Improvement of an Exponential Cohesive Zone Model for Fatigue Analysis

Cohesive zone model is an important tool for fatigue analysis, especially for fatigue crack growth along with an interface. A pioneering model is the one of Roe and Siegmund (Eng Fract Mech 70: 209-232, 2003), in which the damage accumulation is calculated using an irreversible exponential cohesive law. However, it is found in our recent research that the constant unloading and reloading slope in Roe's damage evolution law could cause a discontinuity in the traction-separation curve when the mixed mode ratio changes. This limits its application to single mode cyclic loading or scenarios where the mixed mode ratio is constant. In this paper, the cause of such discontinuity is analyzed, and a robust cyclic loading formulation is proposed, which will help the exponential cohesive law remain continuous under arbitrary mixed mode cyclic loading. Moreover, it is found in this paper that by adding a scale factor to the Roe's damage law, the fatigue failure time can be approximated with less computational cost. The relationship between fatigue failure time and the scale factor is shown to be inversely proportional.