On the number of relaxation regions in polyformaldehyde

The mechanical relaxation of a polyformaldehyde homopolymer free from surface grease and the additives normally used as stabilizers has been studied at a frequency of 10^–2 Hz in the temperature region 77–413°K. Six relaxation regions are observed on the curve of tangent of angle of mechanical losses as a function of temperature.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 5, pp. 925–927, September–October, 1973.     

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.     

Dielectric investigation of the molecular mobility of silicone ladder polymers

Dielectric spectroscopy has been used to study the molecular mobility in polyphenylsilsesquioxane, polyphenylisobutylsilsesquioxane with a 1:1 ratio of phenyl to isobutyl groups, and poly-m-chlorophenylsilsequioxane on the temperature interval from –196 to 300°C at frequencies from 10² to 10⁶ Hz. The investigation was carried out in air and in a nitrogen atmosphere. The flexibility mechanism of silicone ladder polymers is considered and the development of molecular mobility is shown to be discrete.Institute of Heteroorganic Compounds, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 3–7, January–February, 1976.     

Pyroelectric effect in polarized PVC

The pyroelectric effect has been detected in polarized PVC, and the temperature dependence of the pyroelectric constant p has been measured. The latter proved to be constant and equal to 0.1 cgse/deg·cm² at –130 to +30° C. The data show that p is proportional to the piezoelectric modulus d, with the proportionality factor k=3 · 10⁶ at room temperature. As the temperature falls, k decreases.Mekhanika Polimerov, Vol. 4, No. 2, pp. 377–378, 1968     

Polymer fractography and fracture kinetics

The fractographic method makes it possible to determine the test temperature and time at which anomalies appear in the temperature-time dependence of the strength of polymethyl methacrylate and polycaprolactam by finding the conditions of disappearance of specular zones from the fracture surfaces of these polymers. For PMMA these values are –40°C and 10^–2 sec, for PCL –120°C and 10^–7 sec, respectively.For communication 1 see [2].Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 232–237, March–April, 1971.     

Impact strength of high-density polyethylene with various molecular weight distributions

The Charpy impact strength of high-density polyethylene specimens prepared under low pressure with average molecular weight from 60·10³ to 1.5·10⁶ and differing substantially in molecular weight distributions has been studied at room temperature and at –190°C. It is shown that, both at room temperature and at temperature considerably below the glass-formation temperature, the impact strength of polyethylene in the range of molecular weights mentioned is determined mainly by the content of fractions with molecular weights about 10⁵ and more and does not depend on the width of the molecular weight distribution."Plastpolimer" Scientific-Research Association, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 919–921, September–October, 1973.     

Heating of polymer surfaces during the vacuum deposition of metals

Conclusions 1. The heating of polymer surfaces associated with vacuum metal deposition is determined by the deposition rate and the deposition time and also by the thermo-physical characteristics of the substrate—growing film system, and at high deposition rates may reach the phase-transition temperatures of the polymers.2. At deposition rates up to 5 Å/sec the rise in surface temperature can be calculated by solving the usual heat-conduction equation, and at higher rates by solving the nonstationary heat-conduction equation, which makes it possible to take into account the heat transfer characteristics of the substrate— growing film system.3. The temperature of the polymer condensation surface can be regulated by varying the initial substrate temperature and, moreover, by using the pulsed metal vaporization process.Institute of Mechanics of Metal—Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel'. Translated from Mekhanika Polimerov, No. 1, pp. 50–55, January–February, 1977.     

Creep of fluoroplastic under the joint action of tension and hydrostatic pressure

Conclusions 1. The effect of hydrostatic pressure on the creep of Teflon has been investigated under isothermal conditions. The applicability of the principle of reduced variables for reduction of creep curves with respect to pressure has been shown.2. It has been ascertained that in the pressure region from atmospheric to 1600 kgf/cm² there are two subregions, which are separated by a transition at a pressure of 700–800 kgf/cm². It has been shown that in these subregions the occurrence of relaxation processes has different characters.3. A direct measurement of the free volume of Teflon has been made in the temperature range from 40 to 120°C. A sharp increase in free volume in the region of the temperature transition has been shown.Leningrad Technological Institute of the Refrigeration Industry. Okhtinsk Scientific and Industrial Union "Plastpolimer," Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 434–438, May–June, 1977.     

