Boundary conditions applied on bearing corner in direct aluminum extrusion

Abstract

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. The problems concerning number of degrees of freedom, calculation time can be overcome by simplifying the model 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 bearing corner node and loss of flow conservation. A sharp corner and modified corner geometry are examples of the simplified modeling. Moreover, boundary conditions will be applied at the bearing corner node in order to solve the problem of its locking and to satisfy the flow conservation condition. These boundary conditions include specifying a normal or formulating a constraint equation. This paper focuses on the calculation of the normal or constraint equation that can be applied either at a sharp corner or after modifying the corner geometry. Different elements are checked in this study such as plane strain, axisymmetric and tetrahedron elements. Finally, the extrusion force and average exit velocity are investigated and compared with a reference model. In the reference model a round corner with 0.5mm radius is built, contact boundary condition is applied between the die and aluminum, and Arbitrary Lagrangian Eulerian formulation is applied. The finite element analysis is performed in the in-house implicit finite element code "DiekA".

Coupled analysis of material flow and die deflection in direct aluminum extrusion

“…The contact surface between the die and the backer is divided into two regions C 1 and C 2 where the degrees of freedom of the nodes belonging to region C 1 are connected in the extrusion direction only while those belonging to region C 2 are connected in all directions. A conditional normal is defined at the bearing corner to prevent the change in material flow [2]. The degrees of freedom of the nodes at the interface between the die and billet are connected in all directions except at the bearing and bearing corner.…”

Measuring the Deformation of a Flat Die by Applying a Laser Beam on a Reflecting Surface

“…3Free in the extrusion direction at the outflow. 4A constraint equation is determined at each corner node between its displacement components in order to satisfy the material conservation condition [10].…”

Creep-Fatigue Interaction in the AISI H11 Tool Steel

“…The amplitude of the mechanical load on the die is large, varying from zero to a peak value at the beginning of each ram stroke. When a thermal balance of the press is attained after a small number of ram strokes, the die temperature remains fairly stable [2]. Thus, for simplification purpose, the thermal oscillations of the die may be neglected.…”