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.     

Deformative characteristics of plastics reinforced with high-modulus anisotropic fibers

The independent elastic constants of plastics unidirectionally reinforced with transversely isotropic fibers have been determined. It has been assumed that the distribution of reinforcement in a transverse section of the plastic is regularly rectangular or hexagonal. To determine the transverse elastic modulus and the shear modulus in the plane of reinforcement, a constancy-of-plane-sections hypothesis was used. Values of deformative characteristics determined by the assumed calculational dependences have been compared with the experimental ones for plastics reinforced with graphite fibers.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 631–639, July–August, 1972.     

Effect of hydrostatic pressure on the deformation properties of polymer materials

It is suggested that the bulk modulus of homogeneous polymer materials is a function of the specific volume only. The dependence of the bulk modulus and Young's modulus on temperature and hydrostatic pressure is determined on the basis of this assumption. It is shown that the Young's modulus must be higher in compression than in tension. The experimental data are confirmed by the relations obtained. The effect of hydrostatic pressure on the relaxation properties of materials is discussed.Institute of Polymer Mechanics, ASLatSSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 986–991, November–December, 1968.     

Probability characteristics of the shear modulus of glass-reinforced plastics

The results of tests on wound glass-reinforced plastic specimens based on ÉFB-4 epoxy-phenolic-butyral composition and NS 55/6 glass strand reinforcement with a paraffin finish have been subjected to a statistical analysis with the object of determining the probability characteristics of the shear modulus. The shear modulus is determined for unidirectional structures and structures with reinforcement ratios of 1:1, 1:2, and 3:2. The results of the tests are used to determine the mathematical expectation, variance, and probability density function of the shear modulus.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 1, pp. 160–162, January–February, 1973.     

Correlation of the elastic characteristics of Arimid PM with the elasticity modulus of its crystal lattice

Studies were made of the elastic characteristics (longitudinal elasticity modulus, elastic recovery) of Arimid PM fibers and of the longitudinal elasticity modulus of the crystal lattice of these samples. The elasticity modulus of the crystallites was determined by x-ray diffraction studies of loaded fibers. It is shown that the studied samples practically instanteneously recover their starting length after removing the load; the sample and its crystal lattice have comparatively low elasticity moduli with nearly identical values. Based on this data, reasons are discussed for the high elastic recovery of Arimid fibers and for the low elasticity modulus of its crystal lattice.Leningrad Branch, All-Union Scientific-Research Institute of Synthetic Fibers. Translated from Mekhanika Polimerov, No. 5, pp. 771–773, September–October, 1972.     

Effect of the rate of deformation on the mechanical properties of compact bone tissue

Conclusions The results of this study show that the ultimate stress increases with increasing deformation rate from 10^–5 to 1 sec^–1 but the initial elasticity modulus remains virtually constant. A characteristic feature of bone tissue is the significant increase or even maximum in specific deformation energy for destruction in the range of deformation rates corresponding to normal physiological conditions for bone function. The deformation diagrams of human bone tissue for the same values of moisture content and deformation rate in tensile testing do not differ from the analogous curves for the bone tissue of cattle. Quantitatively, the ultimate stress ₁₁ and the initial elasticity modulus E₁ are 5–10% and 15–25% greater, respectively, than for cattle bone tissue, while the ultimate deformation eu is virtually the same. An increase in the moisture content of bone tissue leads to a more pronounced dependence of the mechanical parameters on the deformation rate.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 512–517, May–June, 1982.     

Dynamic method of determining the mechanical characteristics of the surface layer of polymers

A thin polymer film is treated as a three-layered plate, the inner layer being characterized by the bulk and the outer layers by the surface properties of the polymer. Using the equations describing the vibrations of a cantilever element of rectangular section, the authors propose formulas for the thickness, modulus of elasticity, and mechanical loss factor of the surface layer. The mechanical characteristics of the surface layers of PMM and nitrocellulose have been determined by electromagnetically exciting and photometrically recording vibrations in film specimens of varying thickness.Institute of the Chemistry of High-Molecular Compounds, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 3, pp. 548–550, May–June, 1969.     

