Monte Carlo simulations of the growth of small fatigue cracks

Abstract

In this paper are presented Monte Carlo simulations of small, plane embedded or surface-breaking fatigue cracks propagating under mode I cyclic loading through stochastic microstructures. Unlike most prior statistical models of surface-breaking fatigue cracks, which study only the behavior of the visible surface tips of the crack, the simulations calculate the advance of the entire crack front. The rate of growth of any segment of the crack front is determined by empirical or postulated laws that quantify the influence of its immediate microstructural environment. To make feasible the generation of many simulations at reasonable computational expense, approximate, simple algorithms have been derived for estimating the Mode I stress intensity factor around a plane, embedded or surface-breaking crack of any shape. The computational procedures used to carry out the simulations are defined. The potential of the simulations for analysing experimental measurements of fluctuations in crack shape and velocity is explored. The dependence on crack length and the variance of the aspect ratios of small surface-breaking cracks in Al 7075-T6 are accounted for successfully by the effects of microstructure-dependent plasticity-induced closure. Various other statistics of crack shape and velocity that can be predicted by the simulations and compared to experiment are considered. Laws describing the mechanics of crack growth both at and below the surface can be inferred from such comparisons.