An analytic model for TC4 titanium alloy tube bending springback considering temperature effects

Abstract Existing theoretical models for tube bending springback can hardly accurately predict the springback under warm bending conditions. Thus, a springback model was proposed by considering temperature effects. Specifically, the influence of temperature on the material performance was analyzed. Secondly, the area formulas of the tensile plastic zone and elastic zone of the outside section as well as that of the compressive plastic zone of the inside section during the formation of tube bending under temperature effects were derived. Furthermore, the stress distribution characteristics of the above zones were calculated. Then, a theoretical springback model of tube warm bending springback angle was established according to the mechanical equilibrium equation in the springback process. This new model was verified by finite element simulations and warm bending forming experiments of TC4 titanium alloy tubes. Results show that the prediction accuracy of this new model has reached 93%. Moreover, a higher temperature results in a smaller springback angle because it reduces tubes’ elastic layer area and axial stress. Above all, this research clarifies the problem of the unclear springback mechanism under the effect of long-term temperature rise, which provides a reference for subsequent research.