The fatigue crack initiation and propagation phases have been widely studied by the scientific community. There are several models to describe low-cycle fatigue behaviour based on strain damage criteria, but the most widely used is the Coffin-Manson-Morrow relationship, normally used for the fatigue crack initiation modelling. In addition, strain-life models based on hardness measurements and monotonic properties of metals have also been suggested. There are also integrated fatigue models that describe both the fatigue crack initiation and propagation phases, such as the UniGrow, Huffman, Peeker, among others, where the concept of successive crack re-initializations (increments) based on local approaches is adopted. In this paper, the low-cycle fatigue modelling based on Huffman approach using the strain energy density and considering dislocations density is investigated and discussed. For this, various methodologies to evaluating low-cycle fatigue strength based on Huffman approach and exploring different dislocation density parameters are suggested: (i) critical dislocation density driven by the highest strain amplitude; (ii) the mean value of the dislocation density of the available experimental fatigue data and, (iii) Monte Carlo (MC) stochastic prediction considering the variability of dislocation density and the cyclic strain hardening coefficient. Besides, the Monte Carlo stochastic simulations for obtaining the strain-life parameters, fatigue strength and ductility coefficients, it allows the generation of probabilistic fields for the low-cycle fatigue behaviour of metals. In this research, the experimental fatigue data of 1050, 6061-T651, and AlMgSi0.8 aluminium alloys are used to apply the suggested methodologies. A comparison between the experimental fatigue data and strain-life curves based on various suggested methodologies is made.

疲劳裂纹萌生和扩展阶段已被科学界广泛研究。有多种模型可以根据应变损伤准则来描述低周疲劳行为，但应用最广泛的是 Coffin-Manson-Morrow 关系，通常用于疲劳裂纹萌生建模。此外，还提出了基于硬度测量和金属单调特性的应变寿命模型。还有描述疲劳裂纹萌生和扩展阶段的集成疲劳模型，例如 UniGrow、Huffman、Peeker 等，其中采用了基于局部方法的连续裂纹重新初始化（增量）的概念。在本文中，研究和讨论了基于 Huffman 方法使用应变能密度并考虑位错密度的低周疲劳建模。为此，提出了基于霍夫曼方法评估低周疲劳强度并探索不同位错密度参数的各种方法：(i) 由最高应变幅驱动的临界位错密度；(ii) 可用实验疲劳数据的位错密度平均值，以及 (iii) 考虑位错密度和循环应变硬化系数可变性的蒙特卡罗 (MC) 随机预测。此外，蒙特卡罗随机模拟获得应变寿命参数，疲劳强度和延展系数，它允许为金属的低周疲劳行为生成概率场。在本研究中，1050、6061-T651 和 AlMgSi0.8 铝合金的实验疲劳数据用于应用建议的方法。基于各种建议的方法对实验疲劳数据和应变-寿命曲线进行了比较。