Page 86 - 3D Fibre Reinforced Polymer Composites
P. 86
Micromechanics Models for Mechanical Properties 75
(4.30)
Ef(8) =1/[1i/E; +(1/GL -2v.:/Ef)l,?mi +m~lEf]
v.:(e) = vzl,? + vLmj
Gc (8) G:1,? + Gimi
=
E:(@ = E: =Ef
D,, 1 - V: (8)' E: / E: (8) (4.31)
=
The angle Bcan be expressed in terms of x as follows:
e(x) = arctan( y) (4.32)
The following formulas were obtained by Ishikawa and Chou (1982b):
(4.33)
where the superscripts F, W and M represent the weft, warp and matrix, respectively.
By inverting the matrices defined by equation (4.33), the corresponding compliance
matrices,a,?(x), bl;(x) and dl;(x) for the undulated portion can be obtained.
Solutions based on the assumption of uniform stress for the infinitesimal pieces in the
straight and crimped regions, as shown in Figure 4.3, were assembled, and the average
compliance properties can be obtained as follows:
