Fourier series based finite element analysis of tube hydroforming

Purpose - The purpose of this paper is to provide an axisymmetric model of tube hydroforming using a Fourier Series based finite element method.Design methodology approach - Fourier series interpolation function, which considerably reduces the size of the global stiffness matrix and the number of variables, is employed to approximate displacements. The material of the tube is assumed to be elastic-plastic and to satisfy the plasticity model that takes into account the rate independent work hardening and normal anisotropy. Numerical solution obtained from an updated Lagrangian formulation of the general shell theory is employed. The axial displacement stroke (a.k.a. axial feed) during tube hydroforming is incorporated using Lagrange multipliers. Contact constraints and boundary friction condition are introduced into the formulation based on the penalty function, which imposes the constraints directly into the tangent stiffness matrix. A forming limit curve based on shear instability and experimental measurements are used as fracture criteria.Findings - The results obtained from this new formulation are compared against the nonlinear finite element code ABAQUS and experimental measurements for isotropic and transversely anisotropic tube materials. The hoop and axial strains predicted with AXHD code compared excellently with those from ABAQUS FEM code using plane stress axisymmetric (SAX1) and four-node shell (S4R) elements. However, in the case of aluminum, the numerically predicted maximum hoop strain underestimated the actual hoop strain measured from the tube bulging experiment.Practical implications - The axisymmetric hydroforming program (AXHD) developed in this work is very efficient in simulating the free-forming stage of the tube hydroforming process under simultaneous action of internal pressurization and displacement stroke.Originality value - Although Fourier Series based finite element method has been used in metal forming, the extended application presented in this paper is novel in the finite element analysis of tube hydroforming.