On the Temperature-Time Dependence of the Mechanical Strength of Polymers

R. M. Kessenikh, A. V. Petrov

(Presented by the scientific seminar of the Department of Electrical Insulation and Cable Engineering)

For a solid body, the dependence of strength on temperature and time is characteristic. The time dependence of the strength of a solid body is not connected with ideas of critical rupture and ultimate strength, since the time from the moment of loading to rupture of the specimen depends substantially on the magnitude of the destructive stress. The lower the temperature, the less pronounced is the time dependence of strength. Thus, fracture is a continuous process occurring in a mechanically stressed body. Moreover, the rate of this process will depend on the magnitude of the applied stress and on time. The smaller the applied load, the longer the “lifetime” of the solid body; and, conversely, the greater the applied load, the shorter the “lifetime” of the solid body.

Relaxation processes, which occur in all solids, manifest themselves most vividly in polymers. Naturally, under the action of mechanical loads, relaxation processes can exert a substantial influence on the regularities and mechanism of fracture. Studies of the temperature-time dependence of strength for a wide range of materials (metals, silicate glasses, ionic crystals, and polymers) made it possible to describe the experimental results by means of the Zhurkov equation, which has the form

\[ \tau = \tau_0 \exp \frac{U_0 - \gamma \sigma}{RT}, \tag{1} \]

where \(\tau\) is the time from application of the load to fracture, called the durability;

\(\tau_0\) is a constant, numerically close to the period of thermal vibrations of atoms \((10^{-12}—10^{-13}\ \text{s})\);

\(U_0\) is the activation energy of the elementary act of the fracture process in the absence of stress, close in magnitude to the sublimation energy for metals and to the energy of mechanical bonds for polymers;

\(\sigma\) is the stress;

\(\gamma\) is the structurally sensitive coefficient;

\(R\) is the universal gas constant;

\(T\) is the absolute temperature in °K.

Measurements of durability were carried out over a wide range of times (up to 10 orders of magnitude), temperatures, and loads. A systematic study of the durability of polymers made it possible to develop physical conceptions—

notions about the nature of fracture as a kinetic, thermofluctuational process.

Thus, the elementary acts of the fracture process are thermofluctuational ruptures of interatomic bonds (chemical and intermolecular), activated by the applied stress.

In connection with the above, great importance is attached to Zhurkov’s formula, since it is an instrument for the physical analysis of fracture. Thermal fluctuations overcome the energy barrier \(U_0\), reduced as a result of mechanical stresses by an amount equal to \(\gamma\sigma\) [1—9].

It turned out that, for many of the polymers investigated, the activation energy of thermal destruction is numerically equal to the activation energy of mechanical fracture. This confirms that the basis of mechanical fracture, as also of the process of thermal destruction of polymers, is thermofluctuational rupture of chemical bonds.

The quantities \(\tau_0\), \(U_0\), and \(\gamma\) can be determined experimentally by using the temperature dependence of the logarithm of the lifetime of the material. In doing so, the condition of invariability of the structure of the polymer under study must be observed during the experiment. Then the graphical dependence \(\lg \tau = f(1/T)\) is expressed by straight lines with different slopes. All the straight lines intersect at a point lying on the ordinate axis at \(1/T = 0\). At \(1/T = 0\) the lifetime \(\tau\) is equal to \(\tau_0\) (Fig. 1). From the slope of the straight lines \(\lg \tau = f(1/T)\), the activation energy \(U = U_0 \gamma\sigma\) can be estimated and the dependence \(U = f(\sigma)\) constructed.

Thanks to the linear character of this dependence, by extrapolating it to the ordinate axis it is possible to calculate \(U_0\) (Fig. 2). The tangent of the angle of inclination of the straight line \(U = f(\sigma)\) corresponds to the structural coefficient \(\gamma\). Figure 3 shows the dependence of \(\lg \tau\) on load at different temperatures. As in the case of Fig. 1, we observe a family of straight lines which, on extrapolation, converge at one point at \(\lg \tau = \lg \tau_0\). This point is called the pole.

