Development of a multi-scale simulation model of tube hydroforming for superconducting RF cavities

This work focuses on finite element modeling of the hydroforming process for niobium tubes intended for use in superconducting radio frequency (SRF) cavities. The hydroforming of tubular samples into SRF-relevant shapes involves the complex geometries and loading conditions which develop during the deformation, as well as anisotropic materials properties. Numerical description of the process entails relatively complex numerical simulations. A crystal plasticity (CP) model was constructed that included the evolution of crystallographic orientation during deformation as well as the anisotropy of tubes in all directions and loading conditions. In this work we demonstrate a multi-scale simulation approach which uses both microscopic CP and macroscopic continuum models. In this approach a CP model (developed and implemented into ABAQUS using UMAT) was used for determining the flow stress curve only under bi-axial loading in order to reduce the computing time. The texture of the materials obtained using orientation imaging microscopy (OIM) and tensile test data were inputs for this model. Continuum FE analysis of tube hydroforming using the obtained constitutive equation from the CP modeling was then performed and compared to the results of hydraulic bulge testing. The results show that high quality predictions of the deformation under hydroforming of Nb tubes can be obtained using CP-FEM based on their known texture and the results of tensile tests. The importance of the CP-FEM based approach is that it reduces the need for hydraulic bulge testing, using a relatively simple computational approach.