Dynamic Shear Modulus measurement of thin plates using Torsional Pendulum

Abstract

Material testing is an essential step in the product development as it determines the quality and lifetime estimation of a product. The shear test is conducted to determine the behavior of a material under shear strain. This thesis aims to determine the dynamic shear modulus of fixed-fixed thin plates using a torsional pendulum. Torsion test is chosen to be a better alternative than tensile and four-point shear test to obtain the shear properties because it causes only shear stresses and provides purer form of shear in the material. Experimentally, torsional pendulum is used to find the dynamic shear modulus. The calculation of dynamic shear modulus is based on the standard ASTM E1876-15. The boundary condition of this standard ASTM E1876-15 is free – free. Whereas, this thesis uses fixed-fixed boundary condition. The test specimen is clamped on both ends to suppress other modes of vibration that are existing simultaneously. The standard ASTM E1876-15 is used to determine the dynamic shear modulus of high-density materials. Whereas, this thesis shows a method to obtain the dynamic shear modulus for light-weight materials. It involves a double clamped torsional pendulum with two equal springs operating in parallel. It is assumed that the coupling of these springs is larger than 2, due to simultaneous contraction while twisting. The coupling parameter is z(L/w) and established using FEA analysis. It is approximately 2.108. The shear modulus calculated using the frequency obtained from COMSOL Multiphysics showed 95% agreement to the tabulated shear modulus of that material. The constructed device showed agreement within 97% of the FEA predicted shear modulus. Experiments were limited to the material with length to width ratio of more than 20 and width to thickness ratio of more than 5 as for larger torsion constants the instrument’s frame deforms as well, making frequency measurements inaccurate. The fundamental difference between the method developed in this thesis and the method of the standard ASTM E1876-15 is that the standard uses a spring with distributed mass only, whereas this thesis uses purposely an external inertia. This results in slower vibrations and consequently smaller measurement errors due to viscous damping. This leads to an improvement compared to the standard ASTM E1876-15.