A New Theory of Size Reduction

Abstract

Since Rittinger proposed his theory on size reduction in 1867, a number of theories for size reduction have been developed empirically as well as semi-empirically and theoretically. Among these theories, Rittinger's theory, Kick's theory and Bond's theory have been widely referred to. However, many examples of discrepancies between these theories and actual size reduction operations have been experienced.The present authors studied theoretically the fracture phenomena experienced in the size reduction process, particularly the mechanism of fracture, from the material strength point of view. According to this theory, the energy required for size reduction is proportional to the 3 (1-2/β) th power of particle size and the square of tensile strength, as well as inversely proportional to Young's modulus where β being coefficient of uniformity when the “size effect” of tensile strength is taken into consideration.This theory is sufficiently general to incorporate all the three older theories mentioned above, and may permit an accurate calculation to be made for a selected size reduction operation from simple laboratory test information on rock specimens.