13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- The Model and Application of Fatigue Life Based on Fracture Mechanics and Fuzzy Theory Xing-liang MA1,* , Hui-li WANG2 , Si-feng QIN3 1. Bridge Science Research Institute Dalian University of Technology, Dalian, Liaoning province, 116023,China 2. Bridge Science Research Institute Dalian University of Technology, Dalian, Liaoning province, 116023,China 3. The corresponding author: Research Center for Numerical Tests on Material Dalian University, Dalian, Liaoning province, 116022,China * Corresponding author: 512792881@qq.com Abstract: Based on fracture mechanics and fuzzy theory, a model of fatigue life is developed to predict the fatigue life of structure. The dangerous point and stress amplitude can be gotten by finite element analysis method. According to fracture mechanics theory, considering fuzziness of fatigue life factors, the Paris' formula is combined with fuzzy theory and the model of fatigue life based on fuzzy theory is developed. The fuzziness of fatigue life factors is considered in the model so the results are more close to real situation. The model offers reference for fatigue life analysis. Keywords : fracture mechanics, fuzzy, fatigue 1. Introduction In vessels, pipelines, bridges, ships, offshore structures and many other engineering structures, there were a lot of disastrous accidents because of fatigue cracks. A report from American National Standards Institute indicates that cracks cause America a loss of 119 billion dollars every year. It is about 4 percents of American cross national products in 1982. According to a survey result of Committee of the Fatigue and Fracture, a sub-committee of ASCE, about 80-90% destruction of steel structures relates to fatigue cracks. From 1978 to 1981, America did a research against 20 states and Ontario Province in Canada. They collected the data of 142 bridges which had cracks. Among them, they found that the cracks on 115 bridges resulted from fatigue fracture[1]. How to analyze and estimate the fatigue life of member in construction correctly has become an important issue. This paper proposes a analysis modal which is based on fuzzy theory and combined with fracture mechanics. 2. Fuzzy phenomenon in analysis of fatigue life The fuzziness of objects means the boundary is not clear, we cannot distinguish the difference between the right and wrong in its implication correctly, and we cannot divide its boundaries in our discussion range. The fuzziness is a natural characteristic of objects, it is a transient process between difference of objects.[2,3] Broadly speaking, strength includes fatigue life, fracture toughness, residual strength and so on. In order to judge a structure is invalid or reliable, we must know the strength of material and structure. But because we get the data of strength from experiment, so it’s inevitable to bring fuzziness.[4,5] It’s feasible to apply the method of S-N curve and fracture mechanics. This paper is based on fuzzy theory, applys the method of fracture mrchanics to predict the fatigue life of structure. Paris formula[9] is a always used to calculate the fatigue life in fracture mechanics, namely ( )m da C K dN = Δ , (1) Among it, a-crack size; N-number of load cycles; C, m-material constants; KΔ - stress strength
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