PREDICTION OF ELASTIC CONSTANTS AND THERMAL EXPANSION
PREDICTION OF ELASTIC CONSTANTS AND THERMAL EXPANSION
5.1 Concepts
The great challenge in modeling the elastic properties of textile composites is
dealing sufficiently well with the very large variations in stress and strain that can occur
within a textile even under uniform applied loads. A textile composite is a highly
heterogeneous structure. It may be viewed (and is often modeled) as a three-dimensional
tessellation of grains, each of which is an approximately unidirectional composite and
therefore transversely isotropic, with the plane of isotropy lying normal to the local fiber
direction. In polymer composites, the anisotropy factor for each grain is high, with
axial
/E
transverse
20 for typical graphite/epoxy. The distribution of stresses among the
different grains therefore depends very strongly on their relative sizes and orientations
and on the degree of order in their organization. In other words, it depends on the textile
architecture.
All models deal with this difficult situation by simplifying the description of the
textile geometry and restricting the allowable internal stress variations. Models can be
categorized into a few main groups according to how this is done. In choosing a
particular model for some class of composites, the user should first ask whether the
simplifying steps are valid for the given architecture. The following discussion of
essential concepts will provide a guide to answering this question.
Isostrain and Isostress
In infinite 2D laminates, uniform in-plane loads cause identical in-plane strains in
each ply. Thus laminate theory for non-bending plates is based on an isostrain condition
for the in-plane coordinates. The analysis of macroscopic elasticity is reduced to the
simple analysis of a few macroscopic stress or strain components. Bending flat laminar
plates causes a gradient in the in-plane strains through the thickness, but since the
gradient is uniform, the relationship between stresses and strains in different plies
remains trivial [e.g., 5.1].
If an infinite 2D laminate is subjected to a uniform through-thickness load,
identical through-thickness stresses arise in each ply and an isostress condition exists for
the through-thickness coordinate. Of course, through-thickness loads are always
nonuniform (unless they are zero); but if they vary slowly over distances comparable to
