Brittle fracture characteristics of thick-walled functionally graded material cylinders

Abstract

This study is concerned with the brittle fracture characteristics of a thick-walled functionally graded material (FGM) cylinder. Two diametrically-opposed radial edge cracks emanating from the inner surface of the cylinder are considered. The crack surfaces and the inner surface of the cylinder are subjected to an internal pressure. The incompatible eigenstrain induced in the cylinder material after cooling from the sintering temperature due to nonuniform coefficient of thermal expansion (CTE) is also taken into account. The nonhomogeneity of the material properties is simulated by an equivalent eigenstrain, whereby the problem is reduced to the solution of a cracked homogenized cylinder with incompatible and equivalent eigenstrains under an internal pressure. Representing the cracks by continuous distribution of edge dislocations, a method is then formulated to calculate the stress intensity factor (SIF) for the cracks emanating from the inner surface of the homogenized cylinder. The method of calculating SIF is applied to the inverse problem of material distribution intending to realize prescribed apparent fracture toughness in the thick-walled FGM cylinder. It is also applied to calculate the SIF for a single radial edge crack at the inner surface of the FGM cylinder. For numerical results, a thick-walled TiC/AbO] FGM cylinder is considered. It is noted that the material distribution in the FGM cylinder has significant effects on the SIF and apparent fracture toughness which can be controlled by choosing the material distributions appropriately.