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

This study treats the inverse problem of evaluating optimum material distri butions intending to realize prescribed apparent fracture toughness in thic k-walled functionally graded material (FGM) circular pipes. The incompatibl e eigenstrain induced in the pipes after cooling from the sintering tempera ture due to the nonhomogeneous coefficient of thermal expansion is taken in to consideration. An approximation method of finding stress intensity facto rs for a crack in the FGM pipes is introduced in which the nonhomogeneous m aterial properties are simulated by a distribution of equivalent eigenstrai n. 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 deter mined for the crack in the homogenized pipes represent the approximate valu es of the stress intensity factors for the same crack in the FGM pipes, and are used in the inverse problem of evaluating optimum material distributio ns intending to realize prescribed apparent fracture toughness in the FGM p ipes. Numerical results obtained for a thick-walled TiC/Al2O3 FGM pipe reve al that the apparent fracture toughness significantly depends on the materi al distributions, and can be controlled within possible limits by choosing an optimum material distribution profile. (C) 2001 Elsevier Science Ltd. Al l rights reserved.