Analysis of the air-bending test using finite-element simulation : application to steel sheets

Abstract : A full mechanical analysis of the air-bending test was performed in order to determine the stress and strain fields involved in this test. Two low alloy TRIP-aided steels and two bending conditions were considered: the first one is commonly used to test the bending ability (sheet thickness 1.6 mm, bending angle up to 150°) whereas the second one involves fairly different loading conditions (sheet thickness 0.75 mm, bending angle up to 180°). Constitutive equations were determined from tensile and shearing tests to accurately represent the flow behaviour of the sheet during both bending and unloading. Predictions from the two-dimensional simulation of air-bending were in good agreement with all experimental measurements (load vs. displacement curves, hardness and strain field measurements of bent then unloaded specimens). While neither using three-dimensional simulations nor representing the contact between punch and sheet were necessary, an anisotropic yield criterion with both isotropic and kinematic contributions to hardening is required. In particular, accounting for kinematic hardening is necessary for the correct simulation of air-bending of a prestrained material. The strain path experienced by the material both at the apex and close to the initial mid-thickness is then discussed. This method can be applied to assess local mechanical loading, prestrain effects and possibility of damage development to any high strength steel grade.