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 halfspace in 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.

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.