Triaxiality alone is not sufficient to account for the role of stress state on ductility in materials that exhibit shear effects on fracture strain. For these materials, it has been proposed that ductility also depends on the third invariant of the stress deviator. Recently, Bonora and Testa [N. Bonora, G. Testa, Plasticity damage self-consistent model incorporating stress triaxiality and shear-controlled fracture mechanisms – model formulation, Eng. Frac. Mech. 271, 108634 (2022).] derived a plasticity damage self-consistent (PDSC) model considering damage contributions due to intervoid necking, shearing, and sheeting for an arbitrary stress state. In this work, the PDSC model has been applied to Al2024-T351 considering the experimental results reported in the literature obtained on several different sample geometries and material batches. The ability of the model to predict the transition from cup-cone to slant fracture for different stress states is shown. In addition, the possibility to predict ductile fracture in the negative stress triaxiality range has been also demonstrated showing that it can occur for stress triaxiality even much less than -0.5 as long as there is a dominant shear deformation state.