Fig. 1. Dependence of the logarithm of lifetime on reciprocal temperature at different loads

Fig. 2. Dependence of activation energy on load magnitude

Fig. 3. Dependence of the logarithm of lifetime on load at different temperatures

Table 1 gives the values of the initial activation energy \(U_0\) and the structural coefficient \(\gamma\) for certain materials [10, 11].

Consequently, there exists a relationship between mechanical fracture and thermal destruction, making it possible to obtain important information by comparing the kinetics of these two processes. To verify the validity of the basic propositions of the kinetic concept of polymer fracture, experiments have been carried out using modern methods that make it possible, by direct investigations, to establish the structure. These methods include EPR, mass-spectrometric analysis, infrared spectroscopy, etc.

Let us consider some results obtained by the indicated methods.

Table 1

Values of \(U_0\) and \(\gamma\) for some materials

In the works of Bresler, Zhurkov, and others, a number of polymers were studied during mechanodestruction by means of electron paramagnetic resonance (EPR). Some results are shown in Figs. 4 and 5. In Fig. 4a the spectra of free radicals of PMMA are presented. The PMMA radical has the structure

\[ \begin{array}{c} \mathrm{CH_3}\\ \vert\\ \mathrm{CH_2}-\dot{\mathrm{C}}\\ \vert\\ \mathrm{COOCH_3}. \end{array} \]

The first EPR spectrum was obtained in liquid nitrogen, the second—in vacuum, and the third—after admission of air. In Fig. 4b the EPR spectra of free radicals of polystyrene (spectrum 1), polytetrafluoroethylene (spectrum 2), and polyisoprene (third spectrum) are given. In all three cases peroxide radicals of the ROO type are formed.

In Fig. 5 the spectrum of free radicals of polyisobutylene after fracture in liquid nitrogen (5a) and of polyethylene after fracture in liquid nitrogen (5b) is presented. The radicals respectively have the formulas

\[ \begin{array}{ll} & \mathrm{CH_3}\\[-2pt] & \vert\\[-2pt] \text{polyisobutylene radical} & -\mathrm{CH_2}-\dot{\mathrm{C}}.\\ \text{polyethylene radical} & -\mathrm{CH_2}-\dot{\mathrm{CH}}- . \end{array} \]

Similarly, radicals are observed during mechanodestruction, irradiation, and thermal destruction, as well as in a gas discharge and for a number of other polymers. It is known that in PMMA one and the same signal of 9 lines of hyperfine structure appears upon irradiation with X-rays and γ-rays, electrons and ultraviolet light, during mechanodestruction, during polymerization, and under the action of an electric discharge in vacuum [12—19].

The developed method for studying the process of thermal destruction in a mass spectrometer, applied to the study of the kinetics of the process and also to determining the composition of the volatile destruction products formed directly while the polymer is under load, made it possible to obtain interesting results. Thus, Fig. 6 shows the time dependence of the height of the peak \(h_{100}\) of the mass spectrum of products released from PMMA samples under a load of \(2.4\ \text{kg}/\text{mm}^2\). From the very moment the load is applied, monomer begins to be released from the samples; the identity of the shape of the curve for the time dependence of monomer release and the shape of the creep curve is noteworthy.

Fig. 6. Time dependence of the height of the peak \(h_{100}\) of the mass spectrum of products for PMMA under a load of \(2.4\ \text{kg}/\text{mm}^2\)

This fact confirms the supposition that the destruction process indeed begins from the moment the load is applied and proceeds with time [1]. Thus, the data obtained by means of EPR and mass spectrometry complement one another and confirm the concept of kinetic destruction of polymers.

Further investigations in this direction showed that there is an unambiguous relation between the rate of accumulation of free radicals and the lifetime of the polymer in the loaded state. In a number of cases the use of the EPR method is hindered because of the rapid death of radicals; in this case infrared spectroscopy (IR spectroscopy) can be of help, making it possible, from the appearance of new bands, to detect the products of mechanochemical destruction. For example, in the presence of oxygen the radicals are oxidized. This leads to the appearance and growth in the intensity of absorption bands associated with vibrations of carbonyl groups \((\mathrm{C}= \mathrm{O})\).

