A framework for predicting the effect of crack-tip triaxiality on fracture toughness is outlined. This methodology is a two-parameter approach that considers the micromechanism of failure. A local damage parameter is used in conjunction with a crack-tip stress analysis to predict the effect of specimen dimensions on toughness. In the case of cleavage fracture, the local criterion involves the maximum principal normal stress, σ1 as well as the volume over which σ1 acts. The agreement between predictions and experimental data is very good in this case. for initiation of ductile tearing, we defined a damage parameter based on a modified version of the Rice and Tracey hole growth model. The analysis indicates that ductile fracture is less sensitive than cleavage to triaxiality. While this result is broadly consistent with experimental observations, further work is necessary to develop improved local criteria for ductile fracture.
The micromechanics approach proposed by the authors was compared with two-parameter fracture mechanics methodologies based on continuum theory, such as the K-T and J-Q approaches. These continuum methodologies, which involve two-term expansions of the crack tip fields, are descriptive rather than predictive. That is, these approaches describe the crack tip triaxiality, but they do not predict the effect of triaxiality on fracture behavior. The micromechanics approach, however, was developed for the purpose of making such predictions. Thus, the continuum and micromechanics approaches to two-parameter fracture mechanics are complementary.