On the self-consistent modeling of elastic-plastic behavior of polycrystals

Abstract The formulations of self-consistent schemes for elastic-plastic deformations of polycrystals are based on the solution of an ellipsoidal inclusion embedded in an infinite matrix. Because of the non-linear nature of the problem, no exact solution is available and simplifying assumptions have to be made. Unlike the classical bounds, the self-consistent models are called for to account for the heterogeneity of deformation from grain to grain within a polycrystalline aggregate. However, because of simplifying assumptions, results from some of these models may turn out to be very close to those of the Taylor's upper bound formulations. This has been the case for elastic-plastic formulations with time-dependent plasticity (elastic-viscoplastic) in which high matrix/inclusion interactions have yielded high flow stresses and negligible deviations of the deformations from grain to grain. In an attempt to soften these interactions, new elastic-viscoplastic formulations have recently been proposed. We present a non-incremental scheme for elastic-viscoplastic deformations along with the discussion of its validity. Results from this simplified formulation are also presented with particular application to FCC metals under axisymmetric and cyclic loadings. We propose a generalization of this non-incremental formulation to include full anisotropic and elastic compressibility. We also give a rational discussion of the existing elastic-plastic self-consistent schemes for both time dependent and time independent plasticity. Based on our comparison of results from different self-consistent approaches, we discuss the validity of the incremental versus non-incremental formulations and the use of tangent versus the secant modulus in these formulations.

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