The analysis of fatigue lifetime using markov chain model based on randomization paris law equation

Abstract

The experimental data of fatigue crack growth scatter even under identical experimental conditions, including constant amplitude loading. Thus, it is important to take into account the data scatter of crack growth rates by using statistical approach analysis. In this study, the distribution of the fatigue crack growth life was estimated using Markov chain approach based on the modified Paris law equation to consider the variability in the growth of the fatigue crack. In this regard, in the Markov Chain model, the Paris law equation was integrated with the probability distribution of the initial crack length to calculate the probability transition matrix. The result shows that the initial probability distribution was represented by lognormal distribution and it can be said that the initial crack will happen only in state 1 and state 2. The consideration of probability distribution into Paris law equation to represent the physical meaning of fatigue crack growth process. The fatigue life estimation using the Markov chain model are found to be agreed well with experimental results and the value of R 2 showed the model is good. The results provide a reliable prediction and show excellent agreement between proposed model and experimental result. This indicates that the model can be an effective tool for safety analysis of structure.