Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media |
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| Affiliation: | 1. Department of Mechanical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka 1000, Bangladesh;2. Department of Aeronautics and Space Engineering, Tohoku University, Aoba-yama 01, Aoba-ku, Sendai 980-8579, Japan;1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China;2. Department of Engineering Mechanics, Hunan University, Changsha 410082, PR China;1. Institute of Construction and Architecture, Slovak Academy of Sciences, 845 03 Bratislava, Slovakia;2. Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, Canada;1. School of Textile Garment and Design, Changshu Institute of Technology, Changshu, 215500 Jiangsu, PR China;2. College of Liberal Arts and Sciences, National University of Defence Technology, Changsha, 410073 Hunan, PR China;3. College of Basic Education, National University of Defence Technology, Changsha, 410073 Hunan, PR China |
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| Abstract: | This study is concerned with the inverse problem of calculating material distributions intending to realize prescribed apparent fracture toughness in functionally graded material (FGM) coatings around a circular hole in infinite elastic media. The incompatible eigenstrain induced in the FGM coatings after cooling from the sintering temperature, due to mismatch in the coefficients of thermal expansion, is taken into consideration. An approximation method of determining stress intensity factors is introduced for a crack in the FGM coatings in which the FGM coatings are homogenized simulating the nonhomogeneous material properties by a distribution of equivalent eigenstrain. A radial edge crack emanating from the circular hole in the homogenized coatings is considered for the case of a uniform pressure applied to the surfaces of the hole and the crack. The stress intensity factors determined for the crack in the homogenized coatings represent the approximate values of the stress intensity factors for the same crack in the FGM coatings, and are used in the inverse problem of calculating material distributions in the FGM coatings intending to realize prescribed apparent fracture toughness in the coatings. Numerical results are obtained for a TiC/Al2O3 FGM coating, which reveal that the apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media can be controlled within possible limits by choosing an appropriate material distribution profile in the coatings. |
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