Probabilistic modeling of double linear damage accumulation and its application in fatigue reliability analysis

In this paper, a probabilistic double linear damage accumulation model is proposed to characterize the uncertainty of damage accumulation using the statistics of material fatigue life. The probabilistic modeling framework is performed under normal distribution assumption of fatigue life. By applying a one-to-one probability density function transformation method, the probability distribution of critical damage and cumulative damage can be extracted and derived. The proposed probabilistic damage accumulation model is then used for fatigue reliability analysis by building the reliability formulas with respect to the cumulative damage and the critical damage under both constant and variable amplitude loadings. It treats the mean and variance of cumulative damage as time-dependent values that dynamically vary with increase in usage life. The reliability can be easily calculated by limited data necessary from fatigue life samples. The applicability of the proposed method is demonstrated using the experimental data of two metallic materials under constant amplitude and two-block loadings. The results show that the model predictions are in good agreement with the experimental observations under constant amplitude loading and L-H loading sequence. In addition, the proposed method provides better predictive ability than the Miner rule under constant amplitude loading and H-L loading sequence. Moreover, the predicted reliability plots can typically present a two-stage fatigue characteristic during crack initiation and crack propagation periods.