Mechanism of quasi-plastic deformations of densely crosslinked epoxy-amine polymers

Polymer Science U.S.S.BL Vol. 22, ~o. 7, pp. 1804-1813, 1980 Printed in Poland

0032-3950/801071804-10507.5010 © 1981 Pergamon Press Ltd.

MECHANISM OF QUASI-PLASTIC DEFORMATIONS OF DENSELY CROSSLINKED EPOXY-AMINE POLYMERS* YE. S. SOLODYSHEVA, E. F. OLEINIK, B. A. ROZE~BERG, G. D. A.~DREYEVSKAYA a n d N. S. YE~ClKOLOPYAN In~titute of Chemical Physics, U.S.S.I¢. Academy of Sciences (Received 13 July 1979)

A study was made of dcfol~nation of densely crosslinked glassy polymers prepared from resorcinol diglycidyl ester and 2,6-diaminopyridino in the yield point region. ~-e Stress/strain curves and compression curves were plotted in the temperature range of 22-100 ° and in the range of rates of deformation ~ ~ 10-~-10 ° min-L Expcrimontal results were analysed in terms of the thcrmo-fluctuation process of flow; the stress applied (Alexandrov-Eyring theory) influences char'lcteristics of this process. Microscopic charact(~ristics were obtained of deformation near a~.: actiwltion energy AE o and shear volume of activation Vsh.Values of V~hare 3000-3900 .~3 and are comparatively low in relation to linear polymer ~lasscs and actiwltion energy values ziE0----51-7l kcal/mole. Values of AEo were higher than activation energies of segmental motion fi)r the crosslinkcd polymer examined. It was sho~m that large-scale motion is only responsible for deformation near ~,. All results were explained within the framework of the hypothesis conccrning the motion of "holcs"--packh~g defects in the polymer examined.

I~¢ S P I T E of the fact t h a t glassy e p o x y crosslinked p o l y m e r s represent a v e r y p o p u l a r class of c o m p o u n d used for pi'od,.ming s t r u c t u r a l materials, e.g. reinforced composite fibres [lJ, the causes which d e t e r m i n e typical features of m e c h a n ical b e h a v i o u r and the t y p e of deforml~tion process on the micro-level, r e m a i n obscure. T h e r e are studies in the literature, which e x a m i n e the d e f o r m a t i o n m e c h a n i s m of glassy p o l y m e r s [2-4], however, these a r e ' r e s t r i c t e d to linear polymers a n d we do n o t k n o w of a n y similar investigation carried o u t using densely crosslinked systems. This s t u d y deals with densely crosslinked d e f o r m e d n e t w o r k s p r e p a r e d b y the solidification o f resorcinol diglycidyl ester ( R D G E ) using an a r o m a t i c a m i n e - 2,6-diaminopyri(tine (1lAP). As a result of the reaction a m o r p h o u s ( X - r a y ) crosslinked p o l y m e r s are f o r m e d with a c o n c e n t r a t i o n of chemical crosslinks in unit v o l u m e of n ~ 1021 cm -3, a dense n e t w o r k of h y d r o g e n b o n d s [5], high coefficient of molecular p a c k i n g a n d glass t e m p e r a t u r e s T g z 1 3 0 - 1 4 5 ° (va~ 10 -2 e/s). As there are only l l skeletal a t o m s in chains between chemical crosslinks * V y s o k o m o l . soyod. A22: No. 7, 1645-1653, 1980. 1804

