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The present study is focused on the distributions in particle size produced in dynamic fragmentation processes. Previous work on this subject is reviewed. We then examine the one-dimensional fragmentation problem as a random Poisson process and provide comparisons with expanding ring fragmentation data. Next we explore the two-dimensional (area) and, less extensively, the three-dimensional (volume) fragmentation problem. Mott’s theory of random area fragmentation is developed, and we propose an alternative application of Poisson statistics which leads to an exponential distribution in fragment size. Both theoretical distributions are compared with analytic and computer studies of random area geometric fragmentation problems, including those suggested by Mott, the Voronoi construction, a variation of the Johnson–Mehl construction, and several methods of our own. We find that size distributions from random geometric fragmentation are construction dependent, and that a conclusive choice between the two distributions cannot be made. A tentative application of the maximum entropy principle to fragmentation is discussed. The statistical theory is extended to include a concept of statistical heterogeneity in the fragmentation process. Finally, comparisons are made with various, dynamic fragmentation data.

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A B S T R A C T The theory of linear elastic dynamic fracture mechanics for Heaviside loading of an isolated crack is employed to formulate the response to constant strain-rate loading of a single crack. Numerical integration of the Heaviside solution is shown to lead to fracture initiation stresses that are dependent upon the imposed strain rate. These fracture initiation stresses are also shown to be relatively independent of the crack size and crack shape. The results are used to explain the strain-rate dependent fracture stress observed in some rocks as being a structural response, rather than a basic material property.

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