Modeling of Slow Plasticity Waves

Abstract

Quasi-static uniaxial loading of a bar with a length L is considered. Mechanical properties of a material in a point are defined by the segment of negative slope on stress-strain diagram which follows the section of elastic deformation. The deformation in specimen is uniform until the stress exceeds the peak yielding stress. The analytical solution shows that stress-strain diagram of the specimen has a yielding plateau. It is shown that the time for a slow wave to advance by a distance equal to the localized band width S is the same as it is required for a plastic wave to run along the whole bar length.