A hybrid method for accurate prediction of multiple instability modes in in-plane roll-bending of strip

The in-plane roll-bending of strip (IRS) is a flexible forming process to produce ring parts with advantages of low forming forces, low material waste and good flexibility. However, if deformation condition is inappropriate, it results in several instability modes including external wrinkling, internal wrinkling, turning-I and turning-II. Solely using pure analytical solution, implicit finite element method (FEM) or explicit FEM cannot predict all these instability modes of the strip. In this study, a new hybrid method is proposed to accurately predict all these instability modes in IRS. First, using two analytical models with two simple support conditions to simplify the actual roll-bending conditions, the eigenvalue buckling analysis and the analytical solution analysis are conducted to generate four kinds of buckling modes, respectively, and a series of imperfections are defined in the shapes of these buckling modes. Second, assigning these geometrical imperfections into the perfect geometry of strip, a series of hybrid FE models for IRS are established. Four specific case studies of external wrinkling, internal wrinkling, turning-I and turning-II are carried out. By comparing with corresponding experimental results, an appropriate imperfection and an optimal scaling factor A_i are obtained. Third, to validate our proposed method, the hybrid method is applied to five cases of arbitrary experimental condition. The comparisons between the predicted results and experiments show that the proposed method is reliable to accurately predict all instability modes in IRS.