Plastic buckling and wrinkling behavior of tubes under combined bending and torsion loads

Bending and torsion processes are commonly used for the forming of spatial tubes. However, buckling and wrinkling pose a significant challenge to the high-quality and stable forming of spatial tubes. To reveal the interaction mechanism of bending-torsion buckling (BTB) during the forming process, a quadratic model of BTB under plastic buckling instability was proposed. According to the buckling phenomena of simulation and experiment, the BTB state was divided into three zones, namely Zone I (torsion-dominated zone), Zone II (bending-torsion transition zone), and Zone III (bending-dominated zone). The characteristics of bending-torsion response changes, buckling wrinkle features, and critical load variation in the three zones were studied. Considering the complex interaction of bending and torsional buckling, an analytical method for the critical load of tubes under combined bending-torsion action has been provided. This method is based on the energy approach, incorporating pure bending and pure torsion buckling, along with the quadratic model of BTB. The effectiveness of the proposed theoretical model was verified by finite element (FE) simulation, and the influence of tube geometric characteristics, material parameters, and initial imperfection amplitude on the BTB interaction was discussed.