This paper theoretically investigates basic conditions required for the path independence of the J-integral and major factors affecting the path independence, including the incremental plasticity, finite strains and residual stresses. Residual stress modified J-integrals are then introduced for ensuring the path independence. With use of a notched beam, detailed elastic-plastic finite element analyses are performed in terms of the incremental plasticity for a crack subject to three-point bending. The path dependence of the J-integral due to the three major factors is then evaluated. Numerical results show that the residual stress modified J-integral is path-independent, and able to describe the fracture driving force for ductile cracks in a residual stress field. This provides a new technology to assess pipeline integrity for cracks coupling residual stresses that offers significant fundamental and practical value to mechanical engineering.
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