Incremental sheet forming was developed several decades ago as a cost-effective forming process for low volume production. The deformation mechanism of this process is completely different from the conventional sheet metal–forming processes. Applying a three-dimensional (3D) yield function such as Yld2004-18p for the simulation of incremental sheet forming is necessary to account for the significant anisotropy and out-of-plane shears that develop in the sheet metal. Since it is difficult to experimentally measure out-of-plane shear stresses, a set of virtual experiments was conducted with crystal plasticity finite element method (CPFEM) to obtain the required data. To that end, five different representative volume elements (RVEs) were constructed and simulated with a rate-independent CPFEM model to assess which model best predicts the anisotropy of the AA7075 aluminum sheet. Of the four CPFEM models based on the associate flow rule, three used RVEs accounting for grain orientations and grain size distributions, while the fourth model used only the grain orientation information (Taylor’s assumption). The fifth CPFEM model was modified based on the Hill’s 1948 non-associated flow rule and used the Taylor’s assumption. It was verified by experimental data that the fifth CPFEM model (Taylor + Hill) provides the most computationally efficient and accurate prediction of flow stresses and R-values as a function of the accumulated plastic work. The results from the Taylor + Hill model were then used to calibrate the Yld2004 yield function used in the simulation of the single-point incremental forming (SPIF) of 45^° and 67^° conical shapes with AA7075 sheet metal. It was found that simulation results obtained with Yld2004 yield function well predicts the deformation characteristics of both cone shapes when compared with experimental results. Also, the yield locus of AA7075 sheet metal after the SPIF process was predicted based on evolved crystal orientations and the critical resolved shear stress.

增量片材成型是几十年前开发的，是一种经济高效的批量生产成型工艺。此过程的变形机理与传统的钣金成形过程完全不同。必须应用三维（3D）屈服函数（例如Yld2004-18p）来模拟增量板材成形，以解决板材中显着的各向异性和平面外剪切的问题。由于很难通过实验测量面外剪切应力，因此使用晶体塑性有限元方法（CPFEM）进行了一组虚拟实验，以获得所需的数据。为此，构建了五个不同的代表性体积元素（RVE），并使用与速率无关的CPFEM模型进行了模拟，以评估哪个模型最能预测AA7075铝板的各向异性。在四个基于CPFEM的模型中，关联流规则中，三个使用RVE来解释晶粒取向和晶粒尺寸分布，而第四个模型仅使用晶粒取向信息（Taylor的假设）。第五个CPFEM模型是根据Hill的1948年非关联流量规则进行修改的，并使用了Taylor的假设。实验数据证实，第五种CPFEM模型（Taylor + Hill）可提供最有效的计算效率和最准确的流变应力和R值预测功能，该函数是累积塑性功的函数。然后，将Taylor + Hill模型的结果用于校准Yld2004屈服函数，该屈服函数用于模拟45 ^°和67 ^°的单点增量成形（SPIF）圆锥形形状与AA7075钣金。结果发现，与实验结果相比，用Yld2004屈服函数获得的模拟结果很好地预测了两种圆锥形状的变形特性。同样，基于演化的晶体取向和临界分辨剪切应力，预测了SPIF处理后AA7075薄板的屈服点。