ON THE SELF-CONSISTENT MODELING OF ELASTIC-PLASTIC BEHAVIOR OF POLYCRYSTALS

The formulations of self-consistent schemes for elastic-plastic deform ations of polycrystals are based on the solution of an ellipsoidal inc lusion embedded in an infinite matrix. Because of the non-linear natur e of the problem, no exact solution is available and simplifying assum ptions have to be made. Unlike the classical bounds, the self-consiste nt models are called for to account for the heterogeneity of deformati on from grain to grain within a polycrystalline aggregate. However, be cause of simplifying assumptions, results from some of these models ma y turn out to be very close to those of the Taylor's upper bound formu lations. 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 s often these interactions, new elastic-viscoplastic formulations have r ecently 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 parti cular application to FCC metals under axisymmetric and cyclic loadings . We propose a generalization of this non-incremental formulation to i nclude full anisotropic and elastic compressibility. We also give a ra tional discussion of the existing elastic-plastic self-consistent sche mes for both time dependent and time independent plasticity. Based on our comparison of results from different self-consistent approaches, w e discuss the validity of the incremental versus non-incremental formu lations and the use of tangent versus the secant modulus in these form ulations. (C) 1997 Elsevier Science Ltd.