# A constructive empirical theory for metal fatigue under block cyclic loading

Patil, Navendu and Mahadevan, Pradeep and Chatterjee, Anindya (2008) A constructive empirical theory for metal fatigue under block cyclic loading. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464 . pp. 1161-1179.

Much modern engineering design work uses S–N curves and empirical applications thereof. In industry, currently popular methods for predicting fatigue life under complex loading use ad hoc cycle counting algorithms along with Miner's rule, in spite of its known weaknesses. Many ad hoc alternatives to Miner's rule have been proposed, each with limited experimental justification. Of these, Manson's double linear damage rule (DLDR) is widely considered to be good. In this paper, we bring a new perspective to empirical, as opposed to mechanistic, fatigue damage evolution models. It is first assumed, with reasonable justification, that there is a scalar, abstract, damage variable \phi, whose evolution under cyclic loading satisfies $\phi= a\phi ^m$, where a and m are unknown functions of load parameters. One main contribution of the paper lies in deducing what the functions a and m must be in order to obtain consistency with fatigue data in handbooks. A small correction to this basic power law model is then developed. The final explicit model initially has 10 unknown fitted parameters, but these are brought down to three unknowns; the accompanying discussion is the other main contribution of the paper. Finally, comparison with Manson's and other data suggests that, with two fitted parameters, our model works as well as the DLDR and much better than Miner's rule. For other parameter choices, our model reduces to Miner's rule. We conclude with speculation about ways in which the model might be extended beyond the scope of the DLDR.