Calculation of dispersed reinforced polymer composite material linear temperature expansion effective coefficients

Аuthors

Fayzullin K. V.^*, Sidorov I. N.^**, Danilaev M. P.^***

Kazan National Research Technical University named after A.N. Tupolev, Kazan, Russia

*e-mail: KVFayzullin@kai.ru
**e-mail: insidorov1955@mail.ru
***e-mail: MPDanilaev@kai.ru

Abstract

Stringent requirements for the reproducibility of physical and mechanical properties are imposed on dispersion-reinforced polymer composite materials (DRPCMs) used in aerospace engineering. One of the approaches to improving the reproducibility of the complex of physical and mechanical properties of dispersion reinforced polymer composite materials (DRPCMs) consists in forming a polymer shell on the surface of dispersed filler particles, i.e., their encapsulation. Such a shell enhances the adhesion of the particles to the polymer matrix and, at the same time, affects the mechanical behaviour of the DRPCM, including its coefficient of linear thermal expansion (CLTE). This paper presents a mathematical model for calculating the effective CLTE of DRPCMs with a small relative volume fraction of submicron filler particles encapsulated by a polymer. The asymptotic homogenization method for periodic media is employed, introducing "fast" and "slow" variables. Within a representative periodicity cell consisting of an isotropic elastic core (filler particle) coated with an outer isotropic shell of constant thickness, the equilibrium equations, interface continuity conditions, and periodicity conditions are formulated. An explicit expression for the effective CLTE of the composite is derived in terms of the effective bulk modulus, the volume fractions of the constituents, and their respective elastic and thermal expansion properties. An algorithm for computing the effective CLTE based on the effective bulk modulus is developed. It is shown that the CLTE of the composition decreases with increasing shell thickness, which is attributed to the lower elastic modulus of the shell polymer relative to those of the matrix material and fillers particles.

Keywords:

dispersion-reinforced polymer composite material; effective coefficient of linear thermal expansion

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