Plastic behaviour of copper sheets subjected to a double strain-path change

ELSEVIER

Journal of Materials Processing Technology 47 (1995) 261 272

Journal of Materials Processing Technology

Plastic behaviour of copper sheets subjected to a double strain-path change M . F . Vieira a, J.V. F e r n a n d e s b'* Departamento de Engenharia Metalio'gica, Faculdade de Engenharia. Universidade do Porto. 4099 Porto Codex. Portugal Departamento ~h" EngeHharia Mec~nica, Faculdade tk" CiPncias e Tecnologia, Universidack' ~k" Coimbra, 3000 Coimbra. Portugal

(Received June 21, 1993)

Industrial Summary Three sequences of three strain paths have been carried out on a polycrystalline copper sheet: tension rolling tension with the rolling direction normal to the tensile axes; rolling-rolling tension, the first and the second rollings being performed parallel and normal to the tensile axis, respectively; and rolling-rolling tension, the first and the second rollings being performed normal and parallel to the tensile axis, respectively. In order to achieve a better understanding of the mechanical behaviour of the copper sheet under complex strain paths, the effects of double strain-path change on the subsequent reloading yield stress and residual uniform strain have been investigated. It is found that the mechanical behaviour after reloading depends mainly on the orientation relationship between the previous and subsequent paths and less on the order in which they have been performed. A "hard" orientation relationship between two strain paths, consecutive or not, strongly imposes the effects of the prestrain path on the subsequent behaviour.

1. Introduction Multiple strain-paths are often observed in elements of stampings during sequential forming operations. The change of strain path modifies the hardening behaviour and, generally, reduces the ductility of the material used. It is of general interest to have a g o o d understanding about the way in which a multiple strain-path change influences the subsequent mechanical behaviour. Previous work [1,2] on copper has shown that, for a sequence of two strain paths, the behaviour during the second loading, in tension, is highly dependent on the

* Corresponding author. 0924-0136/95/$09.50 (© 1995 Elsevier Science S.A. All rights reserved SSDI 0924-0136(95)01318-U

262 M.F. Vieira, J. V. Fernandes/ Journal of Materials Processing Technology 47 (1995) 261-272 magnitude of the strain-path change defined, for example, by a parameter e that corresponds to the cosine of the angle between the two vectors that represent the successive strain tensors [3,4]. (i) The value of the normalized reloading yield stress is a function of ~ and shows its maximum value at about c~= 011,2]. In fact, the number of new active slip systems (not active during the first loading), i.e. the latent hardening effect during the second path, is a maximum when ~ approaches zero [2]. (ii) The reloading yield stress is followed by a transient period with a low strainhardening rate; the amplitude of this effect is also dependent on the c~ value [1,2]. During the transient period, a dynamic recovery takes place inside the grains and the previous dislocation microstructures rearrange, early in the beginning of the second path. With deformation in the second path, this dislocation microstructure evolves to a cell structure typical of the respective strain path and the macroscopic behaviour approaches that without prestrain [2,5]. (iii) After a critical value, the residual uniform strain, during the second path in tension, depends on the amplitude of the change of strain path, being independent of the nature of the prestrain conditions [1]. In the present work, the work-hardening effects associated with the change of strain path are studied for sequences of three strain paths. Particularly, the reloading yield stress and the residual uniform strain during the third path, always in tension, were studied as a function of the previous deformation history under two preloading paths. Its dependence on microstructural events is considered also.

2. Experimental details Oxygen-free high-purity copper (99.95% Cu) sheet, 1 mm thick, previously coldrolled and annealed, was used in this investigation. The mean size is 7 gin, the grains being equiaxed. X-ray analysis [6] revealed the existence of a weak rolling texture, as is usually observed in annealed industrial copper sheets. This crystallographic isotropy is essentially unchanged after rolling or tension up to a von Mises equivalent strain of 0.20. The three sequences of three strain paths were performed at room temperature at a von Mises equivalent strain rate of about 700.10 -6 s-1. (i) TRT: uniaxial tension on wide samples (100 mm x 20 mm) followed by rolling normal to the tensile axis, uniaxial tension tests then being performed on samples (60 mm x 10 mm) cut parallel to the initial tensile axes. (ii) RRTI: sequences of two normal rollings on square samples (104 mm z) followed by uniaxial tension tests performed on samples (60 m m x 10 mm) cut parallel to the first rolling direction. (iii) RRT2: sequences of two normal rollings on square samples (104 mm 2) followed by uniaxial tension tests performed on samples (60 mm x 10 mm) cut parallel to the second rolling direction. For all sequences, the two first paths are considered as prestrain paths, the von Mises equivalent prestrain values used being in the range 0 to 0.20. The third path, in

