Page 181 - Plastics Engineering

164 Mechanical Behaviour of Plastics

2.41 A plastic which behaves like a Kelvin-Voigt model is subjected to the stress history
shown in Fig. 2.87. Use the Boltzmanns Superposition Principle to calculate the strain in the
material after (a) 90 seconds (b) 150 seconds. The spring constant is 12 GN/m2 and the dashpot
constant is 360 GNs/m2.

Stress
( MN/m2)

10

0
50 100 Time (s)

Fig. 2.87
2.42 A plastic component was subjected to a series of step changes in stress as follows. An
initial constant stress of 10 MN/m2 was applied for lo00 seconds at which time the stress level
was increased to a constant level of 20 MN/m2. After a further lo00 seconds the stress level was
decreased to 5 MN/m2 which was maintained for 1000 seconds before the stress was increased to
25 MN/mz for 1000 seconds after which the stress was completely removed. If the material may
be represented by a Maxwell model in which the elastic constant 6 = 1 GN/m2 and the viscous
constant q = 4000 GNs/mZ, calculate the strain 4500 seconds after the first stress was applied.
2.43 In tests on a particular plastic it is found that when a stress of 10 MN/mZ is applied for 100
seconds and then completely removed, the strain at the instant of stress removal is 0.8% and 100
seconds later it is 0.058%. In a subsequent tests on the same material the stress of 10 MN/m2 is
applied for 2400 seconds and completely removed for 7200 seconds and this sequence is repeated
10 times. Assuming that the creep curves for this material may be. represented by an equation of
the form E(r) = Ar" where A and n are constants then determine the total accumulated residual
strain in the material at the end of the loth cycle.
2.44 In a small polypropylene component a tensile stress of 5.6 MNh2 is applied for lo00
seconds and removed for 500 seconds. Estimate how many of these stress cycles could be
permitted before the component reached a limiting strain of 1%. What is the equivalent modulus
of the material at his number of cycles? The creep curves in Fig. 2.5 may be used.
2.45 A cylindrical polypropylene pressure vessel of 150 mm outside diameter is to be pres-
surised to 0.5 MN/m2 for 6 hours each day for a projected service life of 1 year. If the material
can be described by an equation of the form e(r) = Arn where A and n are constants and the
maximum strain in the material is not to exceed 1.5% estimate a suitable wall thickness for
the vessel on the assumption that it is loaded for 6 hours and unloaded for 18 hours each day.
Estimate the material saved compared with a design in which it is assumed that the pressure is
constant at 0.5 MN/mZ throughout the service life. The creep curves in Fig. 2.5 may be used.