Study of tube flaring ratio and strain rate in the tube flaring process

This paper combines the volume incompressible condition, Levy-Mises equation, and explicit die profile description, to provide analytical expressions relating the tube flaring ratio and tube end strain rate to the tool stroke and velocity in the tube flaring process. An elasto-plastic finite element method based on the updated Lagrangian formulation is developed to investigate the flaring tube end radius, tube end downward depth, and tube end strain rate. The high non-linearity of the process was taken into account in an incremental manner and an extended r(min) technique was used to limit the size of each increment within a linear relation. A flaring experiment, using 15 mm arc and 45degrees semi-cone angle curves to describe the head profile, was conducted to validate the theoretical and simulated results. It was found that the relations, tube end flaring ratio and tube end downward depth ratio to the tool stroke depth, showed good agreement with theory, finite element prediction, and experiment. Tube end strain rate predicted by the FEM also has the same trend as the theoretical results. Moreover, the analytical expressions will be able to provide a good reference guide for the tube flaring forming in the industrial category. (C) 2003 Elsevier B.V. All rights reserved.