Biomedical Engineering Reference
In-Depth Information
Fig. 7.2 Curves of stress against strain for steel and aluminum rods. Note that the strain is in
percentage. The elastic limit and the tensile strength (fracture point) are indicated
, that is an equation of a straight line,
where Y is Young's modulus, the slope of the straight line. The larger is the slope of
the straight line with respect to the x axis, in this case the axis of strain
Equation ( 7.4 ) can be written as
σ ¼
Y
ε
, the greater
is Young's modulus. Figure 7.2 shows the graph of stress as a function of strain for
steel and aluminum rods, subjected to tension. Observe that the equation of the
straight line
ε
is represented by dotted lines. In the case of the steel rod, the
slope of the straight line is much greater than that for the aluminum rod. We can
also say that for the same applied stress, the smaller is Young's modulus, the larger
is the strain produced.
The elastic phase of a material corresponds to a regime in which the object
returns to its original shape, when the stress is removed; in terms of stress, it
corresponds to stresses between zero and the elastic limit. Above the elastic limit,
the phase is said to be plastic and the deformation produced becomes permanent
until the tensile or compressive strength is exceeded, when the object breaks
(fracture point). It is important to emphasize that once the plastic limit is surpassed,
it will be very easy to break any piece, even made of metal, by twisting it from one
side to another as we usually do when the opener of an aluminum can is removed.
For metallic objects, generally, Young's modulus has the same value for tensile
or compressive stresses. This is not true for heterogeneous materials such as wood,
concrete, plastic and bones, that, besides a different Young's modulus for tensile or
compressive stresses, have also different elastic limits and fracture points.
Table 7.1 gives Young's modulus, the shear modulus, the elastic limit and the
compressive and tensile strength for some common solids. Observe that either the
elastic limit or the strength in Table 7.1 is the value of stresses the limits the elastic
from the plastic phase and that causes fracture of a given solid and is measured in
pascal (Pa).
σ ¼
Y
ε
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