Deformations of densely crossllnked epoxy-amide polymers

1805

J

( N - - d i a m i n e a t o m s ) , t h e p o l y m e r s e x a m i n e d f o r m p a r t o f t h e class o f m i c r o I n e t w o r k s [7]. N e v e r t h e l e s s , o n s u b j e c t i n g t h e s e p o l y m e r s to m e c h a n i c a l stress in t h e glassy s t a t e a n d a t m o d e r a t e r a t e s o f d e f o r m a t i o n , a clearly e x p r e s s e d m a x i m u m ay [8] a p p e a r s o n t h e s t r e s s / s t r a i n c u r v e (a-e, 22 °) w h i c h is, e v i d e n t l y , d u e to flow processes [3]. Since d e f o r m a t i o n s e x a m i n e d in this s t u d y are fully r e v e r s i b l e (while h e a t i n g p o l y m e r samples), to d e n o t e t h e m we a d o p t e d t h e t e r m o f quasi-plastic d e f o r m a t i o n . As in linear p o l y m e r s [9], d e f o r m a t i o n of t h e m i c r o - n e t w o r k s e x a m i n e d is heterogeneous. W i t h a stress m u c h lower t h a n ay (usually n e a r t h e p r o p o r t i o n a l i t y ]imit) s h e a r b a n d s a p p e a r in t h e s a m p l e , w h i c h are clearly visible in t h e microscope. I t is well k n o w n t h a t for densely crosslinked p o l y m e r s creep c a n n o t t a k e place w i t h o u t chemical b o n d r u p t u r e . I t w a s s h o w n p r e v i o u s l y t h a t residual d e f o r m a t i o n s are negligibly low for d e n s e l y crosslinked p o l y m e r s [10], therefore, d e f o r m a t i o n processes t a l d n g place in t h e s y s t e m s e x a m i n e d n e a r a~ differ f r o m plastic flow in metals, as t h e y are reversible. H o w e v e r , t h e f o r m a l a p p e a r a n c e of t h e yield p o i n t on a-~ d i a g r a m s p o i n t s to t h e existence of flow; this p a p e r seeks t o e x a m i n e this process.

Analysis of experimental results. I t is widely accepted in modern literature to approach the deformation mechanism as a kinetic thermo-fluctuation process, the activation energy of which decreases as a result of stress applied to the sample. This approach has been developed for polymers in studie~ by Alexandrov and Eyring [l 1-13] and is also widely used for the analysis of plasticity of metals and ionic crystals [I4]. For polymers this approach is applied when studying creep, stress relaxation and temperature-velocity properties of the limit of forced elasticity in elongation and compression [3, 4, 13]. A formal foundation for the study of these effects within the framework of the thermofluctuation approach is a linear relation (within a fairly wide range of temperature and rate of deformation) between the rate of deformation and yield point (forced elasticity) [4, 15, 16]. These relations are observed for a number of crosslinked polymers [17, 18] slid a system examined in this paper. I f we assume that the rate of deformation ~ is inversely proportional to the time of relaxation, from a study of the thermo-fluctuation equation it is easy to derive a linear relation between % and log ~ [4], i.e. the experimental existence of these relations enables the thermo-fluctuation approach to be used bearing in mind mechazfical stress when studying quasi-plastic flow. For the quantitative description of deformation we use the equation on [12, 13, 19] e=A0exp

~E0~

-- - ~ /

W (~) sinh let

(I)

where AE0 is the effective activation energy of plastic deformation with zero stress and W (x) -- the energy of shear stress ~ t . The work W (z) performed ]~y effective shear stress ~ in the sample may be presented as

where V,, is the activation shear volume, V , , - ~ - ~0~o~

\ ~r /T,

structure

180~

YE. S. SOLODYSIIZVA ~ ~g~.

In pure shear deformation F ~ is equal to the product of area ~q of the elementary fragment of a solid talcing part in plastic flow deformation and its displacement b, i.e. Vsh----~q.b [14]. The effective activation energy JEo and activation volume ]rsh are characteristics of molecular regroupings of a solid deformed in each elementary process of deformation [ 13]. I t is known that with high stress levels and at low temperature flow processes of "reverse transfer" of molecular fragments through the energy barrier •E0 m a y be ignored and then equation (1) takes the form e=A0 exp \

~-~

-]

(3)

Using the flow criterion of Coulomb-Navier [3, 20] which gives a satisfactory description of the dependence of at in polymers on hydrostatic pressure or the spherical component of stress tensor, Brady and Yeh [21] modified equation (3) introducing into it normal stress a s acting perpendicular to the shear plane mad the coefficient of internal friction r e , = r e r --a6 t a n ~, where tan ~ is the coefficient of internal friction and rer--critical shear strees. As a result formula (3) in the modified form is as follows

