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