Effect of stress ratio on crack propagation life distribution under random loading

Abstract

A stochastic crack growth model under stationary random loading has been constructed based upon the Walker's growth law which accounts for the effect of the stress ratio. By use of this model, the crack length distribution and the crack propagation life distribution have been successfully derived both in a closed form with the aid of the Markov approximation method and renewal process theory. The validity and applicability of the derived distributions as well as the effect of the stress ratio on the life distribution have been discussed on the basis of the results obtained by Monte Carlo simulation techniques. From these results, first, the crack propagation life distribution based upon the Walker's law is revealed to be of the Birnbaum-Saunders' type, similar to that based upon the Paris-Erdogan's law. Secondly, the mean and the variance of the life distribution in consideration of the stress ratio prove to be both smaller than those of the life distribution without consideration of the stress ratio. Finally, the coefficient of variation of the life distribution is, however, almost identical between both cases with and without consideration of the stress ratio. Though the coefficient of variation at the early stage of propagation becomes large, it gradually decreases to a certain value as the crack length increases.