Applications of the Monte Carlo Method for Estimating the Reliability of Components Under Multiple Cyclic Fatigue Loadings

In reliability-based mechanical design, reliability replaces the traditional factor of safety as the measurement index of the safety of mechanical components. More than 90% of metal components under cyclic fatigue loadings in industries fail because of fatigue. The P-S-N curve fatigue theory (Probability - Stress level - Number of cycles) is one of the current important fatigue theories. It is very important to know how to determine the reliability of components under different loading-induced cyclic stresses for reliability-based mechanical design. The Monte Carlo method is a powerful numerical simulation in almost every field such as optimization, numerical integration, and generating draws from a probability distribution. Literature reviews show the Monte Carlo method is successfully implemented to estimate the reliability of components under single loading-induced cyclic stress. However, there is little literature about implementing the Monte Carlo method to estimate the reliability of components under multiple loading-induced cyclic stress by using the P-S-N curve fatigue theory. The purpose of this paper is to develop a new Monte Carlo computational algorithm to calculate the reliability of components under several cyclic loadings using the P-S-N curve fatigue theory. Two key concepts in the widely-accepted Miner rule in fatigue theory are that fatigue damage is linear cumulative and the fatigue damage because of different cyclic stress is independent. Based on these two key concepts, this paper has successfully developed a new Monte Carlo computational algorithm to calculate the reliability of components under multiple loading-induced cyclic stresses using the P-S-N curve fatigue theory. The results obtained by the developed computational algorithm is validated by results obtained from two published methods. The results by the developed computational algorithm is again validated by the K-D probabilistic model. Based on validation studies, the relative differences in the results between the proposed method and the published methods are in the range of 0.66% to 2.98%. Therefore, the developed Monte Carlo computational algorithm is validated and can provide an acceptable estimation of the reliability of components under several cyclic fatigue loadings using the P-S-N curve fatigue theory.