Page 177 - Plastics Engineering

160 Mechanical Behaviour of Plastics
2.16 The stiffness of a closed coil spring is given by the expressions:

Stiffness = Gd4/64$N
where d is the diameter of the spring material, R is the radius of the coils and N is the number
of coils.
In a small mechanism, a polypropylene spring is subjected to a fixed extension of 10 mm.
What is the initial force in the spring and what pull will it exert after one week. The length of
the spring is 30 mm, its diameter is 10 mm and there are 10 coils. The design strain and creep
contraction ratio for the polypropylene may be taken as 2% and 0.4 respectively.
2.17 A closed coil spring made from polypropylene is to have a steady force, W, of 3 N applied
to it for 1 day. If there are 10 coils and the spring diameter is 15 mm, estimate the minimum
diameter for the spring material if it is to recover completely when the force is released.
If the spring is subjected to a 50% overload for 1 day, estimate the percentage increase in the
extension over the normal 1 day extension. The shear stress in the material is given by 16 WR/d3.
Use the creep curves supplied and assume a value of 0.4 for the lateral contraction ratio.
2.18 A rod of polypropylene, 10 mm in diameter, is clamped between two rigid fixed supports
so that there is no stress in the rod at 20°C. If the assembly is then heated quickly to 60°C
estimate the initial force on the supports and the force after 1 year. The tensile creep curves
should be used and the effect of temperature may be allowed for by making a 56% shift in the
creep curves at short times and a 40% shift at long times. The coefficient of thermal expansion
for polypropylene is 1.35 x 10-40C-' in this temperature range.
2.19 When a pipe fitting is tightened up to a 12 mm diameter polypropylene pipe at 20°C the
diameter of the pipe is reduced by 0.05 mm. Calculate the stress in the wall of the pipe after 1
year and if the inside diameter of the pipe is 9 mm, comment on whether or not you would expect
the pipe to leak after this time. State the minimum temperature at which the fitting could be used.
Use the tensile creep curves and take the coefficient of thermal expansion of the polypropylene
to be 9.0 10-50c-1.
2.20 A polypropylene pipe of inside diameter 10 mm and outside diameter 12 mm is pushed
on to a rigid metal tube of outside diameter 10.16 mm. If the polypropylene pipe is in contact
with the metal tube over a distance of 15 mm, calculate the axial force necessary to separate the
two pipes (a) immediately after they are connected (b) 1 year after connection. The coefficient
of friction between the two materials is 0.3 and the creep data in Fig. 2.5 may be used.
2.21 A nylon bush is to be inserted into a metal housing as illustrated in Fig. 2.85 The housing
has a diameter of 40 mm and the inside diameter of the bush is 35 mm. If the length of the bush is
10 mm and the initial extraction force is to be 1.2 kN, calculate (a) the necessary interference on
radius between the bush and the housing (b) the temperature to which the bush must be cooled to
facilitate easy assembly (c) the internal diameter of the bush when it is in the housing and (d) the
long term extraction force for the bush. The short term modulus of the nylon is 2 GN/mZ, its
coefficient of friction is 0.24 and its coefficient of thermal expansion is 100 x 10-60C-'. Poissons
Ratio for the Nylon is 0.4 and its long term modulus may be taken as 1 GN/mZ.
2.22 If the bobbin illustrated in Example 2.6 (Fig. 2.16) is cooled from 20°C to -40"C,
estimate the maximum hoop stress set up in the acetal. The modulus of the acetal at -40OC is
3 GN/mz and Poisson's ratio is 0.33. The coefficients of thermal expansion for acetal and steel
are 80 x 10-60C-' and 11 x 10-60C-', respectively.
2.23 From the creep curves for a particular plastic the following values of creep rate at various
stress levels were recorded for times between 106 and lo7 seconds:

stress
(MN/m*) 1.5 3.0 4.5 6.0 7.5 9.0 12.0

strain
rate (s) 4.1 x lo-" 7 x lo-" 9.5 x lo-" 1.2 x 1.4 x 1.6 x lo-'' 2 x lo-''