National University of Science and Technology MISIS, Moscow, Russia:

R. K. Khalkechev, Candidate of Physico-Mathematical Sciences
K. V. Khalkechev, Doctor of Physico-Mathematical Sciences, Doctor of Engineering Sciences, h_kemal@mail.ru

This article gives an analysis of geomaterial disintegration by crushing and grinding. These disintegration methods are uncontrollable and, thus, low-selective. To deal with this problem, a new concept of the selective crushing and grinding of geomaterials has been developed, which ensures sharp rise in efficiency of recovery of useful minerals. The scope of the discussion covers the theoretical issues of shaping a cardinally new trend in the mineral processing industry based on technologies of selective disintegration of geomaterials. The constructed mathematical model in the framework of the method of similarity and dimensions in the fracture dynamics allows determining conditions of stable and unstable propagation of cracks. Under stable propagation mode, spacing of cracks is unaltered or reduces. Under unstable propagation scenario, spacing of cracks grows. This offers an opportunity to control spacing of cracks and, as a consequence, selectivity of disintegration. A feature of the developed mathematical model is its generality as it is independent of macroscopic mechanical properties of geomaterials. The generality is supported by its insulation from dimensions of elementary volume. This conditions the model adequacy as the processes of crushing and grinding are not bounded to elementary volumes of geomaterials under treatment. This is achieved by considering crack propagation mechanism as the motion of point and linear defects towards the crack tips, characterized mainly by propagation rate, length and spacing. The computer experimentation shows paths of development in industrial practices of solid mineral disintegration at the concurrent stage and in the future.

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