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In this paper, a new formulation for computing ΔJ using the three-dimensional equivalent domain integral method for finite deformation elastic-plastic problem is presented. It is known that J-integral represents the energy release rate per unit crack extension and is useful for the fracture mechanics analysis of elastic-plastic materials. However, J-integral is only valid under the proportional loading condition in elastic-plastic problem. As a method applicable to the cyclic loading problem, ΔJ was proposed and shown that it is valid for evaluating low-cycle fatigue. ΔJ was initially proposed in experimental studies. Later, a contour integral approach for the evaluation of ΔJ was proposed and many numerical analyses have been conducted by engineers and researchers. However, path-independence of ΔJ was shown under the many assumptions and therefore is valid only for limited problems. In addition, the contour integral for ΔJ evaluation was proposed with assuming small deformation formulation, and it was not clear how it could be extended to the finite deformation problem. In this paper, we present a new formulation for the computation of ΔJ using the three-dimensional equivalent domain integral method. This formulation is based on the three-dimensional J-integral formulation for arbitrary load history and finite deformation that was proposed by the authors. It is shown in this paper that proposed ΔJ evaluation method for finite deformation elastic-plastic problems holds the path-independent property in small/finite deformation under any load histories. Finally, small and finite deformation cyclic elastic-plastic analyses using the finite element method are presented. They show that the present method always holds the path-independent property and can be applied to cyclic elastic-plastic fracture problems.

A new formulation of J-integral range ΔJ using three-dimensional equivalent domain integral for finite deformation elastic-plastic problem