This paper proposes an interactive finite element-based method to perform structural reliability of irregular and randomly occurring fatigue cracks as the analysis of such crack configurations by closed-form methods is unrealistic. The performance function is characterized by a material resistance criterion and failure probability is given by the condition that the applied stress intensity factor exceeds the fracture toughness of the material. A benchmark problem is applied to validate the proposed technique. The effect of a single plate and stiffener web crack on the failure probability of ships is studied.
Analysis of fatigue life of cracked structures have in general been based on closed-form analytical expressions and for standard cracked specimens, numerous published empirical solutions, especially in the linear elastic ranges, exist in crack analysis handbooks (Tada et al., 2000; Murakami, 1987). As a contrast with such standard test cases however, fatigue cracks in real applications are randomly occurring and irregular in shape, orientation and location. As a result, not all crack configurations may be evaluated by analytical methods as corresponding closed-form equations only exist for a limited number of simple cases. Given the limitation of closed-form methods, numerical techniques, which have been implemented in the ABAQUSTM commercial finite element code, therefore provide an alternative to crack growth modeling and analyses for such complex crack configurations. An interactive finite element-based probabilistic method is thus proposed here as an alternative to perform structural reliability analysis. The increased capacity to statistically characterize the inherent randomness in deterministic input strength parameters is advantageous in providing a more realistic assessment of structural response from a reliability point of view. The potential interaction between commercial deterministic FE codes and reliability analyses packages have thus been recognized as a viable solution technique for problems requiring such rational treatment of uncertainties (Pellissetti & Schuller, 2006).