ANALYTICAL METHODS FOR TEXTILE COMPOSITES
6-4
6.3 Ultimate Strength
In many aerospace applications, loads are predominantly uniaxial and will be
oriented with one set of tows in the textile. In such cases, ultimate strength will be
dominated by those primary load bearing tows. The first task in predicting strength is to
compute the stress partition between these tows and all other tows in the textile. But the
contribution of off-axis fibers to composite stiffness is lower in proportion to the degree of
anisotropy of individual tows; and the axial modulus of a tow is typically twenty or more
times its transverse modulus, depending on the fiber material and the fiber volume fraction.
Therefore, when loads are uniaxial and aligned, useful estimates of the stress partition can
be based on very simple models of the stress distribution; and estimates of strength follow
by imposing failure criteria for locally aligned loads, which are reasonably well
understood.
Ultimate strength predictions under off-axis and biaxial loads are also important in
design. Since tow segments of all orientations may contribute significantly under general
loads, the problem of computing stress partitions must usually be solved in more detail.
The failure criteria for individual tow segments must also be those for multiaxial loads.
Once again, experience with unidirectional composites is probably a reasonable guide,
although verification for textiles remains a topic for research. Given the state of
uncertainty, computational codes that predict strength under multiaxial loads can be relied
on at most for identifying trends. Absolute values of strength will have to be measured.
6.3.1 Ultimate Tensile Strength
For aligned loads, consistent but high estimates of ultimate tensile strength have
been found for 2D braids and 3D weaves, among other materials, by comparing the local
axial stress predicted for the aligned tows with the measured strengths of either bare fiber
tows or unidirectional composites [6.1,6.5-6.7]. The local stresses are calculated for given
applied stresses by models equivalent to orientation averaging (Section 5). The off-axis
tows may be assumed undamaged to peak load (elastic) or to be progressively damaged,
e.g. elastic/perfectly plastic, with relatively little effect on the outcome, because they carry a
small proportion of the total load.
Table 6.1 compares predictions of ultimate strength for some triaxial
glass/urethane braids and 3D interlock carbon/epoxy weaves with measured strengths. The
predictions are based on the assumption that the local axial stress in the aligned tows
reaches the strength of an equivalent unidirectional composite (in the case of the AS4/1895
composites) or the strength quoted by the manufacturer for the bare fibers reduced by the
fiber volume fraction (glass/urethane composites). They exceed the measured ultimate
strengths for each textile composite by 20-50%. The difference is greater when the bare
fiber strength is used in the predictions. This is to be expected, since the presence of a
compliant matrix will generally weaken a bundle of fibers by concentrating stresses around
the sites of first fiber failures.
3
Since the bare fiber bundle strength is also strongly gauge
3
The ratio of the dry fiber bundle strength and the strength of a unidirectional composite depends strongly
on the gauge length used for testing the former. However, for typical gauge lengths of a few centimeters,
the stress concentrating effect of a compliant matrix is probably the dominant factor. It leads to stress
concentrations of approx. 15% in fibers neighbouring a fiber break in a typical polymer composite
[6.8,6.9]. The dry fiber bundle strength is then often greater than the strength of the unidirectional
composite. In contrast, in a composite with a stiff matrix, such as a ceramic matrix composite, the stress
concentration in fibers neighbouring a broken fiber is negligible. Furthermore, the ability of the matrix to
restore the axial load in a broken fiber over a relatively short distance via interfacial friction introduces a
material gauge length, much shorter than the specimen length, which becomes the relevant length for
