Finite element simulation of multi-stage deep drawing is performed in ABAQUS software, version 6-9-1. Analysis of the drawing process is based on the axisymmetric condition.
Hence, only the right half of the tools such as punch, die and blank holder is modeled according Fig. 2.
The continuum or solid elements, the shell elements and the membrane elements are three main types of finite elements that can be used in the computer modeling of the blank and tooling elements, and various references may be cited in the development of element formulations capable of modeling large deformation kinematics in the total, updated or corotational sense for these finite element types [8].
The finite element meshes of the forming tools are usually intended to impose the forming loads to the sheet metal through the forming interface.
Because of the fact that the forming tools should be, theoretically, designed to be rigid and the die-face deformations should be elastic with minimal shape changes, Hence, tools deformations are negligible and have been modeled as discrete rigid parts and only the surface geometry of the forming tools are included in simulation models.
Also, sheet is modeled as deformable shell. Entire modeling data is taken from designed dies dimensions and has presented in Table II. Mechanical properties of sheet are introduced to software from Table I and Fig. 3.
Since, majority of metal forming processes are quasi-static problems, therefore, Dynamic Explicit method is suitable for these types of problems. Penalty function method was used to treat the contact algorithm.
The friction coefficient between the punch and sheet was assumed 0.2 and sheet with die and blank holder was 0.1.