Characterization of anisotropic yield surfaces for titanium sheet using hydrostatic bulging with elliptical dies

• Developed anisotropic yield functions for titanium sheet.
• Studied biaxial tension and shear stress states.
• Novel approach to use elliptical bulge data to calibrate yield functions.
• Analytical, finite element simulation, and experimental characterization.

Progressive testing methods are required to accurately characterize the yield surface and large-strain plastic deformation behavior of anisotropic sheet metals. In the current work, hydrostatic bulging through elliptical dies with various biaxial ratios, coupled with full-field strain mapping, was used to generate sheet metal yield surface data for commercially-pure titanium and an exhaust grade titanium alloy. Supplementary characterization was provided by shear tests and tension test specimens taken at various orientations with respect to the rolling direction. The biaxial and tensile data were used to calibrate linear transformation-based anisotropic yield functions. To accurately apply the elliptical bulge tests results for yield function calibration, it was required to accurately calculate the hoop and longitudinal stresses at the pole of the ellipsoidal dome. The optimized yield function coefficients were calibrated for anisotropic response of the sheet metals to high levels of plastic deformation, up to 50%. Finite element simulations using the calibrated yield functions were then shown to provide accurate predictions of the elliptical bulge tests.