Fatigue Damage Mechanism-Based Dependent Modeling with Stochastic Degradation and Random Shocks

This paper proposes a dependent modeling method for reliability estimation of metal structures under constant amplitude loading and random shocks considering the nonlinear damage accumulation mechanism. It is well known that a large monotonic plastic zone ahead of a crack tip caused by a spike overload will retard subsequent fatigue crack growth. However, most existing degradation-and-shock dependent models cannot account for this retardation phenomenon. Moreover, the increase in damage caused by shock is usually assumed to be independent of fatigue degradation. In this investigation, both fatigue degradation and applied random shock damage are considered to have a coupled effect on the crack propagation process. The nonlinear damage superposition approach is utilized herein to model the interaction between fatigue loading and random shocks. Fatigue degradation is considered as a stochastic process influenced by the uncertainties in material properties, and the applied shocks are regarded as random incidents. Next, the piecewise deterministic Markov process is employed to describe the coupling relationship between this stochastic degradation and the random shock process. In the proposed algorithm, Paris' equation is utilized to describe fatigue degradation, and the Willenborg model is employed to describe retardation caused by random shock loads. A simulation is performed to validate the proposed method, and the proposed method is compared with the traditional method.