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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

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The model of an ideal incompressible liquid is now being used to good effect in the theory and practice of explosive breaking. Thus, on the basis of this model, Lavrent'ev [i] solved the problem of formation and action of a shaped charge. Vlasov [2] calculated the size of the crater created by an underground explosion for ejection. The theory of an ideal incompressible liquid is used with complete success by and other authors [10][11][12][13][14]. The authors of [4][5][6][7] solved the problem of the principles of an absolutely directed explosion; the authors of [3,[10][11][12][13][14] the problem of the explosion crater; and the authors of [8] the problem of the principles of uniform crushing of rocks.This model was used for the first time for impact breaking of rocks by Kuznetsov and Sofronov [15].A more detailed description of the model of an ideal incompressible liquid is given in [16]. Below we briefly describe the principle of this theory with regard to the problem of impact breaking.We will assume that the fracture of solid bodies by an impact takes place in two stages. In the first stage the energy of the impact is transmitted to the rock by the formation of a shock wave in the medium; it is assumed that the duration of this stage is vanishingly small. In the second stage the medium itself is moved.From the supposition that the energy is transmitted over a vanishingly short period, it readily follows that the modulus of elasticity of the medium, E, will be infinitely great.This means that the medium can be regarded as incompressible.We can also show that during the period of action of pressure, infinitely large stresses arise in the medium, but deformation of the latter will not be observed. Hence, it follows that the medium behaves like an ideal liquid, Thus the medium being broken can be regarded as an ideal incompressible liquid.In the absence of mass forces, the general equation of motion of such a medium in the Euler form has the following appearance in vector form [17]:where v is the velocity vector of the medium; t, time; p, pressure induced by the impact; and 0, density of the medium.Integrating this equation within the limits from 0 to T and assuming that at the initial moment (t = 0) the medium was quiescent, we obtain ~=--V --P , (i) P where P is the pressure pulse calculated from the equationwhere 9 is the period over which the impact energy is transmitted to the medium.The velocity is a potential function; therefore, from the function @ = --P/p and from the condition of incompressibility it is clear that the velocity field potential satisfies the Laplace equationwhere ~ = ~2/~x2 + ~2/8y2 + 82/8z 2 is the Laplace operator.Institute of Mining, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk.