Rupture prediction for induction bends under opening mode bending with emphasis on strain localization

Abstract This study focuses on the opening mode of induction bends; this mode represents the deformation outside a bend. Bending experiments on induction bends are shown and the manner of failure of these bends was investigated. Ruptures occur at the intrados of the bends, which undergo tensile stress, and accompany the local reduction of wall thickness, i.e., necking that indicates strain localization. By implementing finite element analysis (FEA), it was shown that the rupture is dominated not by the fracture criterion of material but by the initiation of strain localization that is a deformation characteristic of the material. These ruptures are due to the rapid increase of local strain after the initiation of strain localization and suddenly reach the fracture criterion. For the evaluation of the deformability of the bends, a method based on FEA that can predict the displacement at the rupture is proposed. We show that the yield surface shape and the true stress–strain relationship after uniform elongation have to be defined on the basis of the actual properties of the bend material. The von Mises yield criterion, which is commonly used in cases of elastic–plastic FEA, could not predict the rupture and overestimated the deformability. In contrast, a yield surface obtained by performing tensile tests on a biaxial specimen could predict the rupture. The prediction of the rupture was accomplished by an inverse calibration method that determined the true stress-strain relationship after uniform elongation. As an alternative to the inverse calibration, a simple extrapolation method of the true stress-strain relationship after uniform elongation which can predict the rupture is proposed.