Page 108 - 3D Fibre Reinforced Polymer Composites

Micromechanics Models for Mechanical Properties 97
Similar to unidirectional prepreg, woven composites have fibres or fibre tows embedded
in resin matrix in specific patterns, which can be different depending on the
manufacturing procedure used and the selected processing parameters. The basic
constituents are fibre and resin, which can be treated as being homogeneous and
orthotropic. However, finite element modelling of each individual fibre and its
interaction with resin and adjacent fibres in 3D composite materials makes the task
extremely expensive and difficult, if not impossible, and even unnecessary for
evaluating macroscopic properties of the materials. This is a natural and intrinsic
modelling level without any assumptions or with limited assumptions with respect to
fibre paths only.
The next possible modelling level is to treat the fibre tows or bundles as a whole
large ‘fibre’ or yarn, in which all fibres are aligned or closely aligned following a
specific pattern. In this model, a number of assumptions must be introduced to define
the geometry and material properties of each yam. The definition of the yarn geometry
can include the cross sectional shape and size of the yarn, path of the centreline of the
yam, and fibre distribution across the cross-section of the yarn. As all fibres in a yarn
are aligned or closely aligned in one direction at a cross-section, the material properties
of a unidirectional composite can be used in conjunction with coordinate transformation
to determine the properties of a spatial yarn. Finite element methods have been widely
used to model the interaction between the fibre yarns and resin.
The general procedure to predict the mechanical properties of a 3D textile composite
using FEM is the same as that described in Section 4.3.4.

4.4.3.1 30 Finite Element Modelling Scheme
In the 3D finite element modelling scheme, three-dimensional brick, wedge and
tetrahedral elements are usually utilised to generate a mesh that models all the yarns and
matrix in a unit cell. It is possible to model in detail the true geometric shape of all the
yarns and the yarn-matrix interfacial surfaces. Such a model depends on accurate
measurement of yarn geometry in a unit cell, and may not be cost-effective. Accurate
measurement of yarn geometry can also be difficult due to limitations of current
measurement techniques, and may not even be necessary due to geometrical
irregularities found in all textile composites, including inconsistency in tow spacing,
tow waviness and tow pinching.
As an approximation, the cross-sectional shape of a yarn is often assumed to be
uniform along an idealised centreline of the yarn path. Typical cross-sectional shape of
a yarn can be rectangular, circular, elliptical and lenticular. For an idealised yarn with a
uniform cross-section and a defined centreline path, it is easy to develop a computer
program that automatically generates the mesh for a unit cell of a woven composite
material manufactured following a selected weaving process. Figures 4.18 and 4.19
depict a full 3D finite element model for a unit cell and a laminate block of a 3D
orthogonal woven composite material.
The mechanical properties of the composite constitutes in the unit cell of a 3D
woven composite material can be assumed to be homogeneous and isotropic for the
matrix and orthotropic for the impregnated yarns with respect to their corresponding
principle material axes. The mechanical properties of each yarn can be determined
using the properties of the fibre and matrix, the fibre volume fraction as well as the fibre
direction and equations (4.6), (4.39) and (4.46).