Effects of loading path on the fracture loci in a 3D space

Axi-symmetric and 3D unit cell analyses with continuous non-proportional loading paths are performed to investigate the path dependence of the fracture loci in a 3D space. The loading pattern utilized is the generalization of a number of non-proportional paths recorded in real tests. Failure of the unit cell is predicted when localization of plastic flow occurs, and the failure strains are plotted against the strain history averaged stress triaxiality and Lode parameter to construct fracture loci in a 3D space. The fracture locus with a non-proportional loading path deviates from that with a proportional loading path along the axis of stress triaxiality and becomes non-monotonic in high triaxiality regime. Meanwhile, such deviation occurs only when a certain level of triaxiality is reached. Agreement with the proportional locus as well as monotonicity maintains over a large range of stress triaxiality that covers most cases in reality, as long as the non-proportionality of the loading path is sufficiently low. This provides the rationale for utilizing the average triaxiality based fracture locus as an acceptable approximation in practice. Deviations of the non-proportional loci along the axis of Lode parameter are also observed. Further study on the Lode history dependence suggests using the final value of Lode parameter instead of the averaged one as the Lode axis in the fracture loci, which can alleviate the severity of path dependence for the loading patterns concerned. Based on these results, the effectiveness of the average stress state based fracture loci reported in the literature is discussed.