Abstract Based on an experimental result of the literature showing that the crack remains in the grain of its initiation up to about 20% of the lifetime at low cycle fatigue of austenitic stainless steels, the lifetime of a polycrystal made out of these steels undergoing uniaxial isothermal or thermomechanical fatigue from 30 to 340 °C at constant total strain amplitude is calculated. The stresses and strains in the grains and polycrystal are determined in term of mean field with the Hill-Hutchinson model. Dipolar slip markings in the grains are predicted and assumed sites of initiation and propagation of the cracks calculated in terms of critical stress and of shear plastic strain, depth and grain boundary, respectively. There is agreement of the macroscopic stress and plastic strain, but at the residual stress, making the modelling not suitable for thermomechanical fatigue. For isothermal fatigue, the lifetime is in agreement. The lifetime - plastic strain power relationships are addressed to the Coffin-Manson law assumed to derive from the kinetic equation of the crack in a dimensional approach. The calculated constants of the power relationship of five austenitic steels of the literature are in qualitative agreement with those measured of the law. The relationships between the constants of the power relationship, law and kinetic equation are determined. The results and modelling are discussed.

中文翻译：

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由奥氏体不锈钢制成的多晶的等温和热机械疲劳模拟以及与 Coffin-Manson 定律的关系

摘要 根据文献的实验结果表明，在奥氏体不锈钢的低周疲劳寿命的 20% 左右，裂纹仍保留在其起始晶粒中，由这些钢制成的多晶的寿命经过单轴等温或在恒定总应变幅度下计算 30 至 340 °C 的热机械疲劳。晶粒和多晶中的应力和应变是根据使用 Hill-Hutchinson 模型的平均场确定的。晶粒中的偶极滑移标记是根据临界应力和剪切塑性应变、深度和晶界分别计算的预测和假设的裂纹萌生和扩展位置。宏观应力和塑性应变一致，但在残余应力下，使建模不适用于热机械疲劳。对于等温疲劳，寿命是一致的。寿命 - 塑性应变功率关系针对 Coffin-Manson 定律，该定律假设从尺寸方法中的裂纹动力学方程导出。文献中五种奥氏体钢的幂关系计算常数与法测得的常数一致。确定了幂关系常数、定律和动力学方程之间的关系。讨论了结果和建模。文献中五种奥氏体钢的幂关系计算常数与法测得的常数一致。确定了幂关系常数、定律和动力学方程之间的关系。讨论了结果和建模。文献中五种奥氏体钢的幂关系计算常数与法测得的常数一致。确定了幂关系常数、定律和动力学方程之间的关系。讨论了结果和建模。