AN ANALYTICAL MICRO-MACRO MODEL FOR TEXTURED POLY[CRYSTALS AT LARGE PLASTIC STRAINS

An analytical micro-macro model of evolving plastic anisotropy is pres ented that is suitable for numerical simulation of forming processes. The model is based on the combination of a polycrystal model and diffe rent analytical procedures for writing anisotropic plastic potentials, expressing their coefficients in terms of texture coefficients, and u pdating the texture coefficients as function of the (tensorial) strain increment. The use of a fourth-order dual plastic potential (''C4'') in the analytical micro-macro model is studied, and this use is compar ed with that of Hill's [1948] yield criterion and also with the usual run of the Taylor model. The coefficients of the C4 potential depend l inearly on the texture coefficients, which are updated using a variati onal polycrystal model. The analytical operation of this updating lies on the method first proposed by Esling et al. [1984] and is described and checked in some detail. The predictions of the analytical micro-m odel compare well with measurements of the Lankford coefficient, provi ded the C4 potential is used. The predicted texture evolution is also in a good experimental agreement: a better one than with the Taylor mo del, which, in some cases, gives a poor updating. The theoretical stre ss evolution during biaxial or plane-strain tension is experimentally consistent too, although in that case the C4 potential, closer to Tayl or's model, makes no improvement as compared with Hill's quadratic cri terion.