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Strain hardening of copper single crystals at high strains and dynamical recovery processes
kro mud. Printed in
Vol. 30, pp. 1961 to 1968, 1982
OCGI-6160 82.101961-08SO3.00~0 IYS? Pergamon Press Ltd
Great Britain. All rights reserved
Copyright 0
STRAIN HARDENING OF COPPER SINGLE CRYSTALS AT HIGH STRAINS AND DYNAMICAL RECOVERY PROCESSES A. KORBEL
and XL SZCZERBA
Institute for Metals Working and Physical Metallurgy. Academy of Mining and Metallurgy, Krakow, Poland (Receiced 29 December 1981) Abstract-Single crystals of copper were deformed by rolling at room temperature in two orientations. Different stress-strain characteristics were found. In hard orientation (Rolling Plane 11 (1ii). Rolling Direction 11[145]) a period of rapid strain hardening is followed by the constancy of the Row stress. In soft orientation (Rolling Plane 11 (321).Rolling Direction 1I [ i45]) a two-stage process of the strain hardening was found but no plateau of stress was observed up to strains of the order of three. On the basis of strain rate change and temperature change experiments and structural observations (optical and electron microscopes) two different mechanisms of dynamical recovery were identified. In particular. a new dynamical recovery process (D.R.-2) was found to be the result of activation of the formally inactite slip direction. The intensity of this process in hard-oriented crystals leads to localization of strain inro well-defined shear bands resulting in a plateau on the b-e curve. Resume-Nous avons deforme des monocristaux de cuivre de deux orientations par laminage a la temperature ambiante. On trouve des courbes contrainte-deformation differentes. Dans le cas dune orientation dure (plan de laminage 11 (I i I). direction de laminage I I [ i45]). on observe une contrainte d’tcoulement constante, apris one pCriode de fort durcissement. Dans le cas dune orientation douse (plan de laminage I I (321). direction de laminage ( I [i45]). on observe un durcissement en deux itap. mais pas de palier de la contrainte jusqu’a des deformations de l’ordre de trois. G&e a des experienm de sauts de vitesse de deformation et de temperature, ainsi qu’a des observations de la structure (microscopies optique et electronique), nous avons pu identifier deux mecanismes differents pour la restauration dynamique. En particulier. un nouveau processus de restauration dynamique (R.D.-3 resulte de I’activation dune direction de glissement en principe inactive. L’intensite de ce phenomenc dans le cas des cristaux &orientation dure conduit a une localisation de la deformation dans des bands de cisaillement bien d&ties, ce qui donne le palier de la courbe u-e. Zusammenfassung-Kupfereinkristalle wurden bei Raumtemperatur durch Walzen in zwei Orientierungen verformt, welches zu unterschiedlichem Spannungs-Dehnungsverhalten fbhrte. In der harten Orientierung (Walzeben (I i 1).Walzrichtung [ i45]) folgt auf eine rasche Verfestigung ein Bereich konstanter FlieBspannung. In der weichen Orientierung (Walzebene (32 I), Walzrichtung [ i45]) wurde ein zweistufiger Verformungsablauf beobachtet; ein Spannungsplateau wurde jedoch bis zu einer Dehnung der GrSBenordnung drei nicht gefunden. Mit Dehngeschwindigkeits- und Temperaturwechseln und der Untersuchung der Mikrostruktur in Licht- und Elektronenmikroskop wurden zwei verschiedene dynamische Erholungsmechnismen identihziert. Insbesondere wurde ein neuer dynamischer ErholungsprozeB aufgefunden. der von der Aktivierung einer vorher inaktiven Gleitrichtung herriihrt. Die Starke dieses Prozesses in den Kristallen der harten Orientierung verursacht Dehnungslokalisierung in wohldefinierten Scherblndern. Diese Bander fuhren zu dem Plateau in der Spannungs-Dehnungskurve.
INTRODUCTION
It is commonly accepted that an observed strain hardening rate depends upon the intensity of dynamical recovery (D.R.) processes and hence upon the deformation conditions and material itself. An increase of the intensity of D.R. in the course of deformation decreases the rate of strain hardening and makes the flow stress more sensitive to temperature and strain rate changes [ 1-33. If the increase of the D.R. rate is sufficient, it may in essence lead to zero strain hardening rate at high strains. Then the geometrical (athermal) strain hardening is being balanced by the thermally controlled softening (recovery) process. The plastic flow becomes then a steady-state which means that flow stress satu-
rates and does not depend upon the strain although it depends on temperature and strain rate. From the structural point of view it means that the microstructure is essentially constant during the period of steady state flow. A phenomenological description of the steady-state flow, which applies to creep and under high temperature deformation conditions, relates the strain rate to the stress and temperature by the following equation (4 < = A sinh (30,)” exp
where A, r, n and Q are constants. One could expect therefore, that even at low temperatures, the steady-state flow may occur. In other
1961
1962
KORBEL
AND
SZCZERBA:
STRAIN HARDENING AND DYNAMIC RECOVERY
words, the plateau on the stress-strain curve should follow monotonic strain hardening range. In contrast to this prediction. a number of observations indicate that strain hardening rate at high strains does not decrease in a monotonic manner [5-9). A gradual decrease of the strain hardening rate is of course conditioned by the homogeneity of plastic flow. Several experimental works report the inhomogeneous nature of deformation at high strains [lo]. Thus, pseudosteady-state regions of plastic flow are expected because temporary constancy of plastic flow may be caused by the spreading of inhomogeneous deformation. The aim of this work is to verify this suggestion. The strain hardening rate before the steady or eventually pseudo-steady flow stage is reached, depends upon the crystal orientation (number of active slip systems). Crystal orientation controls also the rate of accumulation of the energy stored in the
a)
b)
course of deformation. The energy stored in crystal is the driving force for the D.R. processes. It seems to be very useful to know how the crystal orientation
influences the D.R. and disposition deformation.
