Energy-release rate and crack kinking in anisotropic brittle solids

Abstract

The energy-release rate is calculated for the inception of crack kinking in a general anisotropic solid containing a pre-existing crack. First, the stress intensity factors at the tip of an infinitesimally small kink ( K I ( k) and K II ( k) ) and the kink opening displacements (KODs) are numerically calculated by modeling the kink as continuously distributed edge dislocations. The energy-release rate, G kink, is obtained directly by calculating the work required to fully close the kink gap (KOD) and restore the required normal and shear stresses ( σ ωω and σ r ω ) that existed before kinking. This energy-release rate, G kink, is compared with that (denoted by G Irwin) obtained by applying the Irwin formula in terms of the stress intensity factors K I ( k) and K II (k) at the tip of the vanishingly small kink, for various kink angles, material properties, material symmetry orientations, and loadings. It is observed that the two methods yield exactly the same value for the rate of energy released, even though G kink corresponds to kink nucleation, whereas G Irwin to kink extension. Therefore, Irwin's formula for the energy-release rate is valid for any kink angle, material anisotropy, and loading condition (any combination of modes I and II), provided that the stress intensity factors in the formula are taken equal to those calculated at the tip of a vanishingly small kink, but not those associated with the stress components σ ωω and σ r ω prior to kinking. For different loading and material symmetry conditions, the energy-release-rate fracture criterion is compared with different stress-based fracture criteria of the fracture-path prediction.