It is of interest to determine whether the concentration of carbonyl groups will change when the magnitude of the load applied to polypropylene and polyethylene and the time of its action are varied. Under the action of a uniaxial load of \(50\ \text{kg}/\text{mm}^2\) for \(30\ \text{min}\), the intensity of the bands \(1707\ \text{cm}^{-1}\), \(1735\ \text{cm}^{-1}\), and \(1745\ \text{cm}^{-1}\) increased substantially. As is known, these bands are assigned to vibrations of \(\mathrm{C}= \mathrm{O}\) bonds in acid groups \(-\mathrm{CH}_2-\mathrm{C}(=\mathrm{O})-\mathrm{OH}\), aldehyde groups \(-\mathrm{CH}_2-\mathrm{C}(=\mathrm{O})-\mathrm{H}\), and ester groups \(-\mathrm{CH}_2-\mathrm{C}(=\mathrm{O})-\mathrm{OR}\) [12—13].

A quantitative estimate of the carbonyl groups under tensile load was made using absorption coefficients. The results of the estimate are given in Table 2.

Thus, systematic studies by direct methods of the products of macromolecular decomposition under mechanical loading and purely thermal action, the detection of the appearance of free radicals in the volume of a polymer body under load, and the appearance of absorption bands of considerable intensity clearly confirm and broaden ideas about the kinetic nature of the fracture of polymers, and also confirm the temperature–time dependence of strength. It should be noted that sometimes a discrepancy is observed between equation (1) and experimental data. This discrepancy is due to the fact that equation (1) has its limits of applicability, which are determined by the range of changes in loads and temperature, and also by the particular properties of the materials studied. From experimental data it is known that the observed deviations from equation (1) can be grouped as follows [20]:

Table 1

Increase in the concentration of groups C=O (1·10¹⁸ cm⁻³) in polypropylene and polyethylene under load \(\delta = 50\) kg/mm² over 30 minutes

1. In the region of small loads, a nonlinear dependence \(\lg \tau = f(\sigma)\) is observed. This deviation is inherent in all materials without exception.

2. The pole turns out to be shifted along the abscissa toward positive values of \(1/T\). This pole-shift effect is observed only for some materials.

3. In the dependence \(\lg \tau = f(\sigma)\), breaks are observed for some materials.

In the cases indicated, it is no longer possible to describe durability as a function of stress and temperature by equation (1), since an uncertainty appears in the dependence on temperature and load of all three coefficients. Up to the present time there is no generally accepted physical description of the three deviations from Zhurkov’s equation. Therefore different authors attempt in different ways to describe durability analytically, introducing corrections into equation (1).

As was already indicated above, the dependence of \(\lg \tau\) on \(\sigma\) at different temperatures can be represented by a family of straight lines, fanwise emerging from a single pole. Moreover, this pole must lie on the ordinate axis, i.e., at \(1/T = 0\), and \(\lg \tau_0 \simeq -13\). However, it has been found experimentally that in uniaxial tensile tests at \(\sigma = \mathrm{const}\) a deviation from the above is observed. The essence of this deviation is that the pole in the coordinates \(\lg \tau\)—\(1/T\) turns out not to be on the ordinate axis, but is shifted somewhat along the abscissa toward positive values of \(1/T\), while remaining, in ordinate, at the same level \(\lg \tau_0 \simeq -13\). This effect is called “pole shift.”

Up to the present time the cause of pole shift is unclear. Indeed, it has been found experimentally that for polymers whose destruction follows a random law, the pole is in place. Pole shift, however, is observed in polymers whose destruction does not obey a law—

case, but proceeds along a more complex path, accompanied by secondary radical reactions. In this process, the macroradicals formed during degradation accelerate the decomposition of polymers.

In [21] it is shown that inhibitors that suppress radical reactions shift the pole to the left, toward its normal position on the ordinate axis; catalysts, on the other hand, shift the pole still farther to the right of the ordinate axis. Consequently, secondary radical reactions affect the rate of the process of polymer destruction.

