Plane Elastic Behavior and Stress Intensity Factor for an Inhomogeneous Slab with a Griffith Crack

摘要

A plane elastic problem for inhomogeneous and isotropic solids such as functionally graded materials is treated theoretically. An inhomogeneous slab with a Griffith crack subjected to uniformly distributed loading such as internal pressures on the crack surfaces is considered. It is considered that the Griffith crack is located on the middle plane of the slab. It is assumed that inhomogeneous material property such as the shear modulus of elasticity varies in a form of a power of a transverse coordinate, and the material inhomogeneity in the slab is symmetric with respect to the middle plane. The mixed boundary value problem is developed theoretically using a fundamental equation system for such inhomogeneous and isotropic solids derived in our previous paper. Thereafter, considering a variation of inhomogeneity in the shear modulus of elasticity, displacements and stresses in the slab, and a stress intensity factor for the mode I deformation at the tip of a crack are examined numerically. An effect of inhomogeneity in the shear modulus of elasticity on plane elastic behavior and stress intensity factor for the mode I deformation is discussed.