The Surface Crack Problem for a Plate With Functionally Graded Properties

TLDR

The Young’s modulus of the medium varies continuously in the thickness direction. In this study the plane elasticity problem for a nonhomogeneous layer containing a crack perpendicular to the boundaries is considered. The problem is solved under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the crack region. Mode I stress intensity factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and location of the crack and the material nonhomogeneity, and sample results for crack‑opening displacement and stress distribution are also given.

Abstract

In this study the plane elasticity problem for a nonhomogeneous layer containing a crack perpendicular to the boundaries is considered. It is assumed that the Young’s modulus of the medium varies continuously in the thickness direction. The problem is solved under three different loading conditions, namely fixed grip, membrane loading, and bending applied to the layer away from the crack region. Mode I stress intensity factors are presented for embedded as well as edge cracks for various values of dimensionless parameters representing the size and the location of the crack and the material nonhomogeneity. Some sample results are also given for the crack-opening displacement and the stress distribution.