PREDICTION OF ELASTIC CONSTANTS AND THERMAL EXPANSION
5.4 Code Calibration
The macroscopic elastic constants of any continuous fiber polymer composite can
be loosely divided into those that are fiber dominated and those that are matrix
dominated.
2
The fiber dominated constants are those for which the associated material
deformation involves axial straining, either in tension or compression, of some group of
fibers. The matrix dominated constants are the rest. In a composite designed for any
application requiring high stiffness, the critical elastic constants should all be fiber
dominated.
5.4.1 Fiber Dominated Elastic Constants
The most important geometrical consideration in predicting fiber dominated
elastic constants is simply the number of fibers per unit volume that point in any given
direction. For example, in estimating the in-plane stiffness of a quasi-laminar textile,
getting the correct fiber count for in-plane directions is paramount. Out-of-plane
components of the fiber orientations, whether they are a necessary consequence of the
architecture or arise as accidental waviness, are secondary. They introduce relatively
small modifications to predicted in-plane elastic constants. If the fiber count is right, then
fiber dominated elastic constants will be predicted to within experimental scatter,
regardless of how well the details of stress partitioning throughout the textile are
computed. A simple scheme such as orientation averaging, i.e. the assumption of isostrain
conditions, will suffice.
While corrections to in-plane elastic constants due to out-of-plane components of
fiber orientation should not be ignored, the level of precision required in specifying the
out-of-plane components is not high. Any error will cause an error in a small contribution
to the overall stiffness. Therefore, there is generally not much difference between the
predictions of models in which the geometry of quasi-laminar textile composites is
treated by different approaches.
2
The division is clearest if most fibers are straight or almost straight. Exceptions to this rule obviously
arise. In a knitted composite, all fibers follow highly curved paths, which nevertheless may contain
significant if short straight and roughly aligned segments. The straight segments collectively will raise the
modulus in the direction of their alignment an order of magnitude above that of the matrix; yet not so high
(because they are short) that the contribution of the surrounding matrix dominated material is unimportant.
The modulus is neither clearly fiber nor matrix dominated. But such exceptions arise in composites whose
macroscopic stiffness would not meet the requirements of airframe structures, for this very reason.
