Premium
Simple formulae for the effective moduli of unidirectional aligned composites
Author(s) -
Hui C. Y.,
Shia David
Publication year - 1998
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.10243
Subject(s) - materials science , moduli , composite material , modulus , composite number , simple (philosophy) , flake , fiber , aspect ratio (aeronautics) , young's modulus , physics , philosophy , epistemology , quantum mechanics
Simple closed form expressions for the effective tensile moduli of an unidirectionally aligned two phase composite reinforced by fiber‐like or flake‐like inclusions of aspect ratio α are obtained. The case of α ≫ 1 corresponds to fiber‐like inclusions whereas the case of α ≪ 1 corresponds to flake‐like inclusions. These expressions are based on the exact results obtained by Tandon and Weng, who used the Mori‐Tanaka method to obtain the effective moduli of such composites. These expressions are then compared with various empirically based formulae such as the Halpin‐Tsai equation and the Modified Rule of Mixtures equation. It is found that very large discrepancies result when the modulus ratio E 0 / E 1 is sufficiently small compared with the aspect ratio of the flake‐like inclusions, where E 1 and E 0 are the Young's modulus of the inclusions and the matrix, respectively. Simple criteria for the validity of the rule of mixtures relation are also given. Also, the predictions of the simple closed form expressions are compared to available experimental results and favorable agreements are obtained.