Equivalent drawbead model

Drawbeads are commonly used in the deep drawing process to control the flow of the material during the deformation operation. In the drawbead a sheet material is forced to flow along a sort of threshold and as a result the material is restrained to flow into the die to fast. The force needed to pull the sheet through the drawbead is called the drawbead restraining force, D.B.R.F.. During the flow through the drawbead the strain distribution in the sheet changes and the sheet usually becomes thinner; the drawbead causes an extra plastic thickness strain. The blankholder is lifted by a liftforce which appears when the material flows through the drawbead. In finite element simulations of the deep drawing process the drawbead geometry’s are seldom included because of the small radii. As a result of these small radii a very large number of elements is required to describe the geometry accurately. Therefore an equivalent drawbead model has been developed. In this model the geometry of the drawbead is replaced by a line on the tool surface. When material passes this ‘drawbead line’ an additional D.B.R.F. and a plastic thickness strain is added to the material. At the same time the liftforce is subtracted from the total blankholder force. In this report two different mathematical descriptions of the equivalent drawbead model are pointed out. The implementation of the D.B.R.F. and the liftforce are the same for both descriptions. The implementation of the plastic thickness strain differs for both descriptions. In the first descriptions the algorithm is based on adding stresses to the right hand side of the finite element equations. In the second description the algorithm is based on a penalty constrained method. Simulations are done with both models. From the results of these simulations it can be concluded the algorithm based on the penalty constrained method gives the best approximation of the prescribed plastic thickness strain. Table of contents 3