DISCRETE DISLOCATION PLASTICITY - A SIMPLE PLANAR MODEL

A method for solving small-strain plasticity problems with plastic flo w represented by the collective motion of a large number of discrete d islocations is presented. The dislocations are modelled as line defect s in a linear elastic medium. At each instant, superposition is used t o represent the solution in terms of the infinite-medium solution for the discrete dislocations and a complementary solution that enforces t he boundary conditions on the finite body. The complementary solution is nonsingular and is obtained from a finite-element solution of a lin ear elastic boundary value problem. The lattice resistance to dislocat ion motion, dislocation nucleation and annihilation are incorporated i nto the formulation through a set of constitutive rules. Obstacles lea ding to possible dislocation pile-ups are also accounted for. The defo rmation history is calculated in a linear incremental manner. Plane-st rain boundary value problems are solved for a solid having edge disloc ations on parallel slip planes. Monophase and composite materials subj ect to simple shear parallel to the slip plane are analysed. Typically , a peak in the shear stress versus shear strain curve is found, after which the stress falls to a plateau at which the material deforms ste adily. The plateau is associated with the localization of dislocation activity on more or less isolated systems. The results for composite m aterials are compared with solutions for a phenomenological continuum slip characterization of plastic Row.