Numerical and experimental analysis of elastic–plastic pure bending and springback of beams of asymmetric cross-sections

• Bending and springback of beams with asymmetric cross-sections are considered.
• Algorithms for updating stress–strain relations are presented.
• A particular set of forming parameters to obtain planar deformations of asymmetrical beams is determined.
• Experimentally obtained results showed an excellent agreement with the theoretically predicted results.

We present a procedure for numerical computation of elastic–plastic bending and springback of beams with asymmetric cross-sections. Elastic-nonlinear hardening behavior of the material is assumed and both isotropic and kinematic hardening models are considered. The strains are described as a function of rotation and shift of the neutral axis and the curvature of the beam. Exact geometric expressions for large deflections and large rotations are taken into account during bending process. A complete loading history is taken into account including the effect of the local loading during the monotonic decrease of the load. Numerical examples confirm a strong influence of the load on the final and springback rotation of the neutral axis, its shift, and curvature of the beam for different cross-sections and materials. A custom made forming tool was designed and manufactured in-house to experimentally evaluate the proposed solution procedure. It is shown that relative difference between experimentally and theoretically predicted results of the final radius of curvature of the formed beam is 0.177±0.683%, if also the effect of pre-strain on elastic modulus is taken into consideration.