Study of tube flaring forming limit in the tube flaring process

Abstract

The aim of the current paper is to develop analytical theories for industry to predict the relations between the punch stroke, flaring ratio, tube thickness, and flaring forming limit in the tube flaring process. The volume incompressible condition, Levy-Mises equation, and explicit die profile description are combined to derive the analytical expressions relating the flaring ratio to the punch stroke and velocity in the tube flaring process. Then, according to the stress equilibrium state of a small tube element, the relation of the tube-end thickness ratio to the flaring ratio is developed on the basis of Tresca's criterion. Combining these two analytical theories and the fractured thickness at the tube end, the flaring forming limit can be determined. An elastoplastic finite element method based on the updated Lagrangian formulation is also developed to verify the analytical theories. A flaring experiment, using a 30° semi-cone angle to describe the conical die, is conducted to validate the analytical theories and simulated results. It is found that relations such as tube thickness ratio to flaring ratio, and punch stroke ratio to flaring ratio, show good agreement between analytical theories, finite element prediction, and experiment.