A modified fatigue damage model considering loading sequence effect

Abstract

A modified fatigue damage model is proposed considering the loading sequence effect under variable amplitude loading conditions. The transition sequence is obtained from the counting sequence by an equivalent rainflow counting method and is used to provide the loading sequence information for fatigue damage accumulation prediction. Rainflow counting matrix and sequence transition matrix are formulated based on the rainflow counting sequence and the transition sequence. The relation between the two matrices and the original loading sequence is evaluated in detail. In the deterministic fatigue estimation, the rainflow counting matrix and the sequence transition matrix are integrated into the proposed modified damage model based on the linear damage rule. Mean stress transition is applied to the rainflow counting matrix for loading level effect. Existing experimental data are used to validate the fatigue damage estimation from the deterministic framework. In order to evaluate the fatigue under random loading conditions, the rainflow counting matrix and sequence transition matrix are mapped to one-dimensional exponential and Laplace distributions based on the stationary random process. Numerical simulation is conducted to validate the proposed mapping distributions. Meanwhile, the impact of the correlation length on the proposed distributions under stationary random loading sequence is investigated as well. Finally, with the given distributions of the rainflow counting matrix and sequence transition matrix, a reconstruction procedure is simulated and discussed for probabilistic fatigue estimation. The proposed model provides a sophisticated approximation to the original loading sequence with a sequence transition effect. The proposed modified fatigue damage model corrects the deficiencies of the linear damage rule with sufficient sequence information from the originally applied loading. Furthermore, the probabilistic fatigue estimation can evaluate the accumulated fatigue damages under a random loading process with the sequence transition effect.