Propagation of Plane Elastic-Tough-Plastic Waves in the Material with Yield Delay

Received: December 24, 2016
Revised: February 14, 2017
Accepted: June 26, 2017
Lviv Polytechnic National University

The use of electromechanical model of ideal elastic-tough-plastic material with yield delay while investigating the propagation of plane one-dimensional waves is being considered. The materials being investigated possesses the property of toughness only in the plastic region and is elastic up to the plastic state. The solving of the problem is being carried out in the conditions of one-parameter loading when the permanent (steady) uniformly distributed stress is being suddenly applied to the boundary surface of non-deformed half-space. The value of applied stress exceeds the limit level of elastic state in the case of static deformation and remains unchanged for the whole region of disturbed half-space. In order to conduct the corresponding calculation the dependence between the components the tensor of normal stress and linear deformations along the load axis is being determined. The defining equations of elastic-tough-plastic medium behind the front of the wave of transition from elastic to plastic state are being derived and the simple relationship for determination of the time (duration) of yield delay is deduced. The basic solution of these equations is obtained for the stresses in elastic and plastic region of the half-space. The special representation of the basic pattern of changing of lateral (transverse) stresses and longitudinal deformations for the region of active loading of material is defined. The distribution of velocities of the half-space points in the plastic region is obtained. The difference between the characters of propagation of plane elastic-plastic wave and the wave processes in the material with yield delay is shown.
It is noted that two different solutions are obtained despite of the simple type of loading. The first one detects the strange character of medium’s behaviour when the material of disturbed halfspacein the plastic region is in the state of “trembling”, which causes the pulsations of lateral (transverse) stresses and the impulses of deformations along the axis that is normal to the boundary surface of the half-space.