On the Initial Slope of Elastic-Plastic Boundaries in Combined Longitudinal and Torsional Wave Propagation

Abstract

The elastic-plastic boundaries which start at the end of a tube in wave propagation of combined longitudinal and torsional stresses are studied. The longitudinal and torsional stresses applied at the end of the tube are assumed to be continuous and the initial slope of the boundaries are determined analytically for all possible combinations of the time derivatives of stresses before and after the elastic-plastic boundaries occur. It is seen that a continuous loading into a higher yield surface at the end of the tube does not necessarily produce a continuous plastic region near the end of the tube. Also, more than one elastic and plastic region can be generated near the end of the tube even though the stresses at the end of the tube are continuously increasing to a higher yield surface. These and other unexpected results are presented in this paper.