In addition, the authors of [22] found that introducing an active filler into a polymer leads to a shift of the pole along the temperature scale \(1/T \to 0\) from its position for the unfilled polymer. At a content of 32% of this filler, the coordinate of the pole lies, in accordance with the thermofluctuation theory of strength, on the ordinate axis. A similar effect on the position of the pole is exerted by prior uniaxial orientation of specimens in the highly elastic state. The observed effect is explained by the authors as an increase in intermolecular interaction, and they believe that an increase in intermolecular interaction stabilizes the structure of the polymer, i.e., during testing the specimen retains a stable state and no anomalous shift of the pole is observed.

Structural changes during destruction lead to a change in the coefficient \(\gamma\), which reflects the influence of overstresses. The coefficient \(\gamma\) then varies with temperature according to a hyperbolic law, sometimes increases with plasticization, and decreases with orientation of polymers. The effect of pole displacement is proposed to be described by the expression

\[ \tau = \tau_0 \exp \left[ \frac{U_0 - \gamma' \sigma}{R} \left( \frac{1}{T} - \frac{1}{T_{\mathrm{p}}} \right) \right]. \tag{2} \]

This expression corresponds to the case when \(\gamma\) and \(U_0\) depend linearly on temperature,

\[ \gamma = \gamma' \left( 1 + \frac{1}{T_{\mathrm{p}}} \right); \qquad U_0 = U_0' \left( 1 + \frac{T}{T_{\mathrm{p}}} \right), \tag{3} \]

where \(\tau_0\) and \(U_0\) are constants, as in equation (1), and \(T_{\mathrm{p}}\) is the temperature corresponding to the position of the pole.

In addition, all complications of the functional dependence of the structural coefficient \(\gamma\) on load and temperature can also be assigned to it. In this case one obtains the formula

\[ \tau = \tau_0 \exp \left( \frac{U_0 - \gamma(\sigma, T)\sigma}{RT} \right), \tag{4} \]

Thus, one can propose a whole series of other variants of writing equation (1), but these forms do not make it possible to calculate \(U\) and \(\gamma\).

In the works of Butyagin and co-workers [23], the rate of mechanodestruction of polymers at low temperatures (from \(+25\) to \(-196^\circ\mathrm{C}\)) was studied. As a result it was shown that the rate constant of destruction is constant in time and does not depend on temperature. The absolute values of the rate constants are large. This indicates that the results obtained do not fit within the framework of the thermofluctuation theory of destruction.

The authors of [23] believe that there is a fundamental difference in the mechanisms of high- and low-temperature mechanodestruction: in high-temperature destruction, structural relaxation predominates; in low-temperature destruction, the rate of structural relaxation is greatly reduced, and relaxation begins to play the main role.

energy over the internal degrees of freedom of the molecule [24]. For rubber-like polymers, the form of the temperature–time dependence, according to Bartenev, is written as follows [11]:

\[ \tau = A\sigma^{-m} e^{U_0/RT}, \tag{5} \]

where \(A\) and \(m\) are material parameters.

As is known, in this case the activation energy of fracture is observed to be independent of stress. This independence is explained by the molecular-kinetic nature of the elasticity of highly elastic materials [1].

In studying the durability of thermosetting non-rubber-like polymers over a wide temperature interval, the following has been established. In the glassy state, the durability of these polymers is described by Zhurkov’s equation, and the activation energy of the fracture process decreases with increasing stress. Conversely, in the highly elastic state this energy increases with increasing stress, while remaining, in absolute magnitude, considerably lower than the activation energy of fracture in the glassy state [25]. In addition to Zhurkov’s thermofluctuation theory, there are also a number of other theories of fracture of a solid.

The well-known Griffith theory [1, 11], based on the application of the law of conservation of energy, has been tested experimentally by many authors. The tests showed that in some cases the critical stress of a number of polymers (PS, PMMA) varies proportionally to \(1/\sqrt{l_0}\). There are experimental data showing the limitations of this theory. Therefore it became necessary to refine the theory and to take into account mechanical losses of various natures arising during crack formation.

