Axisymmetric problems of a penny-shaped crack at the interface of a bi-material under shear and compression

Abstract

This paper studies an axisymmetric problem of a penny-shaped interface crack of a bi-material subjected to compression and radial shear at the crack surfaces in cylindrical coordinate system. The Hankel transform technique is applied to convert the problem to dual integral equations. Closed-form solutions for mode-I and II stress intensity factors are obtained for arbitrary radial shear loading at the crack surfaces. Obtained results indicate that no oscillation singularity occurs. Explicit expressions for the stresses and displacements in the whole bi-material elastic space are derived for constant and linear radial shear stress acting on the crack surfaces, respectively. Under uniform radial shear stress, normal and shear stresses have a usual square-root singularity behind and ahead of the crack front, respectively, and the induced normal stress exhibits a logarithmic singularity at the crack center. Under linearly-distributed radial shear stress, the logarithmic singularity at the crack center disappears, and the square-root singularity is still present for the normal and shear stresses near the crack front. The induced mode-I stress intensity factors depend on Dundurs’ parameter and on applied shear loading. Numerical results for a penny-shaped interface crack in Al2O3/PMMA bi-material are presented to show the influence of the bi-material properties on the stress distribution.