to non-uniform
EXPERIMENTAL c) Single crystals were grown in a graphite split mold by zone melting of 99.99% copper in a natural temperature gradient furnace in vacuum better than 5 x lo-’ Torr. The crystals had a rectangular cross section with constant width (4mm) but different thickness ranging from 0.8 to 4 mm. They were grown from the seed so that one face of crystal was parallel to (i II) while another one to (321) crystal plane. The crystal’s longest axis (rolling direction) was kept parallel to [i45] direction. Deformation was imposed on crystal by rolling in the true strain range from 0.03 to 3.0. The final thickness of crystals after rolling deformation, was 0.8 mm except for the two highest strain values. Deformation was carried out in steps under good lubrication conditions. The rape oil was used as the lubricant. To protect the crystals from the development of texture gradient across the thickness in each step of deformation, the ratio of the length of arc of contact to specimen thickness was kept constant at the value of 1 (11). The rolling was performed in two orientations: (a) Rolling plane (R.P.) 11 (321) and rolling direction (R.D.) 1/ [ i45]-soft orientation; (b) R.P. [ I (1il) and R.D. I I [i45]-hard orientation (Fig. 1). After each step of deformation, the thickness and the width of crystals were measured. The specimens were then subjected to mechanical tests and structural observations. The tensile tests at room temperature and at 78 K, strain rate experiments at both temperatures and temperature change experiments, were performed. The value of G,,~ proof stress was determined at strain rate lo-“s-l. Nine measurements of co,*
Fig. 1. The crystal orientations used in the experiments R.D.-rolling direction, T.D.-transvcrjz direction
proof stress were done for each deformation. During the strain rate experiments, the strain rate was increased by one order of the magnitude when stress reached the ao.s value. Corresponding tlow stress increase was determined accordingly to Basinski’s proposal [12]. The structure of crystals was observed in two sections: parallel to rolling plane and parallel to roiling direction but perpendicular to rolling plane using both optical and electron microscopy techniques. RESULTS AND DISCUSSION The influence of crystal orientation on the mechanisms of plastic deformation manifests itself in tensile test curves of crystals predeformed by rolling as well as in the rate of strengthening of the material during rolling. Typical differences which occur during the tensile tests of crystals predeformed to 0105 of natural rolling deformation (In h/h,) are shotvn in Fig. 2. As is shown in Fig. lb, crystals oriented: R.P. I ) (lil), RD. 1( [i45], harden at a much higher rate than crystals rolled in orientation “a” in Fig. 1 (R.P. 1I @l), RD. 1I [i45+soft orientation) and they have a strong tendency to unstable flow if tested in tension along the rolling direction. At small rolling deformations (e < 0.1) plastic flow in tension initiates a form of Luders deformation which propagates throughout the crystal at the constant stress. For higher rolling defor-
KORBEL
.4ND
SZCZERBA:
STRIIN
HARDENING
T=293 K iez 8.4-I0-%-’
I !I/
f longotion,
mm
Fig. 1. Typical ditkences which occur during the tensile test of crystals predeformed to 0.105 of natural rolling deformation in two orientations of the rolling plane. The signal of the local gauge length extensometer (lowest curve) proved the Lauder’s front propagation at the onset of plastic Row in hard oriented crystal.
“0.2
2’
marions
T--293 i = 8.4
IOOC
I( lo-%--’
Boa (e
* 2
0.2
0.40.60.8
1.0 I.2
1.4 1.6 1.82.02.2
ttitt 78
K
-
242.62.83.0
the strain in Li.iders band is big enough for
development of the neck in zone of just nucIeating band (Fig. 3). This is however, not the case for crystals predeformed by rolling in soft orientation. Corresponding stress-strain curves for this orientation are also shown in Figs 2 and 3. The tensile deformation is then homogeneous and leads to strain hardening effect. The inguence of the orientation of crystals on the strain hardening rate is shown in Fig. 4 where the tensile proof stress 60.t is plotted against natural rolling deformation. For hard orientation the high strain hardening rate range (up to strain 0.6) is followed by a typical for steady-state flow stage plateau on stressstrain curve. Soft oriented crystals show a lower but continuous increase of the proof stress in the whole examined range of strains.
2:
1963
AND DYNAMIC RECOVERY
800
P 400
200
I
\
\ 2
E longotion,
mm
Fig. 3. The effect of the crystal orientation and the amount of roiling deformation on the toad-elongation curve in tension.
Fig. 4. The tensile proof stress co,2 vs roliing~d:iormation plots for two orientations of crystals in rollrng and two temperatures (78 K and 300 Kj of tensile tests.
The statistical analysis of the shape of stress-strain curve shows however, that there exist two regions of strain where the stress may be related to strain by Holiomon’s type equation [133. For strains 0 c e < 0.6. the following form of equation was found trO.a= 29.7 . E’-
(r’ = 0.993~
(2)
while for strains bigger than 0.6 the best fit follows the equation oe,a = 22.3 . co.26 (8 = 0.993)
(3)
The change of the strain hardening exponent from 0.59 at small to 0.26 at high strains suggests that some relaxation process operates at large deformations. This idea is supported by the results of strain rate change experiments. In Fig. 5, the Row stress response Aa, to the strain rate increase is plotted against the flow stress which in turn reflects the strain imposed on crystal. One can find that at smalI deformations, the relationship obeys to the Cottrell-Stokes law [ 14). At higher stresses however, significant deviation from C-S law occurs. It happens for G > 170 ZlfN,!m’ or aitemativeIy e > 0.6 for which the ~c.: vs E relationship is given by equation (3). Mecking and Kocks[3] postulate that the deviation from the C-S law is caused by activation of the DR. processes. Accepting this suggestion, one would suppose that the D.R.-2 in soft oriented crystals appears not tili then. the stress reaches I70 4IN/m or strain imposed is bigger than 0.6. They both are significantly bigger than stress and strain at which third
1964
KORBEL +.z~DSZCZERBA:
STRAIN HARDENING
f.2 6.8 6.4 6.0 5.6 f y;
3.6 32 2.6 2.4 2.0. 1.6 1.2 0.6,
Fig. 5. The Row stress response Aa,. to the strain rate increase plotted against the uO.J flow stress in tension for two
