STOCHASTIC MODELLING OF METAL FATIGUE CRACK GROWTH USING PROPORTIONAL PARIS LAW AND INVERSE GAUSSIAN PROCESS

Fatigue failure is one of the main failure modes of metal components. In order to describe the uncertainty associated with metal fatigue crack growth, a stochastic description based on the “time t(a) to first reach a predefined crack length a” allows for the process mean in each specimen to equal to a proportional Paris law. Then, a simple model and a random effect model based on the inverse Gaussian process (IGP) are established, which are used to describe the variability across a single specimen and specimens, respectively. Then the model parameters for the simple model and the random effect model are estimated by using the maximum likelihood estimate (MLE) method and the expectation maximization algorithm (EM), respectively. Finally, the proposed models are used to fit the 68 Virkler fatigue datasets and the good-of-fit test is analyzed. The results show that the proposed models are effective candidates for description and interpretation of the uncertainty of metal fatigue crack growth.