Abstract: It is well known that bending of the thin-walled tubes when continuous straightening induces ovalization to the tube cross-section (that is called the Brazier effect), the maximal cross-sectional deformation as the main straightening technical parameter, is used to control the deformation degree under buckling limit, however, it is usually carried out based on the experiential data and chart by skilled labourers, whose art is based on long experience and experiments, the special theoretical model of the maximal cross-sectional deformation is immediately necessary. Therefore, the normal strain components are firstly obtained for the Brazier effect of the thin-walled tubes, and the strain energy of the thin-walled tube per unit length is got subsequently based on the elastic-plastic theory and relevant hypothesis of the thin-walled member, finally the mathematical model of maximal cross-sectional deformation in terms of curvature, material properties and geometric parameters of a tube, is presented by the principle of minimum potential energy. In order to certify whether it is correct, we have done some local experiments and also dynamic simulations by ANSYS/LS-DYNA, the results have shown that that the model is correct. This research can provide the basis for optimizing straightening technical parameters and completing the theory of thin-walled tube straightening.

Key words: Brazier effect, continuous straightening, maximal cross-sectional deformation, thin-walled tube