Determination of the Shear Modulus of Orthotropic Thin Sheets With the Anticlastic-Plate-Bending Experiment

Abstract

The shear modulus of orthotropic thin sheets from three advanced high-strength steels (AHSS) is measured using the anticlastic-plate-bending (APB) experiment. In APB, a thin square plate is loaded by point forces at its four corners, paired in opposite directions. It thus assumes the shape of a hyperbolic paraboloid, at least initially. The principal stress directions coincide with the plate diagonals, and the principal stresses are equal and opposite. Hence, at 45 deg to these, a state of pure shear exists. A finite element (FE) study of APB is reported first, using both elastic and elastoplastic material models. This study confirms the theoretical predictions of the stress field that develops in APB. The numerical model is then treated as a virtual experiment. The input shear modulus is recovered through this procedure, thus validating this approach. A major conclusion from this numerical study is that the shear modulus for these three AHSS should be determined before the shear strain exceeds 2 × 10−4 (or 200 με). Subsequently, APB experiments are performed on the three AHSS (DP 980, DP 1180 and MS 1700). The responses recorded in these experiments confirm that over 3 × 10−4 strain (or 300 με) the response differs from the theoretically expected one, due to excessive deflections, yielding, changing contact conditions with the loading rollers and, in general, the breaking of symmetry. But under that limit, the responses recorded are linear, and can be used to determine the shear modulus.