Analytical and computational study of the moduli of fiber-reinforced composites and comparison with experiments

Abstract

The present article investigates the analytical and computational derivation of the moduli of continuous fiber-reinforced composites. Theoretical expressions for the longitudinal and transverse elastic moduli and also for the longitudinal and transverse Poisson ratios, which were derived taking into account the concept of boundary interphase between fibers and matrix, were obtained as a function of the fiber volume fraction. The micro-scale model considers that the composite material consists of three phases: the fiber, the matrix, and the interphase. The latter is the part of the polymer matrix lying at a close vicinity to the fiber surface. In this investigation, it was assumed that the interphase is inhomogeneous in nature with varying mechanical properties. Different laws of variation of its elastic modulus and Poisson ratio were taken into account in order to define the overall modulus of the composite. Thermal analysis method had been used for the estimation of the thickness of the interphase. An investigation about the influence of an interphase region on the elastic constants given by the rules of the mixtures is also carried out. Finite element analysis was performed in order to obtain the elastic constants and to compare them with the respective theoretical values derived from the interphase model and with those from other models and also with experimental results.

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

“…Thus the overall methodology leading to an upper bound of composite modulus without the consideration of any variation law, cannot be used to improve a theoretical formula arising from elasticity approach, such as the other formulae used from comparison without the adoption of several variation laws to approach interphase Poisson's ratio. Thus, one could not know beforehand which variation law of interphase Poisson ratio would yield the highest predictions of E L in the final expression of longitudinal modulus, although it was observed [25] that the parabolic variation law generally yields the lowest values for the interphase stiffness of unidirectional fibrous composites when compared with other laws that are commonly used. On the other hand, one may also pinpoint that since according to strength of materials approach fibres, matrix and interphase are supposed somewhat as solid blocks the volumes of which are proportional to their relative abundance in the overall material instead of the modified form of Hashin-Rosen cylinder assemblage model presented in Figure 1 one may adopt the following simplified model (see Figure 4) to simulate the microstructure of the unidirectional fibrous composite.…”

Interrelation between Fiber–Matrix Interphasial Phenomena and Flexural Stress Relaxation Behavior of a Glass Fiber–Polymer Composite

“…Models can be accustomed to the type of material, at different scales and for specific applications, depending on the industrial sector involved (aerospace, automotive, marine, etc.). Through the prediction of the final composite’s properties, materials can be combined to obtain ideal characteristics suitable in engineering applications, thus avoiding the trial-and-error method and also maximizing high structural performance and a sustainable safe life [ 24 , 25 , 26 , 27 , 28 ].…”

A Theoretical Consideration on the Estimation of Interphase Poisson’s Ratio for Fibrous Polymeric Composites

“…Further, in [17,18] the adoption of linear variation laws for interphase elastic constants yielded theoretical predictions of the composite moduli in a reasonable accordance with experimental values. Yet, to approach the interphase modulus and Poisson's ratio by a quadratic (parabolic) law with respect to the radius of the adopted model of embedded cylinders is many times more convenient since many times the linear variation law cannot alleviate the fact that the transition of the elastic constants from the matrix to fiber is carried out by "jumps" in their characteristic properties [17,19]. However, a significant problem that remains is the following: letting an interphase property ( ) be approached by a quadratic polynomial in the general form r 2 + r + , there are three coefficients ; ; needed to be found.…”