Journal of Materials Processing Technology 176 (2006) 70–76 A numerical investigation on the use of drawbeads to minimize ear formation in deep drawing Vahid Vahdat, Sridhar Santhanam ∗ , Young W. Chun Mechanical Engineering Department, Villanova University, Villanova, PA 19085, United States Received 18 July 2005; received in revised form 29 November 2005; accepted 16 January 2006 Abstract In the deep drawing of cups, the earing defect is caused by planar anisotropy in the sheet and friction between the blank and punch/die. In the past, several research efforts have been directed toward developing strategies for eliminating or mitigating the formation of ears. In this paper, we consider the concept of using drawbeads to minimize ear formation, thus overcoming the effects of anisotropy and friction. The study conducted and described here is entirely numerical. The object is to establish a numerical algorithm that will lead to an optimal drawbead contour that minimizes the earing defect in deep drawing. The algorithm is iterative in nature and involves performing simulations of the deep drawing process using finite element analysis, constructing an error metric at the end of each iteration, and utilizing the error metric to adjust the drawbead contour at the end of each iteration. The cycle is repeated until the error metric satisfies a preset convergence criterion. This iterative design process leads to an optimal drawbead contour. Several different test problems are considered, including the drawing of circular and square cups. Simulation results are very encouraging with reasonable number of iterations to arrive at the optimal drawbead contour. © 2006 Elsevier B.V. All rights reserved. Keywords: Deep drawing; Earing; Drawbead; Blank; Anisotropy; Finite element 1. Introduction A problem that has attracted some attention in the recent past is the elimination or mitigation of the earing defect in the deep drawing process. Most parts made by this sheet metal forming process are either cylindrical or box shaped like kitchen utensils, beverage cans, pots, etc. These parts are made by forcing a flat sheet blank into a die cavity by a punch. The sheet metal blank is held between the die and the blank holder. The blank holder is loaded by a blank holder force (BHF) to prevent wrinkling and to control the flow of the sheet metal. The sheet metal takes the shape of the punch and the die when it is pushed into the die cavity by the punch, thus forming a cup. The top edges of a cup formed by deep drawing are not usually even. They are often wavy having crests and valleys. These projections along the perimeter of the cup are called ears. Earing is caused primarily by planar anisotropy in the sheet. Anisotropy is acquired during the thermo-mechanical process- ing of the sheet, which results in different material characteristics ∗ Corresponding author. Tel.: +1 510 519 7924; fax: +1 610 519 7312. E-mail address: sridhar.santhanam@villanova.edu (S. Santhanam). along different directions of the rolled sheet. Earing is undesir- able, as it requires some metal to be trimmed from the top of the cup. This consumes money and time. One approach to avoid this problem is to utilize a suitably contoured drawbead that controls the flow of material into the die, thereby producing a final cup shape that is ear-less. An experimental trial and error process to determine the best drawbead contour for making a defect-free cup is very expensive and time consuming. Numerical simula- tion tools present an attractive and effective alternative. An important aspect of numerical simulation is the use of an effective model for the anisotropic plastic flow of sheet metals. A lot of research has been devoted to characterizing anisotropy of sheet metal and in particular on developing a useful yield function for plastic flow. The quadratic anisotropic yield crite- rion of Hill [1] has been widely used. However this model does not predict the behavior of certain metals, including some alu- minum alloys. A number of non-quadratic yield criteria were subsequently developed including Gotoh [2], Bassani [3], and Logan and Hosford [4]. None of these criteria are effective for modeling planar anisotropy in sheet metal under general load- ing conditions. Barlat and Lian [5] proposed a non-quadratic planar anisotropic yield function where three parameters de- scribe the anisotropy in the sheet metal. This yield function is 0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.01.017