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-organization of collective dislocations in FCC metals. The theory is described by geometrical tenser quantities of crystal defect fields such as dislocation density tenser, representing net mobile dislocation density and geometrically necessary boundaries, and the incompatibility tenser representing immobile dislocation density. Conservation laws for the two kinds of dislocation density are formulated with dislocation products and interactions terms. Based on the second law of thermodynamics, we drive basic constitutive equations for the dislocation flux, production and interaction terms of dislocations. We also derive a set of reaction-diffusion equations for the dislocation density tenser and incompatibility tenser which describes the vein and persistent slip band (PSB) ladder structures. These equations are analyzed 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 by analyzing the stress fields of various possible dislocation configurations using discrete dislocation dynamics. (C) 2001 Elsevier Science B.V. All rights reserved.