A numerical process control method for circular-tube hydroforming prediction - Johnson, K.I.; N. Nguyen, B.; Davies, R.W.; Grant, G.J.; Khaleel, M.A. (International journal of plasticity, 2004)
A numerical control algorithm is described that predicts the axial end-feed and internal pressure loads to give maximum formability of circular tubes during hydroforming. The controller tracks the stresses, strains and mechanical response of the incremental finite element solution to estimate the proper axial feed (end-feed) and internal pressure increments to apply in the next increment as the tube deforms. The algorithm uses the material stress–strain curve and the deformation theory of plasticity with Hill's criterion to relate the current stress and strain increments (from the finite element model) to the next applied load increments. A controlled increment in plastic strain is prescribed for the next solution increment, and the pressure and end-feed increments are calculated to give a constant ratio of incremental axial and hoop strains. Hydroforming simulations using this method were conducted to predict the load histories for controlled expansion of 6061-T4 aluminum tubes within a conical die shape and under free hydroforming conditions. The predicted loading paths were applied in hydroforming experiments to form the conical and free-formed tube shapes. The model predictions and experimental results are compared in this paper for deformed shape, strains and the extent of forming at rupture.