Similitude criteria in models of the fracture of a solid body by an explosion

Abstract

The study of industrial explosions is made difficult by the high pressure and temperatures arising from the detonation of large charges, and by side factors which are difficult to allow for. Simulation by models enables us to cut down the number of costly industrial experiments while maintaining identical conditions so that laboratory resuits can be applied to the full-scale prototypes. The breakup of a medium is governed by its physical and mechanical properties, the characteristics of the explosion, and the conditions of blasting. These factors must be taken into account when designing a model of the process.Breakup is a complex nonstationary process, which can arbitrarily be divided into three main stages: propagation of the stress field, fracture formation, and separation of the fragments formed. In previous work on models of breakup by blasting, the similitude criteria do not allow for the fracture-formation stage, which is critical for the fragmentation process, or the time characteristics of the breakup process. The aim of our present work is to establish similitude criteria which will take account of one phase of the breakup process, namely, fracture formation.The theoretical analysis of the breakup process is based on the hypothesis of A. A. Griffiths and M. V. Machinskii, who postulate that in any body there are defects (microfractures) from which macrofractures originate when a stress field passes. In the propagation of the stress field due to the explosion of a charge, in some volume dv of the medium, dn fractures will open up. The density of sites of origination of individual fractures n o is governed by the maximum applied stress and by the strength properties of the real and model materials, no= ,(s) ds, Ser O)where S is the surface area of a crack, ~(S) is the differential distribution function of the dimensions of the cracks, o is the applied stress, and Scr(O) is the surface area of the smallest crack opened by the stress.As the stress wave spreads, the maximum stresses in it will decrease owing to geometrical expansion and dissipative energy losses in real media: The density of crack initiation sites will be some complicated function of the distance from the charge center, ,r%= (r)]where n o is the number of initiation centers in unit volume, o 0max is the maximum stress at the wail of the blast hole (charge cavity), lob] is the breaking stress under static load, r0 is the radius of the charge, and r is the distance from the charge center.If the body is cylindrical, the total number of crack initiation sites will be R It~ (r)]rc, r n : 2~H, f[-[-~cO 7~o0 where H is the length of the body and R its radius.

Simulation of overcrushing pressure in coal

“…Therefore, the model parameters determining the processes of fusion and evaporation, were not taken into acccount. The other parameters were chosen as in [2,3]. We took account of the similarity in blasting with a counterpressure ~, the charge shape, and the energy emission determined by the composition and weight of explosives.…”