Page 110 - Mechanics Analysis Composite Materials

Chapter 3. Mechanics of a unidirectional ply 95

Thus, we have found the exact solution, but its agreement with experimental data is
rather poor (see Fig. 3.37) because the material model is not quite adequate.
As follows from the foregoing discussion, micromechanical analysis provides only
qualitative prediction of the ply stiffness. The same is true for the ply strength.
Though micromechanical approach in principle can be used for the strength analysis
(Skudra et al., 1989), it provides mainly proper understanding of the failure
mechanism rather than the values of the ultimate stresses for typical loading cases.
For practical applications, these stresses are determined by experimental methods
described in the next section.

3.4. Mechanical properties of a ply under tension, shear, and compression

As shown in Fig. 3.29, a ply can experience five types of elementary loading, i.e.,
0 tension along the fibers,
0 tension across the fibers,
0 in-plane shear,
0 compression along the fibers,
0 compression across the fibers.
Actual mechanical properties of a ply under these loading cases are determined
experimentally by testing specially fabricated specimens. Because the thickness of an
elementary ply is very small (0.1-0.2 mm), the specimen consists usually of tens of
plies having the same fiber orientations.
Mechanical properties of composite materials depend on the processing type
and parameters. So, to obtain the adequate material characteristics that can be used
for analysis of structural elements, the specimens should be fabricated with the
same processes that are used to manufacture the structural elements. In connection
with this, there exist two standard types of specimens - flat ones that are used to
test materials made by hand or machine lay-up and cylindrical (tubular or ring)
specimens that represent materials made by winding.
Typical mechanical properties of unidirectional advanced composites are
presented in Table 3.5 and in Figs. 3.4CL3.43.
Consider typical loading cases.

3.4.1. Longitudinal tension

Stiffness and strength of unidirectional composites under longitudinal tension are
determined by the fibers. As follows from Fig. 3.35, material stiffness linearly
increases with the rise of the fiber volume fraction. The same law following from
Eq. (3.75) is valid for the material strength. If the fibers ultimate elongation, Ef, is
less than that of the matrix (which is normally the case), longitudinal tensile strength
is determined as