Biomedical Engineering Reference
In-Depth Information
Figure 5.8
Stress-strain behavior: (a) different regions and (b) a comparison to other structural
materials.
plate is desirable for internal fixation purposes, allowing the surgeon, within limits,
to plastically contour the plate to bone without incurring brittle fracture.
Maximal tensile forces or compressive forces in the structure are generated on
a plane perpendicular to the applied load (i.e., the normal force). Consequently,
failure typically occurs along this plane. As in pure tension, maximal stresses oc-
cur on a plane perpendicular to the applied load; however, the stress distribution
and resultant fracture mechanics in compressive failure are often very complicated,
particularly for an anisotropic material such as bone.
5.3.2.1 Stresses Due to Pressure
Many conduits in the body transport fluids under pressure. For example, blood ves-
sels carry liquids under pressure. In these cases, the material comprising the vessel
is subjected to pressure loading, and hence stresses, from all directions within the
conduit. The normal stresses resulting from this pressure are functions of the radius
of the element under consideration, the shape of the pressure vessel (i.e., cylinder,
or sphere), and the applied pressure. The method of analyses can be grouped into
thick-walled pressure vessels and thin-walled pressure vessels. Generally, a pressure
vessel is considered to be thin-walled if its radius
r
is larger than 10 times its wall
thickness. For most engineering applications, the thin-wall pressure vessel can be
used and is discussed later. For thick-walled pressure vessels, equations are called
the Lame's equation and detailed derivations can be obtained from textbooks re-
lated to the strength of the materials.
Consider a cylindrical pressure vessel with a wall thickness,
, and an inner
radius,
r
(Figure 5.9). The fluid within this vessel has a gauge pressure of
P
and is
flowing in the
z
-direction. Two types of normal stresses are generated based on the
direction:
δ
Longitudinal (or axial) stress and, if the end of the vessel is closed, stress
experienced by the end cap;
Hoop stress,
σ
h
, the stress in a pipe wall acting circumferentially in a plane
perpendicular to the longitudinal axis of the cylindrical vessel.
