The effect of aspect ratio of inclusions on the elastic properties of unidirectionally aligned composites

Abstract

This paper examines the influence of aspect ratio α, from zero to infinity, on the effective elastic moduli of a transversely isotropic composite. The reinforcing inclusions, which could be flakes or short fibers, are assumed to be spheroidal and unidirectionally aligned. Of the five independent elastic constants, the longitudinal Young's modulus E11 and in‐plane shear modulus μ12 appear to increase with increasing aspect ratio, while the transverse Young's modulus E22, out‐plane shear modulus μ23, and plane‐strain bulk modulus K23, generally decrease. It is further noted that E11 is more sensitive to α when α > 1 but the others are more so when α < 1. The present analysis was carried out by the combination of Eshelby's and Mori‐Tanaka's theories of inclusions.

The mechanical properties and fracture behaviour of epoxy-inorganic micro- and nano-composites

“…The full set of equations required to calculate the predicted modulus, including the components of the Eshelby tensor, are given by Tandon and Weng [40]. In the present work, this model will be refereed to as the 'Mori-Tanaka parallel' model.…”

Graphene nanoplatelet-modified epoxy: effect of aspect ratio and surface functionality on mechanical properties and toughening mechanisms

“…Equations for the MoriTanaka model for platelets with an aspect ratio not equal to one were derived by Tandon and Weng [52]. The composite modulus when the platelets are aligned with the long axis parallel to the loading direction, E 11 , is given by:…”

“…where V f is the filler volume fraction, v m is the Poisson's ratio of the matrix, and the variables A 1 , A 2 , A 3 , A 4 and A 5 are functions of volume fraction, aspect ratio and Poisson's ratio of the matrix and fillers, and are given in [52]. Finally, the modulus of a composite with randomly oriented particles can be estimated using [50]:…”

Influence of carbon nanotube–polymeric compatibilizer masterbatches on morphological, thermal, mechanical, and tribological properties of polyethylene

“…The CLTE value is the average of three measurements. properties of the filler and matrix [26][27][28].…”

“…Both theories assume that the filler is firmly bonded to the matrix, and the effect of the filler-matrix interface is not considered. The principles and details of the theories can be found in the literature [5,[26][27][28][29][30][31].…”