Abstract: A mathematical description of fatigue toughness is set up through analysing the hysteresisenergy and using the cyclic stress - strain curve. The agreement between the description and the avail2able test data is good. The description enables the fatigue toughness of a material to be satisfactorilyestimated only by means of the monotonic and cyclic properties. Through studying the strain - con2trolled low cycle fatigue test data of several materials with different cyclic properties , it is found thatthe fatigue toughness depends on the material and the fatigue life and increases generally with the fa2tigue life , and that under the condition of the strain - controlled low cycle fatigue (Nf < 104 cycle) ,the fatigue toughness - fatigue life curve can be divided into two parts and described separately by twostraight lines on a doubl - logarithmic scale.

Key words: fatigue, toghness, stress analysis