Page 83 - 3D Fibre Reinforced Polymer Composites
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72 30 Fibre Reinforced Polymer Composites
where N and M are the membrane stress resultant and bending moment vectors, E and K
are the vectors of in-plane strains and changes of curvature on the middle plane of the
laminate, and A, , B, and D, (i,j=1,2,6) are the in-plane stretching, bendingktretching
coupling, and bending stiffness matrices,’which can be calculated using:
x
(A, B, D,)= jaj(l z z2)z (4.22)
-x
where Gj are the elastic constants of a lamina, which is a function of fibre orientation,
(see Jones, 1975).
Figure 4.2 Mosaic Model for woven composites (Ishikawa and Chou, 1982a)
As a first order approximation, an iso-strain field is assumed in the middle plane. The
effective stiffness constants for the unit cell of a 2D woven composite idealised as an
asymmetrical cross-ply laminate can be expressed as:
(4.23)
Where the bar on top of a variable indicates an average of that variable over the area of
the unit cell Aut. When these stiffness constants are inverted, lower bounds of the
elastic compliance constants can also be obtained. For non-hybrid weaves, the averages
can be simplified as:
