Page 107 - 3D Fibre Reinforced Polymer Composites

96 30 Fibre Reinforced Polymer Composites

c33 1

c,3s =c33 , C22 =NAC22AVA+NBC2FVB,

C,,S = c C33AC33B
NAVAC,B + NBVBC3; ’

c,s = CMACMB c,,s = C,5AC,5B
NAVACUB + NBVBCMA ’ NAVAC,B + NBVBC,,A ’

It is worth pointing out that the principal axes of material block A and B are assumed to
coincide with the Cartesian coordinates, x, y and z, for all the three assemblage schemes
shown in Figure 4.17.
As shown in Figure 4.16, the woven fabrics unit cell is divided into four cubic
blocks (see Figures 4.16(a)-(d)). The elastic constants for the blocks in Figure 4.16(a),
(b) and (c) can be evaluated using the “X assembly” equations and the stiffness
constants for yarns and resin. The stiffness constants for the combined block (a) and (b)
and the combined block (c) and (d) can be further evaluated using the Y assembly
equations. The overall properties are finally obtained using the z assembly formula.
This was referred to as the XYZ model by Tan et al. (1998, 1999a, 199b) as assemblage
of micro blocks follow the sequence in x, y and z direction respectively. Similarly, three
other models were developed following the similar concepts and were referred to as
“YXZ model”, “ZXY and ZYX models.
A laminate model was also proposed by Tan et a1 (1998) to take into account the
contribution of the z yarn on the upper and lower surfaces of the 3D orthogonal woven
composite material as shown in Figure 4.13.

4.4.3 Applications of Finite Element Methods
Finite element methods (EM) have also been widely used to model characteristic
behaviours of 3D textile composites (see Tan et al., 1997). FEM is a powerful and
versatile numerical tool that allows detailed modelling of complex geometry and
various material properties. Current research focuses on practical applications of
existing elements and solution schemes in commercially available software to
modelling of 3D composite materials of various constituents. There exists limited work
on formulation and development of particular elements and solution schemes that are
specifically formulated and implemented for analysis of 3D composite materials. Thus
we will briefly describe the modelling concepts and methods that are currently being
widely used by researchers in both materials and mechanics communities.