A Random Fatigue Crack Growth Model Using Random Fields and Its Improvement Compatible With Computer Simulations

Abstract

A new probabilistic model is developed for descibing random fatigue crack growth reflecting spatial inhomogeniety of materials, where (i) mean behavior of fatigue crack growth is assumed to obey the well known Paris’s law, (ii) the randomness associated with materials property is modeled as a spatially homogeneous random field, (iii) a random differential equation driven by a random field is transformed into a random differential equation driven by a random process and (iv) the transformed system of random differential equations is of diffusive type so that it is compatible with computer simulations. The proposed model consists of a bivariate diffusion process given as a solution of the system of random differential equations driven by a Wiener process, which leads to a simple algorithm for generating sample functions of fatigue crack growth. Simulation analyses indicate that (i) the proposed model can well reproduce probabilistic properties associated with residual life of fatigue crack gorwth and (ii) a transformed random process descrbing fatigue crack growth resistance can well reproduce a gradual reduction of a correlation time which is caused by a gradual acceleration of fatigue crack growth rate.