temperatures of tensile tests. stage (pa~boiic one) on stress-strain curve of single crystat of copper if tensile atong [i45] direction is observed (oJ = 50 MN/m* and .s3 = 0.15 in our case). In Basinski’s approach, the deviation of Ari, vs d plot from the linearity results from the progressive increase of the log term of the line tension of dislocation rather than from any relaxation process which take place in the third stage [U]. Thus it is necessary to make distinction between the relaxation process which operates at high strains and the cross slip which is thought to be responsible for stage three of deformation of single crystals. This last feature, at least in copper does not introduce a measurable contribution to da, value or else its intensity is proportional to stress so that the Cottrell-Strokes law is stilt fulfilled. It may be violated however, if a new slip system (new slip direction) is being activated [19,20]. One can expect therefore, that the relaxation process which occurs at high strains is caused by the activation of non-active yet slip direction. This meets the evidence in Fig. 6 where the relative change of the width of crystal is plotted against the rolling deformation. Figure 6 shows the curves for both orientations. In particular case of just discussing soft orientation the specimens do not widen until the rolling deformation imposed is bigger than approximately 0.6. Thereafter, a sudden widening of crystat was observed. The analysis based upon the Schmid criterion for yielding [16], which in fact is useful only at the onset of deformation, shows that compression of crystal along [321] direction activates B4 slip system (see Fig. Ic). As the conjugate Cl slip system GilI be activated. the slip directions are then [OJ I] for primary
AND DYNAMIC RECOVERY
and [lOi] for conjugate slip system. If projected on the rolling piane they lie afong the rolhng direction SO that they do not give of any widening of crystal. Sudden widening at strains bigger than 0.6 means that new slip direction began to operate. This creates the possibility for recombination of already existing dislocations on primary systems with those generated in new secondary ones. This process may be thermally activated as in formation of attractive junctions, for example, and influences the flow stress and strain hardening rate due ta the reduction of the long stress fields in existing dislocation arrangements. (This point will be discussed later.) The experiments have shown that at Ieast two physically different mechanisms can lead to dynamical recovery of crystal. In the first case (I3.R.I) the diminishing of the strain hardening rate is caused by intensification of the cross slip of dislocations originally gliding on B4 and Cl slip systems. This process however. does not violate the C-S law in copper at room tem~rature. The change of the active slip direction induces another mechanism of dynamical recovery (DR.-2). it is accompanied by decrease of the strain hardening rate and sudden increase of the strain rate sensitivity. This idea is supported aIso by the analysis of the rate controlling process. Basing upon the strain change and temperature change experiments, the apparent activation enthalpy was Found according to the formula [ 171.
Fig. 6. The relative change of the width of crystals plotted against the rolling deformation.
KORBEI.. ANDSZCZERBA:
STRAIN HARDEMNG
AND DYNAMIC RECOVERY
Taf8 K ( = 8.4 10‘45’
I
so
100
150
200
230
Elongation,
Fig. 7. The apparent activation enthaipy of the plastic flow rate controlling processes vs room temperature 00.s flow
mm
Fig. 9. The toad-elongation curves recorded in tensile of 78 K of crystals prestrained in hard orientation.
stress in tension.
The results are shown in Fig. 7 vs the room tempetature how stress. Two distinct ranges of constancy of AH may setve as the evidence that different mechanisms control the plastic flow in particular regions of strain. it should be noted that the data for single crystals which were explicitly deformed in tension coincide with those obtained for crystals predeformed by toiling. The first region of constancy of A?iHoriginates at stress (cr z 50 MN:m?) which corresponds to the onset of the third stage of deformation of single crystal. Thus AH value of the order of 0.7 eV is monitoring the activation enthalpy of the cross-slip. Strengthening of crystai to 170 MN/m’ initiate another relaxation process which becomes a dominating one at stresses higher than 230 MN/m’ (second region of AH constancy). AH is then as much as twice smaller than
-
uii)tT45) G2l)(T45)
d
only tensile test
20
II
IO
1
I./ 0
200
250
300
Fig. S. The ffor stress Lwclor response to the change of the temper?tutr of tensile test from 320 K to 78 K 6o.J room temperature Stress for two orientations of the rolling plane.
that for D.R.-I, so that the process might be very effcient. it is conditioned however, by activation of new slip system. An identification of the D.R. processes in crystals predeformed in hard orientation is much more difficult. Existing differences between two examined orientations of crystal are shown in Fig. 8 where the results of temperature change experiments are plotted in Aar vs d coordinates, Instability of the plastic deformation from the very beginning of the tensile deformation at room temperature makes the strain rate experiments questionable [18]. For this reason it was impossible to determine the activation enthalpy of the rate controlling process. The strain rate experiment could be however, performed at 78 K because then the plastic flow in tensile is stable (Fig. 9). On the base of the experimental data. it was possible to plot the activation area for two orientations vs low temperature Row stress (Fig. 10). The influence of temperature on stability of plastic flow has important im~Iications for ident~cation of the relaxation process which is responsible for sudden drop of strain hardening rate and the plateau on the stress-strain curve. Another indication which helps to understand the nature of the phenomenon is the behaviour of crystal only slightly predeformed by rolling, so that the Schmid criterion for Row still can be used for analysis. .%cording to this criterion. the following slip systems have the same chance to be activated during compression along [ 1i 1J direction: AZ. A3, B2, BS, C3 and C5 (01 = 0.27). None of these operates however, in tension along fi45] (m = 0). In the tensile test, a new slip system must be activated and the most probable is B4. As shown in Fig. 2, this slip system is a highly relaxing one from the point of view of the stress fields of already introduced by rolling arrangements of dislocations. The stress-strain curve reveals a prolongated instability (Fig. 3) which suggests softening of crystal in the zone of tocalized flow. This result coincides with Basinski and Jackson observations. The?; showed that an “ahen” dislocation
i966
KORBEL
“a
600
2
500
AND
SZCZERBA:
STRAIN HARDENING
400
L
too
w
200
300
400
500 r
GY
Fig. 10. The plots of activation area A vs stress for crystals prestrained by rolling in two orientations. i is the crystal ori~nt~~io~ Factor.
