RESUMO Os materiais compósitos comumente apresentam delgadas regiões ou interfases localizadas entre a matriz e as inclusões. Estas interfases têm influência no comportamento efetivo do compósito. Em diversas aplicações, os compósitos estão sujeitos a variações significativas de temperatura e, consequentemente, a condutividade térmica efetiva desses materiais se torna parâmetro essencial para compreensão do seu comportamento. O objetivo desse trabalho é determinar a influência de interfases na condutividade térmica efetiva de compósitos reforçados com fibras unidirecionais distribuídas periodicamente, utilizando a formulação paramétrica da Teoria de Volumes Finitos. Para isso, são avaliados os efeitos da espessura e condutividade térmica da interfase, assim como do raio da fibra e de sua fração volumétrica. Compósitos com fibras naturais são apresentados dentre os exemplos analisados. Os resultados obtidos com a Teoria de Volumes Finitos são confrontados com outros encontrados por métodos numéricos ou experimentos. Desse modo, observa-se que a interfase possui mais influência quanto maior for a fração volumétrica de fibras e quanto menor o raio das mesmas. Quanto mais espessa a interfase, mais suas propriedades influenciam a condutividade térmica efetiva do compósito, quando a fração volumétrica de fibras é mantida constante. Conclui-se que os efeitos de interfase sobre o comportamento térmico de compósitos são de extrema importância e, consequentemente, eles precisam ser considerados para proporcionar predições consistentes e realísticas.

ABSTRACT Composite materials commonly present thin regions or interphases located between the matrix and inclusions. These interphases influence the effective behavior of the composite. In many applications, composite materials are submitted to significant temperature variations and, consequently, the effective thermal conductivity of these materials becomes essential to understand their behavior. The purpose of this paper is to determine the influence of interphases on the effective thermal conductivity of periodic fiber reinforced composites, by using the parametric finite-volume theory. To this end, the effects of the thickness and thermal conductivity of the interphase are evaluated, as well as the fiber radius and its volumetric fraction. Composites with natural fibers are included in the analyzed examples. The results obtained with finite-volume theory are compared with other results found by numerical methods or experiments. Thus, it is noted that the interphase has a more pronounced influence on the composite effective thermal conductivity for larger fiber volume fraction and smaller fiber radius. The larger the interphase thickness, more its properties influence the effective thermal conductivity, when the fiber volume fraction is fixed. In conclusion, the interphase effects on the behavior of composite materials are extremely important and, consequently, they need to be considered to allow consistent and realistic predictions.

Abstract In this paper, a micromechanical extension of the finite-volume direct averaging micromechanics theory (FVDAM) is presented for evaluation of the homogenized relaxation moduli of linear viscoelastic unidirectional fiber reinforced composites with periodic microstructures. Such materials are assumed as composed of repeating unit cell with arbitrary internal architectural arrangements of fibers coated by thin flexible interphases. These interphases are replaced by equivalent imperfect interface elements with imposed continuity in tractions and discontinuity in displacements. Indeed, the proposed computational procedure allows an easy and efficient treatment of the displacement discontinuity condition across the interfaces. The viscoelastic behavior of the constituent phases is modeled using the generalized Maxwell model. The formulation is particularly derived for the range of small strains, operating directly in the time domain using a numerical incremental time-stepping procedure based on the concept of internal stress variables. The performance of the proposed approach is demonstrated through homogenization of viscoelastic fiber reinforced composites and periodic multilayer materials with flat and wavy architectures.

This paper presents a new micromechanical extension of the parametric finite-volume theory for evaluation of effective thermal conductivities of periodic unidirectional fiber reinforced composites. Such materials are assumed as composed of repeating unit cells with arbitrary internal architectural arrangements of fiber coated by thin interphase with low thermal conductivity. The parametric homogenization approach uses quadrilateral subvolumes for discretization of the repeating unit cell microstructure, thereby allowing an efficient modeling of the details of fibers with arbitrarily shaped cross sections. The interphases are replaced by imperfect interface elements with continuity in normal heat flux and discontinuity in temperature. The performance of the homogenization model is demonstrated for several numerical examples, including two-and three-phase composites with regular squared and hexagonal arrays of fibers. The ability of the model to accurately predict the effective thermal conductivity of those composites is demonstrated by means of comparisons of results obtained using finite-element and analytical solutions.