Biomedical Engineering Reference
In-Depth Information
This section will define the most important mechanical criteria and how they
are evaluated. table 5.2 offers a comparison of mechanical data for several
different types of replacement materials, along with those of bone.
5.2.1 The stress-strain curve
One of the most familiar diagrams to a materials scientist or engineer, a
stress-strain graph provides several pieces of key mechanical data. Various
strength tests can produce a stress-strain curve, the most common being
uniaxial tension and compression tests (Dowling, 1998c). in these tests,
the specimen is fitted between two plates and a load is applied either to
squeeze the specimen together (compression) or to pull it apart (tension).
Figure 5.2(a) shows a schematic of this procedure. As load is applied at a
specified rate, the deformation of the specimen is measured, or vice versa.
By dividing the load by the cross-sectional area of the specimen we get a
value for stress (
s
), while strain (
e
) is calculated by dividing the change in
length of the specimen by its original length. Using stress and strain values
rather than load and deformation values normalises the data for a specimen's
size and geometry.
By plotting stress against strain, we can get a good picture of the material's
behaviour and work out some of its mechanical properties. Figure 5.3 shows
a sample plot with examples of the shapes of curves for several different
types of material behaviour. In the first region of a curve, between (1) and (2),
the material's behaviour is elastic. Stress and strain are directly proportional
to one another and deformation is recoverable, as atoms in the material's
structure are displaced only slightly by the stretching of atomic bonds. the
second, plastic region of a curve (if present) lies between (2) and (3). At
a certain point, stress and strain are no longer proportional and permanent
deformation occurs as whole arrays of atoms move to a new location in the
crystal structure by breaking and reforming atomic bonds.
From the curves, we can obtain the following pieces of data:
∑
Elastic (Young's) modulus, E
. Often referred to as the stiffness, it is the
slope of the linear, elastic region of the stress-strain curve. the steeper
the slope, the higher the Young's modulus and the higher the stiffness
of a material. Some materials, mainly many polymers, do not have a
linear elastic portion (see curve D). in this case either a tangent modulus
is used, by drawing a line tangent to the curve at a specified stress and
using its slope, or a secant modulus is taken from the slope of a line
drawn from the origin to a specified point.
∑
Yield strength
,
s
ys
.
this is the stress at the point when elastic deformation
ends and plastic deformation begins (2). Many times the yield strength is
cited as the 'strength' or 'tensile strength' of a material, since it represents
