Page 107 - Plastics Engineering

90 Mechanical Behaviour of Plastics

and recovery. It is clear therefore that some compromise may be achieved by
combining the two models. Such a set-up is shown in Fig. 2.38. In this case
the stress-strain relations are again given by equations (2.27) and (2.28). The
geometry of deformation yields.

Total strain, E = e1 + €2 + &k (2.41)

52

Fig. 2.38 Maxwell and Kelvin models in series

where &k is the strain response of the Kelvin Model. From equations (2.27),
(2.28) and (2.41).

(2.42)

From this the strain rate may be obtained as

(2.43)

The response of this model to creep, relaxation and recovery situations is the
sum of the effects described for the previous two models and is illustrated in
Fig. 2.39. It can be seen that although the exponential responses predicted in
these models are not a true representation of the complex viscoelastic response
of polymeric materials, the overall picture is, for many purposes, an acceptable
approximation to the actual behaviour. As more and more elements are added
to the model then the simulation becomes better but the mathematics become
complex.
Example 2.12 An acrylic moulding material is to have its creep behaviour
simulated by a four element model of the type shown in Fig. 2.38. If the creep
curve for the acrylic at 14 MN/m2 is as shown in Fig. 2.40, determine the
values of the four constants in the model.