechens beobachtet werden. Das Kriechen bei kleinen mittieren Spannungen zeichnete sich durch einc vergleichsweise symmetrische mcchanische Hys&Ieife BUS, das Kriechen bci hoher mittlerer Spannuag war gekcnnzeichnet durch dcutlich asymmetrische Hystcrcscschleifen. Di Untersuchung der Zellstruktur wies darauf hin, daB sich solche Strukturen wiihnnd der yklischen Verformung kontinuierlich veriindem. Die Verfonnung IHuftliber das Zusammenbrechen von Zellwiinden, wodurch lokale Bereiche g&hfi%mig hoher Versetzuagsdichtc entstehen. Daraus k&men neue Z&en entstehen und bei da na~fol~en zyklischen Verformung wachsen, his sic wieder ~rnenb~~. Demnach ist dii soeannte station&e xyklischc V~o~~g in Wi~~i~~t ein gemitteiter Effekt iiher tine groBe Anxahl von ineinander iibergehenden Verformungsereignissen.
INTRODUCITON
When metals are plastically deformed, well defined dislocation sub-structures are formed within grains. Such aggregations may take the form of bundles, walls or all structures and have been observed during monotonic loading [l] and cyclic loading [Z-s]. For cyclic loading, with which the present inv~ti~tion is concerned, different types of sub-structure are formed depending on the plastic strain amplitude (6). For polycrystalline copper it has been suggested that there are four kinds of structure which are, in order of increasing strain amplitude: (I) Formation (II) Formation
of dislocation dipole veins of persistent slip band ladders
(III) Formation of secondary dipole wall or cell structures with cell structures predominating at higher strains (IV) Formation of structures similar to those observed in monotonic loading. Because of the different dislocation densities in wall or vein structures as compared to the material in the intervening spaces, glide in the regions between dislocation aggregates is expected to be relatively easy and such regions would have a lower Row stress than the walls. This had led to a number of “composite model” approaches to describe various aspects of inelastic deformation behaviour. Examples include high temperature transient creep f7j and creep acceleration [8,9] which have been modelled by assuming
1121
1122
CHANDLER and BEE: POLYCRYSTALLlNE
that walls and regions between walls obey different steady state power law creep equations. Studies have also been carried out on the Bauschinger effect [lo] and other aspects of cyclic deformation behaviour using composite models of different degrees of com-
plexity [I l-,14].The basic assumption in such models is that strains are compatible which leads to different stress distributions in walls and intervening regions due to different flow stresses of the different components. For cyclic deformation between fixed strain limits it has been suggested that plastic flow is primarily due to the movement of dislocation loops which are nucleated at cell walls and traverse the intervening spaces [Z].These loops 8re blocked by neigh~u~ng walls and micro-plastic behaviour results. At higher stress levels, however, it is thought that dislocations arriving at a cell wall may nucleate other dislocation loops in neighbouring cells thus effectively rendering the walls transparent to dislocation movement and resulting in macro-plastic flow [14]. The foregoing views envisage dislocation cells 8s being essentialIystatic structures with little change or reorganization occurring once steady state conditions have been achieved. However, some structural changes must be wrpected during transient creep [IS] or settling towards saturation in cyclic deformation. One rn~~~srn suggested for such structurat changes is that cell walls may split, thereby increasing the number of cells and reducing their size [16]. Most work on cyclic plastic behaviour has been carried out between Bxed strain or displacement limits rather than stress or force limits. When metafs 8re cycIed between @ted stress limits, ~~farly if a steady mean stress is superimposed on the cyclic stress, cyclic strain induced creep occurs. Curves of strain accumulation plotted against number of cycles resemble stress-time curves for thermally induced creep in that transient, steady state and tertiary creep 8re observed. A difference is that in cy& creep the creep strains may be relatively large and can approach values close to the elongation at fracture in a conventional tensile test. Although cell structures may be static when the material is cycled between strain limits, it is difficult to envisage from compatibility conside~tions that such large cyclic creep deformations can be accommodated without considerable dislocation sub-structure rearrangement. A phenomenon observed in the cyclic deformation of single crystals which is associated with substructure breakdown is the occurrence of “strain bursts” f17, 181. When f.c.c. or h.c.p, crystals are cycled between slowly increasing force limits, periodic large increases in the strain amplitude occur which fast for a few cycles and then die out. Observation of dislocation sub-structures before and during such strain bursts [18] in copper single crystals indicate that during bursts there is a large increase in the dislocation density and that new ceils are being formed. In addition to single crystals. strain bursts
