Adaptable dies to minimize distortion in non-axisymmetric extrusions

An upper bound model for the extrusion of a round billet into a round-corner rectangular product has been developed for use with the adaptable die design method. The analysis shows the use of the adaptable die design method for minimizing distortion in the extrusion product. The flow fields are a modification of previous axisymmetric models, but are extended to permit rotational movement to occur during deformation. The extrusion die is analyzed in two segments. A streamlined segment imposes the deformation, and a bearing length segment is attached at the end. The power terms associated with the deformation process are derived. Similar to the axisymmetric analysis, the use of a streamlined die shape at the entrance and exit regions for the deformation zone produces no internal shear power losses along the two internal surfaces, which separate the initial and final rigid body material from the deformation region. The extrusion die shapes are determined by the adaptable die design method, where adjustable coefficients for characterizing the streamlined die are found by minimizing the volumetric effective strain rate deviation. The adaptable extrusion die shapes, based on minimizing the volumetric effective strain rate deviation in the deformation zone, produce minimum distortion in the extrusion product and are equivalent to a controlled strain rate die shape. Confirmation is obtained by analyzing the results from three-dimensional finite element models for extrusion through the adaptable die shapes. The analysis presented can also be modified to analyze other non-reentrant extrusion product shapes.