An analytical micro-macro model for textured polycrystals at large plastic strains

An analytical micro-macro model of evolving plastic anisotropy is presented that is suitable for numerical simulation of forming processes. The model is based on the combination of a polycrystal model and different analytical procedures for writing anisotropic plastic potentials, expressing their coefficients in terms of texture coefficients, and updating 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 compared 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 linearly on the texture coefficients, which are updated using a variational polycrystal model. The analytical operation of this updating lies on the method first proposed by Eslinget al. 1984] and is described and checked in some detail. The predictions of the analytical micro-model compare well with measurements of the Lankford coefficient, provided the C4 potential is used. The predicted texture evolution is also in a good experimental agreement: a better one than with the Taylor model, which in some cases, gives a poor updating. The theoretical stress evolution during biaxial or plane-strain tension is experimentally consistent too, although in that case the C4 potential, closer to Taylor's model, makes no improvement as compared with Hill's quadratic criterion.