Cu UNDERGOING
CYCLIC CREEP
have also been reported during the cyclic deformation of polycrystalline copper [19,20]. As with single crystals, strain bursts in polycrystals were regarded_as being discontinuous events which occur during a few cycles and die down as deformation proceeds. The object of the present investigation was to carry out cyclic tests on polycrystalline copper specimens between a fixed stress amplitude with various superimposed mean stressesto obtain different degrees of cyclic creep. Dislocation cell structures were then examined to try and determine whether different deformation mechanisms are operating at different creep conditions and to assess whether cell structures are static or dynamic entities. RXPERIMRNTAL The material used was commercial purity copper which ~8s annealed to give 8 grain size of about 250 pm. Button head type specimens having a paraflef -test se&on of 27 x 7.5 mm dia were rna~hin~ from the bar after annealing. Mechanical testing was carried out on an BSH servo-hydraulic machine of 250 kN maximum capacity and strains were measured using a IOmm gauge length clip type strain gauge extensometer. Six specimens were tested betwm cyclic force limits w~ch were adjusts so 8s to give f8irly similar true stress amplitudes after steady state conditions had been reached and after allowing for changes in specimen diameter due to different amounts of cyclic creep in different specimens. Two specimens were tested with zero mean stress, two with a tensile mean stress of 17 MP8 and two with a tensile mean stress of 28 MPa. All specimens were tested at a frequency of 0.01 Hz. For each value of the mean stress, one specimen was unloaded from the tensile phase of the cycle and one from the compressive phase prior to microscope examination. Discs were cut from each specimen transverse to the specimen axis and foils suitable for TEN prepared using standard techniques. The structures were studied using a JEOL 1OOCmicroscope operating at 100kV. MECHANICAL BEHAVIOUR
Figures 1 to 3 show steady state mechanical hysteresis loops for specimens tested at mean stresses of zero, 17 and 28 MPa respectively and true stress amplitudes of 346, 346 and 339 MPa. The plastic strain amplitude from Fig. 1 is 3.38 x lo-’ corresponding to defo~ation regime III [6] in which dislocation wall and cell structures should predominate. In the present tests, strain burst behaviour of the kind reported in Ref. [ 191was not observed. This may be either because such strain burst behaviour only occurs during the first few cycfes before steady state cycling conditions are reached or it may be a toading rate effect, the cycling frequency in the present in-
CHANDLER
200
Stress @Pa)
and BEE: POLYCRYSTALL[N~
Cu UNDERGOING
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c
150 -
100so0
10
Strain x 1W
-50 -
-100 -150 -
-200
-200 t
t
Fig. 1. Steady state mechanical hysteresis loop for a specimen cycled at a stress amplitude of 346 MPa and zero mean stress.
Fig. 2. Steady state mechanical hysteresis loop for a specimen undergoing type I cyclic creep. Stress amplitude is 346 MPa and mean stress is 17MPa.
vestigation being 0.01 Hz as compared to 0.3-0.5 Hz in Ref. 1191. The mechanicai behaviour of spechnens tested under different mean stress conditions shows some differences. In Fig. 1, the hysteresis loop is symmetrical about the zero stress axis and the specimen is undergoing very little creep (in practice it is difficult to completely suppress cyclic creep when testing between force limits). In Fig. 2, the specimen is undergoing creep at a strain rate of about 0.4 x lop3 per cycle with a plastic strain of 3.4 x lo-’ in the tensile phase of the cycle and 3.0 x 10q3 in compression. Thus, although the true stress amplitude is the same for this specimen as for that shown in Fig, 1, the mechanical behaviour when a mean stress is
applied appears to be stiffer both in tension and compression. The behaviour illustrated in Fig. I has previously been referred to as type I cyclic creep PI]. in this mode of deformation, creep rates are relatively small compared to the plastic strains generated during cycling and the stress strain curves are relatively steep in both phases of the cycle. For testing conditions under which creep rates become very small, hysteresis loops for type I behaviour tend towards symmetry about the mean stress axis. As distinct from Fig. & the specimen in Fig. 3 is undergoing type II cyclic creep. In this mode of behaviour the creep strain per cycle is relatively large with hysteresis loops being markedly assymmetrical and flat topped in the mean stress phase of the cycle.
