Analysing crack growth

Abstract

Deterministic models of crack growth can be fitted to experimental data. This paper shows that stochastic growth models are easy to use and provides a simple framework for data analysis. A simple transformation allows the standard linear regression model to be used and opens the way for a fully Bayesian analysis. The Bayesian analysis allows the incorporation of prior information and coherent predictions of crack length to be made. The parameters of the Paris-Erdogan model are readily evaluated directly from crack length data without the need for intermediate estimates of the crack growth rate. The approach lends itself to the analysis of properly designed experiments to determine the effect of environmental factors on the parameters of the Paris-Erdogan equation through the medium of accelerated failure time models. The paper also emphasizes the need for adequate communication between experimenter and statistician to ensure efficient experimental designs.