M.F. Vieira, J.V. Fernandes / Journal (~f Materials Processig Technology 47 (1995) 261 272

263

uniaxial tension, is always parallel to a reference direction: the transverse direction of the sheet. A strain gauge was used to measure the extension, a microcomputer being interfaced with the tensile test machine and the signals from load and extension being converted and stored through computer software in the form of true stress a - t r u e strain e. For further processing of this data, computer software was developed to allow graphic outputs of cr = f ( O and O( = da/de) =f(a).

3. Results

Examples of true stress-true strain curves obtained during the third path in tension along the reference direction (the transverse direction of the sheet) for the three sequences studied TRT, RRT1 and RRT2 are shown in Figs. 1, the reference curve, RC, without prestrain being shown also. The prominent features of these curves can be summarized as follows. (i) The macroscopic reloading yield stress (which can be defined as the backextrapolated stress abe for instance [1,2]) is always greater than the stress ar reached at the same strain along the reference curve RC (without prestrain). For the same total prestrain value along the two first paths, the greater is the strain value in rolling normal to tension the greater is the ratio abe/at whatever the sequence, as summarised in Fig. 2. (ii) The slope of the stress-strain curves of prestrain samples is lower than the slope of the monotonic curve, at the same total equivalent strain. Examples of the work-hardening behaviour during the last path in tension are shown in Fig. 3 by plotting 0( = da/de) versus a. (iii) After a critical prestrain value, which depends on the prestrain mode and sequence, flow localization appears immediately after the yield stress (Fig. 4~.

4. Discussion

The above results show the effect of a double strain-path change on the subsequent yield and flow behaviour during the third path in tension. The three kinds of triple sequential strain paths which have been investigated in the present paper allow an understanding of the influence of the deformation during the second path on the vanishing of the deformation memory of the first path and on the development of a new deformation memory typical of the second mode of deformation. For this purpose, a parameter :~ will be used, which is equal to the cosine of the angle between the two vectors representing the successive strain tensors [-3,4], in order to characterize the magnitude of the strain-path change. 4.1. Reloading yield stress

The results concerning the values of the reloading yield stress during the last path in tension are analysed initially in sequences of two strain paths, rolling-tension, the

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change. In fact, microstructural analyses have shown that, when c~decreases from 1 to 0, the number of new active slip systems (i.e., the systems that are active during the second path but not during the first path) increases [-2]; consequently the value of the normalized reloading yield stress defined as abe/G increases also. In the present case, the results agree with this previous observation, the values of abe/O, being clearly greater for ~ = 0 than for ~ = 0.87 (Fig. 5). For both cases, a dependence of the normalized reloading yield stress on the prestrain value was observed (Fig. 5): when this increases, the value of abe/at decreases. This dependence certainly finds its origin in the physical meaning of the definition of the von Mises equivalent strain, which does not take into account

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(Fig. 6): the first tension is followed by orthogonal rolling, this being followed by a further tension, the axis of which is parallel to the first tensile axis. The intercalation of an orthogonal rolling path between two parallel tensile tests results in an increase of the initial flow stress during the second tension (crh,,)compared with the stress at the same von Mises equivalent strain in monotonic tension (G). For the same total prestrain value (during the first two paths), the value of abe/G increases with the increase of the amount of strain in rolling, the value of a~e/ar being slightly greater when the prestrain is performed in rolling only (i.e., there does not exist the first path in tension) than in the other cases (Fig. 2). Further, the value of ab,,/G decreases with the increasing of the total amount of prestrain. Nevertheless, it is possible to conclude that, even for large prestrain in tension (for example 0.10), a low value of rolling prestrain (for example 0.02) clearly implies a high ~rb~/ar value (1.06 in the example) i.e., a similar value to that obtained for the same total prestrain in rolling only (1.08 in the example). This means that the second path in rolling quickly imposes

M.F. Vieira, J.V. Fernandes/ Journal ~[ Materials Processig Technology 47 (1995) 261 272

