Mechanical properties - Orthopaedic Biomaterials in Research and Practice - page 66

probability of failure at a stress (above the endurance limit) is called
the fatigue life.
As the number of cycles increases, the stress that produces a 50%
probability of failure decreases. However, for many materials, includ-
ing iron-base, cobalt-base, and titanium-base alloys, the curve flattens
out in the region of 10 6 -10 7 cycles and becomes horizontal. This part of
the curve is called the “knee,” and the constant stress value is called the
fatigue or endurance limit . Designs for cyclic load applications attempt
to keep peak stresses below this value so that an infinite amount of cycles
may be sustained without failure. In many metallic alloy systems, it is
observed that this endurance limit is an essentially constant proportion
of σ u (as fabricated), typically between 0.5 and 0.3.
Types of fatigue failure Failures occur in two types as a result of
cyclic load. The first is the region on the left side of Figure 3.8 and is
called high-stress, low-cycle failure. The peak cyclic stress required to
produce this type of failure is high (designated here as σ H ) and may even
exceed the yield stress. The other type of failure occurs to the right of the
figure and is called low-stress, high-cycle failure . The peak stress that
produces this type of failure is low (designated here as σ L ) and may be
near the endurance limit.
PROBLEM 3.3
For the material represented by the S - N curve in Figure 3.8, what are the
fatigue lives for σ y , σ H , and σ L ?
ANSWER:
σ y yields a fatigue life of 100 cycles, and σ H yields a fatigue life of 300
cycles. Both of these stresses would produce very early failure. σ L would
probably exceed 10 7 cycles in air, since it is so close to the endurance
limit. However, in vivo, it might be limited to 5 × 10 5 cycles or several
months of ordinary use.
Fatigue processes may produce modest changes in elastic behavior by
an accumulation of work hardening, if local stresses exceed σ 0 owing to
stress concentration effects. This is rarely reflected in measurable prop-
erties. However, composites often show marked reductions in elastic
modulus before fracture, owing to sequential failure of the interfaces
between the various phases in those materials. In such cases, a failure
criterion, usually a modulus reduction of between 10% and 30%, may be
selected, and the S - N curve may be plotted to reflect the 50% probability
of that reduction occurring.
Each stress-strain cycle has the ability to do a certain amount of work
per unit volume of material. In high-stress situations, this work is enough
to either initiate or propagate a fatigue crack. However, in low-stress
situations, the stress may be inadequate either to form a new crack or to
propagate a previously formed crack. Outside of stress magnitude, the
difference in response to stress may be affected by other factors, includ-
ing the following: