Theoretical and numerical study for unsteady tube expansion using hemispherical dies

Unsteady hemispherical die expansion process was investigated theoretically and numerically, using a 48 mm base diameter die. Brass specimens of 32 mm inner diameter, and 1.5, 2, and 3 mm initial wall thickness were simulated using Coulomb’s friction concept with a coefficient of 0.1. The governing equation was derived, and solved for the perfect plastic condition. Reasonable agreement was found between the theoretical and the finite-element results for the relation between forming stress vs. expansion ratio which was noticed to be less affected by the wall thickness. The wall plastic bending at the die entrance was developed to wall curling and waving for all cases. The three components of strains were also studied using the finite-element method. It was noticed that the circumferential strain is always tensile, whilst the radial strain is compressive at the expanded end but turns to tensile at the die entrance. The complexity of expansion process was reflected clearly through the longitudinal strain distribution, it begins as a compressive strain at the expanded end with increasing compressive strain until it reaches its maximum compressive value at a distance about 5 mm from the expanded end, then vanishes at the die entrance.