An Analytical Investigation of Inhomogeneous Straining, Subgrain Formation, and the Initiation of Microshear Bands in Bicrystals

Abstract

It is common in metal polycrystals that, as plastic deformation proceeds, the effects of initial grain boundaries cause grains to subdivide into differently-oriented lattice regions, or subgrains, with different strains among regions and microshear bands forming along some of the subgrain walls. Recent experimental work that clearly shows this behaviour includes that of Hughes and Nix [1], Bay et al. [2], and Hughes [3], among others. Moreover, subgrain and microshear band formation have been shown experimentally to take place from the very beginning of plastic deformation (Hughes [4]). These phenomena have been explained in a qualitative way in terms of dislocation structures, but a rigorous mathematical prediction of the phenomena was not available until Wu and Havner [5]. In that work the hyperbolic partial differential equations governing stress and velocity fields in symmetric f.c.c. bicrystals in (110) channel die compression are derived, based upon the formulation in Havner et al. [6], and are solved for a particular range of lattice orientations — namely, channel lateral-constraint directions lying between [0011 and [112]. In the present paper we present further analyses and results corresponding to the range of lateral constraints between lattice directions [112] and [l T. 1]. The formation of subgrains (at the outset of finite multiple-slipping) and the initiation of tangential velocity discontinuities along certain subgrain boundaries are rigorously demonstrated.