Crack propagation in structures with uncertain-but-bounded parameters via interval perturbation method

Abstract

Fatigue crack growth prediction plays a crucial role in structure design. This paper presents a method for crack propagation analysis in structures with uncertain-but-bounded parameters. Although the parameters of engineering structures are uncertain due to many factors, the range across which they vary can be determined from practical experience and engineering knowledge. The crack growth boundary over the life of the structure has great significance in preventing structural failure. Uncertain-but-bounded parameters are regarded as interval numbers in the proposed method, and expressed alongside time-varying crack length under Paris law as a perturbation series after introducing a small parameter. By combining the perturbation method with interval mathematics, boundaries of each term in the perturbation series of time-varying crack length are determined to obtain the upper and lower boundaries of time-varying crack length. The proposed method is verified based on two examples; both the Monte-Carlo method and probabilistic method are applied for the sake of validation. The results demonstrate the feasibility and efficiency of the proposed method for predicting crack propagation in structures with uncertain-but-bounded parameters.