deformation and fracture of polymers

$: Deformation and fracture of polymers$
DEFORMATION AND FRACTURE OF POLYMERS*

V. A. Stepanov UDC 539.375:539.4

On the basis of experimental research it is suggested that in polymers under load two physically different kinetic processes --deformation and fracture -- develop simultaneously. Their rates depend on different components of the stress tensor; accordingly, the relation between these rates can be experimentally controlled. It is suggested that these processes involve the overcoming of physically different potential barriers and that their elementary events embrace essentially different activation volumes. Deformation involves the overcoming of the forces of intermolecular interaction, and fracture, with the rupture of the main chains.

The study of the mechanical properties of polymers began with the investigation of the nature of their deformation. It was shown that the deformation is re!axational in character and based on the process of straightening of the polymer molecules [i].

A large contribution to the study of the nature of forced-elastic deformation, i.e., the deformation of polymers below the glass transition temperature Tg, was made by Aleksan- drov [2] when he postulated the dependence of the relaxation time T r not only on temperature T, but also on the applied stress ~:

Q0- ¢zo ~r=,o exp R T (i)

Here Q0 is the activation energy of the relaxation process; T O and ~ are certain material constants; R is the universal gas constant.

If it is assumed that the strain rate ~ is inversely proportional to the relaxation time, then

RT (2)

From expression (2) it is possible to obtain the dependence of the stress corresponding to the appearance of inelastic deformation -- the limit of forced-elastic deformation of -- on temperature and loading rate:

Qo R T ~. ~f= In =A-BTlg~: . (3)

~ ~o

*Review of work carried out in the Materials Laboratory of the A. F. Institute, Academy of Sciences of the USSR.

loffe Physico-Technical

A. F. loffe Physico-Technical Institute, Leningrad. Translated from Mekhanika Polimerov, No. i, pp. 95-106, January-February, 1975. Original article submitted May 21, 1974.

l © 1976 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.

8a

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Tlm 2

3

t

0

*f

-2

3

fib kgf/ram2 ° 3 - - " " ~ ,k I aH G

. . - . X X u t,o - . ~ ;, , '

bo i [ ,~ ~,~, . ~.', . . . . r ' ~

- qO0 5 0 0 $ 0

Fig. I Fig. 2

Fig. I. Stress dependence of the rupture life of polymethyl methacrylate [14]. Test temperature, °C: 80 (I); 60 (2); 30 (3); -30 (4); -60 (5); -i00 (6); -196 (7); above 80, sche- matically (8).

Fig. 2. Temperature dependence of the fracture strain (i), the breaking stress (2), and the NMR line width (3) for polyvinyl alcohol [18].

On a limited interval of temperatures and rates this dependence is well justified by the experimental data [3, 4]. In fact, relations (i) and (2) remain the physical basis for describing the polymer deformation process even today [I].

In the work on deformation, fracture was not taken into consideration.

The systematic investigation of polymer fracture as a physical process began with Zhur- kov and coworkers [5, 6].

It was shown that fracture is also a thermal-fluctuation process and determined by the kinetics of accumulation of chemical bond breakages [6, 7]. The lifetime of the specimen T, which in integral form reflects the continuous process of damage accumulation [8], is described by the well-known expression

Uo-vo (4) • =~oexp RT '

from which it is possible to obtain the dependence of the breaking stress a b on temperature and the time of action of the load,

Uo RT %= - - l n S - = A i - B J ' l g ~ .

y y ~o

Here, U 0 is the activation energy, which approximates the energy of thermal degradation; T O and y are material constants [6].

Expressions (2) and (4) are identical in form. Moreover, in a series of experimental creep studies on metals [9, i0] and highly oriented polymers [ii] it was found that

~= e~, = const, (5)

where E k -- for polymers -- is the inelastic creep strain at failure. It follows from (5) [9] that the activation energies of the processes of deformation (creep) Q0 and fracture U 0 are either equal or very similar. For unoriented polymers, however, there are data [12, 13] from which it follows that ~z # const, i.e., the constants in expressions (2) and (4), including Q0 and U0, may differ.

