Propagation of elastic-tough-plastic wave in a rod of ideally plastic materialwhich possesses the property of yield delay

Abstract

The great number of theoretical and experimental investigations indicate that it is necessary to consider plastic deformation of metals as a process which proceeds in certain time interval. However, in such approaches, contradictive points of view emerge concerning investigation of wave processes in materials which possess peculiar properties. In order to describe different mechanical effects, new models of plastic medium are being improved. The phenomenon of emergence of a tooth yield in the strain diagram belongs to such properties of materials. In this article, investigation of propagation of elastic-tough-plastic wave is conducted in a semi-infinite rod; it is conducted on the basis of the electromechanical model of ideal elastic-plastic material with yield delay. The dynamic criterion of plasticity, which is stated by the author is used here. The solving of the problem is conducted according to the statement where constant force is abruptly exerted on a bult of an unloaded rod. the main solution is obtained in stresses, both for elastic and plastic domains of the rod. It is established that characteristic curves which separate an elastic domain from a plastic one and vice versa are frontal lines of weak rupture. On the basis of calculations, fields of stresses? strains, rates of displacements of cross-sections of the rod in a plastic domain are determined. for a fixed instant of time, graphs of changes of stresses and displacements of points on the whole segment of a disturbed rod are plotted. The obtained results have been verified as to exactness of satisfaction to the boundary condition.