An imperfection-based perturbation method for plastic wrinkling prediction in tube bending under multi-die constraints

The prediction of plastic wrinkling in sheet metal forming process with multi-die constraints is difficult. In this paper, taking rotary draw bending of large diameter thin-walled Al-alloy tube bending as research objective, combined with initial imperfection and finite element (FE) method, an imperfection-based perturbation method is proposed to accurately predict wrinkling in tube bending process under multi-die constraints. Considering the distribution of compressive stress in the tube bending process, two simplified models, i.e., tube under pure bending and tube under axial compression, are employed to obtain the buckling modes of a tube in rotary draw bending. By using the eigenvalue buckling analysis and Timoshenko's energy method, two kinds of geometrical imperfection are generated based on the above simplified models, respectively; These geometrical imperfections are embedded into a series of explicit FE models to induce wrinkling in tube bending under multi-die constraints; By updating the wavelength and the magnitude of the imperfection, the imperfection leading to the lowest deformation energy is chosen as the appropriate imperfection; The predictive capability of the imperfection-based perturbation method is validated by using two types of bending experiments, viz., bending with wrinkling and wrinkling-free bending. It is shown that the proposed predictor is more sensitive to the wrinkling compared with the pure explicit FE results with perfect geometry. By providing an over prediction of wrinkling, a "lower bound" forming conditions are obtained, which ensures a reliable wrinkling-based process design for complicated forming process under multi-die constraints.