Computational Methods for Debonding in Composites

2 Material and Failure Models for Textile Composites 33
Another advantage of the approximate meshing is that it simplifies the discretization
of complicated geometries in the mesomechanical unit cell and the application
of periodic boundary conditions. The geometry of fiber bundles has to be approximated
anyway because it is irregular due to the manufacturing process. In addition
the definition of clear boundaries between fiber bundle and epoxy is problematic
as the fiber bundle itself contains epoxy. Therefore Gunnion [7] has shown that the
voxel method is well suited to determine stiffnesses of textile composites.
2.2.3 Micromechanical Unit Cell
For transversely isotropic UD-material state of the art mixture rules give a good
estimation of the elastic properties, but lack to predict inelastic properties such
as strength and hardening of the fiber bundle. So, the micromechanical unit cell
is needed to determine these parameters when experimental data is not available.
This is often the case for textile composites, because the tests required cannot be
done with the whole preform, but only with a part of it, the fiber bundles. Thus the
specimens have to be produced especially for these tests.
A micrograph of unidirectional composite material is shown in Fig. 2.4a. It can
be modelled with a representative volume element on the microscale that consists
of fiber and matrix. Neglecting the random fiber distribution over the cross section,
a regular square fiber arrangement, that can be reduced to the unit cell shown
in Fig. 2.4b, is assumed. It has been shown previously [19], that this is a good
approximation.
As mentioned above, the micromechanical unit cell consists only of one fibre,
that can even be reduced to a quarter of a fiber, see Fig. 2.5 when a symmetric load
is applied due to symmetry reasons.
In the examples given here glass fibres and epoxy matrix are used. Both are
isotropic materials, whose material parameters are well known from test and are
summarized in Table 2.1. Strength of the epoxy resin is neglected in fiber direction
and therefore strength in fiber direction R t,c
� can be computed analytically from the
(a) Micrograph [3] (b) Square arrangement
Fig. 2.4 Micromechanical unit cell
Matrix
Fiber
(c) Unit cell geometry