Page 76 - Plastics Engineering

Mechanical Behaviour of Plastics 59

Table 2.1
Qpical tensile and shear moduli for a range of polymers
Tensile Shear
modulus modulus Poisson’s
Density (E)? (G) ratio (u)
Material (kg/m3) (GN/m2) (GN/mZ)

Polystyrene (PS) 1050 2.65 0.99 0.33
Polymethyl Methacrylate (PMMA) 1180 3.10 1.16 0.33
Polyvinyl Chloride (PVC)
(Unplasticised) 1480 3.15 1.13 0.39
Nylon 66 (at 65% RH) 1140 0.99 0.34 0.44
Acetal Homopolymer (POM) 1410 3.24 1.15 0.41
Acetal Copolymer (POM) 1410 2.52 0.93 0.39
Polyethylene - High Density (HDPE) 955 1.05 0.39 0.34
Polyethylene - Low Density (LDPE) 920 0.32 0.1 1 0.45
Polypropylene Homopolymer (PP) 910 1.51 0.55 0.36
Polypropylene Copolymer (PP) 902 1.13 0.40 0.40
Pol yethersulphone 1390 2.76 0.98 0.41
-
tl00 second modulus at 20°C for small strains (t0.2%)

Note that the ratio of the ratio of the hoop stress (pR/h) to the axial stress
(pR/2h) is only 2. From the data in this question the hoop stress will be
8.12 MN/m2. A plastic cylinder or pipe is an interesting situation in that it is
an example of creep under biaxial stresses. The material is being stretched in
the hoop direction by a stress of 8.12 MN/mz but the strain in this direction is
restricted by the perpendicular axial stress of OS(8.12) MN/m2. Reference to
any solid mechanics text will show that this situation is normally dealt with by
calculating an equivalent stress, a,. For a cylinder under pressure a, is given
by OSa& where a0 is the hoop stress. This would permit the above question
to be solved using the method outlined earlier.
Example 2.4 A glass bottle of sparkling water has an acetal cap as shown
in Fig. 2.14. If the carbonation pressure is 375 kN/m2, estimate the deflection
at the centre of the cap after 1 month. The value of Poissons ratio for acetal
may be taken as 0.33.
Solution The top of the bottle cap is effectively a plate with clamped edges.
The central deflection in such a situation is given by Benham et al. as

PP Eh3
6 = -
where D =
640 12(1 - v2)
To calculate 6 after 1 month it is necessary to know the 1 month creep modulus.
The stresses at the centre of the cap are biaxial (radial and circumferential) both