Strength of polyethylene and capron as a function of stretch ratio

The relation between the strengths and stretch ratios of a capronmonofilament and a high-pressure polyethylene film has been investigated for various stretching temperatures and stretching rates. The strength, measured at –196°C (_–196), is directly proportional to the stretch ratio (). For a given , _-196 does not depend on stretching temperature and stretching rate. The breaking load at –196° C (for a given initial cross section of the starting unoriented specimen) does not vary with . A possible explanation is offered.Mekhanika Polimerov, Vol. 3, No. 4, pp. 591–595, 1967     

Analysis of possible combinations of local stresses in local strain theory

In determining the strain tensor e_ij instead of all the components of the local stress deviator, it is possible to use only the shear stress _xz acting on a small local area. This fact makes it easy to establish the incremental loading conditions in solving complex loading problems for a plastic material. It is shown that in the local strain theory, distinct from the deformation theory, at degrees of nonlinearity n>3 the effect of the third, as well as the second, invariant of the stress deviator is taken into account.Mekhanika Polimerov, Vol. 3, No. 4, pp. 636–644, 1967     

Determination of the characteristics of viscoelastic media from the data of quasi-static tests

By representing memory-influence functions in the form of generators of the Dirac -function in order to describe the relaxation processes on a small initial interval [3], formulas are constructed for determining the true characteristics of viscoelastic media from the data of quasi-static creep tests and relaxation tests by means of the irreversibility effect [2], i.e., the dependence of the relaxation processes on the initial loading conditions.Mekhanika Polimerov, Vol. 3, No. 5, pp. 803–811, 1967     

Construction of the nonlinear relations of thermoviscoelasticity

Nonlinear stress-strain relations, constructed for a viscoelastic medium, have been extended to the temperature region where the temperature-time superposition principle applies. The nonlinearity is introduced into the viscous elements in power-law form. The six parameters entering into the equations are determined from simple specified tests A method is proposed for constructing the functiona _T(T) from the data of quasi-static creep tests at different temperatures or from diagrams obtained at constant loading or strain rates.Mekhanika Polimerov, Vol. 3, No. 6, pp. 989–998, 1967     

Variation of the properties of glass laminate in cyclic tension-compression

The deformation and dissipative properties of glass laminate have been investigated under extended cyclic loading. It is shown that the glass laminate fails at certain critical values of the absorption coefficient and compliance J, which have constant values at any load level for given cycle asymmetry, scale factor, and heat transfer conditions. The effects on and J of temperature and the accumulation of damage with increase in the number of loading cycles are determined separately. Possible variants of the solution of the temperature equation are considered with allowance for the variation of the dissipative properties of the material with temperature and fatigue damage.Mekhanika Polimerov, Vol. 3, No. 5, pp. 864–872, 1967Fourth All-Union Conference on Strength and Plasticity, Moscow, 2 February, 1967.     

Effect of temperature on the chemical relaxation process in rubbers

The effect of temperature on the chemical relaxation of rubbers has been investigated. With reference to nine industrial rubbers it has been shown that during storage in the stressed state (at =const) chemical relaxation is chiefly determined by two processes proceeding at different rates. Furthermore, the chemical relaxation of rubbers is determined not only by the rate constants of these two processes but also by the pre-exponential constants C_0i, the relationship between which varies with increase in temperature. It is possible to extrapolate the rate constants (k_i) and pre-exponential constants (C_0i) from elevated temperatures (110–50° C) to temperatures in the range 20–25° C. An equation is proposed that makes it possible to calculate the change in the elastic properties of rubbers in the stressed state at storage temperatures (20–25° C) by means of results obtained at elevated temperatures.Mekhanika Polimerov, Vol. 3, No. 3, pp. 448–454, 1967     

The stressed state and certain fracture characteristics of glass-reinforced plastics loaded in tension at an angle to the direction of reinforcement

The stressed state of glass-reinforced plastic specimens with various structures is investigated experimentally in the case of tensile loads acting at 45° to the direction of reinforcement. A relation is established between the stress distribution over the cross section and the scale factor associated with the relative width of the understressed zones along the edges of the specimen. The fracture characteristics of GRP specimens with different structures are analyzed. Recommendations are given for testing GRP with different structures in tension at an angle of 45° to the direction of reinforcement.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1030–1034, 1967     

Dynamic adhesive strength of fiber-polymer systems

A new device for studying the dynamic adhesive strength is created. A procedure for determining the dynamic adhesive strength in fiber—polymer systems under impact loading (pull-out technique) is developed. The adhesive strength of the interface of polymer—steel wire joints formed by polymers of different chemical nature (epoxy resin, polysulfone, and polypropylene) is examined. It is shown that the dynamic adhesive strength grows as the loading rate increases for all the systems under investigation and that the relationship between the adhesive strength and the loading rate, , over a wide range of rates can be described by two straight lines corresponding to the quasi-static and impact loading, respectively. When passing from the quasi-static to dynamic loading, the character of scale relations of the adhesive strength does not change.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 689–700, November–December, 1999.     

