Forming characteristic of sheet hydroforming under the influence of through-thickness normal stress

Sheet hydroforming is different from conventional sheet forming due to the existence of liquid pressure. Through thickness normal stress induced by liquid pressure is derived by solving the normal force equilibrium equation. The theoretical prediction is in a good agreement with that determined by experimental data at cup wall. As the third principal stress, through thickness normal stress cannot be reflected in two dimensional yield locus. The variables of η and ω as new coordinates were introduced. Accompanied with stress triaxiality β _av and effective strain ε _eq, they were used to describe the change of typical stress states in sheet hydroforming. As liquid pressure increases to infinity, sheet hydroforming covers the stress states from equi-biaxial tension to uniaxial compression. The numerical simulation in Marc shows that, the stress states of non-free bulging zones are away from plane stress in the (β _av, ε _eq) and (η, ω) based spaces.