On the virtual crack extension method for calculating the derivatives of energy release rates for a 3D planar crack of arbitrary shape under mode-I loading

Abstract

This paper generalizes the analytical virtual crack extension method presented by Lin and Abel [Int. J. Fract. 38 (1988) 217] by providing the energy release rates and their derivatives at all points along a three-dimensional (3D), planar crack front of arbitrary shape. It is shown that the local variation of curvature along the crack front and interaction between crack front perturbations at adjacent crack points must be considered to properly calculate the derivatives of the energy release rates. The main advantage of the method is that the energy release rates and their derivatives at all points along the crack front in a multiply cracked, 3D body can be accurately calculated by the present virtual crack extension method in a single analysis. Comparisons of the energy release rates and their derivatives with exact solutions show that the present method can achieve sufficient accuracy for calculation of the energy release rates and their derivatives. All the advantages and accuracy of the two-dimensional virtual crack extension method presented by Hwang, [Engng. Fract. Mech. 59 (4) (1998) 521] are maintained for the 3D case. The present method has immediate application to the following and related problems: the shape prediction and stability analysis of an evolving 3D crack front in brittle fracture, configurational stability in fatigue crack propagation prediction, investigation of bifurcation in brittle fracture.