Simple formulae for the effective moduli of unidirectional aligned composites

• Published in: Polymer engineering and science 1998-05, Vol.38 (5), p.774-782
• Main Authors: Hui, C. Y., Shia, David
• Format: Article
• Language: English
• Subjects: Applied sciences; Composites; Exact sciences and technology; Forms of application and semi-finished materials; Polymer industry, paints, wood; Technology of polymers
• ISSN: 0032-3888; 1548-2634
• DOI: 10.1002/pen.10243

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 E0/E1 is sufficiently small compared with the aspect ratio of the flake‐like inclusions, where E1 and E0 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.