An evolutionary yield function based on Barlat 2000 yield function for the superconducting niobium sheet

Superconducting radio frequency (SRF) niobium cavities are widely used in high-energy physics to accelerate particle beams in particle accelerators. The performance of SRF cavities is affected by the microstructure and purity of the niobium sheet, surface quality, geometry, etc. Following optimum strain paths in the forming of these cavities can significantly control these parameters. To select these strain paths, however, information about the mechanical behavior, microstructure, and formability of the niobium sheet is required. In this study the Barlat 2000 yield function has been used as a yield function for high purity niobium. Results from this study showed that, due to intrinsic behavior, it is necessary to evolve the anisotropic coefficients of Barlat's yield function in order to properly model the plastic behavior of the niobium sheet. The accuracy of the newly developed evolutionary yield function was verified by applying it to the modeling of the hydrostatic bulging of the niobium sheet. Also, in a separate attempt crystal plasticity finite element method was use to model the behavior of the polycrystalline niobium sheet with a particular initial texture.