arrangements are unstable with respect to the new slip system (slip direction) which is being tested-934 in our case. It is aiso consistent with observations that the strain then localizes into the coarse slip lines [Zl, 223. The first dislocations generated in I34 slip system, interacting with the alien dislocations of formerly acting systems form a path in which the local flow stress is reduced. This path of easy slip is responsible for the
AND RYNAILIIC RECOVER1
s strain ~oca~~tion in this zme but u;ili at xqrx stage harden and srop, Very sudden developmenr of strain lccafization in crystals presrrained LOhigher strains where the energy stored is bigger, coincides well to this model and indicates that small deformations on new slip system lead to substantial relaxation e!Tects. Retard&ion of the strain localization in tension due to decreasing of temperature is another evidence for the thermally activated nature of the pkenom~on. One can expect therefore. that the plateau on the stress-strain curve results from the D.R.-2 process although it has now (hard orientation) different intensity than that for soft oriented crystals. The reason for this is different amounts of the energy stored in crystals before the D.R.4 process starts to operate, (new slip direction is activated)_ More energy stored in crystals rolled in hard orientation will efficiently intensify D.R.4 process and should Iead to remarkable strain focaiizatioa This is supported by structural observations. Figure t f shows the evolution af the crystal strutture, revealed by etching on the side-&1 @I) of crystal (optical micrographs) if deformed in plateau region. There are two important observations. First, is the appearance of the shear bands fS,Bsl which were not observed in earlier stages of deformation. Shear bands tie at IS’ to rolling direction. In the course of deformation, they rotate towards rolling direction. In the course of deformation, they rotate towards rolling direction (Fig. 11 a-d). In result, crystal splits into the layers consisting of “old” (rotated) S.Bs and matrix. Deformation proceeds due to formation of new S.Bs in matrix which maintains the same angle with respect to rolling direction a~tkough frequently in alternative position (- 15’). No shear bands were found in soft oriented crystals. In tke Light of these observations. it is evident that the plateau on the stress-strain curve IFig. 4) rep
Fig_ I I. The evolution of the crystal structure in the course of roiling deformation revealed by ercbing on the side-waif (%I) of crystal (optical micrographs) if deformed in plateau ~0,~ region (al E -s 0.56 Ibf e = 0.69 (c) 6 = 0.96 (d) E = t.3.
KORBEL ANDSZC2ERB.A:
STR.413 HARDENING
AND DYN.AMlC RECOVERY
1967
Fig. 11. The electron micrograph of the structure of crystal prestrained to 0.5 of rolling strain, R.P. : : (lili side-wall (j?i) view.
resents a pseudo-steady-state of plastic flow during which the matrix is being replaced by the S.Bs structure. In the sense, one can say that there exist soft (unstable) matrix and hard (stable) S.Bs. As long as the matrix is not exhausted. the flow stress on the average is constant. The details of the crystal structure were observed on thin foils taken parallel to side-wall (321 t (Figs 12-14). In particular. the structure of SBs which were observed in specimens deformed in plateau stress region. is shown in Figs 13 and l-1. It has the form of the channel with no apparent cell-structure inside. The apparent cell or subgrain structure exists however. in matrix regions. From the obvious differences in arrangements of dislocations in S.Bs and matrix becomes evident that the relaxation process changes the long-range stress field picture in crystal and makes crystal softer in this zone.
No such drastic differences in structure were observed on (lil) side-wail of crystals rolled in soft orientation. At high strains however, the microbands were seen (Fig. 15). One can conclude therefore that the mechanisms of deformation are the same for both orientations. unless the intensity of particuk modes of deformation (uniform deformation or localized deformation) depends strongly upon the number and mutual relation of active slip systems. The orientation of crystal also controls the tendency to non-uniform deformation.
rlcknun~lu~lgrments-The authors wish to thank 51. Orkisz for assistance in electron microscope observations. Appreciation is also expressed to Dr J. D. Embur); for reviewing the manuscript and making valuable suggestion2
_ Fig. 13. The structure of the crystal prestrained to 0.7 of roiling strain, R.P. / 1Cli 1) side-wall (%l) vie*-.
KORBEL
1968
ASD
SZCZERBA:
STRAIN HARDENING
AND DYNAMIC RECOVERY
Fig. 14. The structure of the crystal prestrained to 0.9 of rolling strain. R.P. / / (1i 1I side-wail (321I view.
6. G. Langford and M. Cohen, Trcln~..&II. Sot. ,lfetctls 62.
699 (1969). 7. J. H, Cairns, J. Clough. P. Devey and J. Nutting. J.
Inst. 12fcrais.99. 1 (1971I. 8. D. J. Lloyd. H. Sang. J. D. Embury. P. Wycliffe and G. LeRoy, %furrr. Sci. Engny 36. 35 (19781. 9. D. J. Lloyd and D. Kenny. Acta meralf. 28, 639 (1980).
10. J. Gil Sevilano, P. Van Houtte and A. Xemoudt, in Large Deformation Wrk Hardening and Texrures. Progress in %farerial Science (edited by J. X-. Christian er
a!.) Pergamon Press. Oxford (1980). H. Mecking, lnt. Cot< Trrtwes qf Merati (edited by G. Gottstein and K. Lucke), Vol. 1. p. 27. Springer Verlag, Berlin (1978). 12. S. J. Basinski and 2. S. Basinski, in Disiocafion in Solids (edited by F. R. N. Nabarro). p. 261. %rth Holland. Amsterdam (1979). 13. H. Hollomon, iTram. .-lrn. Inst. .Cfi,z. Eqrs 162. 268 ( 1945). 14. A. H. Cottrell and R. J. Stokes. Proc. R. Sot. 223A. 17 (1955). 15. 2. S. Basinski. Scripta metal/. 8. 1302 \ 197-1). 16. E. Schmid, Proc. fnr. Gong. App(. Meek. Delft, p. 342 II.
t
1
1 w-n
Fig. 15. The structure of the--crystal prestrained fo 0.9 of roIIing strain. R.P. 1/ (321) side-wall (111) view.
REFERENCES I. .A. Korbel. L. Blaz. H. Dybiec, J. Gryziecki and 1. Zasadzinski. :\frrals 7&h& p. 391 (1979). 2. U. F. Kocks. in Dislocution Model&w of Phrsicul Svsterns (edited by C. S. Hartley). Pergamon P&s, Oxford (1980). 3. H. Xfecking and U. F. Kocks. clcra tr~erafl.To be pub-
lished. 4. J. J. Jonas. C. M. Sellars and W. J. McTegart, .Cfer. Rer. .Merals Marer 14. I (1969). 5.-H. P. Stuve and H. Turck, 2. .~fetallk. 55. 699 (1964).
(1924).
17. J. C. M. Li, in Dislocarion D_wamics [edited by A. R. Rosenfield cr al.). p. 87. IMcGraw-Hill. New York, (1967). 18. A. Korbel and H. Dybiec. ,4cta merull. 29, 89 (1981). 19. Z. S. Basinski and P. J. Jackson, Physiw status solidi 9, 805 (1965). 20. Z. 5. Basinski and P. J. Jackson. Physica starus so/i& IO, 45 (19651. 21. J. U. Sharp and M. J. Xlakin. Can 1. Phys. 45. 519 (19671. 22. J. Washburn. G. Murty. Carl J. Phxs. 15. 513 (1967).
