Simplified Model for the Influence of Inclusion Aspect Ratio on the Stiffness of Aligned Reinforced Composites

Abstract

A simplified model for the Young’s Modulus of aligned composites possessing spheroidal inclusions, of any aspect ratio α, is developed herein based on a triply periodic array of parallelpiped inclusions. The Young’s Modulus of continuous unidirectional fiber composites (α→∞), particulate composites (α = 1) and periodically bilaminated composites (α = 0) are obtained as limiting cases based on the Parallel-Series and Series-Parallel schemes of analyses. A reinforcing parameter, R, of the inclusion is then identified from the limiting cases such that R ∊ [0,1]. By curve-fitting for a relationship between the reinforcement parameter and the inclusion aspect ratio for α∊ [0,∞], the Young’s Modulus for aligned short fiber composites (α > 1) and aligned flake composites (α < 1) are obtained. For verification, the present model at limiting cases (α =0, 1, ∞) were reduced to other simple models and/or compared with experimental results. For nonlimiting cases (α <1, α > 1), comparison with other theoretical models show reasonable agreement.

A closed-form, hierarchical, multi-interphase model for composites—Derivation, verification and application to nanocomposites

“…Several researchers (Vernerey et al, 2008;Liu and Brinson, 2006;Liu and Hu, 2005;Tan et al, 2005;Sharma and Ganti, 2004;Barnard and Curtiss, 2005;Lim, 2003;Lim, 2005) have examined the particle size effects in composites. For example, Lim (2003Lim ( , 2005 included interatomic energy at the interface of the matrix and the inclusion in his model to study how nano-scale inclusions influence the mechanical properties of the nanocomposites. Sharma and Ganti (2004) modified Eshelby's tensor of spherical and cylindrical inclusions with surface energy incorporated via a continuum field formulation of surface elasticity.…”

Simplified Transverse Young’s Modulus of Aligned Ribbon-Reinforced Composites by the Mechanics-of-Materials Approach

“…The partial resultant composite stiffness is then evaluated in parallel to the remaining purely matrix block, y 2 ½ y 1 , Áy, to give the transverse Young's Modulus. Detailed PS and SP schemes for rectangular blocks arranged in triply periodic array have been given as [12]…”

“…A practical solution is developed herein for the industry based on a semi-theoretical method for the convenience of the designer, which includes the effect of aspect ratio on both the ribbon width and thickness directions. The present model is an extension to an earlier model for aligned spheroidal-inclusion reinforced composites [12].…”

Young's Modulus of Coated Inclusion Composites by the Generalized Mechanics-of-Materials (GMM) Approach

“…Expected range of R and r for > 1 and < 1 are given as well. A relationship between f () and has been previously given [21] as…”

“…In the foregoing development, two schemes of analyses are adopted for analysis of coated inclusion problem using rectangular three-phase model. These are the Parallel-Series (PS) Scheme and the Series-Parallel (SP) Scheme which has been developed for the limited cases of ¼ 0, 1, 1 [20], the more general cases of > 1 and < 1 [21] and a special case of ribbon reinforcement [22] for two-phase composites, as well as three-phase composites with two phases of noncontacting reinforcements [23]. In this paper, coated inclusion composites are considered as three-phase composites whereby the two reinforcing phases (inclusion and coating) are in contact.…”