"e=Ao exp

\ kT

4-~

where ¢ is the angle of internal friction and ay, yield point. E q u a t i o n {4} was of fundamental importance for the analysis of experimental results derived in this study. The same Brady in Yeh equation was used to analyse deformations a n d the process of cold flow of a n u m b e r of linear polymers [22]. I t follows from equation {4} t h a t gradients of dependences of log k on % give the activation shear volume VBh and from the gradient of dependences of a/T on I/T using Van values derived the value of AEo may be calculated. Samples for mechanical elongation tests taking the form of dumb-bell test pieces (GOST 1162-68, type 51) With a diameter and length of operating part of d = 5 m m and l----40 ram, resq3ectively were prepared with teflon inserts. A stoichiometric mixture of R D G E a n d D A P melted at a temperature of 60 ° was placed into moulds after vacuum treatment. Solidification was carried out in dry argon under step-by-step temperature conditions: 80 °, 4 hr; 100 °, 4 hr. The degree of solidification ~ measured calorimetrically and by 'IR spectra (aeeording to the consumption of epoxy groups) reached the m a x i m u m (~= 0.91-0.93) [23] and remained practically unchanged during subsequent heat treatment. Solidified samples were placed into closed ampoules containing dr T argon and subjeered to subsequent heat treatment (two types} -- annealing mad quenching. Annealing: heating of samples to 160-170 °, retention at this emperature for 5 rain, followed by slow cooling at a rate of 10 dcg/hr to room temperature (in argon). Quenching: heating as in the former case and rapid cooling (the ampoule containing the samples was lowered into cold water at 5-10°). We pointed out previously that heat treatment results in a marked change, in the form of stress/strain curves and limiting mechanical characteristics of the polymer in the glassy state [6]. Mechanical elongation tests wore carried out in a RM-250 machim, in the range of rates of deformation of. 0.1-160~o/min (10-s-10 ° rain-a), which were determined from the movement of clamps gripping the samples. Elongation tests were carried out in heated chambers at temperatures of 22-100 °, compression tests, at room temperature using cylindrical samples with d = 5 m m and l = 10 m m and ~ 0.1--15°/o/rain, (10-s-10-~ rain-a). I n order to plot diagrams of elongation and compression, we used true stress values obtained taking into account variations in the cross-sectional area of samples during deformation with conversion according to the formula at~=a0(l±e) [20], where a is the engineering strew, c--instaattaneous deformation (sic,ms " + " mad " - - " correspond to elongation and compression).

D e f o r m a t i o n s of densely crossllnked e p o x y - a m i d e p o l y m e r s

1807

Figure 1 shows elongation curves atr-e of annealed and quenched samples, respectively at 22-100 ° and a rate of testing of ~ 10 -2 min-L Each curve in the diagrams is the result of averaging using seven to eight samples. Figure 2 shows dependences of yield points a~r on temperature for three rates of deformation and Fig. 3, semi-logarithmic dependences of a~r on the rate of deformation log cat different temperatures. Experimental points in Figs. 2 and 3 are satisfactorily ~t,..e , kg/mrnz

b

!

I

8

I

Iij L

I

16 24

O

1624

?2, E, %

Fro. 1. D i a g r a m s of O'true--e (elongation (1-5) and compression (6)) of a m m a l e d (a) and q u e n c h e d (b) samples of R D G E - D A P (1 : 1) w i t h ~ ~ 10 -2 rain -1 a n d a~ t e m p e r a tures of" 22 (1, 6), 40 (2), 60 (3), 80 (4) a n d 100 ° (5).

arranged on straight lines, which suggests (at least formally) that the Eyring equation (3) is valid for this system. From the gradient of straight lines in Fig. 3 at each temperature the shear volume of activation Vsh m a y be determined; however, for this it is essential to know the size of the member related to the angle of internal friction in curled brackets of equation (4). A popular method of determining the angle of internal friction ~b is by drawing tangents to Moor circles using maximum tensile and compressive stress. It is known that this tangent is inclined to the horizontal at angle ~ [22]. Table 1 shows values of maximum TABLE

1. T R U E

S T R E S S V A L U E S fly F O R A N N E A L E D A N D Q U E N C H E D S A M P L E S O F

RDGE-DAP

ay at 22 ° , k g / m m ~ ~,

ammale~i

ini]),-l

elongation 10-1 10-2 10-a

17.0 16.0 15.0

quenched

comprcssioa ]7.3 16.2 15.1

elongation 14-2 ]3-2 12.2

compres.siott 15.1 13.9 12-9

......................

