A Fundamental Study on the Evaluation and Applicability as a Mixed-mode Fracture Criterion of Crack Energy Density in an Arbitrary Direction

It has previously been shown that crack energy density can be defined in any direction at a crack tip without any restrictions on constitutive equations. The crack energy density, ε_φ, in an arbitrary direction can be divided into the contributions of each mode (ε_φ= ε^I _φ+ε^II _φ+ε^III _φ;ε^I _φ,ε^II _φand ε^III _φ are the contributions of modes I, II and III, respectively), which can be evaluated by path-independent integrals corresponding to each. These are defined for a completely sharp crack as the limits where the notch root radius ρ approaches zero in a notch model. Therefore, it is necessary to use a notch model with a sufficiently small value of ρ in evaluations of the quantities through FEM. In this paper, ε_φ and ε^I _φ are evaluated by path-independent integrals through elastic-plastic finite element analyses varying the value of ρ, and we discuss which of ρ should be adopted in evaluations of them. Moreover, by applying these results to an experimental result of ductile fracture under a mixed mode, we show that ε^I _φ is a potential parameter for expressing elastic-plastic fracture criterion under a mixed mode.