Page 102 - Plastics Engineering

Mechanical Behaviour of Plastics 85

they do aid in the understanding and analysis of the behaviour of viscoelastic
materials. Some of the more important models will now be considered.

(a) Maxwell Model
The Maxwell Model consists of a spring and dashpot in series at shown in
Fig. 2.34. This model may be analysed as follows.

Stressa

Fig. 2.34 The Maxwell model
Stress - S train Relations
The spring is the elastic component of the response and obeys the relation

01 = (. &I (2.27)
where (TI and ~1 are the stress and strain respectively and 4 is a constant.
The dashpot is the viscous component of the response and in this case the
stress a2 is proportional to the rate of strain E2, ie
(2.28)
02 = r) ’ E2
where r) is a material constant.

Equilibrium Equation
For equilibrium of forces, assuming constant area

Applied Stress, (T = (T~ = 02 (2.29)

Geometry of Deformation Equation
The total strain, E is equal to the sum of the strains in the two elements.
so
&=&1+&2 (2.30)