Random fracture of a brittle solid

A brittle solid may be defined as one having a tenacity small in comparison with its rigidity. Such a material readily yields new surface by shattering under random impulsive or crushing forces producing deformation by action at the boundary. Many solids upon which the crushing or grinding mill acts fall into this category. The problem of the mill may be defined as one which concerns itself with the relations between the fragment statistics, the properties of the material, and a set of random mechanical boundary conditions. The production of cracks and fissures in brittle solids under random and organized boundary conditions has been studied by Suzuki,14 Terada l1 and Hirata.12 Hirata has shown that a fundamental statistical attack on the problem is possible by his use of the Poisson series to describe fracture statistics. The grinding mill has been studied extensively by empirical methods and attempts have been made to relate the fragment statistics to the boundary work. The names of Martin 8* g and Gaudin lo are identified with much painstaking work here. The need for a rational approach to the task of specifying and predicting the probable size and shape of the fragment is widely felt. The purpose of this paper is to map out such an approach. Despite numerous complications of the general case, the applicability of three general principles is quite clear. In all discussions “ chance ” must be assumed to play a dominant role.