Continuum theory of shear disintegration of solid bodies
Urgency of the research. Material strength issues are fundamental in any technical science. The issues of destruction are especially relevant in mining, where the main technological processes are aimed at the destruction of rocks (drilling, blasting, crushing, etc.); the production method (method of working) or mining is selected from the condition of stability (strength) of the mining array.Purpose of the work. The work is devoted to determining the laws of plastic deformation and disintegration of rocks (solids) based on their representation as a continuous (continuum) medium.Research methods, results and conclusions. The author proposes some new laws of plastic deformation obtained analytically on the basis of continuum fracture mechanics such as the functions of the yield surface and plastic potential, the strength criterion of solids, the equation that determines the intrinsic moment of blocks (formed structures) during plastic deformation, dynamic equations (evolutionary) of the fragmented structures behavior, the variational principle of the disintegration of solids, the criterion for the growth or appearance of a crack of any scale (hierarchical level), closely related to the fundamental parameter of the hierarchy of mountain ranges and the number of Phidias. Some effects and phenomena of the processes occurring during plastic deformation, disintegration (destruction) have been identified, explained and discussed. In particular, it has been experimentally shown, that the main sign of plastic deformation at the hardening stage is the partial or complete (at the elastic limit) loss of the retaining effect of internal friction in the minute movement sites under the action of the minimum primary stress and its gradual strengthening during hardening, which is a consequence of the phenomenon of dilatancy, i.e., an increase in volume in the direction of the minimum primary stress. It is shown that, turning of shear areas (structural elements) from continuum positions is an inevitability that postpones the fracture moment; in the absence of rotational deformation, an instantaneous cut of the sample will occur. This explains the proximity of the elastic and tensile limits for brittle materials. That is, a criterion for the separation of materials into brittle and plastic is outlined. The possible mechanism of the transition from the accumulation of volumetric damage during plastic deformation to the growth of the main crack (fading of the deformation activity) and the corresponding drop of potentials, which can be explained in terms of tiny fractures: when appearance (while fracturing) they are pointed out at one angle, and a further change in their orientation (turn) is impossible (increase in elastic resistance) and, due to stress concentrations, they are connected according to the anisotropic substance. Keywords : plastic potential function, plasticity and strength criterion, dilatancy, hierarchy parameter, variational principle, moment of blocks, sin-Gordon equation.