Self Friability of Falling Objects

Abstract

When a brittle body falls under its own weight and strikes a rigid surface, tensile stresses are set up that cause fracture. This is called self friability. A recent paper (1) has experimentally investigated the self friability of disc shaped bodies with central hole. This paper applies dimensional analysis to this problem in order to gain a better understanding of the physics involved. It is found that a nondimensional quantity that is proportional to the ratio of the specific elastic energy at the critical point of crack initiation to the specific kinetic energy at impact is controlling. This nondimensional group(the self friabilitu number=N_SF) is useful in understanding the relationship between the uniaxial francture stress in tension (σ), the modulus of elasticity (E), the specific weight of the material (γ) and the height of fall (h). [numerical formula]It is also shown that the maximum tensile stress criterion for uniaxial tension may be replaced by a maximum tensile elastic energy per unit volume criterion when an applied force is replaced by an energy per unit volume as the input to the body. The paper suggests a new method of proof testing grinding wheels and the relation of the self friability test to the droppinf weight type of impact test employed in testing spectacle lenses and other brittle objects.,