tensile stress and compressive stress at. different rates of deformation ( T = 2 2 °) for R D G E - D A P polymers. The Table shows that in annealed samples maximum tensile stress and Compressive stress practically agree. For quenched samples the tr comp difference between a~ and ay is somewhat greater, but even this is negligible. Using the Moor circle to draw tangents produced values of 4)~ l ° and a member

1808

Y ~ . S. SOLODYs~usvX

.

e~ a/.

incorporating a combination of trigonometric functions in equation (4) very close to one. This means t h a t quasi-plastic flow of a crosslinkod polymer in uniaxial stress takes plaee in practice in the direction of maximum tangential stress Zm~x, i.e. at a n g l o 45 ° to the axis of elongation. * The fact that maximum tensile stress and

1o9~

\

a

b

0

a 2 •

-I -2 6

~ 20

,

I 60

I " ~\ I00

20

60

/00

9

15

6

IZ

T°

FIo. 3

FIG. 2

Fxo. 2. Dependence of ctyru®on test temperature for a~nealed (a) and quenched (b) samples with ~----1 (1), 10-s (2) and 10-= rain -1 (3). Fxo. 3. Dependence of ctrue on the rate of deformation log ~ for annealed (a) and quenched (b) aamples: 1-5--elongation at temperatures of 100 (1), 80 (2), 60 (3), 40 (4) and 22° (5); 6 - compression at 22 ° .

compressive stress are equal (i.e. tan ¢~=0) deserves serious attention since as far as we know, this has not been observed previously for amorphous polymers. A detailed explanation of physical principles of this unusual behaviour of polymers is still to come. We can only note now that this effect is, apparently, due to high coefficients of molecular packing of the polymers studied [6]. The fact observed also means that the spherical component of the stress tensor has no effect on deformation near a~ of the polymer studied, which distinguishes it from well-known linear glassy systems [3, 19, 22]. From the gradient of straight lines in Fig. 3 activation volumes Vsh were calculated. For annealed samples (Fig. 3¢) values of Vsh in elongation varied between 3000 and 3940 A 8 at temperatures of 100-22 °, respectively and for compression, this value was 3490 A 8 (at room temperature). For quenched samples the shear volume in elongation varied between 3200 A s at 100 ° and 3630 A 3 at 22 ° while in compression (at T = 2 2 °) it was 3260 A. Using these values of V~ from gradients of straight lines in Fig. 4 values of AE 0 were calculated and found to be 51-71 kcal/mole for annealed samples and 52-59 kcal/molo for quenched samples. All values of V,h and AE0 for different rates of deformation * Results obtained by S. A. Artemenko and L. K. Pakhomova.

Deformations of densely crosslinked epoxy-amide polymers

1809

different thermal backgrounds are shown in Table 2. Let us exalninA p a r ~ meters of quasi-plastic deformation of a crosslinked polymer, shown in Table g. The physical interpretation of parameter Vab is normally given in two w a y m . F o r substances with well organized crystalline structure V~h is presented as t h e volume of a deformed material element, in which the elementary process of plastic deformation took place. This volume is formed from dislocation, area element and the movement of this elementary "element of area" to distance b under conditions of shear stress z.h [13, 14, 20]. For crystalline bodies b is the Burgers vector of moving dislocation.

and

TABLE 2. SHEAR VOLU]~ESA_NI)ACTIVATIONE~T]~R(~IESOr PLASTIC DEIPOItMATIONOr RDGE-DAP

Sample Annealed

}' min-t

Test temperature, *C

V~, .~,

AE,, kcal/mole

10'-10-* (elongation)

100 30 60

3OO0 3360 3625 3610 3940 3490 3200 33O0 3380 3510 3630 3260

51-54

40 22

Annealed Quenched

Quenohod

•

G L ~ S S Y C~aOSSLn~Z~D P O L ~ R

10-L10 -8 (compression) 10'-10 -s (elongation)

lO-a-lO-S (compression)