Linear Viscoelasticity of Liquid-Crystalline Polymers

A linear (small-amplitude) periodic shear deformation of anisotropic viscoelastic liquids obeying the Akay–Leslie rheological model is considered. The frequency dependences of the real and imaginary components of the complex shear modulus and complex normal-stress coefficient are determined. A comparison between calculation results and test data on the shear flow of poly(-benzylglutamate) in m-cresol is carried out. It is stated that, if the material is characterized by some initial orientation, both components of the complex shear modulus contain a multiplier which depends on the degree of the initial orientation and increases the values of the components compared with those for an initially isotropic material. The model predicts that, in a periodic shear flow, the components of shear and normal stresses are constant and, like the components of shear modulus, are independent of deformation frequency. If the parameter d ₀ of the Akay–Leslie model is equal to zero, the values of its other parameters can be determined from experimental results on periodic shear flow.     

Possibilities of a nondestructive one-parameter method of checking the strength of anisotropic glass-reinforced plastics in uniaxial compression

A nondestructive method of checking the strength of glass-reinforced plastics (GRP) in finished products is proposed. This method is based on the correlation, investigated by the authors, between the modulus of elasticity and the compressive strength determined by a standard method. Various orientations in the plane of reinforcement of glass-reinforced plastics with different ratios of the orthogonally arranged fibers are investigated. It is proposed to determine the modulus of elasticity from the propagation velocity of an ultrasonic pulse measured under conditions of one-sided access to the surface of the product."Ritm" Research-Production Association, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 909–919, September–October, 1974.     

Investigation of the thermophysical and antifriction properties of polyethylene compositions

The coefficient of linear expansion of polyethylene compositions has been determined. Metals, oxides, and silicates were used as fillers. The coefficient depends significantly on the geometry of the filler particles. Powdered fillers reduce the coefficient by 10–20% (an amount somewhat greater than their volume concentration). Fillers consisting of material with a low coefficient of linear expansion and a high modulus of elasticity in chopped-fiber form may reduce the coefficient of linear expansion by one order as compared with pure polyethylene.Mekhanika Polimerov, Vol. 3, No. 5, pp. 873–880, 1967     

Calculation of elastic characteristics and creep functions of hollow-sphere plastics by the effective medium method

Conclusion Solutions for the elastic characteristics and the creep functions of a composite containing hollow spherical fillers as applies to the four-phase nucleus/jacket/binder/equivalent-homogeneous-material model are obtained in the study when the method of self-correspondence is used. It is demonstrated that if the two-stage approach (when the elastic characteristics of the nucleus + jacket system, and the composite are calculated in the first and second stages, respectively) yields an exact solution for the bulk modulus K_* of the composite, it is highly approximate when the shear modulus G_* of the composite is determined. The error of determination of G_* increases considerably (by a factor of 2–2.5 when = 0.4) when Kerner's approximate solution (2) is used in lieu of solution (8) for the three-phase model within the framework of the two stage approach. Dzenis and Maksimov [5] establish by comparison with experimental data that the four-phase model provides a rather exact solution for the elastic modulus of a composite when the bulk content of hollow spheres 0.4. It is also demonstrated that use of Kerner's approximate solution (2) within the framework of the two-stage approach in predicting the creep of a composite yields an inadmissibly high error in the region of the principal relaxation transition of the binder from the glassy to the highly elastic state.This work was sponsored at the Iberoamericana University in 1993 by the Mexican National Council of Science and Technology (CONACYT).Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 2, pp. 177–188, March–April, 1994.     

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     

Exact constant in the Jackson inequality in the space L2

We investigate the lowest (exact) constants in Jackson-type inequalities with the second-order modulus of continuity for the case of approximation of differentiable periodic functions by trigonometric polynomials in the space L₂.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1261–1265, September, 1994.     

Determination of the static strength of plastics from the elasticity and internal friction characteristics

It has been shown experimentally that the tensile or compressive strengths of various plastics on a broad temperature range can be estimated from the values of the dynamic modulus of elasticity and logarithmic decrement measured by a vibration method.All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 551–554, May–June, 1976.     

