A Generalization of the Taylor-Bishop-Hill Theories and the Rate-dependent Slip Model in Crystal Plasticity

Abstract

In the Taylor-Bishop-Hill theories of crystal plasticity for the prediction of deformation textures, the problem of determining the shear rate on a slip system in a particular crystallite is reduced to the optimization procedures under linear constraints. On the other hand, the rate-dependent slip theory which is modeled by a power law relationship between the shear rate and the resolved shear stress on a slip system is formulated as the non-linear simultaneous equations system with respect to the stresses. It has been recognized to date that the Taylor-Bishop-Hill theories are essentially distinct from the rate-dependent slip one. This paper is to generalize the Taylor theory by considering in terms of the mathematical programming scheme as a norm minimization problem in the finite dimensional Banach space, and then to demonstrate that the rate dependent slip theory is included in such generalized Taylor-Bishop-Hill crystal plasticity ones. Finally, the mathematical formulation for the extended relaxed constraints model including the rate-dependent slips is comprehensively presented based on the generalized Taylor-Bishop-Hill theories.