Determining the effective characteristics of a composite with hollow fiber at longitudinal elongation

Abstract

When solving problems on the mechanics of composites, it is convenient to use a composite model in the form of a continuous homogeneous medium with effective constants, which adequately reflect its most essential characteristics. Modern engineering and construction commonly use the composites, reinforced with hollow fibers. Unknown for today are the analytical dependences for the effective elastic constants of such composite materials with transtropic components. The task on constructing such dependences is resolved in this paper. We have derived analytical dependences for the effective longitudinal modulus of elasticity and the Poisson’s coefficient in the unidirectional fiber composite, consisting of a transtropic matrix and hollow fiber. The composite is simulated by a solid uniform transtropic material. The conditions for a perfect connection are satisfied at the interphase surfaces. In order to obtain the analytical dependences, we have solved two boundary problems: on the longitudinal elongation of a composite cylinder, whose components are the transtropic matrix and hollow fiber, and a solid homogeneous cylinder that models the transtropic composite. The application of conditions for displacements alignment and stresses, found by solving these problems, provided an opportunity to derive formulae for the effective longitudinal modulus of elasticity and Poisson’s coefficient. These formulae reflect the dependences of effective characteristics of a composite on elastic characteristics of the matrix, fibers, and volumetric shares of the fiber and the cavity inside it. We have compared results of calculations using the formulae derived with the calculation results based on previously known ratios for the isotropic ratios. This comparison has shown that their relative deviation does not exceed one percent. Application of the obtained dependences makes it possible to design structures with elements made from the composite materials