In the framework of the phenomenological scheme a self-consistent description of the transition from the solid state to the plastic flow was presented taking into account the point defects such as interstitials and vacancies. On the basis of the system of synergistic equations the dependencies of the internal stresses and curvature of the velocity profile of the shear displacement on the order parameter as well as the stationary distribution of the concentration of vacancies were found.

The processes occurring during the deformation of solids have attracted attention for a long time [

In this paper we propose a phenomenological scheme, within framework of which the transition from a solid state to a plastic flow is presented as a self-organization process of the elementary particles of a material taking into account the ensemble of vacancies and the external influence. Section

Let us consider the dynamics of the material in the case of shear strain, when the displacement is given by the function

The understanding of the basic laws of plastic flow can be achieved in the framework of the hydrodynamic theory [

The last one meets the local fraction of the free volume. On the other hand, the parameter

In the case of amorphous solids the concept of the “lattice sites" and “vacancies" or “interstitial atom" is not so obvious, and it is necessary to give a more general interpretation of the density

For crystals

It turns out that the value of

The dynamic equations for the density and momentum density in the deterministic case can be represented in a standard way [

Using the definition of

Parameter

It should also be noted that in [

Based on the above it is natural to assume that the third parameter characterizing the system under study is the field of elastic stresses

In contrast to the original relation (

The system of (

As a result of the behavior of solids under external loading with the ensemble of vacancies there is a dimensionless system of equations

Here the prime denotes the coordinate, and the additional parameters characterizing the ratio of the constants and parameters of the material are given by

Despite a significant simplification of the system (

Since the rate of change of the dimensionless

Thus, as shown in Figure

Dependence camber shift offset (a) and internal stresses (b): the concentration of vacancies in

Further, substituting the first relation (

As shown in Figure

The dependence of the vacancy formation energy of its concentration when

The dependence of the steady-state value of the system parameters

In this case, substituting the value of (

Consider the solution of (

It should be noted that at the boundary of the material (

Using the approximation

The final expression for the concentration of vacancies in the definition (

The spatial distribution of the concentration of vacancies at

In this case the constant

The spatial distribution of the elastic stresses at

As follows from Figure

However, in determining the spatial dependence of the shear displacement difficulties, for example, the first equation (

When

Our analysis shows that the use of the system (

In the framework of the adiabatic approximation, it is shown that an increase in the curvature of the vacancy rate of the shear displacement increases and the internal voltage drops below the level fixed by external factors. Obtained from the Ginzburg-Landau-Khalatnikov vacancy formation energy becomes non-zero minimum