The main stages of research development of researches into fracture mechanics and strength of materials in the second half of the XX century have been considered. The principal attention was paid to the analysis of the calculation models of limiting equilibrium of deformed solids, containing sharp stress concentrators (cracks), to the development of the methods of the stress intensity factor calculations, to the methods and means of experimental development of the material crack growth resistance, concepts of fatigue crack initiation and propagation and also to the processes of materials crumbling in the zone of two bodies cyclic contact. New approaches to establishing the period of fatigue macro-crack initiation at the stress concentrator, using the conventional v-K curves for the given material have been formulated. Some prospective problems in this field of science have been proposed.
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