In this study, an anisotropic constitutive model based on the non-associated flow rule was developed for anisotropic sheet metals. This model was defined in the quadratic form of the Hill’s anisotropic function under a general three-dimensional stress condition. The anisotropic parameters for the yield function were identified using the directional planar yield stresses, bulge yield stress and shear yield stress, while those for the plastic potential function were identified using the directional r-values. A full expression related to the non-associated flow rule was applied and the model was implemented into the finite element code ABAQUS. A static-implicit analysis and the solid element were applied. Capability of the developed model for predicting the anisotropic behavior of sheet metal was investigated by considering two different sheet metal forming processes: cylindrical cup drawing of AA2090-T3, A6061P-T6 and SPCE; and hole expansion forming test of A6016-O. Cup heights and through-thickness strain distributions obtained from the simulations were compared with the experimental data. Results demonstrate that the developed material model considering 3D condition can improve accuracy of predicting the anisotropic behaviors. Furthermore, the simple formulations are efficient and user-friendly for computational analyses and solving the common industrial sheet metal forming problems.

中文翻译：

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基于非关联流规则的本构方程用于各向异性板材的成形分析

在这项研究中，建立了基于非关联流规则的各向异性本构模型。该模型是在一般三维应力条件下以希尔各向异性函数的二次形式定义的。使用定向平面屈服应力，凸起屈服应力和剪切屈服应力确定了屈服函数的各向异性参数，而使用方向性r值确定了塑性势函数的各向异性参数。应用了与非关联流规则相关的完整表达式，并将该模型实现为有限元代码ABAQUS。应用了静隐分析和固体元素。通过考虑两种不同的钣金成形工艺，研究了开发的模型预测钣金各向异性行为的能力：AA2090-T3，A6061P-T6和SPCE的圆柱杯形拉拔；和A6016-O的扩孔成型试验。从模拟获得的杯高和贯穿厚度的应变分布与实验数据进行了比较。结果表明，考虑3D条件开发的材料模型可以提高预测各向异性行为的准确性。此外，简单的配方对于计算分析和解决常见的工业钣金成型问题是高效且用户友好的。从模拟获得的杯高和贯穿厚度的应变分布与实验数据进行了比较。结果表明，考虑3D条件开发的材料模型可以提高预测各向异性行为的准确性。此外，简单的配方对于计算分析和解决常见的工业钣金成型问题是高效且用户友好的。从模拟获得的杯高和贯穿厚度的应变分布与实验数据进行了比较。结果表明，考虑3D条件开发的材料模型可以提高预测各向异性行为的准确性。此外，简单的配方对于计算分析和解决常见的工业钣金成型问题是高效且用户友好的。