Cumulative fatigue damage taking the threshold into account

Prediction of fatigue life at variable amplitude often demands considerations about the contribution of loads below the nominal fatigue limit. Different engineering approaches include acceptance of the limit, neglecting of the limit, or making ad hoc corrections for damage contributions originating from loads below the limit. Theories that consider the fatigue limit as controlled by crack thresholds suggest that the limit decreases as the damage accumulates, i.e. as the dominating crack grows. This idea is used here to find an extension of the Palmgren-Miner rule to the case with a fatigue limit decreasing with increasing damage.