Crack propagation under random loading

Abstract

A theory of metal fatigue under randomly distributed stresses is presented which takes into account the probability distribution of the amount of damage done after any number of cycles. The theory takes the form of a set of integral recurrence relations which in general must be solved by computer. A model is considered which is qualitatively close to the physical situation, and for which these integral relations reduce to a set of algebraic relations for the probability of failure at the nth cycle. These latter can be solved approximately, and the leading term in this solution corresponds to the solution obtained by ignoring the spread in the amount of damage, a method which has been adopted hitherto. Thus we are able to state conditions under which these previous methods are valid, and to obtain the major corrections to their results. Throughout this paper we treat the fatigue process in terms of the propagation and final catastrophic failure of a dominant crack.