Page 130 - Plastics Engineering

Mechanical Behaviour of Plastics 113

Log (4
Fig. 2.55 Typical variation of El, E2 and loss tangent for a viscoelastic material

Solution As illustrated above, the stress and strain will be given by
CT = 00 sin(wr + 8)
E = EO sin wt
However, in this type of question it is preferable to utilise complex numbers
and so the transformations will be used so that

CT = ,oei(wr+6) (2.73)
F = EOe'af (2.74)
(i) As shown earlier in this chapter, the governing equation for the Maxwell
model is given by
1. 1
&=-U+-CT
617
Then from equations (2.73) and (2.74)
1
Eoiweiar = looiWei(otC6) + --aOei(0t+6)
4 D
iw -aoei(ot+a) 1 a,,ei(ot+a)
iw=-. &Oeio' + ; &OeiWf
6
.