Reliable sheet metal forming simulations depend on accurate descriptions of real process conditions. These conditions include material behavior, lubrication systems, tool deformations, press dynamics, and more. Research on material models is the most mature area for describing these conditions in a reliable way. Several advanced and flexible models exists. This study focuses on two versions of yield criteria for sheet materials that are assumed to follow the plane stress assumption: the BBC05 model with integer exponent and the BBC05 model with non-integer exponent. The literature has previously described the BBC05 model with integer exponent. This paper elaborates on a modified version with non-integer exponent that offers more flexibility in the mathematical description. Furthermore, it outlines the implementation of this material model and similar yield criteria as user subroutines in finite element software. As mathematical flexibility increases, it enables more physically correct material approximations. However, it also becomes more challenging to calibrate because of ambiguities due to a larger number of mathematical variables. These ambiguities is demonstrated by using a Nakajima test without lubrication during inverse modeling of parameters for the BBC05 model. It shows that it is impossible to accurately identify the physically correct combination of friction coefficient and the yield surface exponent, k, using strain distributions and punch force. It is suggested to use two Nakajima tests in the inverse modeling process where friction can be neglected due to testing conforming to ISO12004-2. One test that corresponds to equi-biaxial strain of the sheet, and one that corresponds to plane strain in the transverse direction of the sheet. By utilizing these samples in the inverse modeling it is possible to separate friction from the exponent k. A non-integer value of k is found to yield the most reliable prediction of strains and forces in the simulations, thereby also demonstrating the need of flexible yield surface models such as BBC05 with non-integer exponent, YLD2000, Vegter and more advanced yield criteria.

可靠的钣金成型仿真取决于对真实工艺条件的准确描述。这些条件包括材料性能，润滑系统，工具变形，压力机动力学等等。材料模型的研究是可靠描述这些条件的最成熟领域。存在几种先进且灵活的模型。这项研究着重于假定遵循平面应力假设的板材屈服准则的两个版本：具有整数指数的BBC05模型和具有非整数指数的BBC05模型。文献先前已经描述了具有整数指数的BBC05模型。本文详细介绍了具有非整数指数的修改版本，该修改版本在数学描述中提供了更大的灵活性。此外，它概述了此材料模型的实现以及与有限元软件中用户子例程相似的屈服准则。随着数学灵活性的提高，它可以实现物理上更正确的材料近似。但是，由于存在大量的数学变量，因此模棱两可也使校准更具挑战性。通过在BBC05模型参数的逆向建模过程中使用不润滑的Nakajima测试，可以证明这些歧义。它表明不可能准确地识别摩擦系数和屈服面指数的物理正确组合，由于大量的数学变量的不确定性，校准也变得更具挑战性。通过在BBC05模型参数的逆向建模过程中使用不润滑的Nakajima试验，可以证明这些歧义。它表明不可能准确地识别摩擦系数和屈服面指数的物理正确组合，由于大量的数学变量的不确定性，校准也变得更具挑战性。通过在BBC05模型参数的逆向建模过程中使用不润滑的Nakajima测试，可以证明这些歧义。它表明不可能准确地识别摩擦系数和屈服面指数的物理正确组合，k，使用应变分布和冲压力。建议在逆建模过程中使用两个Nakajima测试，由于符合ISO12004-2的测试可以忽略摩擦。一种测试对应于片材的等双轴应变，一种测试对应于片材的横向方向上的平面应变。通过在逆模型中利用这些样本，可以将摩擦与指数k分开。在仿真中发现非整数值k可以最可靠地预测应变和力，从而也表明需要灵活的屈服面模型，例如具有非整数指数的BBC05，YLD2000，Vegter和更高级的屈服准则。