Page 180 - Plastics Engineering

Mechanical Behaviour of Plastics 163

Fig. 2.86 Standard model for viscoelastic material
2.36 Show that for a viscoelastic material in which the modulus is given by E(t) = At-”, there
will be a non-linear strain response to a linear increase in stress with time.
2.37 In a tensile test on a plastic, the material is subjected to a constant strain rate of lo-’ s. If
this material may have its behaviour modelled by a Maxwell element with the elastic component
6 = 20 GN/m’ and the viscous element q = loo0 GNSlm’, then derive an expression for the
stress in the material at any instant. Plot the stress-strain curve which would be predicted by
this equation for strains up to 0.1% and calculate the initial tangent modulus and 0.1% secant
modulus from this graph.
2.38 A plastic is stressed at a constant rate up to 30 MN/m2 in 60 seconds and the stress then
decreases to zero at a linear rate in a further 30 seconds. If the time dependent creep modulus
for the plastic can be expressed in the form
h
E(t) = -
o+B
use Boltzmann’s Superposition Principle to calculate the strain in the material after (i) 40 seconds
(ii) 70 seconds and (iii) 120 seconds. The elastic component of modulus in 3 GN/m’ and the
viscous component is 45 x lo9 Nslm’.
2.39 A plastic with a time dependent creep modulus as in the previous example is stressed at
a linear rate to 40 MN/m2 in 100 seconds. At this time the stress in reduced to 30 MN/m’
and kept constant at this level. If the elastic and viscous components of the modulus are
3.5 GN/mz and 50 x lo9 NSlm’, use Boltzmann’s Superposition Principle to calculate the strain
after (a) 60 seconds and (b) 130 seconds.
2.40 A plastic has a time-dependent modulus given by

where E(t) is in MN/m2 when ‘t’ is in seconds. If this material is subjected to a stress which
increases steadily from 0 to 20 MN/mz in 800 seconds and is then kept constant, calculate the
strain in the material after (a) 500 seconds and (b) loo0 seconds.