On the path independence and invariant of the J-integral for a slant crack and rigid-line inclusion using degenerate kernels and the dual BEM

The J-integral and stress intensity factor (SIF) are two major parameters in linear elastic fracture mechanics (LEFM) for the fracture criterion. In this paper, we focus on the J-integral of the slant crack and the slant rigid line inclusion under the remote anti-plane shear. By employing the degenerate kernel, the path independence of J-integral is analytically demonstrated by using the elliptic coordinates. The positive and negative J-integrals are also analytically derived and numerically implemented by using the dual BEM for the crack and the rigid-line inclusion, respectively. It is interesting to find that the J-integral is not an invariant by using different observer systems but is one component of the vector of the first order tensor. Transformation law of the J-integral with respect to different observers is analytically proved and numerically demonstrated. Finally, the tensor property of order one is examined.

Automated summary

This paper focuses on the J-integral of slant crack and slant rigid line inclusion under remote anti-plane shear, demonstrating path independence and transformation properties with respect to different observer systems. The study analytically and numerically derives positive and negative J-integrals, showing that J-integral is a component of a first order tensor rather than an invariant under different observer systems. The tensor property of order one is examined in this research.