Analytical derivation of earing in circular cup drawing based on simple tension properties

In the circular cylindrical cup drawing process of sheet materials, an earing profile develops, incurred by the planar anisotropic properties of sheets. Therefore, proper analysis of earing in cup drawing is important to evaluate anisotropic properties and also to control the development of earing. Even though anisotropic properties are commonly measured in the simple tension test, deformation in circular cylindrical cup drawing is in a near plane strain mode (at the flange) so that numerical simulations utilizing yield functions are common practices to analyze earing. In this work, simplified analytical derivation of earing development in circular cylindrical cup drawing is proposed, based on two simple tension anisotropic properties: the yield stress and the r-value. Good performance of the analytical derivation was verified for AA2090-T3, which has strong anisotropy and six ears in cup drawing. Since the current approach directly utilizes measured simple tension data without involving any yield functions, computational cost is significantly lower. Besides, the current derivation can handle any set of detailed anisotropic measurements in the simple tension test, unlike numerical approaches involving yield functions, which need the development of sophisticated yield functions in the first place.