Extraction of uniaxial stress–strain curve from bending test using DIC measurements

Abstract

This paper presents a novel methodology for the analytical determination of the uniaxial tensile/compressive stress–strain curve derived from the four-point bending test without a pre-assumed constitutive model. While the concept of extracting the stress–strain curve from a bending test is not new, the proposed methodology differs from existing methods by recognising the force equilibrium in a deformed configuration, resulting in a temporal variation of both a bending moment and an axial force. In addition, the deformation of the beam cross-section is taken into account according to the principles of finite strain theory either via Poisson’s ratio or by assuming volume conservation. The crucial data for this methodology are obtained from an experimentally conducted bending test in which the loading force, displacement and strain fields at the top, bottom and front faces of the specimen are measured using a stereo DIC. While the method is completely analytical, it reconstructs the stress–strain curve in discrete form by solving a system of linear equations. While the existing methods for the four-point bending test allow extraction of the stress–strain curve from a single experiment only for strains up to a few per cent, our methodology allows the extraction of the stress–strain curve in tension and compression up to five times the strains obtained with methods that neglect the above features.