ANALYTICAL METHODS FOR TEXTILE COMPOSITES
the thickness of a single ply, isostress conditions may be considered to prevail locally in
estimating the lumped stiffness of many plies.
The isostress or isostrain assumption works in 2D laminates because of
translational invariances in the laminar structure. For example, when an observer scans
along the load axis in Fig. 5-1, the composite he sees does not change. This translational
invariance implies that planes normal to the load axis have no cause to deform under the
load; they remain plane and the isostrain condition prevails. Translational invariance
along two orthogonal in-plane axes is required for isostrain conditions to hold under in-
plane shear; for isostress conditions to exist locally under through-thickness loads; and
for strain gradients to be uniform in bending.
loading
direction
SC.4059T.072795
Figure 5-1. Translationally invariant 2D laminate.
Textile composites are frequently analyzed by assuming an isostrain or isostress
condition. Under combined in-plane and bending loads, quasi-laminar textile composites
are also usually represented by laminate theory. Whether these steps are valid will be
determined by the extent to which the textile composites are translationally invariant on
the scale over which stress variations are being modeled.
5.1.2 Tow Properties
With no exception known to the writers, it is always adequate in modeling the
elastic properties of textile composites to regard tows as being internally homogeneous.
The fibers and resin within tows need not be modeled separately. Furthermore, in every
case studied, the distributions of the fibers in any two directions normal to the tow axis
are equivalent, whatever the tow aspect ratio. Therefore, in the absence of twist, the tows
are transversely isotropic over any gauge length significantly greater than the fiber
diameter.
Thus tow properties can be equated to the macroscopic properties of an equivalent
unidirectional composite. Various closed form approximations for estimating the latter
