Selfsimilar problems of star-shaped crack development under the action of a cleaving gas flow

Abstract

The problem of the development of a system of a system of radial slits from zero at a constant rate under plane strain conditions is considered. For instance, this problem occurs in describing fracturing of a stratum by hydraulic rupture cracks. Crack cleavage can be produced by a gas being formed during the explosion of a cylindrical charge /1/ or by special powder pressure generators pressed into a borehole /2/. Selfsimilar solutions of problems on the development of normal separation crack stars were obtained by the Smirnov-Sobolev method of functionally invariant solutions /3, 4/. The solution of the problem of the cleavage of a star-shaped crack by an isothermal inviscid gas flow being liberated instantaneously at the initial time is presented. Selfsimilar problems on the development of a star-shaped crack under antiplane strain conditions were examined in /5, 6/. Investigation of the cleaving action of a viscous isothermal gas flow on rectilinear isolated slit propagation is performed in /7/, where it is shown that a deceleration shock is formed in the gas flow under certain governing parameters of the problem.