Abstract One of the most challenging issues in the automotive industry is to reliably predict the fracture limits across a broad range of the deformation modes subjected to various forming processes. Sheet metals in general exhibit anisotropy in both their deformation and fracture behaviors, and accordingly the stress and strain states at fracture strongly depend on both the loading condition and direction. A primary concern here is that there exists no global tendency of the anisotropic fracture limits over the wide range of the loading conditions, which gives rise to a difficulty in modeling the anisotropic fracture criterion. In this paper, a solution to the challenge of modeling anisotropic fracture behavior is proposed based on a decoupled formulation of anisotropic fracture limits with an employment of a Lagrangian interpolation function and an L 2 -norm of the principal stress vector. The anisotropic fracture criterion developed based on the proposed modeling approach was successfully applied to accurately represent the fracture forming severity of the DP980 with a thickness of 1.2 mm over a wide range of the loading condition including in-plane shear, uniaxial tension, plane strain tension, and equi-biaxial tension. Comparison of the experimental results with the predictions of the proposed criterion revealed that the proposed criterion has a remarkable capability in describing the anisotropic strain- and stress-based fracture limits. In addition, it was also theoretically discussed how the proposed modeling approach can be extended to predict fracture even for fully anisotropic materials without any plane of symmetry on the fracture initiation, and for dealing with various physical factors such as the strain rate, temperature, etc. in describing a phenomenological fracture criterion.

中文翻译：

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一种考虑金属板一般各向异性的断裂预测新方法

摘要 汽车工业中最具挑战性的问题之一是可靠地预测各种成形过程中各种变形模式的断裂极限。钣金通常在变形和断裂行为方面都表现出各向异性，因此断裂时的应力和应变状态在很大程度上取决于加载条件和方向。这里的一个主要问题是在很宽的载荷条件范围内不存在各向异性断裂极限的全局趋势，这给各向异性断裂准则建模带来了困难。在本文中，基于各向异性断裂极限的解耦公式，采用拉格朗日插值函数和主应力向量的 L 2 范数，提出了一种应对各向异性断裂行为建模挑战的解决方案。基于所提出的建模方法开发的各向异性断裂准则已成功应用于准确表示厚度为 1.2 mm 的 DP980 在广泛的加载条件下（包括面内剪切、单轴拉伸、平面应变拉伸）的断裂形成严重程度, 和等双轴张力。将实验结果与所提出准则的预测进行比较表明，所提出的准则在描述基于各向异性应变和应力的断裂极限方面具有显着的能力。此外，