Thermodynamically consistent model of dislocation-mediated plasticity

Abstract

ABSTRACT We present a thermodynamically consistent damage theory of deformation where the damage mechanism is determined by the presence of dislocations and their motion is the origin of plasticity. The damage parameter is proportional to the square root of the dislocation density of a network. For the evolution of damage, a gradient-flow equation, which describes the relaxation process of plastic deformation, is derived. Analysis shows that the dislocation-mediated plasticity is an activated process with upper and lower yield points, as opposed to a barrierless plasticity with a single yield point, which may be realised by other mechanisms of deformation. Dislocation nucleation is not a limiting factor of the dislocation-mediated plasticity because the free energy barrier for the nucleation is rather low. Application of the theory to the description of uniaxial deformation revealed many features of the experimentally observed deformation processes of metals, e.g. three stages of strain hardening with various characteristics dependent on the material and rate of loading. Applications of the theory to processes of dynamic loading of materials, which simultaneously undergo phase transformations, can bring deeper understanding of the material behaviour.