Approximate Analysis of a Shear Band in a Thermoviscoplastic Material

Shear localization is systematically examined with the aid of an approximate model for the three stages of deformation in the formation and development of a shear band, which comprise: the growth of inhomogeneous deformation, the stress collapse, and the post-collapse state. A basic model of one-dimensional simple shear deformation for a thermoviscoplastic material is employed with a linear thermal softening in the absence of strain hardening. The evolution of plastic strain rate at the center of the shear band is explicitly obtained, and an approximate scaling law for the critical strain, at which the stress collapse begins, is proposed in terms of material parameters and boundary velocity. All state variables including stress, plastic strain rate, and temperature after the stress collapse are evaluated, and the overshoot of the plastic strain rate during stress collapse is explained in terms of a nondimensional parameter and elastic unloading. Finally, numerical experiments confirm the analytical results.