84

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~0

6f kgflmm ~ - 5 0 "

.t, .2 0

t9~ sec- i

2

I l l , 131t

' ° I ~ ,

- I S -$0 * $ 0

Fig. 3 Fig. 4

Fig. 3. Dependence of the forced elastic limit of polymethyl methacrylate in compression on temperature (il, 2) and strain rate C3, 4). Strain rate ~, see-l: 5.10 -1 (i); 5'10 -4 (2); temperature, °C: 20 (3); 70 (4).

Fig. 4. Temperature dependence of the breaking stress (log T = 3): I) oriented Kapron [19], right-hand scale; 2) unoriented Kaprolon V [14], left-hand scale.

These data pose a number of important problems:

i) to what extent are relations (2) and (4) general, i.e., do their coefficients remain constant over a broad range of experimental conditions (temperature, stress, state of stress, etc.);

2) what is the mechanical significance of the stresses in (2) and (4), i.e., by which of the components of the stress tensor -- deviatoric or spherical -- are they chiefly determined;

3) are the processes of deformation and fracture related and if so how;

4) what is the physical nature of the potential barrier Q0 preventing deformation. Our laboratory's work on polymers is directly chiefly toward solving these problems.

Universality of Expressions (2) and (4)

In [13] in studying the long-term strength of amorphous unoriented polymers it was established that if the quantities U0, T O , and y are constant, relation (4) is valid on a relatively small interval of T and o. Later [14, 15] this was confirmed for amorphou~-crystalline and cross-linked polymers. In general, the stress dependence of T for unoriented or weakly oriented polymers at different temperatures has the form shown in Fig. !. In Fig. 2 we have reproduced the temperature dependence of the breaking stress ~b"

The data obtained show that below the glass-transition point in polymers there exists a series of characteristic temperatures (more accurately, narrow temperature regions Tz, T2, and T3 in Fig. 2.), in which either all three constants U0, TO, and y or some of them vary. It has also been found [16] that when the strain rate and temperature are broadly varied breaks are observed on the of(R) dependence (Fig. 3),* i.e., in expressions (2) and (3) characterizing the resistance to inelastic deformation, the constants e0, Q0, and e do not remain constant.

Subsequent studies [17, 18] have established that the location of the breaks Ti (Fig. 2) does not, within the limits of experimental accuracy, depend on the type of state of stress or on the preliminary orientation. It does depend on the nature of the polymer and plasticization.

For highly oriented polymers the deviations from a fan-shaped log T vs ~ dependence are less strongly expressed. Accordingly, with the accuracy of extrapolation, the experimental log T vs ~ straight lines can be reduced to a single point or "pole" [19]. However, when these data are replotted in ~b(T) coordinates breaks are also observed. In Fig. 4 we

*The results presented in Fig. 3 were obtained by A. B. Sinani.

85

have shown the results of such a conversion based on the data of [19] for highly oriented Kapron and unoriented Kaprolon V which is similar in structure [14].

It has also been established [13, 17, 18] that at the temperature T i there is a sharp change (by several times) in the deformation ~k (see Fig. 2) at failure (at T = const). This indicates a jump in the creep rate, i.e., confirms the data on the variation of the constants in expression (2).

It follows that the characteristic temperatures are related with the changes in intermolecular interaction. In fact, a comparison of the results of mechanical tests with the data of NMR and certain other methods of studying molecular mobility in polymers has shown [13, 17, 18, 20, 21] that the characteristic temperatures obtained at ordinary mechanical testing times (102-104 sec) almost coincide with the temperatures at which free (high- frequency, f ~105 Hz) rotational vibrational motion of the individual molecular groups or units develops in the macrochain of the polymer (see Fig. 2).

