Page 116 - Plastics Engineering

Mechanical Behaviour of Plastics 99

Superposition Principle that the entire stress history of the material contributes
to the subsequent response.
It is worth noting that in exactly the same way, a material subjected to a
continuous variation of strain may have its stress at any time predicted by

(2.58)
-m
To illustrate the use of equation (2.57) consider the following Example.
Example 2.14 A plastic is subjected to the stress history shown in Fig. 2.45.
The behaviour of the material may be assumed to be described by the Maxwell
model in which the elastic component 6 = 20 GN/m2 and the viscous compo-
nent 9 = lo00 GNs/m2. Determine the strain in the material (a) after u1 seconds
(b) after u2 seconds and (c) after u3 seconds.

Stress (MN/m2)

100 U2 T' Time (s)
Fig. 2.45 Stress history to be analysed

Solution As shown in the previous Example, the modulus for a Maxwell
element may be expressed as

6v
E(t) = -
9 + 6t
(a) The stress history can be defined as