The Elastic Longitudinal Modulus and Poisson's Ratio of Fiber Composites

Abstract

A simplified theoretical approach for the prediction of the longitudinal elastic modulus and Poisson's ratio in fiber-reinforced composites is developed in this paper. The method considers that the main parameter affecting the elastic behaviour of com posite materials is the existence of the mesophase layer, between fiber and matrix, which possesses different physico-chemical properties than those of the constituent phases. The simplest and most convenient laws of variation are a linear, a parabolic, a hyperbolic and a logarithmic variation of E, and v, for the mesophase material, versus the polar radius from the fiber-surface. In this paper, therefore, these laws are con sidered for evaluating the overall moduli of the composite. Each one of these laws is applied to the representative volume element of the fiber composite and compares favorably with the unfolding model, introduced by one of the authors (PST), as well as with respective data existing in literature.

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

“…In a simplified approach which was adopted in previous papers [7,8], this natural intermediate phase was assumed to be a homogeneous and isotropic material, whereas in another groups of studies [9][10][11] more advanced and prominent models were introduced, the main feature of which was the fibre to be occupied by a series of successive coaxial cylinders, each of which has a different stiffness in a step-function variation in terms of polar radius. Further, a valuable experimental study towards the estimation of mechanical and thermal properties of unidirectional fibrous composite materials was carried out by Clements and Moore [12] whereas a theoretical and experimental investigation of mechanical properties of polymeric particulate and unidirectional fibrous composites by the interphase concept was performed in a previous paper [13].…”

“…It can therefore be noticed that the process of calculating the longitudinal modulus of the final material has shortened considerably, when compared with the corresponding procedures presented in past studies [11,[14][15][16]. In this context, one may observe that by means of the introduced analytical technique, the interphase elastic modulus has been represented directly in terms of fibre content without having previously been expressed as a single-valued function of the polar radius of the coaxial three phase cylinder model.…”

The Thermal Conductivities of Periodic Fibrous Composites as Defined by a Mathematical Model

“…Furthermore, according to the proposed multiphase model, it is evident that: Concurrently, it has been shown [27,29] that for the unidirectional fiber composites, the following parabolic relationship between the content of the intermediate phase and the filler content holds:…”

“…with C defined from the experimental evidence as C = 0.123 [27,29] Thus, for any ordered couple ( f U , i U ), by the use of Equation (35a-c) along with…”

The Thermal Conductivities of Periodic Fibrous Composites as Defined by a Mathematical Model

“…Concurrently, it has been shown [27,29] that for the unidirectional fiber composites, the following parabolic relationship between the content of the intermediate phase and the filler content holds: 47) with C defined from the experimental evidence as C = 0.123 [27,29]. (36)- (45), one may calculate the radii of the seven-phase model, provided that the diameter of the cylindrical fibers is known.…”