A new three-dimensional J-integral formulation for arbitrary load history and finite deformation

Abstract

In this paper, a new formulation of three-dimensional J-integral for the evaluation of elastic-plastic fracture problem is presented. It is known that the J-integral represents the energy release rate per unit crack extension. The J-integral is a path-independent integral and can be computed on arbitrary integral path or domain. This property requires the assumption of proportional loading when an elastic-plastic material is considered. Because of this assumption, J-integral loses path-independent property under a non-proportional loading condition. We present a new formulation of three-dimensional J-integral representing the energy dissipation inside a small but finite domain in the vicinity of crack front. The dissipated energy includes the energy released by crack extension and the deformation energy that dissipates in the process zone. This formulation is the extension of the three-dimensional J-integral using equivalent domain integral method and derived without any assumptions on the deformation history. Therefore, it is possible to evaluate the J-integral for problems subject to any load histories. Finally, the problems of hyperelastic and large deformation cyclic elastic-plastic analysis using finite element method are presented. They show that the proposed method can be applied to non-proportional loading problem.

Keywords

• j-integral
• non-linear fracture mechanics
• non-proportional loading
• cyclic elastic-plastic deformation
• finite element method
• finite deformation
• domain integral method