Previous works (Devaux et al., 1997; Cheng et al., 2017) have emphasized the effects of strain hardening and elasticity upon ductile rupture of metals under cyclic loading conditions. This work pursues the study and modelling of these two effects by distinct theoretical methods, each coupled with micromechanical finite element simulations of the behaviour of some “representative cell”. For the effect of strain hardening, we employ Morin et al. (2017)’s approach, based on the theory of (Yang, 1993; Leu, 2007; Leblond et al., 2018). This approach is applied to various types of hardening of the metallic matrix: isotropic, linear kinematic, nonlinear kinematic with one or two kinematic variables (Armstrong and Frederick, 2007) , and even a simplified version of Chaboche (1991)’s model accounting for complex cyclic effects. Numerical micromechanical simulations of a hollow sphere made of elastic–plastic materials obeying the various hardening laws considered, and subjected to cyclic loadings at high triaxiality, fully confirm the predictions of the model developed, provided elasticity is made negligible by using an artificially high value of Young’s modulus. When a realistic value is employed, however, the agreement between theoretical predictions and numerical results is degraded, thus emphasizing again the importance of the effect of elasticity in cyclic ductile rupture. To deal with this effect we derive, apparently for the first time, an evolution equation of the porosity accounting for (compressible) elasticity. However, numerical micromechanical simulations reveal that simply using this new evolution law, while keeping all other aspects of the model unchanged, remains insufficient to get a good match of theoretical and numerical results. Such a match is achieved by introducing the hypothesis that the yield criterion and flow rule derived from sequential analysis still apply in the presence of elasticity, but with some “effective porosity” slightly differing from the true one through some heuristic, adjustable factor.

中文翻译：

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高三轴度循环载荷下的延性断裂：应变硬化和弹性的影响

之前的工作（Devaux 等人，1997；Cheng 等人，2017）强调了循环载荷条件下应变硬化和弹性对金属延性断裂的影响。这项工作通过不同的理论方法对这两种效应进行研究和建模，每种方法都与一些“代表性细胞”行为的微机械有限元模拟相结合。对于应变硬化的影响，我们采用 Morin 等人。 (2017) 的方法，基于 (Yang, 1993; Leu, 2007; Leblond et al., 2018) 的理论。这种方法适用于金属基体的各种类型的硬化：各向同性、线性运动学、具有一个或两个运动学变量的非线性运动学（Armstrong 和 Frederick，2007），甚至是 Chaboche（1991）模型的简化版本复杂的循环效应。对由弹塑性材料制成的空心球进行数值微机械模拟，该空心球遵循所考虑的各种硬化定律，并在高三轴度下承受循环载荷，充分证实了所开发模型的预测，前提是通过使用人为的高值使弹性可以忽略不计。杨氏模量。然而，当采用实际值时，理论预测与数值结果之间的一致性就会降低，从而再次强调了弹性在循环延性断裂中的影响的重要性。为了处理这种效应，我们显然是第一次推导了考虑（可压缩）弹性的孔隙率演化方程。然而，数值微机械模拟表明，仅使用这种新的演化定律，在保持模型的所有其他方面不变的情况下，仍然不足以获得理论和数值结果的良好匹配。这种匹配是通过引入这样的假设来实现的：在存在弹性的情况下，从序贯分析得出的屈服准则和流动法则仍然适用，但通过一些启发式的、可调整的因素，一些“有效孔隙率”与真实孔隙率略有不同。