A 2D analytical multiple slip model for continuum texture development and plastic spin

Abstract

A two-dimensional continuum slip model is presented which accounts in an approximate way for texture development in polycrystalline metals during large strain plastic deformations. The basic kinematic model is that of a rigid–plastic laminated material deforming predominantly by slip along its contact planes. A polycrystalline material is then modelled as a continuum of such laminated components, initially oriented in a random fashion. Texture development, in terms of a continuous laminae orientation distribution function (LODF), is then governed by relatively simple partial differential equations. For stationary plastic flow processes, analytical solutions to these equations are obtained and discussed. Particular emphasis is laid on the predicted macroscopic plastic spin, defined as the weighted average of the slip-induced spin in the laminated components. Results for particular deformation processes are compared with rigorous analyses using a Taylor–Bishop–Hill model for the plastic deformation of cubic polycrystals due to crystallographic slip.