A plane stress yield surface using Bézier curve interpolation in two directions

Current advanced yield criteria, like BBC2005, Yld2000 and Yld2004, offer significant flexibility and are proven to be convex. The number of coefficients of the function is fixed, which limits the number of experimental results that can be fitted independently. A common approach is to define an error function. The optimal anisotropy coefficients are established by minimizing the error function. The Vegter yield criterion is very flexible with respect to experimental results. It is in fact defined as a function that smoothly connects experimental results, while ensuring a continuous function for the derivative. Fitting is therefore a non-issue; the experimental results are the coefficients for the yield criterion. Second order Bézier curves are used for the interpolation between experimental results. Extreme values for these results can cause concavity in the definition of the yield locus. Although rarely an issue, convexity needs to be validated as part of the implementation of the yield criterion. Recently we have seen some cases of concavity that could be attributed to the cosine interpolation in the original Vegter yield criterion definition. Cosine interpolation is used between experimental results at different angles to the rolling direction. An improved method is proposed that uses Bézier interpolation not only between biaxial stress states in one orientation, but also between stress states with a different material orientation. The benefits are greater flexibility in defining experimental results and a coherent approach towards a 3D extension. The benefits of this new yield criterion will be demonstrated in a direct comparison with Yld2000 and Yld2004. The comparison will include the definition of the yield locus, showing actual cases, where in particular biaxial stress states like plane strain and shear are difficult to fit accurately. The comparison will also include improved accuracy in forming simulations.