An array of no-slip tensile cracks at a bimaterial interface

Abstract

The tensile strength of interdigitated bimaterial interfaces is strongly affected by the formation of multiple interfacial microcracks. Such is the case with cemented total-joint replacements where loosening and breakdown of the cancellous bone-PMMA cement interface occur by “damage” and formation of interfacial cracks. The problem of an array of interfacial cracks is addressed in this paper within the context of fracture mechanics. An analytical solution is presented for the plane-strain problem of a periodic array of no-slip interfacial cracks under uniaxial tension. A closed-form solution is readily available when the cracks are opened by constant pressure; the corresponding Mode I stress intensity factor is found to be identical to that obtained for an array of collinear Griffith cracks in a homogeneous medium. A more realistic situation involves cohesive stresses over the crack faces. Cohesive zone effects have been incorporated in the present model that allows for quantifying the reduction of the strength singularity at the crack tip, due to the pull-out resistance of cement pedicles to being forced out of mechanical interlocks at the interdigitated, bimaterial interface.