The Fuzzy Reliability Of Mechanical Parts Based On Fracture Mechanics, Life Prediction

Fracture mechanics is an embranchment of solid meehanies in its recent development. It established a method to describe cracked bodies' fields of stress and strain regarding crack as damage, and it also proposed the fracture criteria of the component and the rules of crack growth. Since the 1980s, researchers have used fracture mechanics to predict component's life, which has made the theory of life prediction develop quickly. However, there are many problems to be solved in the process of using fracture mechanics to predict components' life. For example, the technology of the nondestructive inspection used widely to describe defects of crack quantitatively can not provide enough exact information. There isn't a set of integrated theories to describe stochastic properties of crack growth, and people have not known the crack growth fully, etc.To describe the stochastic characters of the crack growth, researchers introduced the theory of the reliability to fracture mechanics and obtained lots of achievements. But, with the development of the research on fracture mechanics, people found that there are two uncertainties in the fracture of the component-both stochastic and fuzzy, especially in the inspection of the initial crack, which promoted the emergence and development of fuzzy probability fracture mechanics. Stochastic theory can be used to describe uncertainty, and fuzzy theory can be used to describe the imprecise property caused by the participation of the people. Currently, there is little research on this. This paper discusses the possibility and the general method of combining the theory of fuzzy reliability with fracture mechanics to predict the life of the component based on the current research achievements.(1) From the purpose of fit on whole sample, defect of the traditional method for determining distribution function of data is pointed out through numerical simulation. With the help of the fuzzy linear regression method, a novel method for determining the distribution kinds is proposed, and this method is validated to be effective taking 2024-T351 CT sample's crack growth data as example. One can see from results that crack growth size under the certain load cycles and crack growth rate under the certain stress intensity factor range can be fitted with the log-normal distribution.(2) Application of the weight function for determining the stress intensity factor based on the current literature is discussed in detail. Stress intensity factor expressions of 2D edge through crack and center through crack in the finite rectangle plate were obtained. This method are validated to be effective by comparing results with those proposed in other literatures.(3) Method for determining the fuzzy stochastic property of the initial crack size and the critical crack size is summarized and developed.(4) This paper proposes a novel linear regression with fuzzy weight method, which can eliminate the effect of the abnormal test data on the linear regression and is used to determine crack growth rate curve.(5) Application of the stochastic process in the reliability analysis of crack growth life is introduced, as well as the application possibility of the fuzzy stochastic process in this aspect.(6) Integrating various stochastic and fuzzy factors and using probability crack growth rate curve andfuzzy probability crack growth rate curve proposed in this paper, a novel method and its formula for analyzing fuzzy reliability of crack life is proposed. The application of the maximum likelihood method for determining the stochastic and fuzzy properties of crack growth.