Reliability assessment from fatigue micro-crack data

Micro-cracks are generally defined to be cracks less than 1 mm in length, which propagate under cyclic stresses until they grow large and cause failure in an item (e.g. component or structure). This paper proposes a method of using data on `fatigue micro-crack growth in a material' to predict its reliability. It is increasingly important to model such cracks effectively, Their growth properties, which differ in several respects from larger cracks, are discussed. The paper develops a hierarchical model for the propagation of micro-cracks in a material. This stochastic model attempts to model the dependence of growth on local conditions, varying throughout the material, that causes variation in growth rates across the specimen. Given the model, data on micro-crack growth are used to compute posterior distributions of model parameters, from which a predictive distribution for reliability can be calculated. Computation of the posterior distributions is by Gibb's sampling and kernel density estimation. The methodology is illustrated with two data sets, one simulated and the other from a cast-iron specimen. Some possibilities for further work are presented