A strain-gradient thermodynamic theory of plasticity based on dislocation density and incompatibility tensors

In this work, we discuss a thermodynamic theory of plasticity for self-orga nization of collective dislocations in FCC metals. The theory is described by geometrical tenser quantities of crystal defect fields such as dislocati on density tenser, representing net mobile dislocation density and geometri cally necessary boundaries, and the incompatibility tenser representing imm obile dislocation density. Conservation laws for the two kinds of dislocati on density are formulated with dislocation products and interactions terms. Based on the second law of thermodynamics, we drive basic constitutive equ ations for the dislocation flux, production and interaction terms of disloc ations. We also derive a set of reaction-diffusion equations for the disloc ation density tenser and incompatibility tenser which describes the vein an d persistent slip band (PSB) ladder structures. These equations are analyze d using linear stability and bifurcation analysis. An intrinsic mesoscopic length scale is determined which provides an estimate for the wavelength of the PSBs. The basic aspects of the model are motivated and substantiated b y analyzing the stress fields of various possible dislocation configuration s using discrete dislocation dynamics. (C) 2001 Elsevier Science B.V. All r ights reserved.