Statistical distribution for initial crack and number of loading in fatigue crack growth process

Abstract

A statistical distribution for crack growth technique is one of the important issues emerging from the fatigue crack propagation process. This study aims to compare three different statistical distributions for providing the best modelling of the fatigue data. The normal, the lognormal and the Weibull distribution are compared for determining a better fit for the variables. Kolmogorov-Smirnov has been chosen as the criterion of the best distribution of the variables. Ten replicate specimens of aluminium alloy A7075-T6 in constant amplitude crack tests were conducted. The number of cycles for the formation of the initial crack and initial crack length were taken as random variables. A Bootstrap approach was applied for ensuring that the chosen distribution was the best representative for this type of variables since small data was incorporated in this analysis, it was not suitable to justify the true population. Thus, the result showed that the lognormal distribution was the best distribution to represent the number of cycles and the length of the initial crack. It was found that whether the normal and lognormal types were suitable for those variables, the lognormal was more conservative for these types of variables. These two variables played the main role in life prediction. Therefore, an analysis of the statistical distribution is highly important. It is believed that these results lead to the significant prediction of fatigue lifetime.

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

“…Where, is a shape parameter and is a scale parameter of the length of the initial crack. The lognormal distribution was chosen as the best distribution through the comparison of Kolmogorov Smirnov value from all three distributions (lognormal, normal and Weibull) [19]. Meanwhile, the transition probability matrix values were computed to show the process of fatigue crack growth happened.…”

Fatigue crack growth analysis using Bootstrap S-version finite element model

“…The known distributions are simulated using the bootstrap resampling method in mathematical statistics technique. Sarah Januri et al [47] had used these distributions to simulate the initial crack length and fatigue life for surface crack growth. Bootstrap resampling method is simulated from a small sample of data and then transformed to a large data sample [41].…”