269

its effects concerning the consequences on the a~e/a~ value in the last path in tension. This remark is in qualitative agreement with metallurgical observations indicating that, after path change, there occurs a rapid multiplication of the dislocations in the new active slip systems [2, 5, 10]. 4.1.2. Case of the sequences RRT1 and R R T 2 The yield behaviour during the sequence RRT1 (Fig. 2) is quite similar to that observed in the sequence TRT, discussed above. This is certainly related to the last change of strain path (~ = 0) for the sequence RRT1 being the same as that for the sequence TRT (Fig. 6). The first strain-path change is more smooth in the case of RRT1 (~ = 0.5) than in the sequence TRT (~ = 0). However, for both cases, the first strain path and consequently the first strain-path change seem not to influence, in a determinant way, the yield behaviour during the third path (Fig. 2). This reinforces the idea expressed above that the second path quickly imposes its presence by a rapid increase of the dislocation density in the slip systems then activated. In the sequence RRT2, the first strain-path change is characterised by ~ = 0.5 and the second by ~ = 0.87 (Fig. 6). Both changes are relatively smooth, particularly the second change. The results shown in Fig. 2 indicate that in this case the memory of the first path is noted even when a strong deformation value is imposed in the second path. For a total prestrain value equal to 0.12, for example, the values of abe/at are not influenced greatly by the deformation value during the second path: a~,,/~r is equal to 1.06 when the strain value in rolling normal to the tensile axis is 0.02, whilst for the same total prestrain value performed in rolling normal to the tension only (change of strain path corresponding to ~ = 0) abe/~ is equal to 1.08, which suggests that the dynamic recovery of the previous dislocation structure during a subsequent strain path [-2, 5, 10 14] occurs in a slow mode. This feature is only apparently contradictory to that observed in the sequence RRT1 where the presence of a second path is the principal factor in determining the subsequent yield behaviour. In fact, the yield behaviour during the third path in tension seems to be determined mainly by the presence of the dislocation structure created during the rolling deformation normal to the tensile axis. In conclusion, the results concerning the two sequences RRT indicate that, within the range of strain values used in the present work, the importance of a given strain path for the subsequent behaviour depends mainly on its orientation relationship with the following paths: a "hard" orientation relationship between two strain paths (defined by the parameter ~ being equal to zero), whether consecutive or not, strongly imposes the effects of the prestrain path on the subsequent behaviour. 4.2. Residual un([brm strain

When flow localization occurs, the hardening curve drops below the instability line represented by the linear relation: 0 = a (Fig. 3). In a general way, the appearance of flow localization in tension immediately after path change can be the result of a relatively high value of the back-extrapolated stress (ab,,) a n d / o r a relatively low slope of the tensile curves (a =f(e.)). In polycrystalline copper and other metals subjected to a sequence of two strain paths [15-20], a high value of(abe/at) is followed

270 M.F. Vieira, J.V. Fernandes/Journal o[ Materials Processing Technology 47 (1995) 261 272 by a low work-hardening rate and by a reduction in the total plastic homogeneous deformation; contrarily, a relatively low initial flow stress is followed by a high work-hardening rate and the total plastic homogeneous deformation is almost unaffected by the path change. From a microstructural point of view, a high value o f abe/at is associated with latent hardening effects, as referred to above, and a low workhardening rate is a consequence of a strong recovery process of the previous dislocation structure during the earlier stages of the deformation in the current path. This kind of behaviour is observed also in the present case of double strain-path change: whatever the sequence considered, a relatively large value of the normalized reloading yield stress (~Tbe/CTr) , in the last path in tension, is accompanied by a relatively low value of the work-hardening rate (Fig. 3). Thus, the minimum deformation values for which the flow localization during the last path in tension occurs immediately after yielding is a measurement of the disturbance induced by the previous deformation history on the subsequent yield and flow behaviours. In Fig. 4 are shown the results concerning the appearance of flow localization immediately after yielding in the last path in tension. In the sequence TRT, the intercalation of an orthogonal rolling path with 0.02 strain value after a strain of 0.16 in the first tension reduces the residual uniform strain to zero. Amongst all cases considered in the sequence TRT, which corresponds to the least severe case concerning the reduction of the residual uniform strain (after a total prestrain equal to 0.18 the residual uniform strain drops to zero). The most severe case corresponds to prestrain in rolling only (which is normal to the tensile axis: 2 = 0); in this case a value of prestrain of not greater than 0.08 is possible before the reduction of the residual uniform strain to zero. This agrees qualitatively with the results concerning the reloading yield stress discussed above. For the two sequences RRT, the total prestrain values (during the two first rollings) that reduce the residual uniform strain to zero are in the range from 0.10, corresponding to the sequence tension after prestrain in orthogonal rolling only (~ = 0), to 0.16, corresponding to the sequence tension after prestrain in parallel rolling only (2 = 0.87). This means that relatively low values of deformation (almost equal to or lower than a half of the value of the uniform strain in monotonic tension, which latter is equal to 0.28) in the prestrain paths, can drastically reduce the residual uniform strain even if the path change is smooth as in the case of tension after prestrain in parallel rolling (2 = 0.87). Further, the minimum total prestrain values in rolling for which the residual uniform strain in tension drops to zero is not influenced greatly by the order of the preloadings in rolling (Fig. 7), the sequence RRT2 being only slightly more favourable than the sequence RRT1. These conclusions agree with those concerning the reloading yield stress as discussed above: a relatively high value of the reloading yield stress is accompanied by a relatively low strain-hardening rate.

