Abstract: For 10 types of specimens with different constraints, ductile fracture tests of 9 metal materials under unidirection loading were performed, and their load-displacement relations were measured. Based on the load-displacement curves of notched round bar, the full-range equivalent constitutive relationships of materials up to failure were obtained by FAT (finite-element-analysis aided testing) method. Further, the simulated force-displacement curves for different specimens were obtained based on the full-range constitutive relations, which agree well with the experimental force-displacement curves. The results demonstrate that the full-range constitutive relations up to failure obtained by FAT method have uniqueness for the materials. The critical fracture parameters such as critical stress, critical strain and critical stress triaxiality are investigated by failure simulations for the 36 specimens with different constraints. The first principal stress is suggested to be the master parameter to control ductile fracture. By analyzing the critical behaviors of the specimens which are smooth, notched and cracked, respectively, a unified strength criterion for ductile materials with stress triaxiality varying from -1 to 3 is proposed.