Chemistry Reference
In-Depth Information
to the Eqs. (4.34) ÷ (4.36) diagrams s − e for PAr at three testing tempera-
tures is adduced. The values is
o
were determined as the product
E
e
Y
[66]. As
it follows from the data of Fig. 4.16, the diagrams s − e on the part from
proportionality limit up to yield stress are well described well within the
frameworks of the Mittag-Lefelvre function. Let us note that two necessary
for these parameters (s
o
and n
fr
) are the function of polymers structural state,
but not filled parameters. This is a principal question, since the usage in this
case of empirical fitted constants, as, for example, in Ref. [67], reduces sig-
nificantly using method value [60, 65].
In the initial linear part (elastic deformation) calculation according to the
Eq. (4.34) was not fulfilled, since in it deformation is submitted to Hooke
law and, hence, is not nonlinear. At stresses greater than yield stress (high-
elasticity part) calculation according to the Eq. (4.34) gives stronger stress
growth (stronger strain hardening), than experimentally observed (that it has
been shown by shaded lines in Fig. 4.16). The experimental and theoretical
dependences s − e matching on cold flow part within the frameworks of the
Eq. (4.34) can be obtained at supposition n
fr
= 0.88 for
T
= 293 K and n
fr
=
1.0 for the two remaining testing temperatures. This effect explanation was
given within the frameworks of the cluster model of polymers amorphous
state structure [39], where it has been shown that in a yielding point small
(instable) clusters, restraining loosely packed matrix in glassy state, break
down. As a result of such mechanical devitrification glassy polymers behav-
ior on the forced high-elasticity (cold flow) plateau is submitted to rubber
high-elasticity laws and, hence,
d
f
→
d
= 3 [68]. The stress decay behind
yield stress, so-called “yield tooth,” can be described similarly [66]. An in-
stable clusters decay in yielding point results to clusters relative fraction j
cl
reduction, corresponding to
d
f
growth (the Eq. (1.12)) and n
fr
enhancement
(the Eq. (4.33)) and, as it follows from the Eq. (4.34), to stress reduction. Let
us note in conclusion that the offered in Ref. [69] techniques allow to predict
parameters, which are necessary for diagrams s - e description within the
frameworks of the considered method, that is,
E
, e
Y
and
d
f
.
In Ref. [70], it has been shown that rigid-chain polymers can be have a
several substates within the limits of glassy state. For polypiromellithimide
three such substates are observed on the dependences of modulus ds/de,
determined according to the slope of tangents to diagram s − e, on strain
e [70]. However, such dependences of
d
s/
d
e on e have much more general
character: in
Fig. 4.17
three similar dependences for PC are adduced, which
were plotted according to the data of Ref. [49]. If in Ref. [70] the transition
