A statistically consistent fatigue damage model based on Miner’s rule

•A statistical damage criterion is established based on linear Miner’s criterion.•A consistent index is introduced in the statistical damage criterion.•A statistical fatigue damage model for variable amplitude loading is proposed.•The model can calculate the statistical characteristics of fatigue damage and life.•The numerical simulation of the model is based on Monte Carlo sampling approach.

With Monte Carlo sampling method, a statistically consistent fatigue damage model under constant and variable amplitude loadings based on linear Miner’s rule is proposed, which can quantitatively depict the probabilistic properties of fatigue damage and life. Numerical simulation shows that linear Miner’s damage criterion is statistically inconsistent; through some modification from a probabilistic point of view, a statistically consistent damage criterion is first established. To validate the statistical model, numerical verification of a supposed two-level cyclic loading and experimental verification of fatigue tests for Al-alloy straight lugs available in the literature are successfully conducted. The model predictions coincide quite well with both engineering hypotheses and experimental observations, compared with Miner’s model, indicating that the model can be regarded quantitatively accurate for engineering application.