In this paper, we have investigated the effect of material orthotropy on the formability of metallic sheets subjected to dynamic biaxial stretching. For that purpose, we have devised an original three-pronged methodology which includes a linear stability analysis, a nonlinear two-zone model and finite element calculations. We have studied 5 different materials whose mechanical behavior is described with an elastic isotropic, plastic anisotropic constitutive model with yielding based on Hill (1948) criterion. The linear stability analysis and the nonlinear two-zone model are extensions of the formulations developed by Zaera et al. (2015) and Jacques (2020), respectively, to consider Hill (1948) plasticity. The finite element calculations are performed with ABAQUS/Explicit (2016) using the unit-cell model developed by Rodríguez-Martínez et al. (2017), which includes a sinusoidal spatial imperfection to favor necking localization. The predictions of the stability analysis and the two-zone model are systematically compared against the finite element results – which are considered as the reference approach to validate the theoretical models – for loading paths ranging from plane strain stretching to equibiaxial stretching, and for different strain rates ranging from $100{\text{s}}^{-1}$ to $50000{\text{s}}^{-1}$. The stability analysis and the two-zone model yield the same overall trends obtained with the finite element simulations for the 5 materials investigated, and for most of the strain rates and loading paths the agreement for the necking strains is also quantitative. Notably, the differences between the finite element results and the two-zone model rarely go beyond 5%. Altogether, the results presented in this work provide new insights into the mechanisms which control dynamic formability of anisotropic metallic sheets.

在本文中，我们研究了材料正交性对动态双轴拉伸金属板成形性的影响。为此，我们设计了一种原始的三管齐下的方法，其中包括线性稳定性分析，非线性两区域模型和有限元计算。我们已经研究了5种不同的材料，这些材料的力学行为用基于Hill（1948）准则的屈服屈服弹性塑性各向异性模型进行描述。线性稳定性分析和非线性两区模型是Zaera等人开发的公式的扩展。（2015）和雅克（2020）分别考虑希尔（1948）的可塑性。有限元计算由ABAQUS / Explicit（2016）使用Rodríguez-Martínez等人开发的晶胞模型进行。（2017年），其中包括一个正弦空间缺陷，以有利于颈缩定位。系统将稳定性分析和两区模型的预测与有限元结果进行了系统比较，有限元结果被认为是验证理论模型的参考方法，适用于从平面应变拉伸到等双轴拉伸以及不同应变的加载路径费率从$100{\text{s}}^{-\mathrm{1个}}$ 至 $50000{\text{s}}^{-\mathrm{1个}}$。稳定性分析和两区模型得出的相同总体趋势是通过有限元模拟对所研究的5种材料获得的，对于大多数应变率和加载路径，颈缩应变的一致性也是定量的。值得注意的是，有限元结果与两区域模型之间的差异很少会超过5％。总之，这项工作中提出的结果为控制各向异性金属薄板的动态成型性的机理提供了新的见解。