A uniaxial material model for fatigue damage accumulation, established on the connection of unit elements, is presented in this paper. Although these units are regarded as micro-elements in the proposed model, they are based on a hysteretic operator that enables calculating hysteretic energy loss as an analytical expression. Further, this unit element represents a mechanical model with elastoplastic damage behavior in function of strain. The second level of modeling is defined by the connection of these units (micro-elements) with different values of total energy dissipated at failure. By changing the distribution of dissipated energy limit, various fatigue damage evolution laws are developed. Calculation of total and hysteretic energy loss in one loading cycle is also affected by fatigue damage as the varying number of unit elements are been eliminated when their maximum dissipation energy is reached. Material parameters for the model were defined based on the experimental monotonic and cyclic stress-strain tests, still, detailed comparison was not performed as the main advantage and aim of the paper was the development of the method for assessment of damage evolution in fatigue analysis. On the other hand, the number of cycles to failure ( Nf) and total heat dissipation are compared in both qualitative and quantitative aspects with experimental results. Finally, based on the proposed model, mean strain and load sequence effect diagrams were constructed. It is shown that the proposed model can provide a reliable estimation of fatigue life in the low-cycle regime of loading. The maximum error for the calculated Nf was 3% for constant strain loading for experiments with strain amplitude less than 5%. In load sequence fatigue life estimation, the proposed model demonstrated good accuracy, with a maximum error of 34%. Further, obtained results were achieved with different types of damage evolution that could be defined for the same material and fatigue life.

中文翻译：

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基于能量的延性材料低周疲劳损伤模型


本文提出了一种基于单元单元连接的疲劳损伤累积单轴材料模型。尽管这些单元在所提出的模型中被视为微元件，但它们基于滞后算子，能够将滞后能量损失计算为解析表达式。此外，该单元单元表示具有随应变变化的弹塑性损伤行为的力学模型。第二级建模是通过这些单元（微元件）与故障时耗散的不同总能量值的连接来定义的。通过改变耗散能量极限的分布，开发了各种疲劳损伤演化规律。一个加载循环中总能量损失和迟滞能量损失的计算也受到疲劳损伤的影响，因为当达到最大耗散能量时，不同数量的单元元件将被消除。模型的材料参数是根据实验单调和循环应力-应变测试定义的，但没有进行详细的比较，因为本文的主要优点和目的是开发疲劳分析中损伤演化评估的方法。另一方面，将失效循环次数（Nf）和总散热量与实验结果进行定性和定量比较。最后，基于所提出的模型，构建了平均应变和载荷序列效应图。结果表明，所提出的模型可以提供低循环负载状态下疲劳寿命的可靠估计。对于应变幅度小于 5% 的实验，对于恒定应变载荷，计算出的 Nf 的最大误差为 3%。 在载荷序列疲劳寿命估计中，该模型表现出良好的精度，最大误差为34%。此外，获得的结果是通过不同类型的损伤演变来实现的，这些损伤演变可以针对相同的材料和疲劳寿命进行定义。