One of the principal conclusions of this series of studies [18] was that there is a close relation between the mechanical properties of polymers below Tg and the intermolecular interactions* characterized by the intensity of molecular motion. The occurrence of free (high-frequency) motion of the molecular groups in the polymer means the elimination of some of the intermolecular bonds preventing the motion of these groups [17, 22]. In the last analysis, this means a change in the system of intermolecular bonds throughout the macrochain.

Whenever high-frequency rotational vibrational motion of certain molecular groups developed in the polymer chains, breaks or jumps were observed on the temperature dependences of the mechanical properties (breaking stress, creep rate, fracture strain). In terms of the kinetic theory this meant a change in the constants in expressions (2) and (4), i.e., a disturbance of the generality of those expressions. It has been suggested [18] that at

T = T i in expression (2) it is chiefly the activation energy Q0 =~'q~ that changes,

where qi is the energy of each of the intermolecular bonds opposing the elementary deformation event. There may also be a change in the activation volume ~. In expression (4) a change in y is physically more probable [13, 17]; however U 0 might also vary if, for example, at low temperature the elementary fracture event embraces not one, but several main chains [23]. These questions have not yet been fully resolved.

Mechanical Significance of the Stresses in Expressions (2) and (4)

In the fundamental research of Aleksandrov and Zhurkov on the deformation and fracture of polymers the question of the nature of the stresses was not raised. All the tests were conducted in linear tension, and it is the axial tensile stress that figures in relations (2) and (4). However, the answer to this question, apart from its obvious practical value, could help in solving the fundamental problem of the relation between the processes of deformation and fracture.

In our laboratory we have investigated the creep of a series of linear polymers (PMMA, PE, PS) in tension, torsion and compression [25]. It has been established that for the temperature region in which the fracture, strain is not very small (true shear gm > 0.05), the creep curves for tension, compression and torsion (Fig. 5) approximately coincide if the maximum shear stresses tm are equal. For tension and torsion the tests always ended in failure. In compression the PMMA specimens did not fail up to --150 and the PE specimens up to --196°C. At low temperatures, when the creep fracture strain for tension and torsion was negligible (gm~O.01), the approach of the creep curves depended not on the shear, but on the maximum tensile stresses (see Fig. 5, temperature~--lO0°C). Under these conditions the curves for compression lie considerable below the first two.

*Here intermolecular interaction means the weak (nonchemical) inter- and intramolecular interaction in the polymer.

86

0 i 2 3 ~- ,' 2 3 4 a ~' 2 J , 6' ,' 2 3 ~,

Fig. 5. Creep curves for polymethyl methacrylate at identical normal ~i (left-hand side of figure) and shear t m (right-hand side of figure) stresses [25]. !) Compression; 2) tension; 3) torsion, a: T =--140°C; ~= = 12.8; t m = 6.4 kgf/mm2; b: --120; 13; 6.5; c: --i00; 15.3; 6.65; (4) d: --50; 9; 4.5; e: -20; i0; 5; f: 20; 5; 2.5; g: 50; 3; 1.5; h: 70; i; i.

From these tests it was concluded that the deviatoric part of the stress tensor, in the first approximation the maximum shear stresses, is chiefly responsible for the deformation. The deviation detected at low temperatures was attributed to the large contribution of microbreakages to the creep strain. The lower creep rate observed at these temperatures for compression indicates a smaller number of microbreakages.

Thus, expression (2) should be written in the form

~_~o exp _ ( Q° - cd'~ ) RT '

or, considering that the energy Q0 must be determined by the total energy of all the intermolecular bonds Zqi opposing the elementary deformation event, in the form

~=~0exp- (~ qi-o~t,, (6) R~ -

The experimentally determined dependence of the deformation processes on the shear stresses has recently been theoretically developed by Argon [24].

