This work aims to give a comprehensive and accurate view of those micromechanical models that have been developed over the past two decades by our research team. We hereby refer to the distinct capabilities and theoretical difficulties of such models published in various journals by discussing them in a more integrated manner. We also believe that our community can find a significant benefit from this work through below mentioned discussions, which answer many of the questions asked by researchers and those interested in this field.

Returning to this work topic, the low-cycle fatigue (LCF) life is highly affected by microstructural instabilities, inhomogeneity and shear bands formation. The first type of damage is related to the nuclei of fatigue microcracks, for several FCC and BCC metals generally governed by continuous irreversible slips within the intensive slip bands. The second type of damage concerns ductile damage caused by cavitation induced by plastic strain and hydrostatic stress. Thereby, fatigue-failure is a relevant topic that requires further explanations to better understand the plausible damaging mechanisms of microcracks and/or microvoids at lower levels of observation.

To model the microcracks initiation, some attempts were conducted via micromechanical models assuming, for example, that the microcracks initiate at the crystallographic slip system level describing the LCF response of metals under simple and complex loading paths. In this overview, the latest development of mixed approach with double character called Micromechanical Determinist-Probabilistic Model (MDPM) coupled with damage will be presented with its generalized structure.

这项工作旨在全面，准确地介绍我们的研究团队在过去的二十年中开发的那些微机械模型。我们在此通过更全面的讨论方式来讨论在各种期刊中发表的此类模型的独特功能和理论上的困难。我们还相信，通过下面提到的讨论，我们的社区可以从这项工作中受益匪浅，这些讨论回答了研究人员和对该领域感兴趣的人提出的许多问题。

回到这个工作主题，低周疲劳（LCF）寿命受微观结构不稳定性，不均匀性和剪切带形成的影响很大。所述第一类型的损伤是与疲劳裂纹，的细胞核数FCC和BCC金属通常通过连续的不可逆单密集滑移带内控制。第二类破坏涉及塑性应变和静水压力引起的气蚀引起的延性破坏。因此，疲劳失效是一个相关主题，需要进一步的解释才能更好地理解在较低观察水平下微裂纹和/或微孔的合理破坏机理。

为了模拟微裂纹的萌生，通过微力学模型进行了一些尝试，例如，假设微裂纹在描述简单和复杂载荷路径下金属的LCF响应的结晶滑动系统水平上萌生。在本概述中，将介绍具有双重特征的混合方法的最新发展，称为微机械确定论-概率模型（MDPM）以及损伤，并结合其广义结构。