Effect of molecular weight on strength and deformation characteristics of oriented amorphous polymers

Tensile tests were carried out on uniaxially oriented films of several amorphous linear polymers (polymethyl methacrylate, polystyrene, and poly-2,2-octamethylene-5,5-dibenzimidazol) of various molecular weights. It was shown that molecular weight has no direct effect on polymer strength, which is determined by structure. However, when polymer fibers and films are formed and stretched, the molecular weight of a given material affects the orientation of macromolecules and so predetermines the structure of the products obtained and, consequently, their strength.Mekhanika Polimerov, Vol. 3, No. 4, pp. 579–585, 1967     

Dependence of the rheological characteristics of filled polypropylene on filler concentration,loading regime and temperature

The rheological characteristics of polypropylene have been investigated in relation to filler concentration, loading rate in the =wt regime, creep stress and time interval and temperature. A study has been made of the relationship between the changes in the rheological characteristics of the material, determined from - curves obtained from tensile tests at different constant loading rates, creep tests and by acoustical methods, with variation in filler concentration and temperature.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 853–858, September–October, 1968.     

Radiation resistance of epoxy and epoxytriazine resins

We have investigated the nature and extent of the changes in the physicomechanical and thermomechanical properties of epoxy and epoxytriazine compositions resulting from exposure to Co⁶⁰ -radiation. The effect of active solvents and catalysts on the radiation resistance of these compositions has been determined. Conclusions are reached concerning the nature of the radiochemical processes involved.Mekhanika Polimerov, Vol. 3, No. 5, pp. 840–845, 1967     

Strength of fibrous composites

Research on the effect of various factors on the strength of fibrous composites in tension, compression, shear, bending and plane stress, published in the journal Polymer Mechanics, is reviewed. The more important future trends are outlined.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 553–562, May–June, 1972.     

Dynamic properties of some polymer materials in loading and unloading

A series of quasi-static tests have been carried out on kapron fiber, vinyl plastic, and fluoroplastic specimens with small cross sections. Stress-strain diagrams have been obtained at strain rates from 1 · 10^–3 to 1 · 10² sec^–1. In the experiments the strain rate changed sign, which corresponded to loading and unloading. In each regime the strain rate remained constant. The experimental data are analyzed using the model of a standard linear viscoelastic solid.Mekhanika Polimerov, Vol. 3, No. 1, pp. 118–122, 1967     

The dynamic properties of polyethylene and an acrylonitrile — Butadiene — Styrene material in a broad range of temperature and strain-rate variation

Conclusions The mechanical properties of an acrylonitrile-butadiene-styrene material and polyethylenes of densities =0.92 and 0.96 g/cm³ are studied within the temperature range of from 100 to –196°C and at strain rates of from 10^–3 to 1.3 · 10³ sec^–1. It is observed that under low-temperature and high-strain-rate conditions, the laws governing the mechanical properties of the acrylonitrile-butadiene-styrene material and polyethylenes are similar. Regions of strain rates and temperatures are found for which the behavior of the test materials is in good agreement with the Ree-Eyring equation, and, consequently, conforms to a temperature-time analogy. No embrittlement of the polyethylene is observed during tests at strain rates to 1.3 · 10³ sec^–1 and temperatures down to –196°C. In approximating these values of and T, the mechanical properties of polyethylenes will cease to be dependent on initial density.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, 1027–1033, November–December, 1978.     

Creep on an initial small interval

The creep processes of hereditary media on a small initial interval are described, using as influence functions the resolvent functions for the generators of the Dirac function, which are employed as relaxation kernels. Equations are constructed for determining the instantaneous modulus and the parameters of these functions from experimental stress-strain diagrams obtained at three different constant loading rates.Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 5, pp. 945–950, September–October, 1970.     

