Axisymmetrical Elastic Behavior and Stress Intensity Factor for a Nonhomogeneous Medium with a Penny-Shaped Crack

Abstract

Axisymmetrical elastic problems for a nonhomogeneous medium with a penny-shaped crack are treated theoretically. It is assumed that the nonhomogeneous material properties of shear modulus of elasticity G vary with the axial coordinate z according to the power product form, i.e., G(z)=G₀Z^m. As an analytical model, a nonhomogeneous infinite body or thick plate with a penny-shaped crack subject to uniformly distributed loading such as internal pressure on the crack surface is considered. The above-mentioned axisymmetric problems with a singular stress field are developed theoretically utilizing a fundamental equation system for such a nonhomogeneous medium derived in our previous paper. Thereafter, numerical calculations are carried out for several cases taking into account the variations of the nonhomogeneous parameter m of shear modulus of elasticity G and the thickness of the slab, and the numerical results for displacements, stresses and the stress intensity factor at a crack tip are shown graphically. The influences of the nonhomogeneous material property and the thickness on the elastic behavior such as displacements, stresses and the stress intensity factor are examined precisely.