Minerals Beneficiation - Theory of the Distribution of Fragment Size in Comminution

Recently, Gilvarry1,2 has given a rigorous derivation of the proper distribution function for fragment size in single fracture, based on a closely defined physical model and deduced strictly by the laws of probability. The physical point of departure is Griffith's theory of brittle strength, identifying sub-microscopic flaws as the cause of the low strength of a solid in comparison with values implied by cohesive energies. Gilvarry and Bergstrom,4-7 and Gilvarry8 have compared the predictions of the theory with experiment, and have found excellent agreement, in general. The purpose of this communication is to sketch the extension of the theory to the case of comminution, and to indicate the applications to some examples in nature. The present treatment represents an amplification of a brief discussion appearing elsewhere. 9 Although the basic ideas of the Griffith theory are perfectly general for rupture of brittle solids, it was originally formulated with very brittle materials such as glass in mind. Moreover, Griffith's original experimental work was carried out on glass specimens. Recently, however, the theory has been extended by race" to apply directly to rocks. This extension makes the theory immediately applicable to the materials generally of interest from the standpoint of comminution. GENERAL CASE To obtain the distribution function for fragment size in single fracture, three assumptions are made, that: 1) Fracture proceeds by activation of preex-istent Griffith flaws in the volume, faces, and edges of a fragment; 2) the distributions of flaws of these three types are independent of each other; and 3) activated flaws of a particular type are distributed at random, individually and collectively, in the sense of Fry.11 The last assumption implies that each distribution is separately of Poisson type.