Dynamic Model for Fatigue Evolution in a Cracked Beam Subjected to Irregular Loading

Abstract

The coupling of vibration and fatigue crack growth in a simply supported uniform Euler–Bernoulli beam containing a single-edge crack is analyzed. The fatigue crack length is treated as a generalized coordinate in a model for the mechanical system. This coupled model accounts for the interaction between the beam oscillations and the crack propagation dynamics. Nonlinear characteristics of the beam motion are introduced as loading parameters to the fatigue model to match experimentally observed failure dynamics. The method of averaging is utilized both as an analytical and numerical tool to: (1) show that, for cyclic loading, our fatigue model reduces to the Paris' law and (2) compare the predicted fatigue damage accumulation with the experimental data for chaotic and random loadings. A utility of the fatigue model is demonstrated in estimating fatigue life under irregular loadings.