FINITE STRAIN SINGULAR FIELD NEAR THE TIP OF A CRACK TERMINATING AT AMATERIAL INTERFACE

The paper contains an asymptotic finite-strain analysis of the deforma tions and stresses near the tip of a traction-free crack terminating a t an interface between two dissimilar compressible elastic half-planes under conditions of plane strain. Each of the two half-planes is assu med to be hyperelastic with a harmonic-type strain energy density intr oduced by John. The near-tip singular field is derived for an arbitrar y meeting angle at which the crack meets the interface and the deforma tions and stresses around the crack tip are found to be free of oscill atory singularities arising in the linearized theory. Regardless of th e loading conditions, the explicit conditions for the strict positivit y of the Jacobian determinant in the vicinity of the crack tip are giv en in terms of the known material parameters and the meeting angle. In particular, these conditions are unconditionally satisfied for an int erface crack tip. As two typical examples, the interface crack and the crack perpendicular to the interface are discussed.