Vol. 30, pp. 1961 to 1968, 1982
OCGI-6160 82.101961-08SO3.00~0 IYS? Pergamon Press Ltd
Great Britain. All rights reserved
Copyright 0
STRAIN HARDENING OF COPPER SINGLE CRYSTALS AT HIGH STRAINS AND DYNAMICAL RECOVERY PROCESSES A. KORBEL
and XL SZCZERBA
Institute for Metals Working and Physical Metallurgy. Academy of Mining and Metallurgy, Krakow, Poland (Receiced 29 December 1981) Abstract-Single crystals of copper were deformed by rolling at room temperature in two orientations. Different stress-strain characteristics were found. In hard orientation (Rolling Plane 11 (1ii). Rolling Direction 11[145]) a period of rapid strain hardening is followed by the constancy of the Row stress. In soft orientation (Rolling Plane 11 (321).Rolling Direction 1I [ i45]) a two-stage process of the strain hardening was found but no plateau of stress was observed up to strains of the order of three. On the basis of strain rate change and temperature change experiments and structural observations (optical and electron microscopes) two different mechanisms of dynamical recovery were identified. In particular. a new dynamical recovery process (D.R.-2) was found to be the result of activation of the formally inactite slip direction. The intensity of this process in hard-oriented crystals leads to localization of strain inro well-defined shear bands resulting in a plateau on the b-e curve. Resume-Nous avons deforme des monocristaux de cuivre de deux orientations par laminage a la temperature ambiante. On trouve des courbes contrainte-deformation differentes. Dans le cas dune orientation dure (plan de laminage 11 (I i I). direction de laminage I I [ i45]). on observe une contrainte d’tcoulement constante, apris one pCriode de fort durcissement. Dans le cas dune orientation douse (plan de laminage I I (321). direction de laminage ( I [i45]). on observe un durcissement en deux itap. mais pas de palier de la contrainte jusqu’a des deformations de l’ordre de trois. G&e a des experienm de sauts de vitesse de deformation et de temperature, ainsi qu’a des observations de la structure (microscopies optique et electronique), nous avons pu identifier deux mecanismes differents pour la restauration dynamique. En particulier. un nouveau processus de restauration dynamique (R.D.-3 resulte de I’activation dune direction de glissement en principe inactive. L’intensite de ce phenomenc dans le cas des cristaux &orientation dure conduit a une localisation de la deformation dans des bands de cisaillement bien d&ties, ce qui donne le palier de la courbe u-e. Zusammenfassung-Kupfereinkristalle wurden bei Raumtemperatur durch Walzen in zwei Orientierungen verformt, welches zu unterschiedlichem Spannungs-Dehnungsverhalten fbhrte. In der harten Orientierung (Walzeben (I i 1).Walzrichtung [ i45]) folgt auf eine rasche Verfestigung ein Bereich konstanter FlieBspannung. In der weichen Orientierung (Walzebene (32 I), Walzrichtung [ i45]) wurde ein zweistufiger Verformungsablauf beobachtet; ein Spannungsplateau wurde jedoch bis zu einer Dehnung der GrSBenordnung drei nicht gefunden. Mit Dehngeschwindigkeits- und Temperaturwechseln und der Untersuchung der Mikrostruktur in Licht- und Elektronenmikroskop wurden zwei verschiedene dynamische Erholungsmechnismen identihziert. Insbesondere wurde ein neuer dynamischer ErholungsprozeB aufgefunden. der von der Aktivierung einer vorher inaktiven Gleitrichtung herriihrt. Die Starke dieses Prozesses in den Kristallen der harten Orientierung verursacht Dehnungslokalisierung in wohldefinierten Scherblndern. Diese Bander fuhren zu dem Plateau in der Spannungs-Dehnungskurve.
INTRODUCTION
It is commonly accepted that an observed strain hardening rate depends upon the intensity of dynamical recovery (D.R.) processes and hence upon the deformation conditions and material itself. An increase of the intensity of D.R. in the course of deformation decreases the rate of strain hardening and makes the flow stress more sensitive to temperature and strain rate changes [ 1-33. If the increase of the D.R. rate is sufficient, it may in essence lead to zero strain hardening rate at high strains. Then the geometrical (athermal) strain hardening is being balanced by the thermally controlled softening (recovery) process. The plastic flow becomes then a steady-state which means that flow stress satu-
rates and does not depend upon the strain although it depends on temperature and strain rate. From the structural point of view it means that the microstructure is essentially constant during the period of steady state flow. A phenomenological description of the steady-state flow, which applies to creep and under high temperature deformation conditions, relates the strain rate to the stress and temperature by the following equation (4 < = A sinh (30,)” exp
where A, r, n and Q are constants. One could expect therefore, that even at low temperatures, the steady-state flow may occur. In other
1961
1962
KORBEL
AND
SZCZERBA:
STRAIN HARDENING AND DYNAMIC RECOVERY
words, the plateau on the stress-strain curve should follow monotonic strain hardening range. In contrast to this prediction. a number of observations indicate that strain hardening rate at high strains does not decrease in a monotonic manner [5-9). A gradual decrease of the strain hardening rate is of course conditioned by the homogeneity of plastic flow. Several experimental works report the inhomogeneous nature of deformation at high strains [lo]. Thus, pseudosteady-state regions of plastic flow are expected because temporary constancy of plastic flow may be caused by the spreading of inhomogeneous deformation. The aim of this work is to verify this suggestion. The strain hardening rate before the steady or eventually pseudo-steady flow stage is reached, depends upon the crystal orientation (number of active slip systems). Crystal orientation controls also the rate of accumulation of the energy stored in the
a)
b)
course of deformation. The energy stored in crystal is the driving force for the D.R. processes. It seems to be very useful to know how the crystal orientation
influences the D.R. and disposition deformation.
