Growth of thermoplastic shear band

Shear localization is a fundamental and widely observed non-equilibrium phenomenon in metallic materials subjected to impulsive loadings. Despite extensive research over several decades, the evolution of shear bands still remains poorly understood. In this study, we propose a two-stage model to describe the evolution of thermoplastic shear band, where the effects of strain hardening, strain-rate hardening, and thermal softening are involved. Our analysis reveals that the growth of thermoplastic shear band is derived by the competition between momentum diffusion and thermal diffusion processes, which is controlled by the solid-state equivalent of the Prandtl number. By incorporating these factors into our model, we find that the presence of hardening effect retards the evolution of shear bands, resulting in a wider shear band and increased dissipation of energy. Theoretical calculation results of shear bandwidth, shear band strain, propagation velocity, process zone geometry and dimensions, critical dissipation energy, shear band toughness, and shear band spacing are well consistent with available experimental data. Additionally, we explore the potential transition to turbulence controlled by Reynolds number within shear bands and investigate the influence of the Taylor-Quinney coefficient on the evolution of shear bands. These findings are expected to offer valuable insights into the mechanism of shear band evolution.