An analytic model for tube bending springback considering different parameter variations of Ti-alloy tubes

Springback after unloading is an issue that directly reduces the accuracy of bent tubes, especially for Ti-alloy tubes which are of high strength and low Young's modulus. The Young's modulus, E; wall thickness, t; and neutral layer, D_e, of a tube vary during the bending process. These variations may influence the bending deformation of components, thus on springback. Considering these variations, an analytic elastic-plastic tube bending springback model was established in this study based on the static equilibrium condition. When these variations were considered individually or combined, the resulting springback angles were all larger and closer to the experimental results than the results when variations were not considered for a D6 mm × t0.6 mm Ti-3Al-2.5V Ti-alloy tube. The t variation contribution is the largest and decreases the prediction error by 41.2%-45.3%. D_e variation ranks second and decreases the error by 21.2%-25.3%. E variation is the least significant, decreasing the error by only 2.4%. Furthermore, the influence of the stable Young's modulus E_a on the springback is larger than the initial Young's modulus E₀. Therefore, for the bending springback of tubes with a small difference between E₀ and E_a and under a normal bending radius, E variation effects can be neglected. While for tubes with large differences between E₀ and E_a, and high springback prediction requirements, the E variation should be replaced by E_a. The influences of the initial tube sizes, material properties and bent tube sizes of the Ti-3Al-2.5V tube on springback were obtained using the newly developed model.