Self-organization of adiabatic shear bands in OFHC copper and HY-100 steel

In this paper we study the self-organization process of adiabatic shear bands in OFHC copper and HY-100 steel taking into account strain hardening factor. Starting from mathematical model we present new numerical approach, which is based on Courant -- Isaacson -- Rees scheme that allows one to simulate fully localized plastic flow. To prove accuracy and efficiency of our method we give solutions of two benchmark problems. Next we apply the proposed method to investigate such quantitative characteristics of self-organization process of ASB as average stress, temperature, localization time and distance between ASB. Then we compare the obtained results with theoretical predictions by other authors

Asymptotic And Computational Analysis Of Large Shear Deformations Of A Thermoplastic Material

. A simplified model for shear-band evolution is presented which neglects the effects of diffusion and stress evolution but still captures much of the important dynamics. A regular perturbation expansion is constructed which follows the true solution until the strain rate and temperature begin to blow up. To attempt to capture this divergent behavior better, a uniform expansion is formed that tracks the blowup behavior. These asymptotic results are compared to a numerical solution. Despite the simplifications in the shear band model presented here, severe computational difficulties exist in the form of finite-time blowup of the temperature and strain rate. A numerical method is constructed which is second-order accurate and has automatic mesh- and time-step refinement capabilities. This adaptive scheme tracks the severe blowup behavior of the strain rate and temperature functions well. Key words. Adaptivity, asymptotics, finite differences, shear bands, singular perturbations, thermop..