A New in-Plane Bending Test to Determine Flow Curves for Materials with Low Uniform Elongation

Abstract

BackgroundFlow curves can easily be obtained by uniaxial tensile tests, but strains are then limited by diffuse necking. For many applications, the flow stress must be known above this limit.ObjectiveThe main objective of this paper is to obtain flow curves for material with low uniform elongation to relatively high strains compared to a uniaxial tensile test.MethodA novel in-plane sheet bending experiment and stress evaluation procedure is presented. The developed bending device can be mounted in a tensile test machine and can produce very high bending curvatures compared to previously proposed pure bending setups. The bending angle and curvature are obtained by image processing and the bending moment is calculated directly from the force measured from the tensile test machine and the bending angle. The moment–curvature relation is used to determine the uniaxial stress–strain relation using an analytical approach, without presuming any hardening model. The bending process and the analytical procedure are validated by a numerical simulation as well as by experiments.ResultsThe numerical validation shows good agreement between the stress–strain curve obtained from the bending process and that of the uniaxial input flow curve up to 12% strain. Experimentally the model is validated by comparing the stress–strain curve obtained from the bending test with the results directly obtained from a tensile test for mild steel. Good agreement is observed up to 12% strain. As an application example, bending tests were performed on a martensitic steel (MS) with low uniform strain (less than 3%). For this material, flow curves could be obtained up to relatively high strains (~12%), compared to a tensile test.ConclusionThis bending test setup allows to study materials with low uniform elongation up to significantly higher strains than are readily obtained in a tensile test.