Dynamic Reliability Assessment of Multi-cracked Structure under Fatigue Loading via Multi-State Physics Model

Abstract

The structure strength abruptly decreases due to the propagation of multiple cracks. The crack interaction renders the multiple crack reliability problem being a challenging one. Most of the existing methods cannot fit the whole multiple crack growth process and quantify the crack linkup effects on reliability estimation. To address this problem, we extend the multi-state physics modelling and computation framework to evaluate the dynamic reliability of multi-cracked structure via implementing piecewise deterministic Markov processes (PDMP). The proposed multi-state physics model (MSPM) incorporates the crack propagation state transitions and the Forman model that describes the crack growth rate within the states. For the former, the probability of the linkup of adjacent cracks is calculated to identify the multiple crack systems and define the discrete states of each system. For the latter, the Forman model is employed to calculate the crack growth rate within the states. Therefore, each multiple crack system in the structure can be quantified by PDMP and a Monte Carlo algorithm is presented to evaluate the corresponding dynamic reliability values. Ultimately, the dynamic reliability formulation of the multi-cracked structure is developed. The accuracy of the proposed approach is verified by using the sample data from the literature and simulation example.