Insight into the deformation transition effect in free bending of tubes

•The deformation transition behavior in tube free bending is analytically solved.•A new correction method employing a modified U-R relationship is proposed.•The correction method is validated to improve the forming accuracy of bent tubes. The deformation transition has a significant impact on the forming accuracy in tube free bending. In this paper, the formation mechanism of deformation transition in free bending is analytically revealed. Considering the bending angle and the length of forming area in the transition segment, a modified relationship between the bending die deviation U and the bending radius R is proposed by introducing a new correction factor k. The developed correction method is carefully verified by free bending experiments and simulations using AA5052 tubes, and further, the influence mechanism of the deformation transition in free bending is clarified. This study provides new insights into the understanding of deformation transition in free bending, providing an effective way to design more accurate and robust bending processes for improving product quality.