Practical Constitutive Equation Based on Multiple Strata Plasticity Model

Abstract

The constitutive equation based on the multiple strata plasticity model proposed in the previous paper contains a term involving the tensor Q describing the activation state of the slip systems in polycrystalline metal. In this work we aim to clarify the characteristic of Q under the proportional and nonproportional loadings. To describe visually the complicated stress state a two-dimensional stress plane is newly introduced by applying each magnitude of normal and shearing deviatoric stress tensors. The stress trajectory can be expressed in terms of two angle parameters, ■ and θ, on the stress plane. All of the quantity of Q can be given by the simulation calculations under various loadings with a virtual specimen of polycrystalline metal. Each component of Q can be systematically related to the deviatoric stress using a specific function of ■ and θ. In addition, it is suggested that the hardening characteristic of the slip system may be presumed analytically by comparing the experimental results with the constitutive equation.