Page 109 - Plastics Engineering

92 Mechanical Behaviour of Plastics
The spring constant, 62, for the Kelvin-Voigt element is obtained from the
maximum retarded strain, ~2, Fig. 2.40.
in

The dashpot constant, q2, for the Kelvin-Voigt element may be determined
by selecting a time and corresponding strain from the creep curve in a
region where the retarded elasticity dominates (i.e. the knee of the curve
in Fig. 2.40) and substituting into equation (2.42). If this is done then q2 =
3.7 x lo8 MN.s/m2.
Having thus determined the constants for the model the strain may be
predicted for any selected time or stress level assuming of course these are
within the region where the model is applicable.

(d) Standard Linear Solid
Another model consisting of elements in series and parallel is that attributed to
Zener. It is known as the Standard Linear Solid and is illustrated in Fig. 2.41.
The governing equation may be derived as follows.

I

u
Stress.
Fig. 2.41 The standard linear solid
Stress-Strain Relations
As shown earlier the stress-strain relations are

01 = 41&1 (2.44)
02 = E2&2 (2.45)
(73 = 7l3E3 (2.46)
Equilibrium Equation
In a similar manner to the previous models, equilibrium of forces yields.
(TI = a3
(J = a1 + a2 (2.47)