NONLINEAR STRESS-STRAIN BEHAVIOUR AND STRENGTH
6-1
NONLINEAR STRESS-STRAIN BEHAVIOUR AND STRENGTH
Predicting the response of a textile composite beyond the proportional limit requires
knowledge of how loads are distributed among different tows. Depending on their
orientation and location, tows will show markedly different degrees of plasticity
1
and will
fail at different external loads. Only some of the elasticity codes described in Section 5
calculate local stresses in the required detail; and of these, only a few have been developed
to deal with evolving, heterogeneous plasticity to peak load or ultimate failure. Even in
these few, the nonlinear constitutive properties of tows are either assumed ad hoc or built
up from barely adequate experimental measurements. There is clearly a need for further
model development.
Most of the following discussion and the codes themselves are concerned with
progressive failure in which damage is distributed continuously throughout the composite,
at least on gauge lengths that are larger than the characteristic scale of the textile
architecture, e.g. the unit cell size in a periodic structure or the macroscopic length scale,
i
, of Section 5.1.5. Uniform damage is a reasonable assumption in predicting unnotched
strength and nonlinearity up to peak load. However, stress-strain response beyond peak
load and notched strength are dominated by localized damage bands or cohesive zones.
For these phenomena, a different class of model is needed altogether.
6.1 Nonlinearity Beyond the Proportional Limit
As discussed in Section 4, nonlinearity prior to peak load in textile composites
arises from matrix failure mechanisms: transverse failure of tows or transverse interply
cracks; plastic straightening of wavy tows loaded in axial tension; and matrix-mediated
axial shear deformation (which may include microcracking or crazing). A general model of
these phenomena will take the form of a yield locus for the material in a single tow defined
in a triaxial stress space together with some hardening rule. No detailed constitutive laws
of this kind based on experimental data have yet been presented. Progress to date relies
instead on simple assumptions. In some work, the validity of the assumptions has been
checked by comparing output of the textile model with limited macroscopic property data;
but whether the assumed constitutive laws are uniquely defined by those data and whether
they will hold up for multi-axial loading or parts of complex geometry remain unanswered
questions.
Tensile (Transverse) Matrix Cracking
Matrix cracking among tows that are loaded in transverse tension is similar to
cracking seen in tape laminates in plies oriented normal to the load axis. However, the
factors determining crack spacing and crack saturation are different. In the tape laminate,
crack spacing is determined by the mechanics of stress relief around each crack. Saturation
is achieved when the zones of stress relief around successive cracks overlap. Further
1
Here plasticity is used in the general sense of irreversible damage, from which a material cannot recover to
its original state upon unloading. Thus plasticity is distinct from nonlinear elasticity. In a polymer
composite, plasticity does not arise from the motion of dislocations, as in a metal, because the polymer is
generally noncrystalline. It comes instead from microcracking, especially arrays of cracks such as those
depicted in Fig. 4-1, coupled with irreversible matrix damage (crazing and tearing of polymer chains) and
possibly friction.
