Analytically described polynomial yield criterion by considering both plane strain and pure shear states

Analytical Poly6–18p yield criterion by considering both pure shear and plane strain states has been developed. The convex relationship of analytical Poly6-type yield criteria between 2D and 3D forms has been derived. The accuracy and effectiveness of the proposed yield criterion have been verified by comparing it with the selected yield criteria and applying it for AA7075-T6 and AA6061-O. The results show that both the pure shear and plane strain states can be accurately predicted from the proposed yield criterion. Anisotropic hardening can be also accurately predicted from the proposed yield criterion without any interpolation method. Besides, the proposed analytical yield criterion can cover the ability of the analytical Poly6-type yield criteria to describe both the directional hardening and r-values. The developed yield criterion has been implemented into the FE method for the simulation of tube hydroforming which includes the tension and compression states. For the different lengths of the tube AA6061-O, the developed yield criterion shows an excellent performance for the predictions of thickness change, bulge position and height.