BBC05 with non-integer exponent and ambiguities in Nakajima yield surface calibration

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.