The mechanics of erosion by liquid and solid impact

Abstract

A solution approach for the general problem of erosion by liquid or solid impact is demonstrated for a simplified attack process where impact areas e.g. craters, of one size only are generated on the target surface. The erosion process is characterized by the specific loss of material (per impact) which is considered to be a random variable, the mathematical expectation of which as a function of time (“erosion curve”) is calculated. Based on the statistical nature of the repetitive loading, the individual impacts are classified according to their effectiveness in removing target material. This effectiveness is measured by the probability PrepN to hit, at the Nth impact, as an ith repetition the same neighborhood e.g. the same crater, on the target surface. The present solution procedure is an extension of that used in Bargmann [International Journal of Theoretical and Applied Fracture Mechanics, Vol. 6, pp. 207–215 (1986)] where the probabilities had been calculated, for the early impacts, via so-called erosion-process configurations, the evolution of which had been shown to be Markov. In the present solution procedure, the general solution for the probabilities is given in closed form, for any time t. and the deterministic calculation of the corresponding values of specific material loss, based on impact dynamics, is outlined. It is demonstrated by an illustrative example that the approach is capable of realistically capturing the time-behavior of the erosion curves for both ductile erosion processes and those governed by fatigue.