In this paper, a 3D J-integral based on the domain integral approach is presented for large deformation elastic–plastic fracture mechanics problems associated with residual stresses and spatially varying mechanical properties of a material. The proposed 3D J-integral has physical significance as the energy dissipation into the process zone. The derivations of the proposed J-integral are presented in detail. Through numerical examples, it is shown that the proposed J-integral is unconditionally path independent. The present formulation is a rigorous extension of the 2D-Tε∗ integral of Okada and Atluri to 3D.
- Domain integral method
- Elastic-plastic fracture
- Energy release rate
- Functionally graded material (FGM)