Three-dimensional J-integral evaluation for cracks with arbitrary curvatures and kinks based on domain integral method for quadratic tetrahedral finite element

•J-integral for arbitrary curved/kinked 3D cracks can be accurately evaluated.•Proposed method does not require any hexahedral FEs along the crack front.•Proposed method requires no surface integral even when the crack is not planar.•Proposed method can compute the three-dimensional J-integral very accurately.

In this paper, a methodology to compute the three-dimensional J-integral by the domain integral method using the quadratic tetrahedral finite element for the absence of crack face tractions is presented. We carefully examined the properties of the domain integral method and propose a methodology that can deal with cracks with arbitrary curvatures and kinks in three-dimensional space without any crack surface integral terms. Some example problems are presented and the accuracy of present J-integral method is critically discussed.