Page 168 - Mechanics Analysis Composite Materials

Chapter 4. Mechanics of a eomposite layer I53
and

where

As can be seen in Eqs. (4.71) and (4.75), the layer under study is anisotropic in plane
xy because constitutive equations include shear-extension and shear-shear coupling
coefficients y and 1.For 5, = 0, the foregoing equations degenerate into Eqs. (4.55)
and (4.56) for an orthotropic layer.
Dependencies of stiffness coefficients on the orientation angle for a carbon-epoxy
composite with properties listed in Table 3.5 are presented in Figs. 4.20 and 4.21.
Uniaxial tension of the anisotropic layer (the so-called off-axis test of a
unidirectional composite) is often used to determine material characteristics that
cannot be found in tests with orthotropic specimens or to evaluate constitutive and
failure theories. Such a test is shown in Fig. 4.22. To study this loading case, we
should take cv= = 0 in Eqs. (4.75). Then

(4.77)

As can be seen from these equations, tension in the x-direction is accompanied not
only with transverse contraction, as in orthotropic materials, but also with shear.
This results in the deformed shape of the sample shown in Fig. 4.23. This shape is
natural because material stiffness in the fiber direction is much higher than that
across the fibers.
Such an experiment, in case it could be performed, allows us to determine the in-
plane shear modulus, G12 in principal material coordinates using a simple tensile test
rather than much more complicated tests described in Section 3.4.3 and shown in
Figs. 3.54 and 3.55. Indeed, if we know E, from the tensile test in Fig. 4.23 and find
El, E?, v21 from tensile tests along and across the fibers (see Sections 3.4.1 and 3.4.2),
we can use the first equation of Eqs. (4.76) to determine