An improved continuous damage model to estimate multiaxial fatigue life under strain control problems

In this contribution, a modification and application of the Lemaitre damage evolution law is proposed for the problem of fatigue life estimate under low number of cycles. For this, the denominator of damage, considered constant for Lemaitre, was replaced by a function dependent on the stress triaxiality. The new function has a nonlinear and thermodynamically consistent behavior. In addition, the evolution law of the backstress tensor is adopted as proposed by Desmorat, where there is no saturation of the limit value. The formulation is implemented in an academic tool for analysis at one Gauss point, through an implicit integration strategy of the flow equations. The Newton-Raphson method is used to solve a system of nonlinear equations, with two tensor and two scalar equations. Thus, in order to demonstrate the robustness of the model, experimental data from the literature for SAE 1045 and S460N steels are adopted. Proportional and nonproportional axial, torsional and multiaxial loading paths are simulated. Finally, the results have shown that the modification formulation is a good strategy to control the damage evolution in predicting fatigue life. In this sense, the calculated lives by the new proposal are within a scatter band of factor three, both under normal or torsional uniaxial loading conditions, as well as proportional or nonproportional multiaxial conditions.