The establishement of a "long-term strength criterion," i.e., the stress causing rupture, has presented greater technical difficulties. A number of indirect data [14, 25, 26] have shown that the long-term strength of polymers is associated with the normal tensile stresses. This was demonstrated somewhat more rigorously in [27] by comparing the long-term strengths in tension and torsion both for brittle fracture and for fracture after large deformation. Considering the experimental errors and the considerable difference between the fracture strains in tension and torsion (at ~I = const) it was difficult to anticipate perfect coincidence ofthe long-term strengths as a function of some simple criterion. However, the ex- periment showed (Fig. 6) that the difference is small if as the criterion one takes the maximum tensile stresses, and more particularly that the fracture surface always coincides with the plane of action of those stresses. It may therefore be assumed that irrespective of the mode of fracture (brittle or "plastic") the spherical part of the stress tensor is

8?

l~q* SeC

kgf / [__l_~. 6, mm 2

':, 6 6' lO q2 a /0 12

Fig. 6. Dependence of the long-term strength of polymethyl methacrylate on the maximum tensile stresses [27]. ~,Y) tension; 0, O, []) torsion. ~, O, @) solid specimens; Y, D) tubular specimens. T, °C = 50 (i); 20 (2); --20 (3); --196 (4).

responsible for failure and is only positive. In the first approximation as a long-term strength criterion it is possible to take the maximum tensile stress ~z, and the Zhurkov equation should then be written in the form

.~___.~o exp ( Uo- Ycr~ ) R T

(7)

Physically, this means that only an increase in interatomic distance will reduce the potential barrier to bond rupture. Of course, this applies to local bonds. Accordingly, for example, in macroscopic linear compression fracture may develop at points at which owing to structural inhomogenei- ties the bonds are stretched~ In principle, however, com- pressive stresses should not cause fracture.

This dependence of the creep rate and long-term strength on different components of the stress tensor indicates that they are physically different.

Interrelationship of the Processes of Inelastic Deformation and Fracture Of Polymers

It was noted above that there are data [9-11, 28] indicating the existence of a relation between the processes of deformation and fracture (see also Fig. 2). The nature of this relation is unclear. At the same time, in order to understand the processes of deformation and fracture and predict the behavior of polymers under load it is important to know the answer to this question. Below an attempt is made to give a schematic picture of the phenomenon based on the results of research carried out in our materials laboratory.

We assume that deformation and fracture are physically different kinetic processes proceeding simultaneously in the loaded solid. The relation between the rates of these processes determines the mode of fracture of the body (brittle or plastic). Depending on the magnitude of the energy barriers Q0 and U 0 and the loading conditions, one of these processes may predominate or exert an important influence on the other.

For noncross-linked polymers deformation involves the relative displacement of part of the macromolecules or their larger associations -- elements of the supermolecular structure [i] -- with overcoming of the forces of intermolecular and intramolecular interaction. This process, whose elementary event it is still difficult to determine more accurately, must be accompanied by the temporary weakening of the intermolecular bonds Zq i with subsequent total or partial recovery [29-31]. The deformation of noncross-linked polymers does not require rupture of the chemical bonds. It can proceed without irreversible changes in the polymer bond system. Shear stresses are responsible for deformation. The rate of deformation (creep) is determined, in general, by an expression of the type (6).

According to the results of the Zhurkov school [6], the fracture of polymers is associated with rupture of the main chains. Obviously, the rupture of even a single chain Will produce irreversible changes in the system of bonds in the body. The maximum tensile stresses are responsible for fracture. The mean fracture rate -- the reciprocal of the long-term strength -- is given by the expression

- A ( U o - y O ~ ) v = - - exp - . ( 8 )

To RT

Or, in accordance with a recent study [7], as the fracture rate it is possible to take the rate of accumulation of broken bonds in time t in accordance with the expression

q = C * ( l _ er,'t), (9)

88

Lilt G

f ~ 15

"ZOO "fO0 0

Fig. 7. Temperature dependence of the relative shear at failure (at a lifetime of 3000 sec) for polyethylene [18]: i) tension, isotropic material; 2) tension after prestretching by a factor of four; 3) torsion, isotropic material; 4) NMR line width.

where

K=Ko exp ( Uo-ycq ) (10) Rir

In expressions (9) and (i0) C t is the variable concentration of broken chemical bonds; C* is the limiting concentration of bonds capable of breaking; K is the fracture rate constant.

