Research On Fatigue And Fracture Reliability Of Bodies Initial Cracks

Fatigue failure is the main failure mode for the machinery parts and engineering structures under alternate loading over a long period of time. Fatigue is an important subject whether in theory or in engineering. It is the main work to predict fatigue life in fatigue damage Analysis. Usually the fracture theory are used in the fatigue crack propagation life estimation. After the Industrial Revolution in the early 19th century, the phenomenon of fatigue was taken into account and studied. A lot of research has been developed during the whole world, however, there are still many problems to be solved for researchers. Usually the fatigue life can be estimated by the determination method. However, the fatigue of structure is such a complicated phenomenon affected by many uncertainties that it is necessary to analyze the structural fatigue from the point of probability and statistics. Probabilistic Fracture Mechanics is a branch of fracture mechanics, so the various parameters affecting the fatigue propagationg are considered as randomized. It is an effective and new method to evaluate the structural fatigue reliability by Probabilistic Fracture Mechanics Approach (PFMA).In this paper, through the statistical analysis of the random factors in the stage of sub-critical propagation of cracks, the statistical correlation equations between the two material coefficients are obtained and can be generalized. Furthermore, it can be concluded that cracks propagation rate is influenced greatly by material coefficients in the condition considered in this study. The paper is based on the following foundational theories: statistics, probability analysis, fatigue and fracture mechanics. The work includes several parts as the following:Firstly, fatigue and fracture reliability theory is introduced, along with the statistics theory and its application in fatigue reliability analysis. The theory of probabilistic fracture mechanics is presented. Then the general rule and influential factors of cracks propagation occurred in fatigue failure are discussed.Secondly, the influences of the random parameters on fatigue propagation are discussed in the fatigue propagation Paris formula. In the existing literature, thematerial coefficients are simply considered as constants. Yet the material coefficients C and n in Paris formula are randomized in this study. Using the least square method, the statistical correlation between C and n is obtained through the numerical value collocation.Then, using Pearson x2 testing method, one of the coefficients n following the rule of distribution in statistics is tested. Furthermore, according to the the statistical correlation between C and n , the influence of both C and n on propagation life of fatigue cracks is discussed.Finally, applying Probabilistic Fracture Mechanics Approach (PFMA), the reliability analysis is carried out for helicopter metal material (aluminum alloy) structure having initial cracks. By an example, each parameters are randomized in the Paris formula, and the propagation life of fatigue of the structure is prognosticated on the presented reliability.