Boundary conditions applied on bearing corner in direct aluminum extrusion

Finite element analysis in aluminum extrusion is faced by several problems such as number of degrees of freedom, calculation time, large deformation and flow conservation. The problem of large deformation is overcome by applying the Eulerian formulation. But the problems concerning number of degrees of freedom, calculation time can be overcome by the model simplification especially at the bearing corner. On the one hand, detailed modeling of the bearing corner will increase the complexity of the analysis. On the other hand, simplified modeling of the bearing corner will face problems such as locking of the corner node and flow conservation. Therefore, boundary conditions will be applied at the corner node in order to solve the problem of its locking and to satisfy the aluminum flow conservation. These boundary conditions include normal and constraint equation. This paper focuses on the calculation of the normal with different elements such as plane strain, axisymmetric and tetrahedron elements. The constraint equation at different positions of the corner node is determined for a plane strain element only. The extrusion force and average exit velocity are investigated and compared with the triple node method and reference model. Where, in the reference model the contact boundary condition is applied between the rigid die and aluminum. Eulerian formulation is applied in finite element analysis unless in the reference model the Arbitrary Lagrangian Eulerian formulation is applied.