Our concept of deformation and fracture as different processes involving the overcoming of physically different potential barriers* makes it possible to explain many aspects of the behavior of polymers under load. It also permits certain predictions. We will illustrate this with examples.

I. Since ~ and v depend on different components of the stress tensor, by varying the type of state of stress, i.e., the ratio tm/Oz = 8, it is easy to control the plasticity of polymers.* This is in good agreement with the known facts (Fig. 7) concerning the greater (by almost an order) increase in deformation for torsion (~ = i) as compared with tension (B = 0.5) at the same lifetimes. For compression in the absence of local tensile stresses the degree of deformation (without fracture) can be arbitrarily large [25].

A sharp increase in plasticity should be observed in tension under hydrostatic pressure p. At p > Ozm, where Ozm are the maximum local tensile stress concentrations, the specimen should fail by contraction of the cross section into a point, i.e., by deformation only. For metals this follows from the data of [33], and, moreover, the later studies [34, 35].

For polymers the picture is more complicated since after the long molecules have been more or less completely extended further stretching of the specimen is impossible without the rupture of main chains. Accordingly it may be assumed that when polymers are stretched under high hydrostatic pressure there will be a point of inflection on the o(s) curve corresponding to transition from deformation involving primarily the overcoming of intermolecular forces to the rupture of main chains.

2. It has been shown [6, 7, 36] that fracture is essentially irreversible. According- ly, in accordance with (4) and (7) any application of a tensile load should reduce the strength. However, experience shows the opposite to be true: prestretching (orientation) usually increases the strength and rupture life. From the standpoint of the two-process theory this is obvious. If the test temperature is high, then the intense deformation process reduces the local stress concentrations, decreases y, and increases r. The strain hardening effect should be multiplied many times if large strains are caused by small tensile stresses, i.e., if the fracture rate is reduced while simultaneously increasing the deformation rater It follows from (6) and (8) that this can be achieved either by varying the type of state of stress (increasing $) or raising the temperature, since this changes the chemical bond energy U 0 only slightly [37], whereas the intermolecular energy (Eqi) should decrease with each new mode of high-frequency vibrational motion of specific molecular groups (see Fig. 2). The jump in Q0 with the appearance of high-frequency vibrations explains the stepped character of the Sk(T) curves and the associated break on the o~(T) dependences in Fig. 2. We note that the nature of the log Sk vs T dependence remains the same for different types of state of stress (see Fig. 7).

At T > Tg the intermolecular energy is negligible [38, 39]; accordingly, straightening of the macromolecules takes place at low tensile stresses, i.e., with low probability of rupture. This method of hardening polpnners has long been put to practical use by orienting them at T > Tg. Even greater hardening can apparently be achieved if the polymer is oriented

*Quantitatively Q(t m) = Eqi(tm) may be close to U@z).

#The coefficient B is analogous to the "softness coefficient" introduced in [32].

89

30 I

20 I /

J 1 '° ! 4 . / ' , i

I , It .......... I m i n 0 iO 2,0 aO ~o

- t o 2. o m ~ m i

.0,5

g

@;sec,i

Fig. 8 Fig. 9

Fig. 8. Creep curves for polyvinyl formal in compression [41]: = 5.0 kgf/mm 2 (i) and 7.0 kgf/mm 2 (2), T = 65°C. Stresses

constant throughout the test.

Fig. 9. Specimen fracture strain (in relative units) as a function of rupture life. i, 2) Ebonite, torsion; at 20°C and --30°C, respectively; 3,4) polymethyl methacrylate, tension at --20°C and --140°C, respectively.

not by stretching (~I > 0) but by the application of lateral pressure (~ < 0). Experiments in our laboratory* have shown that lateral compression can increase the maximum stretch ratio of Kapron to 15 as compared with the values 5-6 obtained in linear tension at T = 190-200°C.

