Material rotating frame, rate-independent plasticity with regularization of Schmid law and study of channel-die compression

Abstract

Metals often exhibit several crystallographic components that rotate when subjected to large plastic deformation. Studying their evolution constitutes a prospect to apply the finite plastic strain theory. In this respect, this research paper formulates a three-dimensional extension of Dogui’s plane kinematics to choose a material rotating frame in which deformation and velocity tensor gradients are represented by upper triangular matrices. This technique facilitates numerical calculation and renders it faster. This can prove to be useful if used for crystalline calculation. We study the kinematics of a channel-die loading to implement the material rotating frame model. The rate-independent formulation, which uses the multi-surface theory to represent the plastic flow of crystals, often leads to slip indeterminacy. Hence, we have developed a phenomenological method to solve such a difficulty using the regularization of Schmid’s yield law. As a significant application of this proposed phenomenological approach, aluminium crystal flow in channel-die compression is numerically simulated for three cases of loadings: (i) classical rolling components Cube, Goss, Brass, Copper and Dillamore orientations; (ii) {110} compression; and (iii) Strange orientation, which has no common element of symmetry with the channel-die. A good correlation between the simulation results and the available experimental ones is observed.