Page 122 - Plastics Engineering

Mechanical Behaviour of Plastics 105

Reduced time, k

Fig. 2.50 meal recovery behaviour of a plastic

describes recovery behaviour with acceptable accuracy (see Fig. 2.50). The
relationship between F, and fR may be derived in the following way.
When creep curves are plotted on logarithmic strain and time scales they are
approximately straight lines so that the creep strain, E,(?) may be expressed as
E,(?) = At" (2.62)

and using this relationship in equation (2.59)
E,(?) = At" -A(? - T)"

and so the Fractional Recovery may be written as
AT" - [At" -A(? - T)"]
F, =
AT"

= 1 - (;)"+ (f - 1)"

F, = 1 +?; - (?R + 1)" (2.63)
In practice this relationship is only approximately correct because most plas-
tics are not linearly viscoelastic, nor do they obey completely the power law
expressed by equation (2.62). However this does not detract from the consid-
erable value of this simple relationship in expressing the approximate solution
to a complex problem. For the purposes of engineering design the expression
provides results which are sufficiently accurate for most purposes. In addition,