Effect of higher order asymptotic terms on the competition between crack penetration and debond at a bimaterial interface between aligned orthotropic materials

Abstract

The effects of the split singularities, i.e. a stronger and a weaker singularity of a crack impinging at bimaterial interface on the competition between crack penetration and debond was recently investigated in [1] for the case of infinite isotropic bimaterial plane. Anisotropy usually lifts a degeneracy of the singularity exponents and strongly influences the direction of crack penetration across the interface. The concept of the Finite fracture mechanics introduced in [2,3–7], conservative line integral derived from Betti’s reciprocal principle, and the matched asymptotic expansion method [3–7] are used to evaluate the energy release rate criteria describing the competition between the crack debond and penetration at a bimaterial interface between aligned orthotropic materials in edge cracked tension specimen. The effect of higher order terms on the crack penetration/debond at a bimaterial interface strongly depends on the elastic mismatch of dissimilar materials and on the crack-specimen configuration. For this reasons, a crack perpendicularly impinging the bimaterial interface and a crack arbitrary inclined to the interface are considered for a wide range of elastically mismatched materials. In the former case, the effect of the T-stress is investigated, in the latter case the combined effect of a weaker singularity and stronger singularity is examined for a range of crack/interface configurations. For the crack arbitrary inclined to the interface, FE solution of near-crack stress–displacement field obtained using a very fine mesh is compared with analytical singular field considering two leading terms of asymptotic expansion. As a side result it is found that the domain of singular field dominance for an arbitrary inclined crack increases with decreasing angle between the crack and the interface.