PREDICTION OF ELASTIC CONSTANTS AND THERMAL EXPANSION
meaningful material property if it is measured over gauge lengths that are macroscopic
according to this definition. If the property is measured over smaller gauges,
unacceptable variance will occur in the measurement. In textile composites, macroscopic
length scales are unusually large and their consideration is therefore unusually important.
3, 7, 11, 15
9
1
13
6
5
14
2
10
4, 8, 12, 16
(a)
body warp weaver
surface warp weaver
filler (weft) stuffer (straight warp) warp weaver
layer-to-layer angle interlock
SC.4170T.121595
Figure 5-5. Schematic of a 3D interlock weave. The numbers at the right show the
sequence of occurrence of warp weaver tows encountered on progressing into the
plane of the figure.
Let
λ
i
, i=1,2,3, denote macroscopic length scales along three linearly independent
directions. Almost always, the three
λ
i
will take different values. An effective empirical
definition of macroscopic length scales is that all sets of measurements of elastic
constants or strains over different gauge lengths greater than
λ
i
will have the same
variance. Some experiments demonstrating the convergence of variance as the gauge
length is increased were discussed in Section 3.
It would also obviously be useful to be able to estimate the
λ
i
from the geometry
of a textile composite alone, avoiding the expense of the empirical approach.
Unfortunately, because of the complexity and variety of textiles, there is no single
definition applicable to all cases. The following remarks are therefore a guide to a
decision that must be made on a case by case basis.
If the textile is periodic, each
λ
i
could be identified with the width of the unit cell
in that direction. If the geometry is ideal and the loads uniform, measurements of strain
