Scale effect of Young's modulus of highly oriented polymers

The scale effect of the acoustic Young's modulus E of oriented polymer fibers has been experimentally revealed. If the fiber length L is smaller than its critical value L₀, the modulus decreases proportionally to the logarithm of the fiber length. An increasing temperature causes a proportional increase in the slope dE/d(In L). The scale effect is explained by the influence of the specimen volume on the probability of initiation of intense thermal fluctuations, which cause a decline in the Young's modulus.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 839–846, November–December, 1998.     

Temperature dependence of Young's modulus and the absorption coefficient of certain polymeric materials

The procedure and the results are described of the experimental determination of Young's modulus and the absorption coefficient as a function of temperature of polymeric materials, polystyrene foam, polyarylite, and others, obtained in dynamic investigations.     

Description of the mechanical relaxation of highly oriented polymers based on their relaxation spectra

Both the shape and width of the relaxation spectra of polymers with different draw ratios are analyzed in regions of relaxation transitions. The analysis substantiates an empirically ascertained linear law governing the frequency distribution of the dynamic modulus E'(ω) of highly oriented polymers in E' = ln ω coordinates, which corresponds to the uniform distribution of a single relaxation time H(τ) ? const. The possibility of describing the temperature dependence of the modulus of highly oriented polymers within a broad temperature range is demonstrated, where a single relaxation time is used and consideration given to the nonuniform distribution of the energy of fundamental vibrations with respect to oscillatory modes.     

A method for determining the dynamic Young's modulus of curvilinear specimens

On the basis of a numerical solution of the problem of the natural frequencies of a rod shaped as the are of a circle, the authors suggest a method for determining the dynamic Young's modulus of a curvilinear specimen. They derive an approximate expression suitable for practical use. The results agree well with experiment.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 335–339, March–April, 1974.     

Small deformations of oriented polymers

On the basis of a phenomenological analysis of the temperature dependence of the modulus of instantaneous elasticity and the stress relaxation process, it is suggested that in the region of small deformations there are no breakages of the macromolecules that might affect the elasto-relaxational behavior of highly oriented polymers (fibers) as in the region of large deformations. To judge from the values obtained for the energy constants, these properties are determined by the number of intermolecular bonds in the amorphous regions (modulus of instantaneous elasticity) and the physical events associated with the reorganization of these bonds and hindered rotation of the chain units (relaxation process).S. M. Kirov Leningrad Institute of Textiles and Light Industry. Translated from Mekhanika Polimerov, No. 6, pp. 976–980, November–December, 1971.     

A new approach to the description of the deformation kinetics and relaxation of mechanical properties of oriented polymers

The reduction of Young's modulus and stress as well as the creep rate of highly oriented polymers with different chemical structure has been investigated. The kinetics of these processes are described by Arrhenius-type equations having the same activation parameters. The deformation and relaxation processes were assumed identical in their physical nature and functions of thermal fluctuation. Evidence for this assumption was obtained by investigating spectroscopically excited extended interatomic bonds of the macromolecules. The generation of excited bonds was found to determine the kinetics of these macroscopic processes in polymers.     

Analytical prediction of Young's modulus of carbon nanotubes using a variational method

Molecular mechanics and solid mechanics are linked to establish, a nanoscale analytical continuum theory for determination of stiffness and Young's modulus of carbon nanotubes. A space-frame structure consisted of representative unit cells has been introduced to describe the mechanical response of carbon nanotubes to the applied loading. According to this assumption a novel unit cell, given the name mechanical unit cell here is introduced to construct a graphene sheet or the wall of the carbon nanotubes. Incorporating the Morse potential function with the strain energy of the mechanical unit cells in a carbon nanotube is the key point of this study. The structural model of the carbon nanotube is solved to obtain its Young's modulus by using the principle of minimum total potential energy. It was found that the Young's modulus of the zigzag and armchair single-walled carbon nanotubes are 1.42 and 1.30 TPa, respectively. The results indicate sensitivity of the stiffness and Young's modulus of carbon nanotubes to chirality but show no dependence on its diameter. The presented analytical investigation provides a very simple approach to predict the Young's modulus of carbon nanotubes and the obtained results are in good agreement with the existing experimental and theoretical data.     

