NONLINEAR STRESS-STRAIN BEHAVIOUR AND STRENGTH
6-9
tow segment or grain for matrix failure. When it occurs, selected terms of the local
stiffness matrix are reduced or set to zero. The code must then iterate to re-establish
equilibrium before incrementing the load. TEXCAD and SAWC employ versions of this
approach. One limitation of these codes is that the user has no control over the stiffness
discount rule or the criteria for onset of nonlinearity.
Figure 6-2. Failure loci for individual tows or plies in terms of the local stress state.
(a) Combined aligned and axial shear loads. (b) Combined transverse and axial shear
loads. The x-axis is aligned with local fiber direction. The axes are not to scale.
6.4.2 Ultimate strength
In most of the codes, ultimate tensile strength is estimated by simply comparing
maximum local stresses with tow or fiber strength data, using calculations in which the
textile is assumed to remain wholly elastic. This is analogous to the first-ply failure method
of determining the strength of laminates. In most of the codes, no provision is made for
entering the tow or fiber strength data (Table 6.2); but several codes provide values for
internal stresses as output. These internal stresses could be compared with empirical failure
loci similar to Fig. 6-2 to predict strength. TEXCAD prints tables of internal stresses
determined using the isostrain assumption. The finite element codes µTex-10, µTex-
20, SAWC, and BINMOD all provide internal stresses as output, typically in the material
axes (orientated with the local fiber direction).
CCM-TEX makes the coarsest of all estimates of composite strength, simply
summing the strengths of the tows weighted by their areas. This can nevertheless be a
useful estimate of tensile strength for a textile containing a dominant set of nominally
straight tows under aligned uniaxial loads, e.g. the 3D interlock weaves studied in
[6.1,6.5.6.6]; or the triaxial braids studied in [6.7], when loads are in the axial tow
direction. It is not useful for compressive strength, since the strength of the tow is
undefined without reference to misalignment angle distributions.
