Page 79 - Plastics Engineering

62 Mechanical Behaviour of Plastics
to bear in mind that the manufacturing method may have introduced anisotropy
which will result in different thermal responses in different directions in the
material.
The coefficient of thermal expansion, UT, is given by

(2.17)

where SL is the change in length in the material
L is the original length
AT is the change in temperature.
There are standard procedures for determining UT (e.g. ASTM 696) and
typical values for plastics are given in Table 1.2. It may be observed that the
coefficients of thermal expansion for plastics are higher than those for metals.
Thus if 50 mm lengths of polypropylene and stainless steel are each heated up
by 60°C the changes in length would be

(a) polypropylene, SZ = 100 x x 50 x 60 = 0.3 mm
(b) stainless steel, SL = 10 x x 50 x 60 = 0.03 mm

If these changes in length take place freely then we will have a thermally
induced strain in the material (= 0.3 x 100/50 = 0.6% in the polypropylene)
but no stress. However, if the polypropylene was constrained in some way so
that the 0.3 mm expansion could not happen when it is heated by 6O"C, then
there would be a thermally induced stress in the material, i.e.
stress = modulus x strain

If the modulus of the material is 1.2 GN/m2 at the final temperature, then the
stress in the material would be given by

stress = 1.2 x io9 (;E) - = -7.2 MN/m2

Note that the stress is compressive because the material is effectively
compressed by 0.3 mm.
Example 2.6 The bobbin shown in Fig. 2.16 has been manufactured by
sliding the acetal ring on to the steel inner and then placing the end-plate in
position. At 20°C there are no stresses in the acetal and the distance between
the metal end-plates is equal to the length of the acetal ring. If the whole
assembly is heated to lOO"C, calculate the axial stress in the acetal. It may be
assumed that there is no friction between the acetal and the steel. The coeffi-
cients of thermal expansion for the acetal and the steel are 80 x 10-6"C-' and
11 x 10-60C-1 respectively. The modulus of the acetal at 100°C is 1.5 GN/m*.