Ceramics and composites - Orthopaedic Biomaterials in Research and Practice - page 216

side, upper curve), it is often said that the strength of a composite is the
strength of its stronger phase.

Stress-strain curve for a composite material The result of the effects
of the matrix and the fiber on composite strength may be seen in the
stress-strain curve of a composite, as shown in Figure 8.5. The same
matrix and fiber properties assumed in Figures 8.3 and 8.4 were used
to construct this curve. For a composite with V f = 0.5, at low strain,
the curve is well behaved. However, when the strain exceeds ε u(f ) , fibers
begin to fracture sequentially and the sustainable stress decreases.
Finally, an ultimate stress is reached. This cannot exceed (1 − V f )σ u(m)
and may be much less if the matrix is notch sensitive. For the same rea-
son, ε u(c) is usually less than ε u(m) .
The point P marked on the stress-strain curve is one at which the
stress has declined to approximately 80% of maximum with a strain
approximately 50% greater than ε u(f ) . If the “modulus” is calculated con-
tinuously (= σ/ε) while the stress-strain curve is generated, it will be
approximately 30% less here than in the initial elastic region. Since σ max
has been exceeded and significant numbers of fibers have broken, the
decrease in instantaneous modulus (in this case, 30%) is often used as an
indication of failure of composites, rather than σ u(c) . This is particularly
useful in fatigue studies during which the peak value of σ/ε is usually
plotted continuously as a function of the number of load-unload cycles,
and a predetermined modulus decrease, usually between 10% and 30%,
is selected as a failure criterion.
It is clear that there are large numbers of trade-offs to be made in
composite design. Is maximum stiffness required? Is maximum strength
required? What is the minimum toughness? And so forth. Combined
with anisotropy effects, it is obvious that composites must be designed
for each application and cannot be kept “on the shelf” in the manner of
more conventional metallic and polymeric materials.

E f = 100 GPa
E m = 4 GPa

Fiber

2000

σ
(MPa)

1000

P

V f = 0.05 Matrix

ε u(f ) 0.05 0.1 0.15 0.2

ε

FIGUre 8.5 stress-strain curve for two-phase voigt composite
( V f = 0.5).