Page 131 - Plastics Engineering
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114 Mechanical Behaviour of Plastics
where E* is the complex modulus. Rearranging gives
iw6
E* = -
6 + oqi
Using the fact that (a + bi)(u - bi) = u2 + b2
E* = iwqe (6 - wqi) - 02q2t + or)t2i
-
(6 + wqi) (t - wqi) w2q2 + 62
and since E* = El + iE2
then storage modulus,
w2 a25
El =
,2172 + 62
and loss modulus,
The variations of El, E2 and tan8 with w are shown in Fig. 2.56. It may be
seen that the variations of E1 and E2 are of the general shape that would be
expected. The tan8 curve does not go through a maximum and so this is a
further shortcoming of this simple model.
Fig. 2.56 Variation of El, E2 and loss tangent for Maxwell model
(ii) For the Standard Linear Solid, the governing equation was derived
earlier as
vb +ha = rl0l + t2P + 4241s
