Page 113 - 3D Fibre Reinforced Polymer Composites

102 30 Fibre Reinforced Polymer Composites

schematically in Figure 4.22, in which the inclined laminae are composed of yarns in
four diagonal directions in the unit cell. The inclination angles of the laminae 8, and the
off-axis angle of yarn segment with respect to the x-axis % are expressed as:

(4.55a)

(4.55b)

This approach is an extension of the one-dimension “fibre undulation model“ developed
by Ishikawa and Chou (1986). No experimental tests were attempted to verify this
model, although it was stated that the relevant predictions showed reasonably good
agreement with the experimental data obtained by several other researchers. As the fibre
volume fraction of 3D braid is normally over 0.5, it maybe possible to model the yarns
as bar elements (rather than dimensionless) in the four diagonal directions.

Figure 4.22 Geometrical schematic of a unit cell of the fibre inclination model
composed of four unidirectional laminae for braided composites (Yang et al, 1986)

All the approaches described above in modelling braided composites are to define a unit
cell geometry for a braided structure without providing any relationship between
processing variables and geometric parameters. Hence, these models may not be used to
study the optimisation of the braided fabric architecture for their structural applications.
Byun et a1 (1991) developed a fabric geometric model using lamination analysis and
the stiffness averaging method. This model combines the micro-cell model and macro-
cell model, and can be utilised to predict the elastic constant of 2-step braided
composites. The micro-cell model is constructed for thin specimens so that the two-
dimensional approximation of the classical lamination theory can be applied. Given the
geometric parameters of the micro-cell, fibre and matrix properties and composite fibre
volume fraction, effective in-plane elastic properties can be calculated based on a
pointwise application of lamination theory. The compliance (or stiffness) constants are