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

Abstract

A simplified transverse Young’s Modulus of aligned, continuous ribbon-reinforced composites is developed herein within the framework of the mechanics-of-materials approach for the convenience of the designer. The chosen geometry is that of doubly periodi carray of rectangular parallel-piped, akin to the method-of-cells approach. Results from the present model compare well with an exact model, which is a combination of Mori-Tanaka’s average stress of the matrix and Eshelby’s stress field for an ellipsoidal inclusion. Furthermore, results reveal that increasing ribbon width at constant ribbon volume fraction leads to significant stiffness enhancement in the ribbon width direction with marginal loss of stiffness in the ribbon thickness direction.

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

“…For verification, the present model, Equations ( 21) and (22), are either reduced to easily recognizable form or compared with results by other approaches. The former is applied for the simple cases of R ¼ 1 and 0, while the latter is attempted for the case of R ¼ (1/2) and (2/3).…”

“…In the commonly encountered case of thin coating, the term (t/L) in Equation ( 27) can be neglected such that both Equations ( 21) and (22) simplify to…”

“…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.…”

“…Results of coated fiber composite's Young's modulus from Pagano and Tandon[22].Material, Nicalon E f ¼ 200 GPa Matrix Material, Barium Magnesium Aluminosilicate (BMAS) E m ¼ 106 GPa Fiber Volume Fraction V f ¼ 0:6 ¼ ðr 1 =r 3 Þ 2…”