Page 99 - 3D Fibre Reinforced Polymer Composites

88 30 Fibre Reinforced Polymer Composites
C13 = N ACAV A + N 'C&V ' c;~ N~C~V~ N'C~V~
+
=
+
c; = N~C:V~ N~C:V' C5,S = c55"55"
+
NAVACSSB NBVBC55A
C6,S = C66AC66B (4.47)
NAVAC,,B + NBVBCGGA

where N" and NB are the number of micro-blocks A and B within a strip, respectively,
and are the volume fractions of a micro-block A and micro-block B, respectively,
Ct. Ct, Ci are the stiffness constants for micro-block A, micro-block B and a strip,
respectively.
When the micro-blocks are assembled in the weft or y direction to form the weft
stripes, equations for the average properties for a weft stripe can be obtained by
exchanging 1 and 4 with 2 and 5, respectively, in equation (4.47).
The overall effective properties of the unit cell can be calculated by assembling the
warp or weft stripes via employing the equations for properties of the weft or warp
stripes, respectively.
The 3D model proposed by Tan et al (1997b) can be extended to take into account
the fibre undulation by employing a large number of micro-blocks.

4.3.4 Applications of Finite Element Methods
Finite element methods (EM) have been used almost universally during the past
forty-five years to solve very complex structural engineering problems (Zienkiewicz
and Taylor, 1989). When applied to characterise textile composites, FEM visualises
them as an assemblage of unit cells interconnected at a discrete number of nodal points.
The unit cell is a periodic square array of fibres embedded regularly in the matrix.
Hence, if the force-displacement relationship for an individual unit cell is known, it is
possible, by using various well-known theories and techniques of elasticity theory, to
evaluate its mechanical properties and study the mechanical behaviour of the assembled
composite structure.
The general procedure to predict the mechanical properties of a textile composite
using FEM consists of 1) dividing the textile composite structure into a number of unit
cells and analysing the mechanical properties of a unit cell using FEM, and 2)
reconstructing the entire reinforcement geometry by assembling the unit cells for
predicting mechanical properties of textile composites. Thus, the ability of a FEA model
to predict mechanical properties depends upon the accuracy of modelling the fibre
geometry in a unit cell. For the theoretical method, analytical models for elastic
properties of composites are generally developed based on classical laminate theory and
rule of mixture. Tan et al. (1997a) provided an overview on modelling of mechanical
properties of textile composites using the finite element method.
Whitcomb (1989) analysed plain weave composites using 3D finite element
analysis, and studied the effect of tow waviness on the effective moduli, Poisson's ratio
and internal strain distributions. It was found that the in-plane moduli decreased almost
linearly with increasing tow waviness, which was found to create large normal and
shear strain concentrations in the composites when subject to a uniaxial loading.