Effects of triaxiality on the growth of crack-like cavities in soft incompressible elastic solids

Abstract

We study the finite deformation of an isolated circular or penny-shaped crack in an infinite block of soft incompressible hyper-elastic solid. The crack is subjected to remote tensile true stresses that are parallel (S) and normal (T) to the undeformed crack faces. Two material models are considered, an ideal rubber (neo-Hookean solid) and a hyperelastic material that hardens exponentially. The energy release rates for different triaxiality ratios S/T from uniaxial tension (S/T = 0) to hydrostatic tension (S/T = 1) are determined using a finite element method (FEM). For small deformations, our results agree with linear elastic theory where the energy release rate is independent of S. This is not the case at finite strains; our results show that the energy release rate increases rapidly with triaxiality. For the special case of pure hydrostatic tension, the energy release rate approaches infinity for the neo-Hookean solid at a finite tension, consistent with a previous result by Lin and Hui (Y.Y. Lin and C.Y. Hui, Int. J. Fract., 2004, 126, 205–221). Our result shows that strain hardening significantly reduces the energy release rate for the same remote loading. In particular, for the case of hydrostatic tension, the energy release rate remains bounded for the exponentially hardening solid.