An analytical model for the coupled-field dynamic fatigue crack growth in a metallic beam under chaotic excitations

Abstract

Dynamic fatigue crack growth (FCG) under chaotic excitations has not yet received due attentions. The current paper presents an analytical model for predicting the FCG in a metallic notched beam subject to external chaotic excitations. The proposed stand-alone analytical model only requires the physical properties of the cracked beam; initial crack conditions; the material constants for the Paris power law; and the time series of the external chaotic excitation. The validity of the analytical model proposed is verified using relevant experimental results from other researchers.The validated model is employed to conduct parametric studies on the coupled field FCG in a notched metallic beam vibrating under external chaotic excitations. The fatigue lives obtained under a group of statistically similar chaotic excitations significantly disperse. The ratio between the maximum and minimum fatigue lives is around 5.2. The ratio remains as high as 2.4, even when only the initial conditions in the chaotic excitations vary.The common practice Palmgren-Miner rule is also used to estimate the fatigue life under chaotic excitations. These predictions differ, by several times, from those provided by the current validated analytical model. Similar shortcomings were noticed in a previous experimental study, where the Palmgren-Miner rule, reportedly, considerably overestimated the fatigue damage under chaotic excitations. In the current study, both under and over-predictions are noted.