Asymptotic Analysis of the Crack Tip Field in the Vicinity of a Bimaterial Interface

Fracture of composite laminates and multi-layer structures have been widely studied. The analysis of the crack tip field is a fundamental topic that has received significant attention. There are solutions for various configurations of cracks perpendicular as well as parallel to the bimaterial interface. The present work is dedicated to stress analysis for a crack perpendicular to a bimaterial interface. It is well recognized that for a crack terminating at a bimaterial interface, the order of singularity, λ, departs from 1/2. λ is smaller or greater than 1/2 depending on material properties on both sides of the interface. The existing analysis suggests an intermediate asymptotic as the crack approaches the bimaterial interface. The asymptotic solution tends either to zero or to infinite depending on the material properties. A dimensional analysis of such behavior has been recently performed. In this paper the asymptotic solution of the crack tip stress field in the vicinity of a bimaterial interface is first derived by means of scale invariance of elastic solution. Then energy method is employed through finite element analysis (FEA). The order of singularity found by FEA correlates well with that resulting from analytical consideration. The FEA is also employed to determine the SIF discontinuity across the interface, various applications of the asymptotic solution in crack propagation in a vicinity of bimaterial interface are discussed.