ANALYTICAL METHODS FOR TEXTILE COMPOSITES
Tow waviness creates fluctuations in the stiffness of short segments of tows, which results
in uneven load distributions. For the waviness typical of 3D interlock weaves, for example,
this will cause strength knockdowns of up to 10% [4.21]. 3) Misaligned or pinched tows
may be weaker than straight tows. 4) Lateral loads imposed on tows by neighbouring
interlaced tows may reduce their strength.
One common manifestation of shear plasticity under tensile loads is plastic
straightening of wavy tows. The criterion for the onset of tow straightening is essentially
the same as that for kink band formation under compression. The resolved axial shear
stress, which is proportional to the local misalignment angle,
φ
, must exceed
τ
c
, the shear
flow stress, leading again to Eq. (1), with
σ
p
, the critical axial stress for shear plasticity,
replacing
σ
k
. Since tow misalignment is a continuously varying random variable, tow
straightening commences at different stresses for different locations on the same tow.
Unlike kinking, tow straightening leads to hardening and can therefore propagate
along a tow. Its progression can be estimated simply by calculating the local rotation of the
tow, which leads to evolution in
φ
and therefore
σ
p
. Tow straightening ceases when the
axial plastic strain equals the fractional difference between the initial arc length of the wavy
tow and its projected length in the axial direction. The contribution to strain to failure from
this source rises as the square of the average misalignment angle [4.22].
When a tensile load is not aligned with a primary group of tows, tow rupture
may
give way to failure by shear or transverse cracking [4.2,4.14,4.23]. For loading at ±45°
with respect to two orthogonal sets of tows, which might be tows in the plain weave of
Fig. 4-2(b) or in a 3D interlock weave, the problem reduces to one of deviatoric shear in
those tows. The stress-strain response will be similar to those shown in Fig. 4-2. Figure 4-
6(a) shows stress-strain curves for a plain weave composite loaded at various orientations.
Response in the 0/90° orientation is nearly linear to failure, while considerable plasticity and
high strains to failure are exhibited for off-axis loads. Figure 4-6(b) shows similar trends
for open hole specimens. The failure stress for off-axis loads can be higher in the notched
than in the unnotched specimen. The authors of Ref. [4.24] attribute this curious result to
plastic tow straightening occurring near the hole. In tubular braided specimens, interesting
lockup mechanisms can come into play when tows interfere with one another at very high
strains, causing pronounced hardening. The hardening enables a form of cold drawing to
progress along the entire specimen, with high levels of plastic work required to achieve
ultimate failure [4.25].
