Springback equation of small curvature plane bending

A new analytical method for springback of small curvature plane bending is addressed with unloading rule of classical elastic-plastic theory and principle of strain superposition. We start from strain analysis of plane bending which has initial curvature, and the theoretic derivation is on the widely applicable basic hypotheses. The results are unified to geometry constraint equations and springback equation of plane bending, which can be evolved to straight beam plane bending and pure bending. The expanding and setting round process is one of the situations of plane bending, which is a bend-stretching process of plane curved beam. In the present study, springback equation of plane bending is used to analyze the expanding and setting round process, and the results agree with the experimental data. With a reasonable prediction accuracy, this new analytical method for springback of plane bending can meet the needs of applications in engineering.