A Review of Path-Independent Integrals in Elastic-Plastic Fracture Mechanics

The objective of this paper is to review the path-independent (P-I) integrals in elastic-plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J-integral. The P-I integrals considered herein are the J-integral by Rice, the thermo-elastic P-I integrals by Wilson and Yu, and by Gurtin, the J*-integral by Blackburn, the Jθ-integral by Ainsworth et al., the Ĵ-integral by Kishimoto et al., and the ΔTp- and ΔT*p-integrals by Atluri et al. The theoretical foundation of these P-I integrals is examined with an emphasis on whether or not the path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradients, and material inhomogeneities. The similarities, differences, salient features, and limitations of these P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.