5. Conclusions

The behaviour described concerns the mechanical behaviour of a polycrystalline copper sheet subjected to a double strain-path change. This study relates to the

M.F. Vieira, J.V. Fernandes/Journal o[" Materials Processig Technology 47 (1995) 261 272 0.12__

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reloading yield stress and to the residual uniform strain during the third strain path in tension. It enables the following conclusions to be drawn. The behaviour after prestrain depends mainly on the orientation relationship between the previous and subsequent paths and less on the order in which they are performed. A "hard" orientation relationship between two strain paths, consecutive or not, strongly imposes the effects of the prestrain path on the subsequent behaviour. This is verified with respect to the values of the reloading yield stress and the values of the critical prestrain above which the residual uniform strain drops to zero.

Acknowledgements The authors are indebted to JNICT and FEDER for financial support through the STRIDE Programme.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

M.F. Vieira, J.-H. Schmitt, J.J. Gracio and J.V. Fernandes, d. Mat. Proc. Tech., 24 (1990) 313. J.-H. Schmitt, J.V. Fernandes, J.J. Gracio and M.F. Vieira, Mater. Sci. Em]. A, 147 (1991) 143. J.-H. Schmitt, E. Aernoudt and B. Baudelet, Mater. Sci. Eny., 75 (1985) 13. J.L. Raphanel, J.-H. Schmin and B. Baudelet, Int. J. Plast., 2 (1986) 371. J.V. Fernandes, J.J. Gracio and J.-H. Schmitt, in J.L. Raphanel and F. Siderof {eds.), Proe. MECAMAT'91, A.A. Balkema, Rotterdam, 1993, pp. 219 228. A.M. Dias, personal communication, 1992. P.J. Jackson and Z.S. Basinski, Can. J. Phys., 45 (1967) 707. P. Franciosi, M. Berveiller and A. Zaoui, Acta Metall., 28 (1980) 273. P. Franciosi, Acta Metall., 33 (1985) 1601. J.V. Fernandes, J.J. Gracio, J.-H. Schmin and E.F. Rauch, Ser. Metall. Mater. 28 (19931, 1335. B.V.N. Rao and J.V. Laukonis, Mater. Sei. Eng., 60 (1983) 125. N. Christodoulou, O.T. Woo and S.R. MacEwen, Acta Metall., 34 (1986) 1553. E.F. Rauch and J.-H. Schmitt, Mater. Sci. Eng. A, 113 (1989) 441.

272

M.F. Vieira, J.V. Fernandes/Journal ~['Materials Processing Technology 47 (1995) 261 272

[14] [15] [16] [17] [18] [19] [20]

J.V. Fernandes and J.-H. Schmitt, Phil. May. A, 48 (1983) 841. D.J. Lloyd and H. Sang, Metall. Trans. A, 10 (1979} 1767. J.V. Laukonis, Metall. Trans. A, 12 (1981) 467. R.H. Wagoner and J.V. Laukonis, Metall. Trans. A, 14 (19831 1487. A. Korbel and P. Martin, Acta Metall., 36 (1988) 2575. A.B. Doucet and R.H. Wagoner, Metall. Trans. A, 20 0989) 1483. M. Zandrahimi, S. Platias, D. Price, D. Barrett, P.S. Bate, W.T. Robert and D.V. Wilson, Metall. Trans. A, 20 (1989} 2471.