A refined method for estimating the interlayer shear modulus by correcting the deflection of polymer composite specimens

Abstract

Shear and interlayer characteristics of polymer fiber composites, in contrast to metals, play a decisive role in the deformation and fracture processes. In this regard, special methods have been developed to determine the interlayer bending strength of a short beam and the interlayer shear modulus by deflection correction. At the same time, the accepted hypotheses about the distribution of shear stresses, for example, by the Zhuravsky formula, are too simple and do not provide the determination of the correction and calculation of the shear modulus with a rather 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 the shear stresses occurring in the beam, as well as their distribution over the height and width of the beam, 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. We present an exact approximation of the strict solution by simpier quadratic dependences, which provides determination of the deflection correction and the shear modulus with a high accuracy. It is shown that for real composite beam-type specimens the use of the refined shear stress distribution with allowance for the heterogeneity of stresses along the beam width gives a negligibly small correction for the deflection compared to the simplified parabolic distribution according to the Zhuravsky formula. The numerical verification was carried out using the finite element. Special tests of fiberglass specimens of different widths for three-point bending also showed no increase in the deflection with increasing beam width, which indicates an insignificant influence of the heterogeneity of tangential stresses on the deflection.