Statistical analysis of the virkler data on fatigue crack growth

Abstract

The extensive data set obtained by Virkler et al. for fatigue crack growth under homogeneous cyclic stressing is the object of statistical analysis. It is based on a previously published stochastic model of the crack growth. The statistical scatter of the experimental data is made up of a random “between” specimen variation and a random “within” specimen variation, the former being of the finite dimensional random vector type and the latter of random independent increment process type. The main results of the statistical analysis are 1. (1) that a random equation of the ParisErdogan type that allows for random material inhomogeneities fits very well to the data and 2. (2) that the distribution type for the number of stress cycles needed to grow a crack by a given length is convincingly described as being inverse Gaussian. Within the basic stochastic model this distribution type is asymptotically correct for large cycle number increments. Furthermore 3. (3) the random vector variation between specimens is reasonably well described by a joint normallog normal distribution. Numerical differentiation of the (basically non-difierentiable) experimental crack growth curves to obtain crack growth rates is avoided in the present model. In place the model points at direct maximum likelihood estimation of the parameters in the Paris-Erdogan equation.