General Design Principles for DuPont Engineering Polymers - Module

Figure 4.01 Creep
Stress (S), MPa (psi)
S oe o
e o
Strain (e), mm/mm (in/in)
S oe t
Creep between time T and T o = e T – e o mm/mm (in/in).
The creep modulus E T Pa (psi) for design in creep
applications at stress S o and time T is the slope of the
secant from the origin to the point (S o e T ).
The stress required to deform a plastic material a fixed
amount will decay with time due to the same creep
phenomenon. This decay in stress with time is called
stress relaxation.
Stress relaxation is defined as the decrease, over a
given time period, of the stress (Pa, psi) required to
maintain constant strain. Like creep, it can occur in
tension, compression, flexure or shear. On a typical
stress-strain curve it is shown in Figure 4.02.
Figure 4.02 Relaxation
Stress (S), MPa
S o
S T
e o
Strain (e), mm/mm (in/in)
S oe o
S Te o
e t
Relaxation between
time T and T o =
S o – S T Pa (psi). The
relaxation modulus
E T Pa (psi) for design
in relaxation applications
(e.g., press
fits) at time T is the
slope of the secant
from the origin to the
point (S Te o).
Laboratory experiments with injection molded
specimens have shown that for stresses below about
1 ⁄ 3 of the ultimate tensile strength of the material at
any temperature, the apparent moduli in creep and
relaxation at any time of loading may be considered
similar for engineering purposes. Furthermore, under
these conditions, the apparent moduli in creep and
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relaxation in tension, compression and flexure are
approximately equal.
A typical problem using creep data found in the
properties sections is shown below.
Cylinder under Pressure
Example 1: A Pressure Vessel Under Long-Term
Loading
As previously noted, it is essential for the designer to
itemize the end-use requirements and environment of
a part before attempting to determine its geometry.
This is particularly true of a pressure vessel, where
safety is such a critical factor. In this example, we will
determine the side wall thickness of a gas container
which must meet these requirements: a) retain pressure
of 690 kPa (100 psi), b) for 10 years, c) at 65°C
(150°F).
The inside radius of the cylinder is 9.07 mm (0.357 in)
and the length is 50.8 mm (2 in). Because the part will
be under pressure for a long period of time, one
cannot safely use short-term stress-strain data but
should refer to creep data or, preferably, long-term
burst data from actual pressure cylinder tests. Data
typical of this sort for 66 nylons is shown in Fig. 4.03
which plots hoop stress versus time to failure for
various moisture contents at 65°C (150°F). Actually,
Zytel ® 101 would be a good candidate for this application
as it has high impact strength in the 50% RH
stabilized condition and the highest yield strength of
unreinforced nylons.
Referring to the curve, we find a hoop stress level of
18.63 MPa (2700 psi) at 10 years, and this can be used
as the design stress. The hoop stress formula for a
pressure vessel is:
t = Pr × F.S.
S
where:
t = wall thickness, mm (in)
P = internal pressure, MPa (psi)
r = inside diameter, mm (in)
S = design hoop stress, MPa (psi)
F.S. = factor of safety = 3
t = (.690) (9.07) (3) (100) (.357) (3)
18.63 2700
= 1.0 mm (0.040 in)
The best shape to use for the ends of the cylinder is a
hemisphere. Hemispherical ends present a design
problem if the cylinder is to stand upright. A flat end
is unsatisfactory, as it would buckle or rupture over a
period of time. The best solution, therefore, is to mold
a hemispherical end with an extension of the cylinder
or skirt to provide stability (see Figure 4.04).