The Influence of Dimensional-Type Mathematical Model for Cylindrical Deep Drawing on the Distribution of Extreme Unitary Stresses

Abstract

The The 3D modelling, compared to the 2D-symmetrical rotation (axial) modelling, is much more complex and one of the reasons for this, with a view to plastic anisotropy, is that 3D modelling adopts normal anisotropy while 2D modelling adopts symmetrical rotational anisotropy. When the finite element method is used for numerical solving, the number of nodes in the discretization network is much larger in the 3D modelling and even when using last generation PCs the processing time is much longer. For this reason, for expedite calculations, as those needed to establish, in a first approximation, the optimal parameters of a deep drawing process I analysed in this paper the possibility to use the 2D-symmetrical rotation (axial) modelling. In a first phase, we intend to create a representative set of deep drawing problems and then to solve them through numerical simulations using Ansys package, using both the 3D modelling, in cartesian coordinates, and the 2D-symmetrical rotation (axial) modelling, in cylindrical coordinates. Runnings shall be carried out for various refinement levels of discretization network in finite elements. The calculation times shall be compared for these two modellings and following the comparative analysis of the results we can deduce the errors entered in the 2D modelling. These errors shall be assessed by analysing and comparing the extreme unitary stresses as follows: normal stress by the Ox and Oy axes , in the 3D modelling, and in the 2D modelling by the Ox / Oy axis; shear stresses by the XZ and YZ planes, in the 3D modelling and in the 2D modelling by the XZ plane.