Wrinkling analysis for forming limit of tube bending processes

Thin-walled tube bending processes may produce a wrinkling phenomenon if the process parameters are inappropriate, especially for tubes with large diameter and thin wall thickness. How to predict this phenomenon rapidly and accurately is one of the urgent key problems to be solved for the development of this process at present. In this paper, a wrinkling wave function is proposed and a simplified wrinkling prediction model to predict the minimum bending radius for tubes is established based on thin-shell theory, forming theory, the energy principle and wave function. The minimum bending radius calculated according to the method established is in agreement with data reported in the literature. Furthermore, effects of parameters on the minimum bending radius are also analyzed: (1) the influence of bending angle on the minimum bending radius is negligibly small; (2) the effect of geometrical dimensions and material properties of tubes on the minimum bending radius is significantly large; (3) the minimum bending radius becomes larger with the original radius and strength coefficient of tubes increasing, whereas with the wall thickness and strain hardening exponent decreasing. The results are helpful to the design and optimization of the relevant processes in practice.