Original paper(Vol.48 No.7 pp.771)

Abstract:In this study, we deal with an axisymmetrical mixed boundary value problem for a nonhomogeneous medium with a crack. It is assumed that the nonhomogeneous material properities of shear modulus of elasticity G varies with the axial coordinate z according to the power product form, i.e., G(ƒÄ)=G₀ƒÄ^m. As an analytical model, a nonhomogeneous half-space with a penny-shaped crack subject to uniformly distributed loading such as internal pressure on the crack surface is considered. Making use of a fundamental equation system for such a nonhomogeneous medium, which is already derived in our previous paper, this axisymmetrical elastic problem with a singular stress field is developed theoretically. Then the simultaneous dual integral equation of Fredholm's second kind derived from the discontinuous boundary conditions on the crack surface and its extended surface is solved numerically. Numerical calculations for the elastic field and singular stress field are carried out, and the numerical results for displacements, stresses and the stress intensity factor at a crack tip are shown graphically. Finally, the influences of the nonhomogeneous material property and the distance from the boundary surface to the crack surface affected on the elastic behavior such as displacements, stresses and the stress intensity factor are examined precisely.

Key Words:Elasticity, Stress intensity factor, Nonhomogeneous half-space, Axisymmetric problem, Simultaneous dual integral equation