Analysis of nonlinear polymer creep

The relaxation properties of polyethylene are analyzed. The nonlinear time-dependent stress-strain relations and the creep and relaxation equations are obtained from the experimental creep data. The analysis is based on an appropriate variant of the nonlinear memory theory with singular functions whose parameters, together with the modulus of elasticity, are determined by the method described in [1].Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 410–414, May–June, 1969.     

Allowance for inertia of test piece in dynamic measurements of the rheological characteristics of polymers

The determination of the dynamic shear modulus and dynamic viscosity of polymer materials on apparatus of the Fitzgerald-Ferry type is discussed. Limiting values of the test piece height for which it is permissible to neglect wave propagation of the oscillations are determined. Agreement of the values of the rheological constants determined with and without allowance for inertia is observed at ratios of test piece height to wavelength not exceeding 0.02–0.05. Above this limit the discrepancy rapidly increases and reaches values excluding the use of the formulas recommended in [1–4]. Relations are presented from which the rheological constants should be determined with allowance for the inertia of the test piece.Mekhanika Polimerov, Vol. 2, No. 1, pp. 130–138, 1966     

Estimation of the length distribution of through polymer chains

The contributions of entropy and elastic forces to the tensile modulus of a polymer chain are estimated. The chain length-distribution function in the amorphous region of highly oriented Lavsan is approximately determined from macroscopic stress-strain dependence. It is found that the length distribution has a width of the order of several percent of the length of the amorphous region of the fibril.A. F. Ioffe Physicotechnical Institute, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 922–925, September–October, 1974.     

Effect of fillers on the structure and properties of cured resins

The elastic (modulus of elasticity and equilibrium high-elastic modulus) and thermal (volume coefficients of thermal expansion below and above the glass transition temperature) properties of compositions based on ÉD-5 epoxy resin cured with polyethylenepolyamine have been investigated. Quartz powder and aluminoborosilicate glass powder were employed as fillers at concentrations from 0 to 0.413. The thermal expansion coefficients of the compositions were studied in a dilatometer, in which the specimen is free of mechanical loads. The Young's modulus at 25°C and the equilibrium high-elastic modulus at 125°C of the compositions were determined in the compression regime in an instrument based on the IZV-2 optical length gage. The thermal expansion coefficients of the polymer matrix were calculated with allowance for the elastic properties of the resin and the filler. It is shown that, as the filler concentration increases, the thermal and elastic properties of the resin in the filled system change. This can be interpreted as a change in the properties of the resin as it approaches the surface of the filler particles. Increased interaction between the filler surface and the epoxy resin tends to stiffen the polymer network.Scientific Research Institute of Precision Technology, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1018–1022, November–December, 1969.     

Rheological characteristics of orthotropically reinforced polymeric materials

It is proposed to calculate the rheological characteristics of orthotropically reinforced polymeric materials using a model in accordance with which the composite is assumed to consist of layered blocks, the planes of the layers having one of three possible orientations with given probabilities. The effective rheological characteristics of each block are exactly determined, while those of the composite as a whole are determined in the Voight or Reuss approximations. The first scheme is convenient for calcuating the shear modulus operators, the second for calculating the Young's modulus and Poisson's ratio operators. A numerical computer analysis has been made for the Young's moduli. It is shown that for the anisotropic composites in question each of the technical elastic moduli is characterized by two resolvent Q* operators of real or complex argument. The conditions under which one of the Q* operators can be neglected are determined. The integral representation of the kernel of the Q* operator of complex argument is given in the case where the latter is fractional-exponential with fractional index =–1/2 and the corresponding curves are presented.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 276–283, March–April, 1972.     

Viscoelasticity of a curing epoxy composition in the "critical branching" region

The curing of an epoxy resin in the "critical branching" region has been investigated by mechanical and infrared spectroscopy. It is shown that the effective molecular weight between network points (M_c) during the polymerization of an actual system can be determined from the relaxation spectrum in the curing stage investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 154–158, January–February, 1976.