Analytical Investigation of Rupture Phenomena in Sheet Hydro-forming Process by Hemispherical Punch

Rupture and wrinkling are two prevalent phenomena that happen in hydro-forming process. Many efforts have been made to achieve the upper and lower bounds for the pressure related to rupture and wrinkling of sheet, respectively. The aim of this investigation is to improve the upper bound of fluid pressure in hydro-forming process by hemispherical punch. In this article, analytical study of the upper bound of fluid pressure based on new assumption of Hill theory is presented. Next, governing equations of the process is derived; and numerical methods are used to solve these equations. In this process, the effect of material and geometric properties on the upper bound pressure is investigated. The results then are compared with experimental and theoretical based on Tresca criterion. The investigation on the effect of geometry and material shows that increasing of the sheet thickness raises the upper bound pressure. Moreover, the reduction of sheet to punch diameter ratio leads to increase of the upper bound pressure. Decrease of the friction force as well as increase of the anisotropic coefficient both causes the rise of upper bound pressure. Finally, the increase of work hardening parameter leads to the rise of rupture place.