Fatigue crack propagation analysis in structures with random parameters based on polynomial chaos expansion method

Abstract

Fatigue fracture is the most common failure for aircraft structures, therefore fatigue life prediction plays an important role in structure design. However, uncertainties widely existing in engineering structures make it difficult to analyze crack propagation and predict fatigue life. This paper presents a novel efficient and accurate approach to crack propagation analysis in structures with random uncertainties based on polynomial chaos expansion (PCE) method. For short fatigue crack in aircraft skin or armor plate of tank, the structure can be regarded as an infinite plate. In this situation, the stress intensity factor range has a simple analytical expression and a basic crack propagation equation is derived based on it. Considering uncertain parameters, crack length is regarded as a random variable and expanded into orthogonal polynomial series after introducing Hermite polynomials. Because crack length is a time-dependent variable, the coefficients in polynomial series are regarded to be time-dependent. In order to determine values of these coefficients, orthogonal polynomial series of crack length is substituted into Paris law and a series equations are obtained considering the orthogonality of Hermite polynomials. Time history of the coefficients is acquired by solving these equations using numerical algorithm. Furthermore, expectation and standard deviation of crack length can be easily obtained. The proposed method is verified based on three numerical examples and Monte-Carlo Simulation (MCS) is applied for the sake of validation. The results demonstrated the accuracy and efficiency of the proposed method for crack propagation analysis of structures with random parameters.