Application of Survival Statistics to the Impulsive Fragmentation of Ductile Rings

摘要

The current study addressed the problem of predicting fragment size distributions resulting from the tensile fracture of impulsive loaded bodies. Theory was restricted to one-dimensional bodies subjected to uniform loading. A rigorous treatment of the statistics of dynamic fragmentation has been attempted using concepts of survival statistics and incorporated here through the relation derived by Johnson and Mehl and Avrami. Physical concepts are introduced through the assumption of a uniform nucleation rate of fracture and the propagation of stress-relief waves governed by the tensile response of an ideally ductile material. An analytic distribution curve was derived for ductile fracture and compared with the fragmentation data of Wesenberg and Sagartz on aluminum rings. The analytic expression was found to provide a good representation of the data although further experimental work in this area is strongly needed. The present analysis and resulting fragment size distribution expressions are fairly complex even for the very simple geometry and loading conditions considered. Direct application of the method to more complicated fragmentation events would probably be difficult. Perhaps the greatest value of the present type of analysis will be the insight that it provides on the statistical nature of impulse fragmentation - hopefully a source of fresh ideas for computational models currently under development. (ERA citation 05:027475)