A phenomenological plasticity model with non-normality effects representing observations in crystal plasticity

An abrupt strain path change has recently been used to determine the shape of the subsequent yield surface near a current loading point. Both polycrystal plasticity calculations and experiments have shown non-normality of plastic flow, with a vertex-type response on the apparently smooth yield surface.

The physical reason for this observation is carefully discussed in the paper, with particular emphasis on the fact that the prediction appears in spite of the normality rule built into each slip system of the crystal plasticity model. To represent the observed non-linear material response, a phenomenological plasticity model is proposed, in which a smooth yield surface for an anisotropic solid is combined with a vertex-type plastic flow rule.

As plastic instability results are particularly sensitive to accurate modeling of material response under abrupt stress path change, the material model is tested on predictions of the onset of necking in biaxially stretched metal sheets. It is shown that the phenomenological plasticity model gives a good approximation of critical strains predicted by direct application of the Taylor polycrystal plasticity model.