Page 203 - Mechanics Analysis Composite Materials

188 Mechanics and analysis of composite materials

Under pure shear of an angle-ply layer, its plies are loaded with the additional
normal stresses. These stresses can be found if we take sx = 0 and sY = 0 in the first
two equations of Eqs. (4.75). The result is

Substituting these expressions into the third equation we get z,,, = Gxyyxy, where

is the shear modulus of an angle-ply layer which is much higher than G.C. (see
Fig. 4.57).
Tension of f45" angle-ply specimen provides a simple way to determine in-plane
shear modulus of a unidirectional ply, G12. Indeed, for this layer, Eqs. (4.72) and
(4.129) yield

and

1 1
E45 = - (A;; + A::)(A;; - A;;), 1 + ~45 = - (A;: + A::) .
A:: A::

Taking into account that A:; -A:; = 2G12 we have

G- E45 (4.132)
I2 - 2(1 + v45)

Thus, to find G12, we can test a f45" specimen under tension, measure and E~,
determine E45 = v45 = -E~/E.~, and use Eq. (4.132) rather than perform
cumbersome tests described in Section 3.

4.5.2. Nonlinear models

To describe nonlinear behavior of an angle-ply layer associated with material
nonlinearity of its plies, we can use nonlinear constitutive equations, Eqs. (4.60) or
Eqs. (4.64), instead of Hooke's law. Indeed, assuming that the ply behavior is linear
under tension or compression along the fibers we can write these equations in the
following general form: