Curvilinear fatigue crack reliability analysis by stochastic boundary element method

Abstract

AbstractIn this paper, the stochastic boundary element method, which combines the mixed boundary integral equations method explored in Reference 1 with the first‐order reliability method, is developed to study probabilistic fatigue crack growth. Due to the high degree of complexity and non‐linearity of the response, direct differentiation coupied with the response‐surface method is employed to determine the response gradient. Three random processes, the mode I and mode II. stress intensity factors and the crack direction angle, are included in the expression of the response gradient. The sensitivity of these random processes is determined using a first‐order response model. An iteration scheme based on the HL‐RF method2 is applied to locate the most probable failure point on the limit‐state surface. The accuracy and efficiency of the stochastic boundary element method are evaluated by comparing the cumulative distribution function of the fatigue life obtained with Monte Carlo simulation. The reliability index and the corresponding probability of failure are calculated for a fatigue crack growth problem with randomness in the crack geometry, defect geometry, fatigue parameters and external loads. The response sensitivity of each primary random variable at the design point is determined to show its role in the fatigue failure. The variation of each primary random variable at the design point with the change of probability of failure is also presented in numerical examples.