200
Stress
t 150 -
-50 -
Strain x 1CP
-200 Fig. 3. Mechanical hysteresis loop for specimen undergoing type II cyclic creep. Stress amplitude is 339 MPa and mean stress is 28 MPa.
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Fig. 4. Dislocation cell structure from a specimen undergoing type I cyclic creep. Typical structures are (A) areas of wall breakdown, (B) small cells indicating recovery, (C), elongated cells and (D) wails terminating within cells.
Cu UNDERGOING
CYCLIC CREEP
Fig. 6. Areas of distributed dislocations which are not surrounded by well defined walls. These are probably due to wall breakdown caused by local strain bursts.
type I cyclic creep unloaded from the tensile phase of the c$zle. These are (as labelled in Fig. 4): All specimens possessed similar dislocation substructures with the exception of a particular structure only observed in one of the specimens undergoing type II creep. Essentially the structures were similar to those described in Refs [18] and [20] and all specimens posses& features which were described as being typical of those present before, during and after
a strain burst. In the present inv~tigation, microstructural observations were made after steady state cycling conditions had been achieved. It is thus likely that the kind of strain bursts which produce noticeable changes in the stress-strain behaviour over several cycles and in which particular structural features appear to dominate before, during and following a strain burst are associated with settling towards a steady state, either at the commencement of cycling, or following load changes. The principal structu!af features are shown in Fig. 4 which was obtained from the specimen undergoing
Fig. 5. Cells showing locally continuous distributions of dislocations. At the bottom. the distributed dislocations may be an obliquety sectioned wall since they are surrounded by a well detmcd wall structure.
(A) Localised areas with fairly uniform dislocation density and poorly defined wall stnlctures. (B) Small cell sects forming within regions such as A. (C) Large relatively dislocation free cells enclosed by well defined walls. Such cells are
fixquently elongated. which terminate within cells.
(D) Wall structures
Figures 5 and 6 show more detailed views of areas with relatively uniform dislocation densities. Such structures may be interpreted as being either cell walls which have been sectioned obliquely or as structures produced by cell wall disruption, i.e. isolated strain bursts. Considering the former inte~retation, it may be expected that walls more or less perpendicular to the plane,of the foil as well as the obliquely sectioned wall would be visible and that the uniform dislocation density would be outlined by relatively well defined structures. This may well be the case for the cell at the bottom of Fig. 5. However, the latter interpretation, that of a localised strain burst, is more likely where there are no well defined surrounding walls such as regions A in Fig. 4, structures at the right and left of Fig. 5 and in Fig. 6. In areas where cell breakdown has occurred producing avalanche dislocations, recovery processes resulting in the formation of new cells are likely to take place over a number of cycles. Structural features such as that labelled B in Fig. 4 are probably nuctei for new cell development. A particular structure which may be associated with recovery is that shown in Fig. 7 which was only observed in the specimen undergoing type II cyclic creep unloaded from the tensile phase of the cycle. Cells are of variable size and irregularly shaped as compared to the more usual structures shown in Figs 4, 5, 6 and
CHANDLER
and BEE:
POLYCRYSTALLINE
Fig. 7. Irregular size and shape cells which were only observed in tt? specimen undergoing type II cyclic creep. Such structures are probably associatedwith recovery in
Cu UNDERGOING
CYCLIC
CREEP
1125
(a)
areas where there has been widespread cell wail breakdown.
8. Under the relatively high stresses at which type II behaviour occurs it is possible that strain bursts are
not as localised as &i type I deformation and that large numbers of neighbouring cells break down. Structures such as that in Fig. 7 possibly arise from the recovery of widespread regions of avalanche dislocations. It is probable that type I and II behaviour differ due to the localised nature of strain bursts in the former and widespread strain bursts in the latter case. Elongated cells (C in Fig. 4) are characteristic features of dislocation sub-structures in cycled metals. Such structures often consist of dense long walls with thinner traversing walls dividing them into cells as,shown in Fig. 4 and the left of Fig. 8. In copper, it has been shown that the long walls tend to lie along the primary (111) and conjugate (trl) slip systems 118,201.The. micrograph in Fig. 9(a) indicates that cell elongation occurs by the absorption of dislocations from traversing walls into long walls and the structure of Fig. 9(a) seems to have formed from a set of equiaxed, mainly hexagonal cells as illustrated
Fig. 9. (a) Elongatedcells showing arts’ of cell walls which probably traversed them and divided the structure into equiaxed polygonal cells as illustrated in (b).
