Improvements of j-integral criterion for ductile fracture characterized by a triaxiality parameter

It is now generally agreed that the applicability of the one-parameter J-based fracture approach is limited to so-called high-constraint crack geometries and the research of alternate methods is needed. This paper proposes to employ damage mechanics models for ductile fracture to correlate the variability of macroscopic fracture toughness values (j_Ic) with crack tip constraint characterized by crack tip stress triaxiality ( S_m S_e). Firstly, a continuum damage mechanics model and an improved micromechanics model for ductile fracture proposed by the author [Engng Fracture Mech. 42, 185-193 (1992); Int.J. Fracture 57, R3-R6 (1992)] are introduced briefly. Then the experimental results on the stress-state dependence of the critical J-value, denoted J_Ic, at crack initiation are reviewed, and the relationships between J_Ic and the stress triaxiality factor, S_m S_e, in the crack tip region are derived on the basis of the two damage mechanics models. Finally, modified fracture parameters J_dc and J_mc and the associated two-parameter (J and S_m S_e) criteria for ductile fracture are proposed, where the J-integral sets the deformation at the crack tip and the stress triaxiality S_m S_e, sets the crack tip constraint, which are the improvements on the one-parameter J-integral criterion. Experiments verified that the newly improved parameters J_dc and J_mc are material constants independent of stress state, i.e. specimen geometry and loading condition-independent constants.