Fatigue Laws via Functional Equations

In routine industrial design, fatigue life estimation is largely based on S-N curves and ad hoc cycle counting algorithms used with Miner’s rule for predicting life under complex loading. However, there are well known deficiencies of the conventional approach. Of the many cumulative damage rules that have been proposed, Manson’s Double Linear Damage Rule (DLDR) has been the most successful. Here we follow up, through comparisons with experimental data from many sources, on a new approach to empirical fatigue life estimation (‘A Constructive Empirical Theory for Metal Fatigue Under Block Cyclic Loading’, Proceedings of the Royal Society A, in press). The basic modeling approach is first described: it depends on enforcing mathematical consistency between predictions of simple empirical models that include indeterminate functional forms, and published fatigue data from handbooks. This consistency is enforced through setting up and (with luck) solving a functional equation with three independent variables and six unknown functions. The model, after eliminating or identifying various parameters, retains three fitted parameters; for the experimental data available, one of these may be set to zero. On comparison against data from several different sources, with two fitted parameters, we find that our model works about as well as the DLDR and much better than Miner’s rule. We finally discuss some ways in which the model might be used, beyond the scope of the DLDR.