An Upper Bound of Longitudinal Elastic Modulus for Unidirectional Fibrous Composites as Obtained from Strength of Materials Approach

John Venetis,Emilio Sideridis

doi:10.3390/fib6030057

Abstract

In this paper, the authors introduce an upper bound of the longitudinal elastic modulus of unidirectional fibrous composites to strength of materials approach, provided that the fibre is much stiffer than the matrix. In the mathematical derivations resulting in this bound, the concept of boundary interphase between filler and matrix was also taken into consideration. The novel element of this work is that the authors have not taken into account any particular variation law to approach the stiffness of this intermediate phase. The theoretical predictions were compared with those obtained from some accurate analytical models as well as with experimental data found in the literature, and a satisfactory accordance was observed.

Highlights

The variational energy principles of classical elasticity theory have been widely used to designate upper and lower bounds on the stiffness of unidirectional fibre-reinforced composites in the longitudinal and transverse direction of fibres respectively
The authors derived an upper bound of the longitudinal elastic modulus of unidirectional fibrous composites reinforced with continuous fibres according to strength of materials approach, provided that the fibre is much stiffer than the matrix a fact that generally concerns polymeric composites
A shortcoming of Equation (21), which illustrates the upper bound of longitudinal composite moludus derived from strength of materials approach, is that the mathematical derivations were based on the hypothesis that the fibre is much stiffer that the matrix i.e., Em + Ei < E f and an analogous expression for Poisson ratio of the composite cannot be obtained according to this reasoning

Summary

Introduction

The variational energy principles of classical elasticity theory have been widely used to designate upper and lower bounds on the stiffness of unidirectional fibre-reinforced composites in the longitudinal and transverse direction of fibres respectively. According to Strength of Materials approach, the longitudinal elastic modulus EL for a fibrous composite material reinforced with unidirectional continuous fibres can be obtained from the following modified form of standard mixtures law, initially introduced previously.

Results

Conclusion