Limit velocity of fracture front and dynamic strength of brittle solids

The theories of propagation of brittle fracture fronts in solid materials are compared with experimental data. Instead of the well-known theory of the limit fracture stress the theory of limit velocity of fracture front is developed. Accordingly between the moving boundary at which the static strength is attained and the front of fracture the material can stand essential dynamic over-loadings. The experimental data on contained explosions in optically transparent intact blocks show that the limit velocity of brittle cracks front takes place immediately after the separation of the shock front and the front of brittle fracture. The hypothesis of the existence of limit front velocity leads to the conclusion that in the two-front structure of plane shock waves the amplitude of elastic precursors, known as “the Hugoniot elastic limit”, exceeds the value of ultimate static strength of a solid material and has to increase with increasing of a finite shock pressure. This effect is justified by a number of experiments with brittle materials. The analogue with the plane problem of a self-supporting brittle burst is shown. The explanation of exceeding of the ultimate static strength and of “the delay time” of fracture under the spall condition is given. The increasing of internal fractures, which is described by the dilatancy loosening of materials is discussed. The well-known laws of “the geometrical similarity” of contained explosions are in accordance with expression of the strength in terms of the ultimate stress but not in terms of Griffith's energy for creating of new cracks. The possibility of the regime of a limit front velocity of fracture at explosion motions in real rocks, for which the dilatancy has place, is discussed.