Propagation of sound in oriented polymers

The propagation of sound in oriented polymers is considered. Starting from an assumption concerning the superposition of relaxation processes in polymers, expressions are obtained for the speed and absorption of sound as functions of the relaxation spectrum, molecular orientation, and crystallinity. It is shown that the orientation dependence of the acoustic properties is more distinctly expressed in the region of the glassy state.Scientific-Research Institute of Plastics, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 437–441, May–June, 1969.     

Strength of rigid oriented amorphous polymers

A method is proposed for obtaining uniaxially oriented specimens of amorphous unfractionated polymer with a particular oriented chain length. The length of the oriented chains and their molecular weight M_c depend importantly on the conditions under which the polymer is stretched. It is shown that the strength of specimens obtained by stretching at constant M_c increases linearly with the relative fraction of oriented phase. The slope of this linear relation increases with the length of the oriented molecular chains. The ratio of the maximum strength of fully oriented polystyrene to the strength of the unoriented material is found to be 78 instead of the value of 6 given in [6].Mekhanika Polimerov, Vol. 3, No. 6, pp. 1048–1053, 1967     

Molecular mechanism of oriented crystalline polymers

It is shown with reference to linear polyethylene that the deformation of an oriented crystalline polymer takes place as a result of elongation of the coiled parts of the macromolecules in the amorphous zones owing to conversion of gauche into extended trans isomers. The decrease in coiled isomer content when the specimen is deformed by approximately 5% is accompanied by a small number of chemical bond breakages. Repeat deformation by the same amount does not result in any additional breakage of polymer chains.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of The USSR, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 584–588, July–August, 1973.     

Temperature - time analogy for thermorheologically complex polymeric materials

Conclusions 1. The viscoelastic properties of mixtures of crystalline polymers with elastomers have been studied as functions of temperature. It is shown that, for mixtures of PP with PIB and TEP, the concept of thermorheologically simple behavior is applicable only within a narrow interval of temperature.2. Parameters of the temperature—time analogy for thermorheologically complex materials have been calculated. It is established that, at temperatures above a characteristic temperature T*, a strong dependence of the correction coefficient on time and a strong dependence of the relaxation function on the ratio of components exist.3. It is shown that use of the concept of thermorheologically complex behavior for prediction of the long-term deformability allows analysis of the contributions of specific components to the viscoelastic behavior of the mixture in different temperature intervals.Paper presented at the Third All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1976.Okhtinsk Scientific-Industrial Association "Plastpolimer," Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 614–620, July–August, 1977.     

Relaxation processes in oriented amorphous and crystalline polymers

Studies were made of the experimental data on the relaxation processes leading to the preferential molecular disorientation and uniaxially drawn amorphous and crystalline polymers.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 787–792, September–October, 1972.     

Relation between fracture and deformation in oriented polymers

The development of submicroscopic cracking under load has been studied (by a small-angle X-ray scattering technique) in such oriented polymers as Kapron (Nylon 6), polypropylene, etc. The increase in crack density (N_cr) is compared with the variation of the tensile strain (). The observed correlation between and N_cr indicates that the processes of fracture and deformation of oriented polymers are closely connected. The presence of a similar correlation in loading-relaxation-repeat loading experiments establishes fracture as the primary process.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 43–47, January–February, 1970.     

Lifetime and relaxation processes in solid polymers

The relationship between relaxation processes and the fracture of solid polymers is examined with reference to the example of repeat loading with recovery. An investigation of polymethyl methacrylate, KAST-V glass laminate, and a Finnish polyester glass-reinforced plastic has shown that this lifetime may be considerably (several orders) shorter than that at the same level of constant stress. This is attributed to the time dependence of the structure-sensitive coefficient in the lifetime equation and is illustrated by means of a model that includes a Regel' fracture element.Moscow Lenin State Pedagogical Institute, Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, No. 4, pp. 629–635, July–August, 1969.