Application of a substructure-based hardening model to copper under loading path changes
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I. INTRODUCTION
THE explosive growth of understanding over the last decade or so, of plastic deformation processes in polycrystals at different length scales (especially at the substructure level), obtained largely through electron microscopy, has brought us near the point where such information may be incorporated in models of bulk polycrystal response. Such substructurebased hardening models could supplement or supplant traditional grain hardening models that resort to phenomenological considerations at the length scale of the grain. While on the one hand a substructure-based approach is much more detailed and intensive than the traditional hardening laws, on the other hand, due to the much more detailed description of the internal state of a grain used by the substructure-based approach, it can capture, for instance, transient response during nonmonotonic loading, which lies beyond the capabilities of typical grain-level phenomenological approaches. Most polycrystal models available in the literature concerned with reproducing the texture evolution and the anisotropy of the aggregate are usually based on relatively simple hardening laws for the active slip systems (Balasubramanian and Anand,[3] Tomé et al.,[4,5] Kok et al.,[6] and Kocks et al.[7]). For example, Tomé et al.[4] consider an extended Voce law of slip system hardening to describe the effect of texture evolution upon the monotonic stress-strain response of oxygen free high conductivity (OFHC) copper: tsc() t0 (t1 u1) [1 exp (u0 /t1 )]
[1]
tsc,
Here, the evolution of the critical resolved shear stress in slip system s, is given as a function of the accumulated strain in the grain . The parameter 0 is the initial yield stress, 0 1 the back-extrapolated yield stress, and 0 and S. MAHESH, Postdoctoral, C.N. TOMÉ, R.J. McCABE, G.C. KASCHNER, and A. MISRA, Technical Staff Members, Materials Science and Technology Division, and I.J. BEYERLEIN, Theoretical Division, are with Los Alamos National Laboratory, Los Alamos, NM 87545. Contact e-mail: [email protected] Manuscript submitted December 5, 2003. METALLURGICAL AND MATERIALS TRANSACTIONS A
1 the initial and final hardening rates, respectively. Such an expression accounts for dislocation hardening in a qualitative way and succeeds in accounting for texture effects on the overall stress-strain response[4] associated with monotonic loading. However, Tomé et al.[4] could not find a unique set of hardening parameters that accounts for the polycrystal mechanical behavior under different loadings: tension, compression, and torsion. They concluded that crystal orientation effects account for about half of the observed von Mises yield stress discrepancy between large strain tension, compression, and torsion and attributed the other half to differences in the dislocation structure associated with each deformation mode. Another disadvantage of simple hardening rules such as Eq. [1] is that they do not suffice to predict the transients associated with strain path changes. To capture the observed tra
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