Page 85 - 3D Fibre Reinforced Polymer Composites

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74 30 Fibre Reinforced Polymer Composites

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1 -sin{ (x
h, (x) = -[ - 1 - sin{ (x - when a, 5 x 5 a 12 (4.29)
when a12 5 x I a2
where a, = (a - a,)/2 and a2 = (a + uu)1 2. Clearly, both functions are independent
of the y-axis, which indicates that the fibre undulation in the warp direction is neglected.

Figure 4.3 Fibre undulation model (Ishikawa and Chou, 1982b)

The unit cell in Figure 4.3 consists of two straight cross-ply regions and one undulated
cross-ply region. For the undulated portion, the angle 8 between the local fibre
orientation and the global coordinate is a function of x only and can be determined from
the function hl(x). The elastic stiffness constants a,! for the undulated weft yarn can
be expressed in terms of the elastic stiffness constants Ql and the angle 8, and these
are defined as follows by Ishikawa and Chou (1982b):