Biomedical Engineering Reference
In-Depth Information
Table 3.1.2-3 Mechanical properties derivable from a tensile test
Property
Units
Fundamental
a
International
English
N/m
2
(Pa)
lbf
b
/in.
2
(psi)
1. Elastic modulus (E)
F/A
N/m
2
(Pa)
lbf/in.
2
(psi)
2. Yield strength (
s
yield
)
F/A
N/m
2
(Pa)
lbf/in.
2
(psi)
3. Ultimate tensile strength (
s
uts
)
F/A
4. Ductility (
3
ductility
)
%
%
%
J/m
3
in lbf/in.
3
5. Toughness (work to fracture per unit volume)
F d/V
a
F, force; A, area; d, length; V, volume.
b
lbf, pounds force.
Creep and viscous flow
influence of an applied stress are forced to move, irre-
versibly, to new locations in the crystal structure. This is the
microstructural basis of plastic deformation. During elastic
straining, on the other hand, the atoms are displaced only
slightly by reversible stretching of the interatomic bonds.
Large scale displacement of atoms without complete
rupture of the material, i.e., plastic deformation, is only
possible in the presence of themetallic bond so onlymetals
and alloys exhibit true plastic deformation. Since long-
distance rearrangement of atoms under the influence of an
applied stress cannot occur in ionic or convolutely bonded
materials, ceramics and many polymers do not undergo
plastic deformation.
Plastic deformation is very useful for shaping metals and
alloys and is called ductility or malleability. The total per-
manent (i.e., plastic) strain exhibited up to fracture by
a material is a quantitative measure of its ductility
(
Fig. 3.1.2-8
). The strength, particularly the 0.2% offset
yield strength, can be increased significantly by reducing the
grain size as well as by prior plastic deformation or coldwork.
The introductions of alloying elements and multiphase mi-
crostructures are also potent strengthening mechanisms.
Other properties can be derived from the tensile stress-
strain curve. The tensile strength or the ultimate tensile
stress (UTS) is the stress that is calculated from the maxi-
mum load experienced during the tensile test (
Fig. 3.1.2-8
).
The area under the tensile curve is proportional to the
work required to deform a specimen until it fails. The area
under the entire curve is proportional to the product of
stress and strain, and has the units of energy (work) per unit
volume of specimen. The work to fracture is a measure of
toughness and reflects a material's resistance to crack
propagation (
Fig. 3.1.2-8
)(
Newey and Weaver, 1990
).
The important mechanical properties derived from a ten-
sile test and their units are listed in
Table 3.1.2-3
. Repre-
sentative values of these properties for some important
biomaterials are listed in
Table 3.1.2-2
.
For all the mechanical behaviors considered to this point, it
has been assumed that when a stress is applied, the strain
response is instantaneous. For many important biomaterials,
including polymers and tissues, this is not a valid assump-
tion. If a weight is suspended from an excised ligament, the
ligament elongates essentially instantaneously when the
weight is applied. This is an elastic response. Thereafter the
ligament continues to elongate for a considerable time even
though the load is constant (
Fig. 3.1.2-9A
). This continuous,
time-dependent extension under load is called ''creep.''
Similarly, if the ligament is extended in a tensile ma-
chine to a fixed elongation and held constant while the
load is monitored, the load drops continuously with time
(
Fig. 3.1.2-9B
). The continuous drop in load at constant
extension is called stress relaxation. Both these responses
are the result of viscous flow in the material. The me-
chanical analog of viscous flow is a dash-pot or cylinder
and piston (
Fig. 3.1.2-10A
). Any small force is enough to
keep the piston moving. If the load is increased, the rate
of displacement will increase.
Despite this liquid-like behavior, these materials are
functionally solids. To produce such a combined effect, they
act as though they are composed of a spring (elastic ele-
ment) in series with a dashpot (viscous element) (
Fig. 3.1.2-
10B
). Thus, in the creep test, instantaneous strain is pro-
duced when the weight is first applied (
Fig. 3.1.2-9A
). This
is the equivalent of stretching the spring to its equilibrium
length (for that load). Thereafter, the additional time-
dependent strain is modeled by the movement of the
dashpot. Complex arrangements of springs and dashpots
are often needed to adequatelymodel the actual behavior of
polymers and tissues.
Materials that behave approximately like a spring and
dash-pot system are viscoelastic. One consequence of
viscoelastic behavior can be seen in tensile testing where