Strength of cylindrical shells of laminar composites under dynamic loading

Conclusion The methods described in the present review paper for the computation of cylindrical shells of laminar composites under various types of dynamic loads make it possible to calculate the stress-strain state at any point of the body of the shell at an arbitrary time and to determine the time of the first failure of a layer (including fatigue failure) using strength criterion of an anisotropic body for the case of a plane stressed state, and also the location of the first flaw in the shell. This makes it possible to determine the magnitude of the applied pulse (the amplitude of a pulsed loading), or the amplitude of a vibratory loading for which the first centers of failure appear in the design.Presented at the Second Soviet-American Symposium on the Problem Failure of Composite Materials (Bethlehem, Pa., USA, March, 1981).Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 460–467, May–June, 1982.     

A. F. Lavrik's truncated equations

By a new method, we obtain some known results of A. F. Lavrik (Dokl. Akad. Nauk SSSR,171, No. 2, 278–280 (1966); Mat. Zametki,2, No. 5, 475–482 (1967); Izv. Akad. Nauk SSSR, Ser. Mat.,30, No. 2, 433–448 (1966)) regarding the truncated functional equations of various L-functions. As an application, we give an estimate of Dedekind's zeta-function of an algebraic number field K of degree n4, _k(1/2+it)t^n/6log^ct,t>1 and a similar estimate for L-series with grössencharacters. The method of the paper allows us to consider fields of degree n12.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 76, pp. 124–158, 1978.     

Mechanical properties and internal shear stress field in reinforced media as a function of the type of microstructure

The effect of type of microstructure and volume content of filler and binder on the internal stress field and shear modulus has been analyzed for various composite materials. There is an "optimum" filler content at which the maximum stresses in the structure are lowest. A quantitative estimate is obtained for the error of the approximate formulas for the shear modulus of various types of structure.Mekhanika Polimerov, Vol. 3, No. 4, pp. 667–670, 1967     

Linear groups

This survey article covers papers abstracted inReferativnyi Zhurnal Matematika during the period 1978–1982 and is a continuation of the surveys Linear groups published in 1967, 1971, and 1977 in the seriesAlgebra, Topology, Geometry (Itogi Nauki i Tekhniki). The main things under consideration are linear groups over rings and the structure of infinite linear groups. Some very recent results are also mentioned.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 21, pp. 135–182, 1983.     

3-Adic Cantor function on local fields and its p-adic derivative

The problem of “rate of change” for fractal functions is a very important one in the study of local fields. In 1992, Su Weiyi has given a definition of derivative by virtue of pseudo-differential operators [Su W. Pseudo-differential operators and derivatives on locally compact Vilenkin groups. Sci China [series A] 1992;35(7A):826–36. Su W. Gibbs–Butzer derivatives and the applications. Numer Funct Anal Optimiz 1995;16(5&6):805–24. [2] and [3]]. In Qiu Hua and Su Weiyi [Weierstrass-like functions on local fields and their p-adic derivatives. Chaos, Solitons & Fractals 2006;28(4):958–65. [8]], we have introduced a kind of Weierstrass-like functions in p-series local fields and discussed their p-adic derivatives. In this paper, the 3-adic Cantor function on 3-series field is constructed, and its 3-adic derivative is evaluated, it has at most order. Moreover, we introduce the definition of the Hausdorff dimension [Falconer KJ. Fractal geometry: mathematical foundations and applications. New York: Wiley; 1990. [1]] of the image of a complex function defined on local fields. Then we conclude that the Hausdorff dimensions of the 3-adic Cantor function and its derivatives and integrals on 3-series field are all equal to 1.There are various applications of Cantor sets in mechanics and physics. For instance, E-infinity theory [El Naschie MS. A guide to the mathematics of E-infinity Cantorian spacetime theory. Chaos, Solitons & Fractals 2005;25(5):955–64. El Naschie MS. Dimensions and Cantor spectra. Chaos, Solitons & Fractals 1994;4(11):2121–32. El Naschie MS. Einstein’s dream and fractal geometry. Chaos, Solitons & Fractals 2005;24(1):1–5. El Naschie MS. The concepts of E infinity: an elementary introduction to the Cantorian-fractal theory of quantum physics. Chaos, Solitons & Fractals 2004;22(2):495–511. [9], [10], [11] and [12]] is based on random Cantor set which takes the golden mean dimension as shown by El Naschie.