Failure of water-filled cylindrical glass-reinforced epoxy shells under internal impulsive loading

Conclusions 1. The explosive failure of water-filled, geometrically similar glass-reinforced epoxy shells, whose dimensions increase by a factor of 1.5–4.4, is not associated with an energetic scale effect. This is attributable to the imperfect similarity of the shells, since although their dimensions changed, the diameter of the glass reinforcing fibers remained the same.2. The relative mass of explosive required to fracture the shells is approximately 0.4%. With respect to this index, glass-reinforced epoxy is comparable to structural steels 20 and 17Mn1Si at R₀160 mm.3. The circumferential deformation of the shells at failure is about 4% and does not depend on the thickness of the shell wall, the dimensions of geometrically similar shells, or the initial strain rate on the interval 0.21 · 10³–1.2 · 10³ sec^–1. Thin-walled shells begin to fail from the outside surface, thick-walled shells from the inside surface.4. The modulus of elasticity of the GRE is 2.4 · 10⁵ kgf/cm² and does not depend on the strain rate on the interval 10^–3–1.5 · 10³ sec^–1. The material deforms elastically up to failure.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 283–289, March–April, 1978.     

Effect of the molecular weight of polystyrene on the viscosity of concentrated solutions

The viscosity of solutions of polystyrene of various molecular weights (from 1.04 · 10² to 3.8 · 10⁵) in a poor solvent (decalin) and a good solvent (ethylbenzene) has been measured at temperatures from 15 to 70°C over a broad range of shear stresses from 10² to 10⁶ dyne/cm². The nature of the solvent has a considerable influence on the critical molecular weight and the absolute value of the viscosities of the solutions over the entire range of molecular weights and on the form of the flow curves of decalin solutions of polystyrene as a function of temperature. The heat of activation of viscous flow increases with increase in molecular weight and shear stress on the interval 20–80°C. The results obtained are explained in terms of the effect of the molecular weight of the polymer, the nature of the solvent, stress and temperature on structure formation in the solution and on the orientation of the macromolecules and structures in the flow process.Ural Gor'kii State University, Sverdlovsk. Translated from Mekhanika Polimerov, No. 5, pp. 920–926, September–October, 1970.     

Study of the role of intermolecular interactions (hydrogen bonds) in the initial stage of orientation of polyvinyl alcohol and vinyl alcohol copolymers

The effect of hydrogen bond rupture on the process of destruction of the starting crystallite structure of polyvinyl alcohol and copolymers of vinyl alcohol and N-vinylpyrrolidone and -vinylcaprolactam has been investigated. The differential spectrum method is used to establish the frequency (3200 cm^–1) of the band corresponding to the vibrations of the bound hydroxyl groups; the temperature dependence of the optical density of the 3200 cm^–1 band has been recorded. The strength of the starting structure is calculated from the stress-strain diagram and its temperature dependence is plotted. It is concluded that the strength of the starting structure is chiefly determined by the presence of hydrogen bonds between the polymer macromolecules.Leningrad Kirov Institute of Textile and Light Industry. Translated from Mekhanika Polimerov, No. 2, pp. 327–329, March–April, 1971.     

On the existence of certain cyclic difference families and difference matrices

A theorem is proved to the effect that if there exists a BIB-schema with parameters (p^m–1,k, k–1), where k¦(p^m–1), p is prime, and m is a natural number, then there exists a BIB-schema (p^mn–1),k, k–1). A consequence is the existnece of a cyclic BIB-schema (p^mn–1, p^m–1, p^m–2) (p^m–1 is prime) that specifies each ordered pair of difference elements at any distance = 1, 2, ..., p^m–2 (cyclically) precisely once. Recursive theorems on the existence of difference matrices and (v, k, k)-difference families in the group Z_v of residue classes mod v are proved, along with a theorem on difference families in an additive abelian group.Translated from Matematicheskie Zametki, Vol. 52, No. 1, pp. 114–119, July, 1992.     

Effect of normal load on the temperature and velocity dependence of the force of friction for high-elastic materials

The problem of the effect of normal load on the temperature and velocity dependence of the force of friction is examined for rubbers based on SKN-18, SKN-26, and SKN-40. In the temperature range from 18°–100°C the force of friction for these rubbers falls linearly with increase in temperature. The effect of loads up to 10⁷N/cm² on the temperature dependence of the force of friction for SKN-18, SKN-26, and SKN-40 rubbers reduces to a change in the real contact area or an increase in the temperature dependence with increase in load.The velocity dependence of the force of friction for SKN-18 rubber reveals a weak dependence of the activation energy and the average "jump distance" of the molecular chains on specific load. In the low-velocity region the force of friction depends linearly on the logarithm of velocity, at velocities above 0.44 cm/min and pressures of 30×10⁵ N/cm² the force of friction increases sharply due to an increase in uncontrolled heating of the friction surfaces.Mekhanika Polimerov, Vol. 1, No. 4, pp. 123–129, 1965     

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.     

