Analytical Prediction of Large Radius Bending by Circular Approximation

Abstract

An accurate analytical method is normally the preferred choice in engineering practice since this approach usually does not require additional software and can be applied for different situations. A number of analytical methods have been proposed for the air bending process, however, none of them has the capacity to deal with large radius bending. Large radius bending is characterized by a high ratio of the punch radius to the die opening and it is often applied for high-strength steels because of their limited bendability. This bending mode is used to fulfill the imposed level of maximum strain during the forming process. This contribution develops an analytical solution based on the assumption that the bent plate profile can be represented by two straight lines and a circular segment. Three different hardening laws—linear, Swift, and Aerens—are used for the bending moment calculation. Unit moment measurements are used in order to avoid extrapolation of hardening curves obtained by tensile testing. The model is compared with a wide range of experiments using the coefficient of determination, relative and absolute average errors, in addition to the mean standard error. The analytical prediction based on the circular approximation is found to be an accurate and robust tool for the calculation of the major bending characteristics for large radius air bending of high-strength steels.