to non-uniform
EXPERIMENTAL c) Single crystals were grown in a graphite split mold by zone melting of 99.99% copper in a natural temperature gradient furnace in vacuum better than 5 x lo-’ Torr. The crystals had a rectangular cross section with constant width (4mm) but different thickness ranging from 0.8 to 4 mm. They were grown from the seed so that one face of crystal was parallel to (i II) while another one to (321) crystal plane. The crystal’s longest axis (rolling direction) was kept parallel to [i45] direction. Deformation was imposed on crystal by rolling in the true strain range from 0.03 to 3.0. The final thickness of crystals after rolling deformation, was 0.8 mm except for the two highest strain values. Deformation was carried out in steps under good lubrication conditions. The rape oil was used as the lubricant. To protect the crystals from the development of texture gradient across the thickness in each step of deformation, the ratio of the length of arc of contact to specimen thickness was kept constant at the value of 1 (11). The rolling was performed in two orientations: (a) Rolling plane (R.P.) 11 (321) and rolling direction (R.D.) 1/ [ i45]-soft orientation; (b) R.P. [ I (1il) and R.D. I I [i45]-hard orientation (Fig. 1). After each step of deformation, the thickness and the width of crystals were measured. The specimens were then subjected to mechanical tests and structural observations. The tensile tests at room temperature and at 78 K, strain rate experiments at both temperatures and temperature change experiments, were performed. The value of G,,~ proof stress was determined at strain rate lo-“s-l. Nine measurements of co,*
Fig. 1. The crystal orientations used in the experiments R.D.-rolling direction, T.D.-transvcrjz direction
proof stress were done for each deformation. During the strain rate experiments, the strain rate was increased by one order of the magnitude when stress reached the ao.s value. Corresponding tlow stress increase was determined accordingly to Basinski’s proposal [12]. The structure of crystals was observed in two sections: parallel to rolling plane and parallel to roiling direction but perpendicular to rolling plane using both optical and electron microscopy techniques. RESULTS AND DISCUSSION The influence of crystal orientation on the mechanisms of plastic deformation manifests itself in tensile test curves of crystals predeformed by rolling as well as in the rate of strengthening of the material during rolling. Typical differences which occur during the tensile tests of crystals predeformed to 0105 of natural rolling deformation (In h/h,) are shotvn in Fig. 2. As is shown in Fig. lb, crystals oriented: R.P. I ) (lil), RD. 1( [i45], harden at a much higher rate than crystals rolled in orientation “a” in Fig. 1 (R.P. 1I @l), RD. 1I [i45+soft orientation) and they have a strong tendency to unstable flow if tested in tension along the rolling direction. At small rolling deformations (e < 0.1) plastic flow in tension initiates a form of Luders deformation which propagates throughout the crystal at the constant stress. For higher rolling defor-
KORBEL
.4ND
SZCZERBA:
STRIIN
HARDENING
T=293 K iez 8.4-I0-%-’
I !I/
f longotion,
mm
Fig. 1. Typical ditkences which occur during the tensile test of crystals predeformed to 0.105 of natural rolling deformation in two orientations of the rolling plane. The signal of the local gauge length extensometer (lowest curve) proved the Lauder’s front propagation at the onset of plastic Row in hard oriented crystal.
“0.2
2’
marions
T--293 i = 8.4
IOOC
I( lo-%--’
Boa (e
* 2
0.2
0.40.60.8
1.0 I.2
1.4 1.6 1.82.02.2
ttitt 78
K
-
242.62.83.0
the strain in Li.iders band is big enough for
development of the neck in zone of just nucIeating band (Fig. 3). This is however, not the case for crystals predeformed by rolling in soft orientation. Corresponding stress-strain curves for this orientation are also shown in Figs 2 and 3. The tensile deformation is then homogeneous and leads to strain hardening effect. The inguence of the orientation of crystals on the strain hardening rate is shown in Fig. 4 where the tensile proof stress 60.t is plotted against natural rolling deformation. For hard orientation the high strain hardening rate range (up to strain 0.6) is followed by a typical for steady-state flow stage plateau on stressstrain curve. Soft oriented crystals show a lower but continuous increase of the proof stress in the whole examined range of strains.
2:
1963
AND DYNAMIC RECOVERY
800
P 400
200
I
\
\ 2
E longotion,
mm
Fig. 3. The effect of the crystal orientation and the amount of roiling deformation on the toad-elongation curve in tension.
Fig. 4. The tensile proof stress co,2 vs roliing~d:iormation plots for two orientations of crystals in rollrng and two temperatures (78 K and 300 Kj of tensile tests.
The statistical analysis of the shape of stress-strain curve shows however, that there exist two regions of strain where the stress may be related to strain by Holiomon’s type equation [133. For strains 0 c e < 0.6. the following form of equation was found trO.a= 29.7 . E’-
(r’ = 0.993~
(2)
while for strains bigger than 0.6 the best fit follows the equation oe,a = 22.3 . co.26 (8 = 0.993)
(3)
The change of the strain hardening exponent from 0.59 at small to 0.26 at high strains suggests that some relaxation process operates at large deformations. This idea is supported by the results of strain rate change experiments. In Fig. 5, the Row stress response Aa, to the strain rate increase is plotted against the flow stress which in turn reflects the strain imposed on crystal. One can find that at smalI deformations, the relationship obeys to the Cottrell-Stokes law [ 14). At higher stresses however, significant deviation from C-S law occurs. It happens for G > 170 ZlfN,!m’ or aitemativeIy e > 0.6 for which the ~c.: vs E relationship is given by equation (3). Mecking and Kocks[3] postulate that the deviation from the C-S law is caused by activation of the DR. processes. Accepting this suggestion, one would suppose that the D.R.-2 in soft oriented crystals appears not tili then. the stress reaches I70 4IN/m or strain imposed is bigger than 0.6. They both are significantly bigger than stress and strain at which third
1964
KORBEL +.z~DSZCZERBA:
STRAIN HARDENING
f.2 6.8 6.4 6.0 5.6 f y;
3.6 32 2.6 2.4 2.0. 1.6 1.2 0.6,
Fig. 5. The Row stress response Aa,. to the strain rate increase plotted against the uO.J flow stress in tension for two
temperatures of tensile tests. stage (pa~boiic one) on stress-strain curve of single crystat of copper if tensile atong [i45] direction is observed (oJ = 50 MN/m* and .s3 = 0.15 in our case). In Basinski’s approach, the deviation of Ari, vs d plot from the linearity results from the progressive increase of the log term of the line tension of dislocation rather than from any relaxation process which take place in the third stage [U]. Thus it is necessary to make distinction between the relaxation process which operates at high strains and the cross slip which is thought to be responsible for stage three of deformation of single crystals. This last feature, at least in copper does not introduce a measurable contribution to da, value or else its intensity is proportional to stress so that the Cottrell-Strokes law is stilt fulfilled. It may be violated however, if a new slip system (new slip direction) is being activated [19,20]. One can expect therefore, that the relaxation process which occurs at high strains is caused by the activation of non-active yet slip direction. This meets the evidence in Fig. 6 where the relative change of the width of crystal is plotted against the rolling deformation. Figure 6 shows the curves for both orientations. In particular case of just discussing soft orientation the specimens do not widen until the rolling deformation imposed is bigger than approximately 0.6. Thereafter, a sudden widening of crystat was observed. The analysis based upon the Schmid criterion for yielding [16], which in fact is useful only at the onset of deformation, shows that compression of crystal along [321] direction activates B4 slip system (see Fig. Ic). As the conjugate Cl slip system GilI be activated. the slip directions are then [OJ I] for primary
AND DYNAMIC RECOVERY
and [lOi] for conjugate slip system. If projected on the rolling piane they lie afong the rolhng direction SO that they do not give of any widening of crystal. Sudden widening at strains bigger than 0.6 means that new slip direction began to operate. This creates the possibility for recombination of already existing dislocations on primary systems with those generated in new secondary ones. This process may be thermally activated as in formation of attractive junctions, for example, and influences the flow stress and strain hardening rate due ta the reduction of the long stress fields in existing dislocation arrangements. (This point will be discussed later.) The experiments have shown that at Ieast two physically different mechanisms can lead to dynamical recovery of crystal. In the first case (I3.R.I) the diminishing of the strain hardening rate is caused by intensification of the cross slip of dislocations originally gliding on B4 and Cl slip systems. This process however. does not violate the C-S law in copper at room tem~rature. The change of the active slip direction induces another mechanism of dynamical recovery (DR.-2). it is accompanied by decrease of the strain hardening rate and sudden increase of the strain rate sensitivity. This idea is supported aIso by the analysis of the rate controlling process. Basing upon the strain change and temperature change experiments, the apparent activation enthalpy was Found according to the formula [ 171.
