The analysis of initial probability distribution in Markov Chain model for lifetime estimation

Abstract

Fatigue crack growth is a stochastic phenomenon due to the uncertainties factors such as material properties, environmental conditions and geometry of the component. These random factors give an appropriate framework for modelling and predicting a lifetime of the structure. In this paper, an approach of calculating the initial probability distribution is introduced based on the statistical distribution of initial crack length. The fatigue crack growth is modelled and predicted by a Markov Chain associated with a classical deterministic crack Paris law. It has been used in calculating the transition probabilities matrix to represent the physical meaning of fatigue crack growth problem. The equation of Paris law provides information regarding the stress intensity factor and material properties in predicting the crack growth rate. The data from the experimental work under constant amplitude loading was analyzed using the Markov Chain model. The results provide a reliable prediction and show excellent agreement between proposed model and experimental result. The reliability of the model can be an effective tool for safety analysis of structure.