Analytical Characterization of Shear Localization in Thermoviscoplastic Materials

Critical conditions for shear localization in thermoviscoplastic materials are obtained in closed form for idealized models of simple shearing deformations. The idealizations, which include the neglect of heat conduction, inertia, and elasticity, are viewed as quite acceptable for many applications in which shear bands occur. Explicit results obtained for the idealized, but fully nonlinear problem show the roles of strain-rate sensitivity, thermal softening, strain hardening, and initial imperfection on the localization behavior. Numerical solutions for two steels are shown to exhibit the principal features reported for torsional Kolsky bar experiments on these steels. Mathematically exact critical conditions obtained for the fully nonlinear problem are compared with critical conditions obtained by means of linear perturbation analysis. Use of relative changes instead of absolute changes in the linear perturbation analysis gives better agreement with predictions of the fully nonlinear analysis.