in Fig. 9(b). The process of cell elongation probably occupies a number of cycles during which the structures are relatively stable until local stresses reach a value such that a strain burst is precipitated. A further possible mechanism for cell growth or division is the contraction or extension of walls which terminate within cells, e.g. D in Fig. 4. Many terrninating walls are probably formed follo~ng absorbtion of cross walls into more stable walls as indicated with an arrow at the top left of Fig. 4. Cell walescence by wall contraction also appears to be occurring at the top of Fig. 8 (arrowed) where there seems to have been a junction between four walb. IX&cation loops have formed at the wall ends and it is likely that glide of these across cells could result in dissipation of parts of the walls. DISCUSSION
Fig. 8. Elongated cells with, at the left, less dense all walls spanning dense continuous walls.
Even under so called steady state or saturation conditions, it appears that cyclic defo~ation is not homogeneous but invoIves spatially localised strain bursts producing regions of relatively uniform dislocation density from which new cells form. The new cells grow during succeeding cycles, often by elon-
I126
CHANDLER
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~LYCRYSTALLINE
gation, until they in their turn suffer strain bursts. This mechanism is able to account for the large strains that may be accumulated under cyclic creep conditions in a more satisfactory way than by considering dislocation sub-structures to be essentially static. Thus the apparently steady state condition is, in fact, the average effect of a large number of transient deformation events. The effect of strain bursts is to cause localised deformations which would relieve the local stress. Stress relief in one area would cause stress increases elsewhere in the material and, depending on c&l orientation and stress magnitude cause other strain bursts to occur. In a single crystal where slip planes have the same orientation with respect to the applied stress, strain bursts should propagate through a large region of the crystal giving the observed large increase in the overall strain [ 17,181, Slip line formation is associated with strain bursts in single crystals of copper [18]. In polycrystals during initial stages of cycling before well defined cell structures have been established, strain bursts may be expected to propagate through a large proportion of a suitably orientated grain and this, over a number of grains, probably gives rise to the less pronoun gross strain burst behaviour observed f19]. However, once cell structures have been fully established, there is probably suiTGent misorientation between cells within an individual grain to prevent strain bursts from extending over more than a few cells (in type I creep) so that noticeable changes in the hysteresis behaviour as cycling proceeds are not observed. Previous work [21]‘indicates that onset of type II cyclic crep as in Fig. 3 does not depend on the stress amplitude but orxurs when the maximum stress reaches a&ticaI value which is close to the ultimate tensile strength of the mate&i. As indicated above, it is likeIy that widespread rather than IocaIisedstrain bursts occur in this mode of deformation and therefore that cell misorientations are not large enough to lo&se. burst behaviour once a critical stress is reached. Type II behaviour can possibly be considered to be strain burst behaviour similar to that described in Ref. [19] which does not die out after a few cycles but continues at the same rate in succeeding cycles. If, during steady state cycling, the force is heId constant at some point during the cycle, creep continues to occur. At low tem~ratur~ (such that steady state thermally activated creep is insignifi~nt) such cr&p practically ceases within a few hours. it is likely that most of this deformation arises from recovery and cell growth and the structure tends to an equilibrium configuration. The material softens during such creep deformation which can be shown by unloading from the hold point and continuing cycling at the same rate as before. The initial stress-strain behaviour is much softer than the steady state curve and the material hardens during the next few cycles to the previous steady state condition. If
