Strain localization in thermoviscoplastic materials

Abstract

Shear localization in thermoviscoplastic materials is examined by way of some approximations and proper numerical techniques. We are concerned with the critical strain of severe localization, the structure of shear band at post state and the stability behavior during stress collapse. Nondimensional parameters and predictions expressed by material parameters and boundary velocity provide a very useful information for understanding the process of formation and development for the shear band in thermoviscoplastic materials. In particular, the instability of the stress collapse is systematically explained by introducing the so-called energy-balance number. The validity of the energy-balance number and the error estimator is demonstrated via numerical experiments in the simple shear and two-dimensional plane strain deformations. Weak contribution of heat diffusion before the critical strain makes the governing equations simplified, and the evolution of strain rate is approximately obtained under this assumption. As a result, we predict the critical strain, and discuss the influences of material parameters upon the formation and development of the shear band. The numerical experiments confirm the prediction of the critical strain. Moreover, we give our efforts for an approximate analysis of the morphology of fully developed shear band. A good approximation to the post behavior is obtained and complete solutions are constructed by tracking the evolution of stress and temperature after the critical strain from assumption of line heat source for the shear band. The basic framework for the instability of the stress collapse in one-dimensional shear localization is presented through analytical and numerical methods. The instability is closely associated with the unloading elastic energy released, which is largely dependent upon material parameters and boundary velocity. As precursory indicators of the instability, introduced are the energy-balance number and the local e...