This is the third of several companion papers dealing with the derivation of material constants for ductile failure criteria under hydrostatic stress. It was observed that the ultimate engineering stresses and elongations at fracture from tensile tests for round specimens with various notch radii tended to increase and decrease, respectively, because of the stress triaxiality. The engineering stress curves from tests are compared with numerical simulation results, and it is proved that the curves from the two approaches very closely coincide. Failure strains are obtained from the equivalent plastic strain histories from numerical simulations at the time when the experimental engineering stress drops suddenly. After introducing the new concept of average stress triaxiality and accumulated average strain energy, the material constants of the Johnson-Cook failure criterion for critical energies of 100%, 50%, and 15% are presented. The experimental results obtained for EH-36 steel were in relatively good agreement with the 100% critical energy, whereas the literature states that aluminum fits with a 15% critical energy. Therefore, it is expected that a unified failure criterion for critical energy, which is available for most kinds of ductile materials, can be provided according to the used materials.