Page 133 - Mechanics Analysis Composite Materials

118 Mechanics and analysis of composite materials

that is the basic element of composite structures. This information is provided
by experimental methods discussed above. As a result, the ply is presented as an
orthotropic homogeneous material possessing some apparent (effective) mechanical
characteristics determined experimentally.This means that on the ply level we use a
phenomenological model of a composite material (see Section 1.l) that ignores its
actual microstructure.
It should be emphasized that this model, being quite natural and realistic for the
majority of applications, sometimes does not allow us to predict actual material
behavior. To demonstrate this, consider a problem of biaxial compression of a
unidirectional composite in the 23-plane as in Fig. 3.72. Testing a glass-epoxy
composite material described by Koltunov et al. (1977) shows a surprising result -
its strength is about 8 = 1200 MPa which is quite close to the level of material
strength under longitudinal tension, and material failure is accompanied with the
fiber breakage typical for longitudinal tension.
Phenomenologicalmodel fails to predict this mode of failure. Indeed, the average
stress in the longitudinal direction specified by Eq. (3.75) is equal to zero under
loading shown in Fig. 3.72, Le.,
01 = 0,Uf + 0yu, = 0 . (3.127)
f
To apply the first-order micromechanical model considered in Section 3.3, we
generalize constitutive equations, Eqs. (3.63), for the three-dimensional stress state
of the fibers and the matrix as

(3.128)

Changing 1 for 2, 2 for 3, and 3 for I we can write the corresponding equations for
€2 and 83.
Assume that the stresses acting in the fibers and in the matrix in the plane of
loading are the same, i.e.,

Fig. 3.72. Biaxial compression of a unidirectional composite.