An analytical model and its corresponding numerical algorithm for viscous pressure bulging process considering the effects of rate-dependent tangential adhesive stress

Abstract

In conventional bulging process, it is usually assumed that sheet metal deforms under normal pressure regardless of the frictional force between the sheet and the pressure-carrying medium. However, there is a phenomenon that sheet metal is bulged under the combined action of normal pressure and beneficial frictional force, which is resulted from the special characteristics of the pressure-carrying medium. Effects of constant tangential stress (beneficial frictional force) caused by rubber or urethane have been studied analytically and experimentally in previous works. Yet, the tangential adhesive stress imposed on sheet metal by viscous medium is correlated with its flow velocity due to its rate-dependent property, which can be controlled and measured by loading equipment. This kind of rate-dependent tangential adhesive stress has been taken into account to establish an analytical model to analyze its effects on the viscous pressure bulging (VPB) process. Then a numerical approach is presented to solve the problem, which utilizes incremental strain to start an iteration loop by considering different magnitudes of adhesive stress. Results have shown that rate-dependent beneficial frictional force in VPB process can promote longitudinal deformation of the bulged part to help make the strain distribution more uniform. The location of maximum thickness strain point deviates from the pole the outer radius, which means that when polar strains remain at the same level, higher bulging height can be obtained for larger magnitude of rate-dependent tangential stress; this characteristic mainly accounts for the postponement of fracture instability of sheet metal in VPB. The theoretical predictions of strain components and geometric parameters are analyzed and compared with experimental results. The comparisons have shown good agreement to validate the analytical model.