Applicability of Fracture Mechanics in Strength Evaluation of Functionally Graded Materials

Abstract

Elastic and elastic-plastic analyses of a crack in a particulate-dispersed functionally graded material (FGM) have been carried out using a newly developed finite element method based on Tohgo-Chou-Weng's(1994, 1996) constitutive relation for particulate-reinforced composites. By setting the mechanical properties of particles and a matrix and their content graded in the thickness direction, FGMs and non-FGM are designed. From comparison of the numerical results for the FGMs and non-FGM, the influence of the gradient of the mechanical properties on a stress intensity factor and the crack tip field is discussed. The following conclusions are derived: (1) The stress intensity factor of a crack under constant boundary conditions is considerably affected by the gradient of the mechanical properties. (2) The elastic and plastic stress singular fields around a crack tip in a FGM are basically described by the fracture mechanics parameters(K 1 and J 1 ) as well as in a non-FGM, using the mechanical properties of the material at the crack tip. (3) The size of the singular field decreases with an increase in the gradient of the mechanical properties. This means that the applicability of fracture mechanics, such as the small-scale-yielding condition and the validity of the J-integral, is affected by the gradient.