Fig. 6. The relative change of the width of crystals plotted against the rolling deformation.
KORBEI.. ANDSZCZERBA:
STRAIN HARDEMNG
AND DYNAMIC RECOVERY
Taf8 K ( = 8.4 10‘45’
I
so
100
150
200
230
Elongation,
Fig. 7. The apparent activation enthaipy of the plastic flow rate controlling processes vs room temperature 00.s flow
mm
Fig. 9. The toad-elongation curves recorded in tensile of 78 K of crystals prestrained in hard orientation.
stress in tension.
The results are shown in Fig. 7 vs the room tempetature how stress. Two distinct ranges of constancy of AH may setve as the evidence that different mechanisms control the plastic flow in particular regions of strain. it should be noted that the data for single crystals which were explicitly deformed in tension coincide with those obtained for crystals predeformed by toiling. The first region of constancy of A?iHoriginates at stress (cr z 50 MN:m?) which corresponds to the onset of the third stage of deformation of single crystal. Thus AH value of the order of 0.7 eV is monitoring the activation enthalpy of the cross-slip. Strengthening of crystai to 170 MN/m’ initiate another relaxation process which becomes a dominating one at stresses higher than 230 MN/m’ (second region of AH constancy). AH is then as much as twice smaller than
-
uii)tT45) G2l)(T45)
d
only tensile test
20
II
IO
1
I./ 0
200
250
300
Fig. S. The ffor stress Lwclor response to the change of the temper?tutr of tensile test from 320 K to 78 K 6o.J room temperature Stress for two orientations of the rolling plane.
that for D.R.-I, so that the process might be very effcient. it is conditioned however, by activation of new slip system. An identification of the D.R. processes in crystals predeformed in hard orientation is much more difficult. Existing differences between two examined orientations of crystal are shown in Fig. 8 where the results of temperature change experiments are plotted in Aar vs d coordinates, Instability of the plastic deformation from the very beginning of the tensile deformation at room temperature makes the strain rate experiments questionable [18]. For this reason it was impossible to determine the activation enthalpy of the rate controlling process. The strain rate experiment could be however, performed at 78 K because then the plastic flow in tensile is stable (Fig. 9). On the base of the experimental data. it was possible to plot the activation area for two orientations vs low temperature Row stress (Fig. 10). The influence of temperature on stability of plastic flow has important im~Iications for ident~cation of the relaxation process which is responsible for sudden drop of strain hardening rate and the plateau on the stress-strain curve. Another indication which helps to understand the nature of the phenomenon is the behaviour of crystal only slightly predeformed by rolling, so that the Schmid criterion for Row still can be used for analysis. .%cording to this criterion. the following slip systems have the same chance to be activated during compression along [ 1i 1J direction: AZ. A3, B2, BS, C3 and C5 (01 = 0.27). None of these operates however, in tension along fi45] (m = 0). In the tensile test, a new slip system must be activated and the most probable is B4. As shown in Fig. 2, this slip system is a highly relaxing one from the point of view of the stress fields of already introduced by rolling arrangements of dislocations. The stress-strain curve reveals a prolongated instability (Fig. 3) which suggests softening of crystal in the zone of tocalized flow. This result coincides with Basinski and Jackson observations. The?; showed that an “ahen” dislocation
i966
KORBEL
“a
600
2
500
AND
SZCZERBA:
STRAIN HARDENING
400
L
too
w
200
300
400
500 r
GY
Fig. 10. The plots of activation area A vs stress for crystals prestrained by rolling in two orientations. i is the crystal ori~nt~~io~ Factor.
