On the Measurement of Shear Modulus of an Orthotropic Plate by Torsional Testing

Abstract

Many of the FRP plates used frequently among various types of composite materials are orthotropic. While the shear modulus G₁₂ in the in-plane shear deformation of an orthotropic plate can be measured by the plate-twisting test method, it is not easy to measure shear moduli G₁₃, G₂₃ in the out-of-plane shear deformation.
This report gives an account on the method to measure these shear moduli by means of torsional testing of an orthotropic rectangular bar.
The relation between the torque M and the angle of rotation per unit length θ in the case when a rectangular bar is cut out along one principal axis of the plane, for instance along the l-axis direction, and subjected to the torsional testing, is as follows:
M=G₁₂θh³b/3F, F=1-192/π⁵h/βbtanhπ/2βb/h
where h is the thickness of cross section, b the breadth of cross section and β² the value of G₁₃/G₁₂.
The values of G₁₂, G₁₃ can be calculated from the forgoing equation by carrying out the torsional testing on two bars of b/h≈1 and b/h=5∼10.
G₁₃(G₂₃) is the value related to the interlaminar shear characteristics of a composite material, and the measurement of this G₁₃ is important in studying the physical properties of composite materials, for instance, in investigating the mechanism of decrease in stiffness due to fatigue.
The present report also refers to the method of torsional testing using Instron type testing machine and the results of the measurement of G on FRP plates.