In this research has been carried a study about the influence of tempering temperature on the fracture toughness of the steel ASTM A-36, in the range from 500 to 650 °C, for a tempering time of 45 minutes. In the regimen elastoplastic integral on applying the analysis based on the mechanics to the fracture elastoplastic. For the study were employed three points bend specimen type SENB (Single Edge Notched Bend), with a wide approximate one of W = 25 mm, and thickness of (B = W/2), according to the norm ASTM E-1820, which were submitted to a state quenching in water (840ºC), and the state of tempering by 500, 550, 600 and 650 °C to a time of 45 minutes. Subsequently the specimens were cracked with a machine of fatigue of flexion in three points until reaching the relation from a/w approximately to 0,6. The cracked by fatigue was carried out with a relation . For the determination of th...