Corrosion fatigue damage can lead to degradation of engineering structures and components. As a major stage of the total corrosion fatigue life, the crack initiation of pitting corrosion and fatigue is studied. A continuum damage mechanics model for predicting the crack initiation life of pitting corrosion fatigue is presented based on a pure fatigue damage model and a fracture-mechanics-based pit-to-crack transition criterion. The synergistic effect of pitting corrosion and fatigue are quantified as a time-varying amplification of the fatigue stress field. The proposed model is validated by corrosion fatigue test data of two different metallic materials. The predicted curves of corrosion fatigue crack initiation life are in good agreement with the test data. The model demonstrates a good prediction of corrosion fatigue crack initiation life, i.e., corrosion fatigue life is always lower than fatigue life, and the lower the stress, the more significant the life reduction.

To alleviate the difficulty of combination explosion, in this work, a generalised equivalent extreme-value event is presented to the problem of multi-component simultaneous failure in system reliability analysis, where m components in total l components are failed simultaneously. Firstly, the generalised equivalent extreme-value event is formulated with rigorous mathematical derivation for single boundary problem. Secondly, based on a mathematical transformation, the generalised equivalent extreme-value event is extended to double boundaries problem. Thirdly, by introducing the point estimation method (PEM) and the principle of maximum entropy to calculate the first four-order statistical moments and the failure probability of the equivalent performance function, an easy-to-implement method is proposed, which is capable of solving the multi-component simultaneous failure problem of static and dynamic systems. Finally, the feasibility of the proposed method is verified through a mathematical example and two engineering examples. The comparison to the Monte Carlo simulation shows that the proposed method is of high precision and high efficiency.

The time-variant system reliability analysis is a challenging and significant topic, which also faces the common obstacles of traditional system reliability methods such as combination explosion and unclear correlation information. In this paper, the probability density evolution method (PDEM) for two types of time-variant system reliability analysis is proposed. First, the system reliability is classified into two types, and the corresponding equivalent performance functions are given, which are further extended to time-variant structural systems. Second, based on the single equivalent performance function, the generalized density evolution equation (GDEE) for time-variant structural system is derived in two different ways. Third, the GDEE is solved by the Dirac sequence method and the time-variant system reliability is evaluated. Finally, several numerical examples are investigated to illustrate the accuracy and effectiveness of proposed method.

Purpose: Conversion of the correlated random variables into independent variables, especially into independent standard normal variables, is the common technology for estimating the statistical moments of response and evaluating reliability of random system, in which calculating the equivalent correlation coefficient is an important component. The purpose of this paper is to investigate an accurate, efficient and easy to implement estimation method for the equivalent correlation coefficient of various incomplete probability systems.Design/methodology/approach: First, an approach based on the Mehler’s formula for evaluating the equivalent correlation coefficient is introduced, then, by combining with polynomial normal transformations, this approach is improved to be valid for various incomplete probability systems, which is named as the direct method. Next, with the convenient linear reference variables for eight frequently used random variables and the approximation of the Rosenblatt transformation introduced, a further improved implementation without iteration process is developed, which is named as the simplified method. Finally, several examples are investigated to verify the characteristics of the proposed methods.Findings: The results of the examples in this paper show that both the proposed two methods are of high accuracy, by comparison, the proposed simplified method is more effective and convenient.Originality/value: Based on the Mehler’s formula, two practical implementations for evaluating the equivalent correlation coefficient are proposed, which are accurate, efficient, easy to implement and valid for various incomplete probability systems.