Abstract
The localization of plastic deformation has been discussed as “stationary discontinuity” characterized by a vanishing velocity of an acceleration wave. Therefore, on the basis of the coincidence of the onset strains between localized deformation and acceleration waves of vanishing velocity, diagrams of diffuse necking, localized necking and forming limit are analyzed by applying the proposed acoustic tensor, which is based on the generalized Christoffel tensor derived by one of the authors, and by solving the cutoff conditions of a quasi-longitudinal wave to determine the onset strains of deformation localization. The purpose of the present study is to analyze the effect of superimposed hydrostatic pressure on localized deformation using the proposed theory of ultrasonic wave velocities propagating in plastically deformed solids. From the analytical results, the catastrophic ductility increase is caused by the mode change of localized deformation beyond the critical hydrostatic pressure.
