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.
