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.

在这篇文章中，针对低循环次数下的疲劳寿命估计问题，提出了 Lemaitre 损伤演化定律的修改和应用。为此，对于 Lemaitre 来说，被认为是常数的损伤分母被一个依赖于应力三轴性的函数所取代。新函数具有非线性和热力学一致的行为。另外，背应力张量的演化规律采用了Desmorat提出的，不存在极限值饱和的情况。该公式通过流动方程的隐式积分策略在一个高斯点分析的学术工具中实现。Newton-Raphson 方法用于求解具有两个张量和两个标量方程的非线性方程组。因此，为了证明模型的稳健性，采用了 SAE 1045 和 S460N 钢文献中的实验数据。模拟了比例和非比例轴向、扭转和多轴加载路径。最后，结果表明，修正公式是在预测疲劳寿命时控制损伤演变的良好策略。从这个意义上说，在正常或扭转单轴载荷条件下，以及在比例或非比例多轴条件下，新提案计算的寿命都在因子三的散布带内。