In the works of Bartenev et al. [26], the allowance for and the form of mechanical losses are substantiated. Thus, Griffith’s theory contains two main shortcomings: 1) the concept of critical stress, 2) the neglect of various kinds of mechanical losses arising during crack growth.

Bartenev and Razumovskaya proposed a time dependence of strength [11, 34, 35]. The essence of this theory is as follows. The fracture process proceeds as a result of crack growth, at the tips of which bonds between atoms break because of thermal fluctuations. At low stresses the probabilities of bond rupture and restoration are equal, and the crack practically does not grow (by low stress is meant a safe stress less than the so-called safe stress \(\sigma_0\)). At \(\sigma > \sigma_0\) the probability of rupture becomes greater than the probability of bond restoration, which leads to the growth of a microcrack. Then the rate of its growth may be taken as equal to \(V = V_1 - V_2\), where \(V_1\) and \(V_2\) are, respectively, the rates of growth and closure of microcracks.

These quantities depend on the probabilities of rupture and restoration of bonds, determined, in turn, by stress, temperature, and other factors. The expression for the rate of growth of a microcrack has the form

\[ V = V_k \left( e^{-\frac{U-w\beta\sigma'}{RT}} - e^{-\frac{U' + w'\beta\sigma'}{RT}} \right), \tag{6} \]

where \(V = \lambda \nu_0\) is the critical rate of growth of a microcrack (\(\lambda\) is the mean distance between neighboring rupturing polymer chains along the path of crack growth, \(\nu_0\) is the frequency of thermal vibrations of atoms in the polymer chain);

\(w\) is the fluctuation volume;

\(\beta\) is the stress-concentration coefficient at the tip of a growing crack;

\(U\) and \(U'\) are, respectively, the activation energies of the processes of fracture and bond restoration.

According to Barten'ev, the lifetime in general form is written as

\[ \tau = A(\sigma, T)\, e^{\frac{U_0-\omega\beta\sigma}{RT}}, \tag{7} \]

where

\[ A(\sigma, T)=\frac{L\cdot n\cdot R\cdot T\cdot e^{-a/R}}{\nu_0\omega\beta\sigma}, \]

\(a\) is a constant taking into account the dependence of the activation energy on temperature;
\(n=1/\lambda\) is the number of chains breaking per unit crack path;
\(L\) is the width of the strip-shaped specimen.

Equation (7) is valid for brittle fracture. In fracture in the high-temperature region (where “silver” cracks mainly grow), the lifetime is determined by the lifetime of the crazes and is described by the relation [1, 11]

\[ \tau=\frac{R}{\lambda\nu_0}\, e^{-a/R}\, e^{\frac{U_0-w'\beta'\sigma}{RT}}, \tag{8} \]

where the coefficients \(\lambda\), \(w\), \(\beta\) have the same meaning as in equation (6), but have different values. Thus, the lifetime of polymeric materials is described by equations (7) and (8), analogous to equation (1).

The approach described above to the theoretical description of the fracture process is analogous to the approach of Tobol'skii and Eyring [1]. This approach is based on the concept of an activation process of rupture of bonds between atoms. According to their concepts, lifetime is determined by the rate of rupture of these bonds, \(-dN/dt\), where \(N\) is the number of unbroken bonds per unit cross section of the specimen; \(t\) is time. The lifetime in this case is described by the equation

\[ \tau=A\,\frac{N_0}{\sigma}\, e^{\frac{\Delta F-\sigma\lambda'}{RT}}, \tag{9} \]

where \(N_0\) is the initial number of bonds;
\(A\) is a parameter;
\(\Delta F\) is the free-energy barrier that is overcome during bond rupture under conditions \(\sigma=0\);
\(\lambda'\) is the deformation of the bond at rupture.