3. We will also consider the case of an increase in the plasticity of polymers (low- ering of the brittle point) after a relatively small prestretch [12, 18, 40] at T > Tg. Such stretching, by equalizing the stresses on the chains, reduces y in (8), i.e., reduces the fracture rate at the same mean stresses ~I and increases the time to failure. At the same time, the creep rate is almost unaffected ~12, 18]; accordingly, before failure the weakly oriented polymer is able to accumulate much more strain (see Fig. 7).

The weak influence of light stretching on the creep curves indicates the lesser sensitiv- ity of the coefficient ~ in (6) to nonuniform distribution of the stresses among the structural elements. This is natural, since the elementary deformation event should embrace a much larger volume then the fracture event, for which in principle the rupture of a single bond between neighboring main-chain atoms is sufficient.

Digressing slightly, we note that the idea of an analogy between the creep curves for polymers and metals is incorrect [41]. The creep curve of unoriented polymers has the general form shown in Fig. 8. It does not have an interval of steady-state creep rate, at which it is usual to take the segment II near the inflection point. The third stage may again be fol- lowed by a drooping branch (at ~ = const) IV, which is missing in the case of metals. The shape of the actual curves obtained in creep tests depends on the stage in which fracture interrupts the deformation process, i.e., on the ratio of the creep and fracture rates. In "soft"states of stress (torsion and, especially, compression) creep may pass through all the stages. In tension it is interrupted by fracture no later than the stage III. The nature of the c(t) dependence indicates that the constants in expression (6) change during the process of deformation. It is probably that here both Q0 [29-31] and ~ vary.

These observations concerning the independence of the processes of deformation and fracture should be understood in the sense that they are physically different processes and can develop independently. However, in reality they do, of course, affect each other. Thus, the coincidence of the breaks in the ~b(T) curves and the "jumps" on the Ok(T) curves (see Fig. 2) is probably the consequence of the effect of deformation on fracture. The abrupt change in intermolecular interaction at the characteristic temperatures affects Q0 and hence the deformation rate or the rate of relaxation of local stress concentrations, i.e., affects y in expression (4).

*Carried out by V. N. Borsenko and A. B. Sinani.

9O

The processes of orientation and stress relaxation that take place during stress-rupture testing at high and low temperatures, respectively, are evidently associated with the degeneration of the inclined log T vs ~ relations into almost vertical straight lines (see Fig. i). The possibility of relaxation of high stresses even at temperatures of --170°C was demonstrated in [15]. Thus, here deformation plays the decisive part in the deviation from dependence (4). However, in this case the relation between the processes of deformation and fracture is not a direct one.

Cases of a Direct Relation Between Deformation and Fracture

The essential independence of the processes of deformation and fracture and, moreover, the observed cases where deformation has an indirect influence on fracture relate morepartic- ularly to bodies in which the elementary displacement events are associated with the overcoming of lower barriers than required for the rupture of interatomic bonds. These bodies include metals, nonmetallic crystals with low Peierls barriers, and linear polymers. For highly cross-linked polymers deformation cannot proceed very far without the rupture of interatomic bonds. Here, the deformation rate must be determined by the rate of bond rupture. Obviously, in this case, T~ = ~k = const. Such data (Fig. 9) were obtained in tests on ebonite [27].

An example of the decisive role of fracture is low-temperature creep [25]. As the temperature falls, even for linear polymers the sum of the energies of the intermolecular bonds may exceed the main-chain rupture energy. Then the probability of deformation will be negli- gibly small. At the same time, even for PS and PP~IA at --196°C a small amount of creep is observed. However, the creep rate is determined not by t m, but by ~I. It is therefore to be assumed that the macroscopic creep strain is caused by elastic deformation in the neighbor- hood of opening submicrocracks. The probability of this mechanism is strengthened by the data on the effect of preliminary loading on the strength [42]. Keeping the specimen under a light load in the temperature region where ~ depends on ~ weakens it. However, holding it at higher temperatures, where creep is determined by the displacements of the chain units (~ depends on tm) strengthens the specimen. In the first case, within the limits of experimental error, T~ = Sk = const, in the second, as in [13], T~ # const (see Fig° 9)~

It is possible to imagine one more case where the polymer deformation (creep) process should be determined by the main-chain breakage rate. Namely, the extension of highly oriented linear polymers, when many of the chains are already extended to the limit and further stretching of the specimen is impossible without breaking the macromolecuies. Such behavior was observed in [ii]. It was shown that T~ = const and that creep is sharply accelerated and bond rupture is intensified by ultraviolet radiation. The creep rate of unoriented polymers was not affected by ultraviolet radiation.

