Stochastic modeling and statistical verification of crack growth under constant amplitude loading

Abstract

Some results of theoretical mechanical analysis are a direct inspiration for the stochastic model of the fatigue crack growth process proposed in this paper. A crack growth equation is formulated in which the effect of the slip line mechanism as well as the effect of the plastic zone at the crack tip are both taken into account. A consequent application of the results of theoretical investigations removes the problem with parameter dimensioning which often occurs for crack propagation laws commonly used in practice, e.g. the Paris or Forman laws, and assures the asymptotic behavior of the crack rate for small and large stress range intensity factors which is usually observed in experiments. Four random variables and a random process describe, in general, the effect of material randomness on the fatigue crack growth process. The statistical analysis of the so-called Virkler and Ghonem-Dore data sets is extensively used to verify the model and to identify the model parameters. A delta-correlated random process is assumed to describe the random nonhomogeneity of the material but its effect on the fatigue crack growth process is derived to be nonstationary with finite correlation length. Accordance with the theory of fatigue crack growth and a very good agreement with the experiment results make the proposed model very promising in further applications.