45 Flexure Test for Measurement of In-Plane Shear Modulus

Abstract

A new method to obtain the in-plane shear modulus GLT for unidirectional oriented composite materials is proposed. The method is based on an original analytic way for calculating middle point displacement in a 3-point flexure test. The bending–twisting coupling effects in such a test induce the lift-off of the specimen at the fixture supports for some geometrical conditions. Thereby, contact points are located at two opposite points of the specimen. Consequently, new bending moments along the width of the specimen and twisting moments appear. By supposing resultant moments and shear forces per unit length are uniformly distributed, these distributions are calculated for static conditions along longitudinal and transverse cross sections of the specimen. After having expressed strain energy as a function of resultant moments and resultant shear forces per unit length, Second Castigliano’s theorem is applied in order to calculate the middle point displacement. No similar analytic way has been encountered in classical laminated beams theory or in classical laminated plates theory. The displacement obtained in this work and the one obtained from classical laminated beams theory are particularised to the case of 45 fibre orientation. GLT expressions have been derived from those displacement expressions in three ways: two of them from the solution of this work, not considering and considering shear effects, respectively, and the third one from displacement obtained from classical laminated beams theory. Experiments have been made for different geometric conditions in order to test the influence of geometric parameters in experimental results. For span-to-width ratios up to two, the values obtained are quite constant and agree well with the in-plane shear modulus value obtained by the material manufacturer using 45 tensile test.