Instabilities and failure in ductile non associated materials have been widely investigated during last decades especially in the case of geomaterials. It has been shown experimentally that collapse of some specimens can occur strictly within the ultimate plasticity limit, which is experimentally characterized by the maximum shear stress in a drained triaxial test. From a theoretical point of view such instability problems are well described using the so called second order work criterion derived from the Hill's stability analysis (Hill [1958]). Hence a question arises as to the experimental characterization of the ultimate plasticity limit with respect to the choice of stress paths. After a few reminders on Hill's theory, we prove in a general framework that the drained triaxial paths allow to determine with certainty this ultimate plasticity limit without any risk of preliminary bifurcation whatever the elasto-plastic material considered. We conclude that the plasticity limit is only slightly sensitive to variation of the internal state of the material, which can be described by different micromechanical quantities such as the void ratio and the fabric tensor. Furthermore, we define the limit of the bifurcation domain as the surface drawn in the 6-dimensional stress space that delimits the unconditionally stable space from the one where instabilities and failures can occur within the plasticity limit. However, we show that this latter limit is itself very sensitive to the evolution of the internal state of the soil sample.