Investigation of the contact area of a rigid spherical indenter and a polymeric surface at various pressures,temperatures, and contact times

The effect of temperature and normal load on the variation with time of the indentation depth of a rigid spherical indenter in polymeric materials has been investigated with the object of obtaining the dependence of the contact area on the principal parameters of the process. Plexiglas, PVC and polyformaldehyde were selected for study. It is shown that at a given temperature the ratio _m/(a/R)^n–2=A is a function of time only and almost independent of the applied load. It is established that the time-temperature superposition principle can be used for investigating metal-thermoplastic contact phenomena. An expression is obtained for calculating the contact area at various temperatures and loading times.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 457–464, May–June, 1971.     

Propagation of and Maxwellian weighted bounds for derivatives of solutions to the homogeneous elastic Boltzmann equation

We consider the n-dimensional space homogeneous Boltzmann equation for elastic collisions for variable hard potentials with Grad (angular) cutoff. We prove sharp moment inequalities, the propagation of L¹-Maxwellian weighted estimates, and consequently, the propagation L^∞-Maxwellian weighted estimates to all derivatives of the initial value problem associated to the afore mentioned equation. More specifically, we extend to all derivatives of the initial value problem associated to this class of Boltzmann equations corresponding sharp moment (Povzner) inequalities and time propagation of L¹-Maxwellian weighted estimates as originally developed Bobylev [A.V. Bobylev, Moment inequalities for the Boltzmann equation and applications to spatially homogeneous problems, J. Statist. Phys. 88 (1997) 1183–1214] in the case of hard spheres in 3 dimensions. To achieve this goal we implement the program presented in Bobylev–Gamba–Panferov [A.V. Bobylev, I.M. Gamba, V. Panferov, Moment inequalities and high-energy tails for Boltzmann equation with inelastic interactions, J. Statist. Phys. 116 (5–6) (2004) 1651–1682], which includes a full analysis of the moments by means of sharp moment inequalities and the control of L¹-exponential bounds, in the case of stationary states for different inelastic Boltzmann related problems with ‘heating’ sources where high energy tail decay rates depend on the inelasticity coefficient and the type of ‘heating’ source. More recently, this work was extended to variable hard potentials with angular cutoff by Gamba–Panferov–Villani [I.M. Gamba, V. Panferov, C. Villani, Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation, ARMA (2008), in press] in the elastic case collision case where the L¹-Maxwellian weighted norm was shown to propagate if initial states have such property. In addition, we also extend to all derivatives the propagation of L^∞-Maxwellian weighted estimates, proven in [I.M. Gamba, V. Panferov, C. Villani, Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation, ARMA (2008), in press], to solutions of the initial value problem to the Boltzmann equations for elastic collisions for variable hard potentials with Grad (angular) cutoff.     

The effect of rate of deformation on the mechanical characteristics of plastics

An experimental investigation of the effect of the rate of deformation on the strength and modulus of elasticity of vinyl plastic and glass-reinforced laminate is described. It is established that when the rate of relative tensile deformation of vinyl plastic at 25°C is reduced from 2000×10^–6 sec^–1 to 5×10^–6 sec^–1, and that for glass-reinforced laminate from 1000×10^–6 sec^–1 to 1.3×10^–6 sec^–1, the decrease in the modulus of elasticity is about 40% and the decrease in ultimate strength 30 and 48%, as the case may be.Mekhanika polimerov, Vol. 1, No. 1, pp. 76–81, 1965     

Estimates for the Rapid Decay of Concentration Functions of n-Fold Convolutions

We estimate the concentration functions of n-fold convolutions of one-dimensional probability measures. The Kolmogorov–Rogozin inequality implies that for nondegenerate distributions these functions decrease at least as O(n ^–1/2). On the other hand, Esseen⁽³⁾ has shown that this rate is o(n ^–1/2) iff the distribution has an infinite second moment. This statement was sharpened by Morozova.⁽⁹⁾ Theorem 1 of this paper provides an improvement of Morozova's result. Moreover, we present more general estimates which imply the rates o(n ^–1/2).     

Effect of cycle asymmetry on the cyclic strength of polymers

Cyclic strength diagrams have been obtained for polymethyl methacrylate and kaprolon at different degrees of loading asymmetry (from a pure compression to a pure tension cycle) on the interval from –100 to +80° C at 2·10³ and 3·10⁵ cycles.M. I. Kalinin Leningrad Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 948–951, September–October, 1968.     

Infrared spectroscopic study of the prefracture state of rigid polymers

A correspondence has been established between the effects of stress and temperature on the half-width and the position of the maximum of the 972-cm^–1 absorption band for polyethylene terephthalate. It is shown that the prefracture state of polyethylene terephthalate is a softened state.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 520–523, May–June, 1976.