Fracture analysis of a functionally graded strip with arbitrary distributed material properties |
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Authors: | Zheng Zhong Zhanqi Cheng |
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Affiliation: | 1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, PR China;2. School of Civil Engineering, Zhengzhou University, Zhengzhou 450001, PR China;1. Yangtse Chair Professor & Dept. Head Department of Engineering Mechanics Tsinghua University, Beijing 100084, CHINA;2. Allen E. & Marilyn M. Puckett Professor Division of Engineering & Applied Sciences Harvard University, Cambridge, MA 02138 |
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Abstract: | In this paper, the plane elasticity problem for a crack in a functionally graded strip with material properties varying arbitrarily is studied. The governing equation in terms of Airy stress function is formulated and exact solutions are obtained for several special variations of material properties in Fourier transformation domain. A multi-layered model is employed to model arbitrary variations of material properties based on two linear-distributed material softness parameters. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Comparisons with other two existing multi-layered models have been made. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the model. Numerical results show that fracture toughness of materials can be greatly improved by graded variation of elastic modulus and the influence of the specific form of elastic modulus on the fracture behavior of FGM is limited. |
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