Abstract This contribution proposes an incremental approach to fatigue life estimate of ductile materials subjected to low cycle fatigue. In this approach, the life prediction is based on the evolution of the internal damage variable of a proposed extension for the Gurson model capable of describing the gradual degradation of the material in function of the number of loading cycles. The extension of the model consists in the inclusion of the Armstrong-Frederick kinematic hardening law [4] and the reformulation of the damage evolution law proposed by Gurson [22], assuming the Nahshon and Hutchinson shear mechanism [43] and a term based on the normalized third invariant with the role to promote asymmetric damage growth under axial (tension–compression) cyclic conditions. An implicit integration scheme is developed, and numerical analyzes are done through simulations at one Gauss point. In this context, the incremental damage approach has applied to experimental data extracted from the literature for thin-walled tubular specimens made of two different materials, S460N structural and hot-rolled normalized SAE 1045 steels. Finally, the predictive capacity of the proposed approach is evaluated comparing predicted and experimentally observed results considering six different proportional and non-proportional loading paths.

中文翻译：

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比例和非比例载荷下疲劳寿命估计中基于 Gurson 的增量损伤：恒定振幅和低周状态应用

摘要 此贡献提出了一种增量方法来估计承受低周疲劳的延性材料的疲劳寿命。在这种方法中，寿命预测基于 Gurson 模型的拟议扩展的内部损伤变量的演变，该模型能够描述材料随加载循环次数而逐渐退化的情况。该模型的扩展包括包含 Armstrong-Frederick 运动硬化定律 [4] 和 Gurson [22] 提出的损伤演化定律的重新表述，假设 Nahshon 和 Hutchinson 剪切机制 [43] 以及基于归一化的第三不变量，在轴向（拉伸-压缩）循环条件下具有促进不对称损伤增长的作用。开发了一个隐式集成方案，数值分析是通过一个高斯点的模拟来完成的。在这种情况下，增量损伤方法已应用于从文献中提取的实验数据，这些数据是由两种不同材料制成的薄壁管状试样，即 S460N 结构钢和热轧正火 SAE 1045 钢。最后，比较考虑六种不同比例和非比例加载路径的预测和实验观察结果，评估了所提出方法的预测能力。