Page 95 - Mechanics Analysis Composite Materials

80 Mechanics and analysis of composite materials

Fig. 3.28. Mechanism of the crack stopping at the fiber-matrix interface.

results not only in higher static strength along the fibers (line l), which is quite
natural. It is also accompanied with elevation of the work of fracture (line 2) and
consequently, in the increase of material fatigue strength (bending under IO6 cycles,
line 3), which shows its sensitivity to cracks.
The reason for such a specific behavior of composite materials is associated with
their inhomogeneous microstructure, particularly, with fiber-matrix interfaces that
restrain free propagation of a crack (see Fig. 3.28). Of some importance are also
fiber defects, local delaminations and fiber strength deviation, which reduce the
static strength but increase the fracture toughness. As a result, combining brittle
fibers and brittle matrix we usually arrive at the composite material whose fracture
toughness is higher than that of its components.
Thus, we can conclude that composites comprise a new class of structural
materials entirely different from traditional man-made materials for the several
reasons. First, using thin fibers we make an attempt to utilize the high strength
capacity that is naturally inherent in all the materials. Second, this utilization is
provided by the matrix material, which increases the fiber performance and makes
it possible to manufacture composite structures. Third, combination of fibers and
matrices can result in new qualities of composite materials that are not inherent
either in individual fibers or in the matrices and are not described by the laws of
mechanical mixtures. For example, as noted above, brittle fiber and matrix
materials, both having low fracture toughness, can provide a heterogeneous
composite material with high fracture toughness.

3.3. Micromechanics of a ply

Consider a unidirectional composite ply under the action of in-plane normal and
shear stresses as in Fig. 3.29. Because normal stresses do not change the right angle
between axes 1 and 2, and shear stresses do not cause elongations in the longitudinal
and transverse directions 1 and 2, the ply is orthotropic, and the corresponding
constitutive equations, Eqs. (2.48) and (2.53) yield for the case under study