CONCLUSIONS

I. It has been shown that the fracture and deformation of polymers are associated with different components of the stress tensor: fracture (brittle and "plastic") with the normal tensile, and deformation with the shear stresses. Deformation (maximum shear stresses) and fracture (maximum tensile stresses) criteria have been determined in the first approximation.

2. It has been established that relations (2) and (4) cannot describe the experimental data over a broad range of variation of the test conditions if the quantities ~0, Q0, and

in (2) and TO, U0, and y in (4) are kept constant.

3. It has been found that below the glass transition temperature the changes in these quantities take place on relatively narrow (10-15 ° ) temperature intervals (characteristic temperatures). The number and value of the characteristic temperatures depend on the structure of the polymer and are related with the intervention or suppression of new types of high-frequency rotational-vibrational motion of specific molecular groups (side chains and elements of the main chain).

4. It is suggested that in polymers, as in other loaded solids, two physically different kinetic processes develop simultaneously, namely, deformation and fracture. Their rates depend on different components of the stress tensor. Accordingly, they can be experimentally controlled. It is postulated that these processes involve the overcoming of

91

physically different potential barriers, and that their elementary events embrace essentially different activation volumes. Deformation involves the overcoming of the forces of intermolecular interaction, fracture involves the rupture of the main chains [6].

5. It is suggested that the observed sharp changes in the temperature dependence of the breaking stress and fracture strain (at constant rupture life) on narrow temperature intervals are mainly associated with changes in y and the intermolecular interaction energy Q0, respectively.

6. A number of examples showing how the concept of two processes makes it possible to explain the behavior of polymers under load are examined.

LITERATURE CITED

I. A. A. Askadskii, Deformation of Polymers [in Russian], Moscow (1973). 2. A. P. Aleksandrov, in: Proceedings of the First and Second Conferences on High-Molecular-

Weight Compounds [in Russian], Moscow (1945), p. 49. 3. Yu. S. Lazurkin and R. L. Fogel'son, Zh. Tekh. Fiz., No. 21, 267 (1951). 4. Yu. S. Lazurkin, Doctoral Dissertation, Moscow (1954). 5. S. N. Zhurkov, Vestn. Akad. Nauk SSSR, No. 3, 46 (1968). 6. V. R. Regel', A. I. Slutsker, and E. E. Tomashevskii, Usp. Fiz. Nauk, !06, 193 (1972). 7. S.N. Zhurkov and V. E. Korsukov, Fiz. Tverd. Tela, 15, 2071 (1973). 8. V. A. Zakrevskii, Vysokomolek. Soed. 13, 105 (1971). 9. S. N. Zhurkovand T. P. Sanfirova, Zh. Tekh. Fiz., No. 28, 1719 (1958).

10. I. E. Kurov, V. A. Stepanov, and V. V. Shpeizman, in: Physics of Metals and Metallography. Transactions of the Leningrad Polytechnic Institute.305 [in Russian], Leningrad (1970)~ p. 71.

ii. V. R. Regel' and N. N. Chernyi, Vysokomolek. Soed. 5, 925, (1963). 12. M. I. Bessonov, Candidate's Dissertation, Leningrad (1961). 13. N. N. Peschanskaya and V. A. Stepanov, Fiz. Tverd. Tela, ~, 2962 (1965). 14. I. N. Sgureva and V. A. Stepanov, in: Physics of Metals and Metallography. Transactions

of the Leningrad Polytechnic Institute. 331 [in Russian], Leningrad (1973), p. 112. 15. Yu. A. Nikonov and V. A. Stepanov, Fiz. Tverd. Tela, 16, 2750 (1974). 16. A. B. Sinani and V. A. Stepanov, in: Transactions Df the Metr~logical Institutes of the

