Optimum material distributions for prescribed apparent fracture toughness in thick-walled FGM circular pipes

Abstract

This study treats the inverse problem of evaluating optimum material distributions intending to realize prescribed apparent fracture toughness in thick-walled functionally graded material (FGM) circular pipes. The incompatible eigenstrain induced in the pipes after cooling from the sintering temperature due to the nonhomogeneous coefficient of thermal expansion is taken into consideration. An approximation method of finding stress intensity factors for a crack in the FGM pipes is introduced in which the nonhomogeneous material properties are simulated by a distribution of equivalent eigenstrain. A radial edge crack emanating from the inner surface of the homogenized pipes is considered for the case of a uniform internal pressure applied to the surfaces of the pipes and the crack. The stress intensity factors determined for the crack in the homogenized pipes represent the approximate values of the stress intensity factors for the same crack in the FGM pipes, and are used in the inverse problem of evaluating optimum material distributions intending to realize prescribed apparent fracture toughness in the FGM pipes. Numerical results obtained for a thick-walled TiC/Al 2O 3 FGM pipe reveal that the apparent fracture toughness significantly depends on the material distributions, and can be controlled within possible limits by choosing an optimum material distribution profile.