YIELDING PROCESS - Fractal Mechanics of Polymers - page 56

The yielding process of amorphous glassy polymers is often considered
as their mechanical devitrification [36]. However, if typical stress - strain
(s - e) plot for such polymers is considered ( Fig. 4.6 ), then one can see, that
behind the yield stress s Y the forced elasticity (cold flow) plateau begins and
its stress is p is practically equal to is Y , that is, is p has the value of order of sev-
eral tens MPa, whereas for devitrificated polymer this value is, at least, on
the order of magnitude lower. Furthermore, is p is a function of the tempera-
ture of tests T , whereas for devitrificated polymer such dependence must be
much weaker what is important, possess the opposite tendency is p enhance-
ment at T increase). This disparity is solved easily within the frameworks of
the cluster model, where cold flow of polymers is associated with devitrivi-
cated loosely packed matrix deformation, in which clusters “are floating.”
However, thermal devitrification of the loosely packed matrix occurs at the
temperature T g ' - which is approximately 50 K lower than T g . That is why it
should be expected that amorphous polymer in the temperature range T g ' ÷
T g will be subjected to yielding under the application of even extremely low
stress (of about 1 MPa). Nevertheless, as the plots in Fig. 6 show, this does
not occur and s - e curve for PAr in T g ' ÷ T g range is qualitatively similar to
the plot s - e at T < T g ' (curve 1). Thus is should be assumed that devitrifica-
tion of the loosely packed matrix is the consequence of the yielding process
realization, but not its criterion. Taking into account realization of inelastic
deformation process in the clusters ( Fig. 4.5 ) one can suggest that the suf-
ficient condition of yield in the polymer is the loss of stability by the local
order regions in the external mechanical stress field, after which the defor-
mation process proceeds without increasing the stress s (at least, nominal
one), contrary to deformation below the yield stress, where a monotonous
increase of s is observed (Fig. 4.6).
Now using the model suggested by the authors of Ref. [37] one can
demonstrate that the clusters lose their stability, when stress in the polymer
reaches the macroscopic yield stress, s Y . Since the clusters are postulated
as the set of densely packed collinear segments, and arbitrary orientation
of cluster axes in relation to the applied tensile stress s should be expected,
then they can be simulated as “inclined plates” (IP) [37], for which the fol-
lowing expression is true [37]:

( ) ( )

tt en n <= + - , 24 G 1 2 (4.10)

Y IP cl 0 2 2

where t Y is the shear stress in the yielding point, t IP is the shear stress in IP
(cluster), G cl is the shear modulus, which is due to the clusters availability