Finite Strain Singular Field Near the Tip of a Crack Terminating at a Material Interface

Abstract

The paper contains an asymptotic finite-strain analysis of the deformations and stresses near the tip of a traction-free crack terminating at an interface between two dissimilar compressible elastic half-planes under conditions of plane strain. Each of the two half-planes is assumed to be hyperelastic with a harmonic-type strain energy density introduced by John. The near-tip singular field is derived for an arbitrary meeting angle at which the crack meets the interface and the deformations and stresses around the crack tip are found to be free of oscillatory singularities arising in the linearized theory. Regardless of the loading conditions, the explicit conditions for the strict positivity of the Jacobian determinant in the vicinity of the crack tip are given in terms of the known material parameters and the meeting angle. In particular, these conditions are unconditionally satisfied for an interface crack tip. As two typical examples, the interface crack and the crack perpendicular to the interface are discussed.