Page 74 - 3D Fibre Reinforced Polymer Composites

Chapter 4

Micromechanics Models for Mechanical Properties

4.1 INTRODUCTION

Composite materials are composed of at least two constituent phases, such as fibres and
matrix, and their overall behaviour is dependent on the mechanical properties of the
constituent phases and the detailed forms in which they interact. Composite materials
are intrinsically heterogeneous at the micro-scale. However, the heterogeneous
structures of composite materials may be idealised as a homogeneous medium with
effective anisotropic properties at the macro-scale, which have been widely and
successfully used in practical structural engineering. The procedure to determine the
effective properties of a representative volume of composite materials from the known
properties of the individual constituents and their detailed interaction is referred to as
micromechanics analysis or characterisation of composite materials in a more general
sense.
The effective overall behaviours of a composite material are dependant on the
mechanical properties of the individual constituents, and their detailed interaction, such
as relative volumetric ratios and micro-structural distribution of the individual
constituents. While it may be relatively easy to determine the mechanical properties of
the individual constituents, comprehensive understanding and accurate consideration of
the interaction between the individual constituents at the micro-scale is of vital
importance and represents a great challenge in micromechanics analysis. Over the past
five decades, many researchers have devoted their efforts to the development of
micromechanics analysis techniques to predict mechanical properties of composite
materials. Treatment of microstructures and their influence in a composite material is
one of the most important efforts. Micromechanics models have been developed to
evaluate some effective linear properties of certain composite materials by completely
ignoring the influence of microstructures of all constituents. For composite materials
with their microstructures having stochastic and probabilistic features, uncertainties of
some effective properties can be estimated by determining their corresponding upper
and lower bounds. Recently, with the advance of computing and measurement
technologies, more accurate evaluation of effective properties for a composite material
can be achieved with the aid of more available information on microstructures of all
constituents.
This chapter will focus on micromechanics analysis of fibre reinforced composite
materials, particularly those materials reinforced long fibres. Typical examples include
unidirectional fibre reinforced composites, 2D woven composites as well as 3D fibre
reinforced composites. Earlier researches were conducted based on a large number of
assumptions for simplifying the analysis procedures. The relevant approaches include
rules of mixture approximations, composite cylinder models and the variation boundary
method. These methods provide approximate estimation of mechanical properties, but