An advanced Crystal Plasticity Finite Element (CPFE) approach is developed to accurately predict the ductility limit strains of thin metal sheets. This method uses polycrystalline unit cells to represent the metal sheets at the macroscopic level. The macroscopic behavior of these unit cells is determined based on that of the constituent single crystals using the periodic homogenization multiscale scheme. At the single crystal scale, the constitutive framework follows a finite strain rate-independent formulation, with the flow rule governed by the Schmid law. The evolution of the single crystal yield surface is described through a physically-based mixed hardening model, where isotropic hardening is characterized by a dislocation density-based formulation, while kinematic hardening is described by the nonlinear Armstrong–Frederick model. The unit cell ductility limit strains are predicted by the Rice bifurcation criterion. The reliability of the mixed hardening model in accurately reproducing mechanical behavior is confirmed through simulations of uniaxial tension/compression loading. Then, the developed computational strategy is used to investigate the impact of key microstructural hardening parameters on the initiation of localized necking under linear strain paths. The numerical predictions reveal the significant influence of these parameters on the formability of thin metal sheets. Additionally, the analysis of ductility limits under non-linear strain paths demonstrates a strong dependency of the numerical predictions on strain path changes. The numerical predictions obtained by the developed CPFE multiscale strategy are compared with experimental results from the literature. In summary, the proposed approach provides a reliable tool for accurately predicting the ductility limits of thin metal sheets, offering valuable insights for engineering applications.

中文翻译：

---

基于物理的混合硬化模型，用于使用 CPFE 方法预测薄金属板的延展性极限

开发了先进的晶体塑性有限元 (CPFE) 方法来准确预测薄金属板的延展性极限应变。该方法使用多晶晶胞来表示宏观水平上的金属板。这些晶胞的宏观行为是根据使用周期性均质化多尺度方案的单晶组成的宏观行为来确定的。在单晶尺度上，本构框架遵循与有限应变率无关的公式，流动规则受施密德定律支配。单晶屈服面的演化是通过基于物理的混合硬化模型来描述的，其中各向同性硬化的特征是基于位错密度的公式，而运动硬化是通过非线性阿姆斯特朗-弗雷德里克模型来描述的。通过莱斯分叉准则预测晶胞延展性极限应变。通过单轴拉伸/压缩载荷的模拟，证实了混合硬化模型在准确再现机械行为方面的可靠性。然后，使用开发的计算策略来研究关键微观结构硬化参数对线性应变路径下局部颈缩起始的影响。数值预测揭示了这些参数对薄金属板的成形性的显着影响。此外，非线性应变路径下延性极限的分析表明数值预测对应变路径变化的强烈依赖性。将通过开发的 CPFE 多尺度策略获得的数值预测与文献中的实验结果进行比较。总之，所提出的方法为准确预测薄金属板的延展性极限提供了可靠的工具，为工程应用提供了有价值的见解。