The experimentally obtained values of \(\Delta F\) are underestimated and are difficult to compare with characteristics of bonds determined by an independent method [1]. V. E. Gul' considers fracture of a polymer by the growth of defects (cracks, tears, cuts). This process is characterized by the transition of a kinetic unit from one state to another. The potential barrier of interaction of the kinetic unit with neighboring ones may be due both to forces of intermolecular interaction and to forces of chemical interaction, as well as to both simultaneously.

In accordance with the theory of absolute reaction rates, Gul' obtains an expression for the shear stress

\[ \sigma_p=\frac{hN}{V_0}\, e^{-\frac{\Delta S^{+}}{RT}}\, e^{\frac{E_{\mathrm{raz}}}{RT}}\cdot V, \tag{10} \]

where \(h\) is Planck’s constant;
\(V_0\) is the molar volume;

\(\Delta S^{+}\) — standard activation entropy;
\(E_{\text{fract}}\) — activation energy of fracture;
\(V\) — rate of bond rupture.

Expression (10) correlates well with the empirical equation

\[ \sigma_p = k_1 V e^{\frac{U}{RT}} . \tag{11} \]

This equation, like the lifetime formula (1), reflects the thermofluctuation mechanism of fracture [36]. Various dependences are used to estimate lifetime in different media [36—42], and most often, under conditions of corrosive fracture, the lifetime of polymers does not obey S. N. Zhurkov’s equation. As for the time dependence of strength proposed by G. M. Bartenev (equation 7), in order to solve applied problems it becomes necessary to determine a larger number of physical constants of the material. Therefore many authors use phenomenological theories of fracture [41—42].

Thus, at the present time there are two main directions in the study of the physical mechanism of fracture of polymer bodies. The first direction includes the thermofluctuation theory, and the second includes the theory of the mechanism associated with the presence of defects in the solid and the development of cracks during the fracture process [1]. It is natural to consider that both directions complement each other. However, for applied engineering problems, a description of fracture processes at the molecular level without taking into account the supramolecular structure, defects, and the mechanism of crack development practically does not provide an analytical apparatus for predicting lifetime over a wide range of temperatures and stresses. From this point of view, S. N. Zhurkov’s equation is not universal, and with its aid it is not possible to make predictions over a wide range of temperatures and stresses [17].

The question is further complicated by the fact that, under the action of mechanical stress on a polymer, in most cases a substantial change in its supramolecular structure is observed during deformation. Failure to take into account the change in morphology during the deformation preceding fracture leads to an incorrect evaluation of the strength characteristics of polymers [43, 44, 45, 46].

REFERENCES

1. A. A. Askadskii. Advances in the Chemistry and Physics of Polymers. Moscow, “Khimiya,” 139, 1970.
2. S. N. Zhurkov, B. N. Narzullaev. ZhTF, 23, 1677, 1953.
3. S. N. Zhurkov, T. P. Sanfirova. DAN SSSR, 101, 237, 1955.
4. S. N. Zhurkov, E. E. Tomashevskii. ZhTF, 25, 66, 1955.
5. S. N. Zhurkov. Vestnik AN SSSR, No. 11, 78, 1957.
6. S. N. Zhurkov, B. Ya. Levin, E. E. Tomashevskii. FTT, 2, 2066, 1960.
7. S. N. Zhurkov, T. P. Sanfirova. FTT, 2, 1034, 1960.
8. S. N. Zhurkov, V. A. Zakrevskii, E. E. Tomashevskii. FTT, 6, 1912, 1964.
9. S. N. Zhurkov, V. R. Regel, T. P. Sanfirova. VMS, 7, 1339, 1965.
10. I. M. Melamedov. Physical Foundations of Reliability. Moscow, “Energiya,” 1970.
11. G. M. Bartenev, Yu. S. Zuev. Strength and Fracture of Highly Elastic Materials. Moscow, “Khimiya,” 1964.
12. Aging and Stabilization of Polymers. Edited by A. S. Kuzminskii. Moscow, “Khimiya,” 1966.
13. S. Bresler, E. Kazbekov, E. Saminskii. VMS, 1, 132, 1959.
14. R. A. Brathay, H. Melville et al. Trans. Farad. Soc., 54, 1133, 1958.
15. I. S. Milevskaya, M. V. Vol’kenshtein. Optics and Spectroscopy, 11, 349, 1961.

