Biomedical Engineering Reference
In-Depth Information
load cell, and cyclic testing in a standard mechanical
testing machine. To do so, Hooke's law is rearranged as
follows:
E
ΒΌ
s
3
:
(3.1.2.3)
Brittle fracture
In real materials, elastic behavior does not persist in-
definitely. If nothing else intervenes, microscopic defects,
which are present in all real materials, will eventually
begin to grow rapidly under the influence of the applied
tensile or shear stress, and the specimen will fail suddenly
by brittle fracture. Until this brittle failure occurs, the
stress-strain diagramdoes not deviate from a straight line,
and the stress at which failure occurs is called the fracture
stress (
Fig. 3.1.2-6
). This behavior is typical of many
materials, including glass, ceramics, graphite, very hard
alloys (scalpel blades), and some polymers like poly-
methyl-methacrylate (bone cement) and unmodified poly
vinyl chloride (PVC). The number and size of defects,
particularly pores, is the microstructural feature that
most affects the strength of brittle materials.
Fig. 3.1.2-7 Mechanical testing machine.
Plastic deformation
reproducibility of results (see the publications of the
American Society for Testing and Materials, 100 Barr
Harbor Dr., West Conshohocken, PA 19428-2959).
Another useful test that can be conducted in a me-
chanical testing machine is the bend test. In bend testing,
the outside of the bowed specimen is in tension and the
inside in compression. The outer fiber stresses can be cal-
culated from the load and the specimen geometry (see any
standard text on strength of materials;
Meriam, 1996
).
Bend tests are useful because no special specimen shapes
are required and no special grips are necessary. Strain gages
can also be used to determine the outer fiber strains. The
available formulas for the calculation of stress states are
only valid for elastic behavior. Therefore, they cannot be
used to describe any nonelastic strain behavior.
Some mechanical testing machines are also equipped
to apply torsional (rotational) loads, in which case torque
versus angular deflection can be determined and used to
calculate the torsional properties of materials. This is
usually an important consideration when dealing with
biological materials, especially under shear loading con-
ditions (
Hummel, 1997
).
For some materials, notably metals, alloys, and some
polymers, the process of plastic deformation sets in after
a certain stress level is reached but before fracture occurs.
During a tensile test, the stress at which 0.2% plastic strain
occurs is called the 0.2% offset yield strength. Once plastic
deformation starts, the strains produced are very
much greater than those during elastic deformation
(
Fig. 3.1.2-8
); they are no longer proportional to the stress
and they are not recovered when the stress is removed.
This happens because whole arrays of atoms under the
uts
yield
Toughness
E
Elasticity
0.2%
ductility
The tensile elastic modulus, E (for an isotropic material),
can be determined by the use of strain gages, an accurate
Fig. 3.1.2-8 Stress versus strain for a ductile material.
