ANALYTICAL METHODS FOR TEXTILE COMPOSITES
unit cell), which typically represents a few cubic centimeters of material and contains a
few thousand tow and effective medium elements. (The representative volume element
needs only to be larger than the macroscopic length scales,
λ
i
, of Section 5.1.5. These
may be defined by experiments or by exercising the Binary Model itself for simulations
of different size.) The whole assembly is analyzed as a finite element calculation. The
effective medium elements are implemented as eight-noded isoparametric solid elements;
the tow elements as 1D springs. If geometrical irregularity has been introduced by
randomly offsetting initial node positions, a single simulation becomes a Monte Carlo
calculation. The effects of irregularity on macroscopic stiffness are determined by
averaging over many Monte Carlo calculations.
5.3 Comparison of Code Predictions for a Plain Woven Textile Composite
Several of the codes in Table 5.3 can predict the stiffness of a plain woven textile
composite. These codes were each run with the input parameters for a typical
carbon/epoxy composite shown in Tables 5.6 and 5.7. In Table 5.6, "yarn" properties are
those of a unidirectional composite having the "yarn fiber volume %" of Table 5.7. They
are quoted for a coordinate system in which the x-axis lies along the fiber direction and
the x-y plane is the plane of isotropy. The matrix properties are assigned to any volume of
the textile composite not assigned to a yarn. The test case matches the parameters in Ref.
[5.28], which also provides experimental data.
The codes were used to compute the properties of a single ply of plain woven
composite. They yielded the predictions for the 3D stiffness matrix shown in Table 5.8
and the thermal expansion coefficients shown in Table 5.9. In these tables, x
3
is the
through-thickness direction of the composite, and x
1
and x
2
its in-plane directions, which
are equivalent in a plain weave. The stiffness predictions for the axial stiffness, E
1
, fall
within a narrow band. The largest variation is in Poisson’s ratio,
ν
12
. The out-of-plane
stiffnesses are not available from codes such as PW, which are purely plate analyses. The
results labeled CLT (classical laminate theory) are provided for comparison. These were
obtained independently of the codes by volume averaging the stiffness matrix for a stack
of flat layers corresponding to warp and weft fibers, with a resin layer added to obtain the
correct overall fiber volume fraction.