Page 104 - Plastics Engineering

Mechanical Behaviour of Plastics 87

Hence, the creep modulus, E(t), is given by

(2.33)

(ii) Relaxation
If the strain is held constant then equation (2.31) becomes

Solving this differential equation (see Appendix B) with the initial condition
o = a,, at t = to then,

-5,
a(r) = aoe 11 (2.34)
a(t) = oOe-f/TR (2.35)
where TR = q/e is referred to as the relaxation rime.
This indicates that the stress decays exponentially with a time constant of
q/t (see Fig. 2.35).

(iii) Recovery
When the stress is removed there is an instantaneous recovery of the elastic
strain, E', and then, as shown by equation (2.31), the strain rate is zero so that
there is no further recovery (see Fig. 2.35).
It can be seen therefore that although the relaxation behaviour of this model
is acceptable as a first approximation to the actual materials response, it is
inadequate in its prediction for creep and recovery behaviour.
(b) Kelvin or Voigt Model
In this model the spring and dashpot elements are connected in parallel as
shown in Fig. 2.36.

+ Stress. u

Fig. 2.36 The Kelvin or Voigt Model