arrangements are unstable with respect to the new slip system (slip direction) which is being tested-934 in our case. It is aiso consistent with observations that the strain then localizes into the coarse slip lines [Zl, 223. The first dislocations generated in I34 slip system, interacting with the alien dislocations of formerly acting systems form a path in which the local flow stress is reduced. This path of easy slip is responsible for the
AND RYNAILIIC RECOVER1
s strain ~oca~~tion in this zme but u;ili at xqrx stage harden and srop, Very sudden developmenr of strain lccafization in crystals presrrained LOhigher strains where the energy stored is bigger, coincides well to this model and indicates that small deformations on new slip system lead to substantial relaxation e!Tects. Retard&ion of the strain localization in tension due to decreasing of temperature is another evidence for the thermally activated nature of the pkenom~on. One can expect therefore. that the plateau on the stress-strain curve results from the D.R.-2 process although it has now (hard orientation) different intensity than that for soft oriented crystals. The reason for this is different amounts of the energy stored in crystals before the D.R.4 process starts to operate, (new slip direction is activated)_ More energy stored in crystals rolled in hard orientation will efficiently intensify D.R.4 process and should Iead to remarkable strain focaiizatioa This is supported by structural observations. Figure t f shows the evolution af the crystal strutture, revealed by etching on the side-&1 @I) of crystal (optical micrographs) if deformed in plateau region. There are two important observations. First, is the appearance of the shear bands fS,Bsl which were not observed in earlier stages of deformation. Shear bands tie at IS’ to rolling direction. In the course of deformation, they rotate towards rolling direction. In the course of deformation, they rotate towards rolling direction (Fig. 11 a-d). In result, crystal splits into the layers consisting of “old” (rotated) S.Bs and matrix. Deformation proceeds due to formation of new S.Bs in matrix which maintains the same angle with respect to rolling direction a~tkough frequently in alternative position (- 15’). No shear bands were found in soft oriented crystals. In tke Light of these observations. it is evident that the plateau on the stress-strain curve IFig. 4) rep
Fig_ I I. The evolution of the crystal structure in the course of roiling deformation revealed by ercbing on the side-waif (%I) of crystal (optical micrographs) if deformed in plateau ~0,~ region (al E -s 0.56 Ibf e = 0.69 (c) 6 = 0.96 (d) E = t.3.
KORBEL ANDSZC2ERB.A:
STR.413 HARDENING
AND DYN.AMlC RECOVERY
1967
Fig. 11. The electron micrograph of the structure of crystal prestrained to 0.5 of rolling strain, R.P. : : (lili side-wall (j?i) view.
resents a pseudo-steady-state of plastic flow during which the matrix is being replaced by the S.Bs structure. In the sense, one can say that there exist soft (unstable) matrix and hard (stable) S.Bs. As long as the matrix is not exhausted. the flow stress on the average is constant. The details of the crystal structure were observed on thin foils taken parallel to side-wall (321 t (Figs 12-14). In particular. the structure of SBs which were observed in specimens deformed in plateau stress region. is shown in Figs 13 and l-1. It has the form of the channel with no apparent cell-structure inside. The apparent cell or subgrain structure exists however. in matrix regions. From the obvious differences in arrangements of dislocations in S.Bs and matrix becomes evident that the relaxation process changes the long-range stress field picture in crystal and makes crystal softer in this zone.
No such drastic differences in structure were observed on (lil) side-wail of crystals rolled in soft orientation. At high strains however, the microbands were seen (Fig. 15). One can conclude therefore that the mechanisms of deformation are the same for both orientations. unless the intensity of particuk modes of deformation (uniform deformation or localized deformation) depends strongly upon the number and mutual relation of active slip systems. The orientation of crystal also controls the tendency to non-uniform deformation.
rlcknun~lu~lgrments-The authors wish to thank 51. Orkisz for assistance in electron microscope observations. Appreciation is also expressed to Dr J. D. Embur); for reviewing the manuscript and making valuable suggestion2
_ Fig. 13. The structure of the crystal prestrained to 0.7 of roiling strain, R.P. / 1Cli 1) side-wall (%l) vie*-.
KORBEL
1968
ASD
SZCZERBA:
STRAIN HARDENING
AND DYNAMIC RECOVERY
Fig. 14. The structure of the crystal prestrained to 0.9 of rolling strain. R.P. / / (1i 1I side-wail (321I view.
6. G. Langford and M. Cohen, Trcln~..&II. Sot. ,lfetctls 62.
699 (1969). 7. J. H, Cairns, J. Clough. P. Devey and J. Nutting. J.
Inst. 12fcrais.99. 1 (1971I. 8. D. J. Lloyd. H. Sang. J. D. Embury. P. Wycliffe and G. LeRoy, %furrr. Sci. Engny 36. 35 (19781. 9. D. J. Lloyd and D. Kenny. Acta meralf. 28, 639 (1980).
10. J. Gil Sevilano, P. Van Houtte and A. Xemoudt, in Large Deformation Wrk Hardening and Texrures. Progress in %farerial Science (edited by J. X-. Christian er
a!.) Pergamon Press. Oxford (1980). H. Mecking, lnt. Cot< Trrtwes qf Merati (edited by G. Gottstein and K. Lucke), Vol. 1. p. 27. Springer Verlag, Berlin (1978). 12. S. J. Basinski and 2. S. Basinski, in Disiocafion in Solids (edited by F. R. N. Nabarro). p. 261. %rth Holland. Amsterdam (1979). 13. H. Hollomon, iTram. .-lrn. Inst. .Cfi,z. Eqrs 162. 268 ( 1945). 14. A. H. Cottrell and R. J. Stokes. Proc. R. Sot. 223A. 17 (1955). 15. 2. S. Basinski. Scripta metal/. 8. 1302 \ 197-1). 16. E. Schmid, Proc. fnr. Gong. App(. Meek. Delft, p. 342 II.
t
1
1 w-n
Fig. 15. The structure of the--crystal prestrained fo 0.9 of roIIing strain. R.P. 1/ (321) side-wall (111) view.
REFERENCES I. .A. Korbel. L. Blaz. H. Dybiec, J. Gryziecki and 1. Zasadzinski. :\frrals 7&h& p. 391 (1979). 2. U. F. Kocks. in Dislocution Model&w of Phrsicul Svsterns (edited by C. S. Hartley). Pergamon P&s, Oxford (1980). 3. H. Xfecking and U. F. Kocks. clcra tr~erafl.To be pub-
lished. 4. J. J. Jonas. C. M. Sellars and W. J. McTegart, .Cfer. Rer. .Merals Marer 14. I (1969). 5.-H. P. Stuve and H. Turck, 2. .~fetallk. 55. 699 (1964).
(1924).
17. J. C. M. Li, in Dislocarion D_wamics [edited by A. R. Rosenfield cr al.). p. 87. IMcGraw-Hill. New York, (1967). 18. A. Korbel and H. Dybiec. ,4cta merull. 29, 89 (1981). 19. Z. S. Basinski and P. J. Jackson, Physiw status solidi 9, 805 (1965). 20. Z. 5. Basinski and P. J. Jackson. Physica starus so/i& IO, 45 (19651. 21. J. U. Sharp and M. J. Xlakin. Can 1. Phys. 45. 519 (19671. 22. J. Washburn. G. Murty. Carl J. Phxs. 15. 513 (1967).