Biomedical Engineering Reference
In-Depth Information
∑
failure Strength, sf.
f
.
this is the stress at catastrophic failure (3). it may
or may not correspond to the ultimate tensile strength.
∑
Work of fracture (toughness).
taken as the area under the entire stress-
strain curve, from origin to failure, this is a measure of the ability of
a material to absorb energy up to fracture. Note that this is a slightly
different concept from values most often cited as 'toughness', which are
actually the fracture toughness and a measure of a material's ability to
resist crack propagation (see Section 5.2.3).
∑
Ductility, %El or %RA.
Ductility is a measure of the amount of plastic
deformation at fracture. Very generally, this can be seen by the shape
of the stress-strain curve. Curve A undergoes extremely little plastic
deformation, whereas Curves B, C and D display considerably more. Values
of ductility can be given as percentage elongation (%eL) or percentage
reduction (%RA) in area according to the following formulae:
l
l
f
-
-
l
0
[5.1]
% =
f
100%
%
E
%
l
×
0
AA
-
AA
-
0
AA
0
A
f
AA
×
f
[5.2]
% =
%
R
%
0
100%
A
A
0
0
where
l
f
and
l
0
are the fi nal and initial length, respectively and
A
f
and
A
0
are the fi nal and initial cross-sectional areas, respectively. A material with
a low value of ductility (0-5%) is said to be brittle, whereas a material
with a high value is said to be ductile.
the four different curves displayed in Fig. 5.3 are typical of different
types of materials. Curve A displays the high modulus and brittle behaviour
common to ceramics and bone cement. As no plastic deformation occurs in
this case, points (2) and (3) are the same. Curve B shows a material with a
moderate modulus, a fair degree of yielding, and the blurred elastic-plastic
transition common to metals and alloys. the more distinct yield point and
yielding behaviour of curve C is common of many polymers. Curve D
displays the typical behaviour of elastic polymers, such as rubber. these are
very general curve shapes and classifi cations, at best, but should give some
idea of how varied material behaviour can be. indeed the shape of a curve
may differ considerably for the same material, depending on the processing
conditions or testing environment.
5.2.2 Other strength tests
While tensile tests work well for most metals and polymers, ceramics pose
more of a problem. First, it is diffi cult to prepare ceramic specimens with
the right geometry (often a dog-bone shape) and their brittle nature makes