22 100 80 60 40 22 22

,

62-67 68-71 52 55 59

For amorphous solids, including polymers, a completely different concept w a s adopted. In this case Vsh is regarded as the volumetric increment required for t h e motion of molecular fragments in the solid on a scale which is sufficient for macroscopic plastic deformation [13, 20, 22, 24]. For amorphous polymers V~h is identified with excess free volume A Vt (apparently, of fluctuation type [3]), which is formed during deformation. The Poisson coefficient in these substances is usually v < 0 . 5 and for epoxy crosslinked polymers it is 0.35-0.37 [25]. At. the moment when the value of A Vt in the polymer becomes high enough to achieve segmental mobility (or other types of medium- and large-scale molecular mobility), the polymer undergoes plastic deformation (yielding) that can be recorded macroscopically. These two different approaches to the interpretation of Vsh essentially reflect physically different mechanisms of plasticity of solids. There are moving dislocations in crystalline solids and this motion (slipping) does not practically require (or almost does not require) further free volume [13, 14].

YE. S. SOLODYS]SL~VAe~ a/.

]St0

In amorphous solids the physical basis for a lattice dislocation model disappears and the scientist can no longer observe the dislocations experimentally: Therefore, theories concerning the effects taking place in micro-regions of amorphous solids during plastic flow are qualitative (at best semi-quantitative) and are based on the physical pattern of kinetio effects observed at the glass-transition, with unit type concepts of free volume [3, 20, 26]. According to those views, .the formation of A Vt during deformation of amorphous glassy polymers is the limiting stage of plastic flow. I t is easy to imagine that in amorphous-crystalline polymers both these mechanisms of plasticity m a y be observed.

fnue

2

-

b

a

! 3 ! 2.7

2.9

3.1

3"3

"b.7

2-8

a.1

a.a 10~/r,K '

I~G. 4. Dependence of a~rue/Ton 1/T for annealed (a) and quenched samples (b) when ~= 1 (1), 10-' (2) and 10-' (3) min-l.

However, results obtained in this study (Table 1) indicate that R D G E - D A P glassy polymers behave differently during deformation from the linear polymers described in the literature. The difference is that the hydrostatic component of the stress tensor has no effect on quasi-plastic flow. This means that the formation of new free volume does not limit the process of flow, i.e. the mechanism of plastic deformation of these objects is nearer, from the point of view of activation volume, to the mechanism observed in metals. This suggests t h a t during quasiplastic flow of the micro-networks examined local regions in existence in the polymer before the start of deformation take part in some form of motion. When applying stress on the polymer these regions start to move by the action of reff, the increase in stress level involving an increasing number of local elements during flow (without increasing overall volume). On reaching stress ay (or more precisely Ty), the velocity component of motion of these local volumes along the axis of stress becomes equal to the macroscopic rate of deformation, which in the diagram is shown in the form of a maximum. "Holes" [27], always present in the glassy polymer m a y be elements of the polymeric solid taking part in flow. Furthermore, micro-networks examined in this study are more prone to form holes, compared with any linear polymer glass, since the packing of networks is more satisfactory [6] and, of course, dense packing can only be observed as a result of the formation o f holes.

