Page 100 - 3D Fibre Reinforced Polymer Composites

Micromechanics Models for Mechanical Properties 89
A finite element model for plain weave textile composites was proposed by Glaessgen
et al. (1994). The yarns forming a unit cell were considered to be elastic bodies
interacting with one another and subject to external loads. The centre line of each yam
was represented as a Bezier curve interpolating a set of discrete support point. The
cross-sectional shapes were assumed to be elliptical. The constituent properties of
textile composites were approximated as transversely isotropic yams in an isotropic
matrix. The quadratic tetrahedral element in ABAQUS was used. Subsequently,
Glaessgen et al. (1996) proposed a method using the textile geometry model combined
with the FEM for studying the internal details of displacement, strain, stress and failure
parameters. In this method, the geometrical and mechanical modelling was carried out
on the structural level of the unit cell,
Since the microstructure of the textile composite is very complex, it is almost
impractical to incorporate all architecture parameters in a simple finite element model.
In order to obtain reasonable predictions of mechanical properties with a minimum
analysis effort, there is a need for more computational efficient methods for performing
the analysis (Whitcomb, 1991; Whitcomb and Woo, 1993a).
A 2D to 3D global/local finite element analysis method has been developed by
Thompson and Criffin (1990, 1992) to determine interlaminar stress fields for
composite laminates with a hole under a remotely loaded uniform uniaxial load. The
initial approach used was a 2D global finite element analysis on the whole body or
global region with 2D plate finite elements, followed by a more detailed 3D local finite
element analysis performed on the local areas of interest with 3D finite elements. The
appropriate displacements of the global/local interfaces from 2D global model were
applied to the edges of 3D local model. A new finite element analysis approach, called
global/local (or macro/micro) analysis method, for textile composite was subsequently
proposed for improving analysis efficiency. It was suggested that an accurate global
analysis, which determines the local effect on a gross scale, be carried out first, and then
as many local analyses as required be conducted.
Whitcomb ( 199 1) proposed an iterative global/local finite element analysis method.
The basic idea of this method is that a coarse global model can be employed to obtain
displacements or forces that can be used as appropriate boundary conditions for local
regions. There may be a potential problem due to the differences in the stiffness of the
global and local models. This method was subsequently used for performing linear
analysis and geometrically non-linear analysis (Whitcomb and Woo, 1993a,b).
A new type of finite element, referred as macro element, was proposed, in which the
tow path was assumed to be sinusoidal (Woo and Whitcomb, 1994). The displacement
field within the macro element was assumed to be single field. Because of this
assumption, the stresses or strains calculated within the macro element may not be
accurate. A new finite element method, referred to as global/local methodology, was
proposed. This method is based on 3 types of special macro elements, referred to as
coarse microstructure transitional microstructure and fine microstructure. A transitional
microstructure is a structure that stands between the coarse and fine microstructures,
and a special finite element is needed. It was reported that the predictions obtained
using the conventional EM and the global/local method were in poor agreement when
near the globaYlocal boundary.
A 3D finile element model was proposed by Chapman and Whitcomb (1995) to
investigate the effect of the assumed tow architecture on the moduli and stresses for
plain weaves. In this model, a yarn is assumed to have a sinusoidal tow path and a