Cu UNDERGOING CYCLIC CREEP
the material is cycled sufficiently slowly, a quasi equilibrium hysteresis loop is formed which may be expected since strain bursts followed by cell formation and growth could occur over a time interval in which there is little increase in load, tending to form a low energy structure. This, therefore, provides some physical justification for describing cyclic deformation in terms of “overstress” theories of viscoplasticity [22-241. In such theories the strain rate is
considered to be not only a function of stress as is the casezwith most plastic flow theories ‘but aIso is a function of the difference in stress (overstress) between the actual stress-strain point and the corresponding strain point on an “equilibrium” stress strain curve. In terms of the microstructural events described above, strain burst behaviour is expected to give rise to the dependence of strain rate on the actual stress and softening processes i.e. cell nucleation and growth would lead to the strain rate being a function of the overstress. CONCLUSIONS
Ex~nation of dislocation sub-structure in polycrystalline copper specimens undergoing differing degrees of cycfic creep deformation under steady state cyclic conditions indicates that cell structures arc not static: Deformation occurs by a process involving localised cell wall breakdown (strain bursts) producing regions of relatively uniform dislocation density (dislocation avalanches). This is similar to that observed in single crystals and in polycrystals during the initial stages of cycling. However, under steady state conditions, the strain bursts are small and isolated and do not produce the fluctuations in hysteresis behaviour seen in single crystals and during settling to steady state conditions. New cells nucleate within dislocation avalanches and grow, mostly by c&I elongation until orientation and local stress conditions render them unstable and they stier strain bursts. These events occur simultaneously in different parts of the specimen tid not co-operatively as in single crystals thus giving an apparently steady state hysteresis loop which is an averaged effect of many transient deformation events. Acknowl~dgetnents-The authors would like to thank the Barlow Rand Group, the C.S.I.R. and the Senate Research Committee of the University of the Witwate~nd for financial assistance.
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CHANDLER
and BEE:
POLY~RYSTALLlNE
5, K. V. Rasmussen and 0. 13. Pederscn. Aeru twtufl. Lx, 1467 (1980). 6. H. Mughrabi and R. Wang, in froc. Second Ri.w It~i. S,vmp. on Mercdlurgy ottci hfulcriuis Scietrcc. Rise. 1980 (cditcd by N. Hansen. A. Horsewell, T. Letfers and H. Lilholt). p. X7. Riser National Laboratory, Roskilde (1981). 7. W. Blum. Scr#ru ntrrt~ll. 16, I353 (1982). 8. T. Mura, H. Shirai and M. Meshii, Mater. .Sci. .!%grzg 17, 221 (1975). 9. M. Meshii, M. Ueki and H. D. Chion. in Proc.,fifib fnr. C~I$ on Strengrh qf Metals and Aiioys, Aachen, 1979 (edited by P. Haasen, V. Gerold and G. Koston), Vol. I, p. 245. Pergamon Press, Oxford (1979). 10. 0. B. Pedersen, L. M. Brown and W. M. Stobbs, Acta mefall. 29, 1843 (1981). II. C. Holste and H. J. Burmeister, Physica stafus solidi A57, 269 (I 980). 12. H. J. Burrneister and C. Holste, Physica status solidi A64 61 I (1981).
Cu UNDERGOING
CYCLIC
CREEP
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13. 0. B. Pcdcrscn atId A. T. Winter, Acra metal/. 30, 71 I (1982). 14. H. Mughrabi, Acw meral/. 31, 1367 (1983). 15. W. D. Nix and B. Ischncr. in Proc.JTfih Int. CO& on /he Sfwrr,~fh r!/‘ Mc/u/.v cud A//o,ws. Aachen, 1979 (edited by P. Haasen. V. Gerold and G. Kostorz), Vol. 3, p. 1503. Pergamon Press. Oxford (1980). and R. 0. Scattergood, 16. U. F. Kocks. T. &Wgdw Scripla /71alcrN. 14, 449 (I 980). 17. P. Neumann, Z. Me/o//k. 58. 780 (1967). 18. F. Lorenzo and C. Laird, Acla mefall. 32, 671 (1984). 19. F. Lorenzo and C. Laird. Muler. Sci. Enpzg 52, I87 (1982). 20. F. Lorenzo and C. Laird, Acta me&i. 32, 681 (1984). 21. H. D. Chandler. Acta ~zer~~li.32, 1253 (1984). 22. M. A. Eisenberg, C. W. Lee and A. Phillips. In<. J. Solids Strut’f. 13, 1239 (1977). 27, 363 (1979). 23. E. Krempl. J. &tech. P!J~s. Solids 24. D. Kujawski, V. Kallianpur and E. Krempl, J. Me& fhys. Solids 28, 129 (1980).