A simple analytical crack tip opening displacement approximation under random variable loadings

A simple analytical approximation is proposed in this paper to calculate the crack tip opening displacement under general random variable amplitude loadings. This approximation is based on a modified Dugdale model for cyclic loadings. The discussion is first given under constant amplitude loading and is extended to several simple cases under variable amplitude loadings. Following this, a general algorithm is proposed under general random variable loadings. Numerical examples are verified with finite element simulations. Following this, hardening effect is included by including a hardening correction function. The proposed analytical approximation is very efficient compared to the direct finite element simulation. The solution can be used for detailed fatigue crack growth analysis under random variable amplitude loadings.