Stress intensify factors for an external circular crack at the interface of a bi-material in shear–compression

Abstract

This paper studies an external circular crack at the interface of a bi-material subjected to shear–compressive loading at the crack surfaces. An axisymmetric problem is solved for an external circular crack where radial shear loadings are applied at the smooth crack surfaces. Across the crack surfaces in contact, there are tangential displacement shift and no normal displacement gap. A mixed boundary value problem is reduced to dual integral equations, and a closed-form solution of the interface stresses is given via the Hankel transform technique. Our results indicate that there is no oscillatory singularity near the interface crack front in shear–compression. Both the radial shear stress and the normal stress exhibit a usual square-root singularity ahead of and behind the crack front, respectively. Explicit expressions for the mode-I and II stress intensity factors (SIFs) are obtained for compressive forces applied at the central axis of the bonding part towards to the bonding center. The mode-I SIFs are proportional to mode-II SIFs, and depend on a Dundurs’ parameter. Numerical results of a bi-material Al2O3/PMMA with an external circular crack subjected to compressive forces are presented to show the influence of the bi-material properties on the stress distribution and the SIFs.