Impact disintegration of rocks by single and twin indentors within the framework of a hydrodynamic model

Abstract

One of the methods actively being advocated today for use in processing hard rocks, including frozen rocks, is the impact method.In this connection, there has been increased interest recently in studying the simultaneous action of twin indentors on a rock. L. I. Baron et al. Conducted experimental investigations of the formation of disintegration regions when single and paired indentors are statically impressed [i]. They arrived at conclusions which confirm the effectiveness of twin indentors when a small impression step is used.We will consider the problem of the impact disintegration of a rock by an indentor with a sharp point.We will assume that the impact takes place over an infinitesimal area. In the plane case this corresponds to a point impact on a half-plane.We will solve the problem within the framework of a hydrodynamic model [2]. For this case, as has been shown previously [3], the complex flow potential has the formwhere M is a constant determined from energy considerations and having a numerical value proportional to the moment of a dipole situated at the origin, and z = x + iy. From (i) we see that the potential of the velocity vector is ~(x, y) = Re ~V(z)=--My/(x 2 + y:).(2)Hence the components of the velocity vector ~ in a Cartesian coordinate system will beThus, the modulus of the velocity vector in a polar coordinate system (r, 8) can be expressed in the formThe equation for the boundary of the disintegration will be found, a~ in [2], on the assumption that the equationis satisfied on it, where c, = const characterizes the physical properties of the rock being disintegrated. It can be seen from (5) and (6) that the region of the disintegration is a semicircle with center at the point of application of the force and radius ~.Let us calculate the crushability criterion From (2) and (7) we haveand the distribution of the dimensions of the disintegrated pieces over the region of disinegration can be described by the equation [2]where u s = Cs/E~0 is the critical rate of disintegration under compression; o s is the yield strength of the medium; E is the modulus of elasticity; 0 is the density of the medium.Northern IGD of the YaF of the Siberian Branch of the USSR Academy of Sciences, Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh