Reliability Estimation for Structure under Fatigue Load Using Probability Theory and Fatigue Crack Growth Model

Methodologies to calculate the failure probability and to estimate the reliability of the damaged structures under fatigue are developed in the present work. The applicability of the developed methodologies is evaluated with the help of fatigue crack growth models suggested by Paris and Walker. Probability theories such as the FORM (first order reliability method) and the SORM (second order reliability method) are utilized for the seven cases. It is found that the failure probability increases with the increase of the initial fatigue crack size and the decrease of the design fatigue life. It is also found that the failure probability calculated by the FORM and the SORM turns out similar for the Paris and the Walker models. And the distribution types of the slope of the Paris equation and the coefficient of the Paris equation dominantly affect the failure probability. Introduction The repeated loads may lead to failure of material even when the load level is lower than the ultimate limit states. Many mechanical structures such as train axles and wheels, load bearing parts of automobiles, offshore structures, and bridges are designed to endure for a long term up to giga-cycle loadings in the actual service. Furthermore, some mechanical structures in the various areas are needed to be investigated if the operation life can be extended beyond the design life because of the economic consideration. In such circumstances, mechanical components of these structures are exposed to tremendous number of stress/strain cycles in the long term service. Thus, the fatigue property of the structural materials under the long term cyclic loadings is an important subject to provide the safety design data for such mechanical structures [1,2]. In the fatigue design, the use of S-N curves is well established. These curves predict fatigue failure under constant amplitude loading, but cannot incorporate information related to crack detection and/or measurement. As a result, the structures must be repaired, if the crack is discovered. However, the use of fracture mechanics techniques can be successfully applied to this problem. The fracture mechanics needs the information about the defects, or cracks to be used in the analysis. Since the size and location of defects are quite random, the deterministic analysis may provide incomplete results about the structure safety. Also the randomness of loads, geometry and material properties influence significantly the reliability of a structure. Therefore, the fracture mechanics with a probabilistic method provide a useful tool to solve these problems [3,4]. In this paper, fatigue models suggested by Paris and Walker are used to formulate the limit state function for assessing the failure of fatigue loaded structures. And the failure probability is estimated by using the FORM (first order reliability method) and the SORM (second order reliability method). The reliability is assessed by using this failure probability, and the application of these methods to the reliability estimation is given for a case study.