Deformations of densely crosslinked epoxy-amide polymers

1811

According to this hypothesis the FB~ value measured in this s t u d y is directly linked with the volume of moving holes and is precisely equal t~ the average volume gh of this hole when e : e y or proportional to Vh if more than one hole is involved in the elementary process of flow. Thus, holes in the polymer are to some e x t e n t similar to dislocations in crystalline bodies. Dislocations models of flow in polymer glass are described in the literature [24, 28] and Bowden and R a h a proposed a theory [24, 29], according to which ay is interpreted as the stress required for forming a dislocation loop in the polymer (it is possible that the loop is formed of holes, which during motion form the configuration required for this loop). The theoretical concept of dislocations has recently been successfully extended to amorphous solids [30]. Let us examine values of Vsh given in Table 2. For annealed samples Vsh varies between 3000 and 3940/~a, which corresponds to average dimensions of spherical holes starting from ~ 1 8 - 2 - 2 0 / ~ a . For quenched samples Vsh----32003600 A a, which gives ~--~18.5-18.8 A 3. Volumes Vsh in compression agree with volumes during elongation, which corresponds to the model examined. I t is interesting that the average size of holes is close to the size of the molecular network fragment, incorporating one R D G E and DAP chain. The variation of VBh with temperature is very slight; this is typical of the glassy state, in which within the temperature interval examined no temperature transitions are observed [6J. The variations observed are, apparently, due to thermal expansion of the sample [27]. Somewhat lower values of Vsh for quenched samples are evidently due to a higher content of small holes, which impart increas~l plasticity to the sample. Small holes begin to move at reduced stress (lower values of the proportionality limit [67) and the maximum on a-~ curves is achieved with lower values of ay. This corresponds to experimental results obtained. Quenched samples break down at much higher values of ~b than annealed samples. Tiffs may also be due to the size of mobile holes, since processes of breakdown [4] taking place in parall(~] with quasi-plastic deformation occur at a lower rate with lower stress. It is not quite clear why values of Vsh for quenched and anuealed samples are practically comparable when T ~ 8 0 °. This is, apparently, somewhat related to diffusion of holes taking place at noticeable rates at 80 ° and processes of coalescence. An empirical correlation was derived [22J betweeu Vsh ~nd the volume of the monomer unit of line polymers. Thus, the Vsh/VM ratio for atactic PS is 17-40, for polycarbonate - 0 and polymethylmcthacrylate -- 10-20. For a R I ) G E DAD network (l : l) calculation established the followiug values: VM -413 ~8 an(l the ratio of Vsh/VM of 8-9. This ratio is considerably lower than for linear polymers, which also points to certain structural features of miero-uetworks. The hypothesis concerning the role of holes in quasi-plastic flow of micronetworks m a y now only be examined as one of the possible approximate assumptions and requires serious further investigation. However, it gives a satisfactory exl)lal~ation to all experimental results available. Investigations carried out 1)y the

1812

Y~-. S. SOLOV~S~CVA ¢t a/.

authors using ~thor micro-networks suggest that the dimensional (energy) distribution of holes and their mutual effect may be important in forming physical and mechanical properties. Activation energy values AE0 calculated from gradients of straight lines in Fig. 4 are shown in Table 2 for various temperatures and rates of deformation. All points are situated on straight lines, which is evidence of the absence of structural rearrangement in the polymer in the entire temperature range studied. This is confirmed by a study of molecular motion in these networks [6]. For linear polymers/lEo often varies with temperature, which is interpreted as the participation of various types of molecular motion in plastic flow [22]. For a R D G E - D A P network quasi-plastic flow in point 8y is probably determined only by a single type of molecular motion. Dielectric measurements of activation energy values of segmental motion in this network [6] (vat-~ 10 -2 sec -1) produced the value of/lE0 ~40 kcal/mole, i.e. a value much lower than in this study. This suggests that fragments larger than segments responsible for softening of the sample near T s take part in quasi-plastic flow of micro-networks. Holes may be fragments of this type. I t is important that AEo values obtained are proportional to Itch, which is apparently due to hole dimensions, as noted previously. It is also clear that small-scale motion has a negligible effect in this case (it does not restrict the process). Fairly high Values of AE0 (Table 2) may suggest chemical bond rupture as a limiting stage of the process. However, an increase in the free volume of the sample may be expected during flow, which conflicts with results obtained (equality of a~ and Irsh during elongation and compression). I t is possible that high values of/lEo are due to the temperature dependence of the barrier [27], however, evaluation (assuming that ~tE0 shows a linear dependence on temperature) indicates that this dependence is too significant for satisfactory agreement with experimental results. The absence of relaxation transitions inside the temperature range examined also forces us to reject this reasoning [4]. It should be assumed, apparently, that the process of quasi-plastic deformation is limited by the rearrangement of intermolecular bonds in the polymer [4]; their number in average elementary volume taking part in flow is fairly high. Hydrogen bonds, no doubt, have a marked effect on this barrier; they form a dense physical network in the system investigated [5, 6]. Results indicate that the process of deformation of densely crosslinked notworks in the glassy state has a number of special features, compared with linear polymer glass. These typical properties are, no doubt, related to structural features of the systems [6]. Hypothesis concerning the role of holes, in which a free fluctuation volume of the polymer is concentrated, enables many features of deformation to be explained. However, a deeper understanding of the process mechanism requires further investigations. Translated

by E. S E ~

Deformations of densely croselinked epoxy.amide polymers

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