Effects of large plastic deformation and residual stress on the path independence of J-integral for cracks in ductile materials

Large plastic deformation and residual stress exist in the oil and gas transmission pipelines with mechanical damages that often contain a gouge or crack. Residual stresses can alter the mechanics behavior of the crack, and cause the standard J-integral to become path-dependent and unable to describe the crack driving force.This paper investigated the effects of large plastic deformation and residual stress on the path independence of the J-integral for a crack in ductile materials. The basic conditions required for the path independence of the standard J-integral were first reviewed, and the major factors that affect the path independence were then analyzed. This includes the theory of plasticity, finite strain formulation, and residual stresses. Then, a residual stress modified J-integral was introduced for ensuring the path independence. After that, the elastic-plastic finite element analyses were performed for a notched beam in terms of the incremental plasticity to create residual stresses and to simulate a crack at the notch root subject to three-point bending. The path independence of the standard and modified J-integrals was numerically evaluated for each of the major factors. Results showed that the modified J-integral is path-independent and able to describe the crack driving force for a crack in a residual stress field, but the standard J-integral cannot do so because of its nature of path dependence when residual stresses are present. Thus, the modified J-integral can be used as an appropriate fracture parameter to assess the pipeline integrity for line pipes containing cracks and residual stresses.