Refined Method for Estimating the Interlayer Shear Modulus by Correcting the Deflection of Polymer Composite Specimens

Abstract

The shear and interlayer characteristics of polymer fiber composites, in contrast to metals, play a decisive role in the deformation and fracture processes. In view of this, special methods have been developed to determine the interlayer flexional strength of a short beam and the interlayer shear modulus by the deflection correction. At the same time, the accepted hypotheses about the distribution of shear stresses, for example, those based on the Zhuravsky formula, are too simple and do not provide the determination of the correction and calculation of the shear modulus with a high accuracy. The use of the Saint-Venant–Lekhnitzky solution for an orthotropic beam instead of the simplest parabolic distribution potentially makes it possible to take into account all shear stresses occurring in a beam and their distribution over the beam height and width, which should increase the accuracy of determining the deflection correction and interlayer shear modulus, respectively. Since the strict solution is presented in a series of hyperbolic functions, its practical use is rather difficult. In this study, an exact approximation of the strict solution by simpler quadratic dependences is proposed, which makes it possible to determine the deflection correction and shear modulus with a high accuracy. It is shown using the proposed approximation that, for real beam-type composite specimens, the use of the refined shear stress distribution with allowance for the nonuniformity of stresses over the beam width yields a deflection correction negligibly small as compared with the case of the simplified parabolic distribution according to the Zhuravsky formula. The numerical verification using the finite element method has been carried out. Special three-point bending tests of fiberglass specimens of different widths have also showed no deflection growth with increasing beam width, which points out an insignificant impact of the heterogeneity of shear stresses on the deflection.