Page 75 - Plastics Engineering

58 Mechanical Behaviour of Plastics
The bulk modulus is appropriate for situations where the material is subjected
to hydrostatic stresses. The proof of equations (2.15) and (2.16) is given by
Benham et al.

Example 23 A cylindrical polypropylene tank with a mean diameter of 1 m
is to be subjected to an internal pressure of 0.2 MN/m2. If the maximum strain
in the tank is not to exceed 2% in a period of 1 year, estimate a suitable value
for its wall thickness. What is the ratio of the hoop strain to the axial strain in
the tank. The creep curves in Fig. 2.5 may be used.
Solution The maximum strain in a cylinder which is subjected to an internal
pressure, p, is the hoop strain and the classical elastic equation for this is

PR
€0 = -(2 - U)
2hE
where E is the modulus, R is the cylinder radius and h is the wall thickness
(See Appendix C).
The modulus term in this equation can be obtained in the same way as
in the previous example. However, the difference in this case is the term
u. For elastic materials this is called Poissons Ratio and is the ratio of the
transverse strain to the axial strain (See Appendix C). For any particular
metal this is a constant, generally in the range 0.28 to 0.35. For plastics
u is not a constant. It is dependent on time, temperature, stress, etc and
so it is often given the alternative names of Creep Contraction Ratio or
Lateral Strain Ratio. There is very little published information on the creep
contraction ratio for plastics but generally it varies from about 0.33 for hard
plastics (such as acrylic) to almost 0.5 for elastomers. Some typical values are
given in Table 2.1 but do remember that these may change in specific loading
situations.
Using the value of 0.4 for polypropylene,

PR
h= -(2-~)
~EE
6.5
from Fig. 2.7, E = - 325 MNlm2
=
0.02
0.2 x 0.5 x 103 x 1.6
... h= = 12.3 mm
2 x 0.02 x 325
For a cylindrical tank the axial strain is given by

PR
Ex = -(1 - 2u)
2hE
2 = (-) 1.6
2-u
so = - = 8
Ex 1 - 2v 0.2