USSR. 91 (151) [in Russian], Moscow--Leningrad (1967), p. 180. 17. E. A. Egorov, N. N. Peschanskaya, and V. A. Stepanov, Fiz. Tverd. Tela, ii, 1325 (1969). 18. N. N. Peschanskaya and V. A. Stepanov, Mekhan. Polim., No. i, 30 (1971). 19. S. N. Zhurkov and S. A. Abasov, Vysokomolek. Soed., 3, 441 (1961). 20. V. G. Nikol'skii and N. Ya. Buben, Dokl. Akad. Nauk SSSR, 134, 134 (1960). 21. N. N. Peschanskaya, ~. S. Pugachev, and V. A. Stepanov, Fiz. Tverd. Tela, 16, 2424 (1974). 22. R. D. Endryus, in: Transitions and Relaxation Effects in Polymers [in Russian], Moscow

(1968), p. 300. 23. G. M. Bartenev, Vysokomolek. Soed., ii, 2341 (1969). 24. A. S. Argon, Phil. Mag., 28, 839 (1973). 25. V. N. Borsenko, N. N. Peschanskaya, A. B. Sinani, and V° A. Stepanov, Mekhan. Polim.,

No. i, 24 (1970). 26. I. E. Kurov and V. A. Stepanov, Fiz. Tverd. Tela, ~, 191 (1962). 27. N. N. Peschanskaya and V. A. Stepanov, Mekhan. Polim., No. 6, 1003 (1974). 28. V. A. Stepanov and V. V. Shpeizman, in: Heat Resistance of Materials and Structural

Elements. 5 [in Russian], Kiev (1969), p. 82. 29. N. A. Kalinina and V. A. Stepanov, Fiz. Tverd. Tela, 13, 3086 (1971). 30. V. A. Bershtein, N. A. Kalinina, S. V. Savin, and V. A. Stepanov, Fiz. Tverd. Tela, 14,

1140 (1972). 31. N. A. Kalinina, in: Physics of Metals and Metallography. Transactions of the Leningrad

Polytechnic Institute. 331 [in Russian], Leningrad (1973), p. 107. 32. Ya. B. Fridman, Mechanical Properties of Metals [in Russian], Moscow (1952), p. 149. 33. P. W. Bridgman, Studies in Large Plastic Flow and Fracture with Special Emphasis on the

Effects of Hydrostatic Pressure, Harvard University Press (1952). 34. Mechanical Properties of Materials Under High Pressure. l [in Russian], Moscow (1973). 35. B. N. Beresnev, E. D. Martynov, K. P. Rodionov, D. K. Bulychev, and Yu. N. Ryabinin,

Plasticity and Strength of Solids at High Pressures [in Russian], Moscow (1970). 36. S.N. Zhurkov, V. A. Zakrevskii, V. E. Korsukov, and V. S. Kuksenko, Fiz. Tverd. Tela,

13, 2289 (1971).

92

37. Ya. I. Frenkel', Kinetic Theory of Liquids [in Russian], Leningrad (1945), p. 35. 38. S. N. Zhurkov and B. Ya. Levin, Dokl. Akad. Nauk SSSR, 71, 89 (1949). 39. S.N. Zhurkov and B. Ya. Levin, Dokl. Akad. Nauk SSSR, 72, 269 (1950). 40. B. V. Perov and M. M. Gudimov, Oriented Acrylic Glass Laminates [in Russian], Moscow

(1961). 41. V. N. Borsenko, A. B. Sinani, and V. A. Stepanov, Mekhan. Polim., No. 5, 787 (1968). 42. V. V. Zhitkov, N. N. Peschanskaya, and V. A. Stepanov, Mekhan. Polim., No. i~ 176

(1972).

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deformation and fracture of polymers

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