Approximate analysis for the formation of adiabatic shear bands

Abstract

Parametric solutions are given for the formation of adiabatic shear bands in the context of the onedimensional nonlinear theory where inertia and elasticity are ignored. When heat conduction is also ignored, the exact solution reduces completely to a sequence of quadratures. For a perfectly plastic material with heat conduction, an implicit parametric solution is also constructed. This is similar to the previous one in many ways, but now it involves two quadratures, a single nonautonomous first-order ODE. and two functions that obey heat equations. This solution appears to be very accurate (compared to the full finite element solution) until the time of stress collapse. Results indicate that for weak rate hardening of the power law type, intense localization depends strongly on the initial characteristics of thermal softening and not at all on the high temperature characteristics. Within the context of rigid/perfect plasticity, a scaling law for the critical strain is given, and a figure of merit is defined that ranks materials according to their tendency to form adiabatic shear bands.