Page 112 - 3D Fibre Reinforced Polymer Composites

Micromechanics Models for Mechanical Properties 101

architecture and material properties of textile reinforced composites to its global
stiffness matrix through micromechanics and the stiffness averaging technique. It was
reported that the self-consistent fabric geometry model gave good predictions of elastic
properties by relating these properties to the constituent material properties and the fibre
architecture geometry.
FEM has also been widely applied to investigate the mechanical properties of
braided fabrics. In 1986, Ma et al. (1986) proposed a ‘diagonal brick model’ for 3D
braided textile composites as shown in Figure 4.21, which was based on the concept of
a simplified fibre unit cell structure. As shown in the figure, it was noted that this model
consists of a brick-shaped element of bulk resin with four parallel bar elements along
four edges of the brick plus four diagonal bar elements, and the unit cell is centred
around an “interlock of yams. The spatial orientation of each diagonal bar element in
the unit cell is defined by its orientation angle with respect to x-axis as:

) Pb2 + p,’
6 = tan-’ (4.53)
Po

The “inclination” and “off-axis” angles a and p are defined as (Whitney and Chou,
1989):

tan8
tana = (4.54a)
JR2 ( 1 + tan2@ + 1
Run8
tanp = - Jz , where R=b/c (4.54b)

However, crimping of fibre, which was assumed to occur at the comers of the cell, was
neglected. The intersection of fibres at the unit cell centre was also ignored (Whitney
and Chou, 1989).

Figure 4.21 Geometrical schematic of a unit cell for a 3D braided composite (Ma et al,
1986)

Yang et al. (1986) introduced a new model called ‘fibre inclination model’ by extending
the lamination theory for predicting the elastic properties of 3D braided composites.
This model treats the unit cell of a composite as an assemblage of inclined
unidirectional laminae. The laminate approximation of the unit cell structure is shown