Biomedical Engineering Reference
In-Depth Information
Fig. 3.1.2-9 (A) Elongation versus time at constant load (creep) of ligament. (B) Load versus time at constant elongation
(stress relaxation) for ligament.
the load is applied at some finite rate. During the course of
load application, there is time for some viscous flow to
occur along with the elastic strain. Thus, the total strain
will be greater than that due to the elastic response alone. If
this total strain is used to estimate the Young's modulus of
thematerial (E
ΒΌ
s
/
3), the estimatewill be low. If the test is
conducted at a more rapid rate, there will be less time for
viscous flow during the test and the apparent modulus will
increase. If a series of such tests is conducted at ever higher
loading rates, eventually a rate can be reached where no
detectable viscous flow occurs and the modulus de-
termined at this critical rate will be the true elastic mod-
ulus, i.e., the spring constant of the elastic component.
Tests at even higher rates will produce no further increase
in modulus. For all viscoelastic materials, moduli de-
termined at rates less than the critical rate are ''apparent"
moduli and must be identified with the strain rate used.
Failure to do this is one reason why values of tissue moduli
reported in the literature may vary over wide ranges.
Finally, it should be noted that it may be difficult to
distinguish between creep and plastic deformation in or-
dinary tensile tests of highly viscoelastic materials (e.g.,
tissues). For this reason, the total nonelastic deformation
of tissues or polymersmay at times be loosely referred to as
plastic deformation even though viscous flow is involved.
though the service stresses imposed are well below the
yield stress. This occurs when the loads are applied and
removed for a great number of cycles, as happens to pros-
thetic heart valves and prosthetic joints. Such repetitive
loading can produce microscopic cracks that then propagate
by small steps at each load cycle.
The stresses at the tip of a crack, a surface scratch, or
even a sharp corner are locally enhanced by the stress-
raising effect. Under repetitive loading, these local high
stresses actually exceed the strength of the material over
a small region. This phenomenon is responsible for the
stepwise propagation of the cracks. Eventually, the load-
bearing cross-section becomes so small that the part fi-
nally fails completely.
Fatigue, then, is a process by which structures fail as
a result of cyclic stresses that may be much less than the
UTS. Fatigue failure plagues many dynamically loaded
structures, from aircraft to bones (march- or stress-
fractures) to cardiac pacemaker leads.
The susceptibility of specific materials to fatigue is de-
termined by testing a group of identical specimens in cyclic
tension or bending (
Fig. 3.1.2-11A
) at different maximum
stresses. The number of cycles to failure is then plotted
against themaximumapplied stress (
Fig. 3.1.2-11B
). Since
the number of cycles to failure is quite variable for a given
stress level, the prediction of fatigue life is a matter of
probabilities. For design purposes, the stress that will
provide a lowprobability of failure after 10
6
to 10
8
cycles is
often adopted as the fatigue strength or endurance limit of
thematerial. This may be as little as one third or one fourth
of the single-cycle yield strength. The fatigue strength is
sensitive to environment, temperature, corrosion, de-
terioration (of tissue specimens), and cycle rate (especially
for viscoelastic materials) (
Newey and Weaver, 1990
).
Other important properties
of materials
Fatigue
It is not uncommon for materials, including tough and
ductile ones like 316L stainless steel, to fracture even
A
B
F
F
Fig. 3.1.2-10 (A) Dash pot or cylinder and piston model of viscous flow. (B) Dash pot and spring model of a viscoelastic material.