1. Symons M. E. R., G. Chem. Soc., 277, 1959; 1186, 1963.
2. Yngram D., Symons M., Towusend M. Tran. Farad, Soc., 54, 409, 1958.
3. A. I. Mikhailov, I. S. Topopova, Ya. S. Lebedev. DAN SSSR, 164, 140, 1965.
4. Lacoste, G. Moleret G. Wind. Revne Generale de L’electricite, 78, No. 1, 53, 1969.
5. V. R. Regel. “Mekhanika polimerov,” No. 1, 98, 1971.
6. S. N. Zhurkov, V. R. Regel, T. P. Sanfirova. VMS, 6, 1092, 1964.
7. S. N. Zhurkov, V. R. Regel, T. P. Sanfirova. VMS, 8, 1339, 1965.
8. P. Yu. Butyagin. Doctoral dissertation. Moscow, Institute of Chemical Physics, Academy of Sciences of the USSR, 1967.
9. A. L. Buchachenko, Ya. M. Lebedev, M. B. Neiman. Advances in the Chemistry and Physics of Polymers. Moscow, “Khimiya,” 409, 1970.
10. A. T. Sanzharovskii, T. A. Grinyute, T. V. Likhtman. DAN SSSR, 157, 1196, 1964.
11. G. J. Bendow, F. G. Roesler. Proc. Soc. B 70, 201, 1957.
12. G. P. Berry, G. Polgmer. 50, 107, 1961; 50, 313, 1961.
13. L. C. Gessna, S. S. Sternstein. J. Polumer Sci., B3, 825, 1965.
14. N. Mott. Engineering, 165, 16, 1948.
15. S. Bateson. Phys. Chem. Glass., 1, 139, 1960.
16. G. M. Bartenev, I. V. Razumovskaya. DAN SSSR, 133, 341, 1960.
17. G. M. Bartenev. “Mekhanika polimerov,” No. 5, 700, 1966.
18. F. Esler. Kunstoffe, 40, 305, 1950.
19. G. M. Bartenev. Izvestiya AN SSSR, OTN, No. 9, 53, 1955.
20. I. V. Razumovskaya. Candidate dissertation, Moscow State Pedagogical Institute named after V. I. Lenin, 1963.
21. V. E. Gul. “Mekhanika polimerov,” 3, 489, 1972.
22. D. F. Kantor. “Plasticheskie massy,” 1968, No. 4, 9.
23. M. N. Bokshitskii, I. Ya. Klipov, N. A. Bokshitskaya. Moscow, “Mashinostroenie,” 22, 1967.
24. W. A. Dukes. “British Plastics,” 34, No. 3, 123, 1961.
25. E. Gaube. “Kunstoffe,” No. 19, 446, 1959.
26. A. M. Karpatnitskii, M. N. Bokshitskii. In the collection “Reliability and Durability of Polymer Materials and Products Made from Them.” TsDNTP, 98, 1969.
27. Polycarbonate in Mechanical Engineering. Ed. by V. N. Kestelman. Moscow, “Mashinostroenie,” 1971.
28. Yu. M. Molchanov. “Mekhanika polimerov,” No. 3, 413, 1972.
29. Yu. S. Zuev, M. A. Revazova, M. F. Bukhina. “Mekhanika polimerov,” No. 2, 222, 1972.
30. G. L. Slonimskii. “Mekhanika polimerov,” No. 3, 387, 1972.
31. T. I. Sogolova. “Mekhanika polimerov,” No. 3, 395, 1972.
32. V. R. Regel, A. I. Slutsker. Durability of Polymers, Encyclopedia of Polymers. Vol. 1, Moscow, 754, 1972.
33. V. R. Regel, A. I. Slutsker, D. E. Tomashevskii. The Kinetic Nature of the Strength of Solids. “Nauka,” 1974.