Effect of relaxation parameters on the behavior of rigid polymers in pure shear

The authors have investigated the effect of the relaxation parameters of a rigid polymer corresponding to the individual terms of the relaxation spectrum on the nature of the theoretical curves calculated for creep, strain relaxation and loading at constant strain rate in pure shear on the assumption that the stress-strain relation is described by the generalized Maxwell equation.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 431–436, May–June, 1969.     

Nonlinear creep of thick-walled polymer tubes under internal pressure

The process of creep in a thick-walled tube of rigid homogeneous epoxide-type polymer under under the action of a steady internal pressure is studied. A theoretical analysis has been made on the basis of a non-linear generalized Maxwell equation, taking account of two terms of the spectrum of polymer relaxation times. A comparison is given with the results of a calculation with a single term of the spectrum and according to linear theory. The theoretical results are compared with those obtained experimentally in a specially constructed apparatus. The possibility is shown of evaluating the long-term strength of a thick-walled polymer tube under the action of a steady internal pressure.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 493–501, May–June, 1970.     

Stress relaxation in a polymer disk

The stress relaxation in a polymer disk with a central hole, into which a rigid metal rod is press-fitted, is considered. The progressive redistribution of the stresses in the disk has been observed by a photoelastic method. In the theoretical solution of the problem the relaxation properties of the polymer are taken into account by means of a generalized nonlinear Maxwell equation with two terms of the relaxation spectrum. It is shown that the linear, as distinct from the nonlinear, theory is not capable of conveying the characteristics of the stress relaxation process in a rigid polymer disk.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1064–1070, November–December, 1971.     

Investigation of the torsion of a circular polymer shaft on the basis of the generalized Maxwell model

The torsion of a long, circular polymer shaft is investigated on the basis of the generalized Maxwell equation, used to describe the stress-strain relation in the polymer. The results obtained with the nonlinear and linearized equations are compared. The error due to linearization is estimated.Mekhanika Polimerov, Vol. 3, No. 5, pp. 906–914, 1967     

Stress relaxation in physically nonlinear polymer materials under simultaneous tension and torsion

Conclusions 1. Application of our method of determining the parameters of physically nonlinear polymer materials from tests in uniaxial tension or in torsion ensures a satisfactory agreement between theoretical and experimental stress-relaxation curves corresponding to other modes of loading.2. Theoretical stress-relaxation curves for shear (tension) calculated on the basis of parameters which have been determined from approximations of stress-relaxation curves for tension (torsion) fall closely within the confidence interval for an individual measurement (with =95%).3. The agreement between theoretical and experimental stress-relaxation curves for a plane state of stress is 2–3 times worse, in terms of the mean-square relative difference, than the agreement between the respective curves for uniaxial tension.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 797–803, September–October, 1977.     

Shear strength and laws of shear deformation of some cross-linked resins

The authors present the results of an experimental investigation and comparison with theory of certain laws of shear deformation and shear strength for rigid cross-linked resins. The possibility of describing the state of strain of homogeneous isotropic polymers by means of the generalized nonlinear Maxwell equation is considered. The results of an investigation of thin-walled tubular specimens of three cross-linked polymers based on epoxy resins and one linear polymer are offered as a check on the corresponding theoretical relations. The agreement between the theoretical and experimental results is perfectly satisfactory. Experimental values of the high-elastic constants in shear and tension have been determined. It is shown that the theoretical and experimental relations coincide with satisfactory accuracy. Certain experimental data on the comparative conditions of failure in shear and tension are presented.Mekhanika Polimerov, Vol. 2, No. 2, pp. 214–228, 1966     

Creep stability of polymer rods

The author examines the problem of the buckling of a hinger rod of rigid homogeneous polymer material under constant load. The results of an experimental investigation are presented. The theoretical calculations are based on the nonlinear generalized Maxwell equation. A numerical solution has been obtained on a computer. The results of this solution are compared with the experimental data. An analytic solution that makes it possible to estimate certain limiting values is obtained for the linearized equation.Mekhanika Polimerov, Vol. 4, No. 1, pp. 145–150, 1968     

Effect of cellular structure on the mechanical properties of plastic foams

A generalized equation for the compressive stress-strain diagrams of plastic foams is derived on the basis of a 14-faced model of the cell. The results obtained make it possible to predict the polymer base and type of cellular structure required to obtain a foam with predetermined mechanical properties in compression. The calculated values are shown to be in satisfactory agreement with the experimental data.Vladimir Scientific-Research Institute of Synthetic Resins. Translated from Mekhanika Polimerov, No. 4, pp. 594–602, July–August, 1970.     

Rheology and molecular structure of polyethylene melts 1. Melt identification from mechanical properties

It is proposed to use periodic deformation for the identification of the molecular structure of polyethylenes. By comparing the dependence of the complex and apparent viscosities on frequency and shear rate, respectively, it is shown that these functions are not equivalent for low-density polyethylene melts. The need for a numerical characteristic of the rheological functions, which should be related to the numerical characteristics of the molecular structure of the polymer, is established. The possibilities of using generalized relations for investigating the molecular structure are discussed. It is shown that the dynamic viscosity of polyethylene melts, described by a three-parameter equation, quite accurately reflects the viscoelastic properties of polyethylene melts and makes it possible, with the aid of the calculated function of the relaxation spectrum, to construct a frequency dependence of the modulus corresponding to the experimental data. Three numbers characterizing the viscoelasticity of polyethylene, which must be related with three molecular characteristics, are established.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 523–532, May–June, 1975.     

Relaxation and optical properties of cured epoxy resin

Epoxy resin cured with methyltetrahydrophthalic and maleic anhydrides has been tested in relaxation, creep, and compression at constant strain rate. The constants characterizing the relaxation properties and the approximate limits of the spectrum of most probable relaxation times have been determined; it is shown that the mechanical properties can be described by means of equations with two relaxation times. The residual optical effect has also been investigated. A linear relationship between the high-elastic strains and the path difference in the birefringent state is preserved at temperatures below the glass transition region.Read at Moscow State University polymer mechanics seminar.Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 15–23, January–February, 1970.     

Creep of polymer materials under periodically varying loads

A method is proposed for constructing the creep curves of a material whose nonlinear memory properties are described by Rozovskii's nonlinear integral equation [2] (with allowance for the stress dependence of the relaxation time) under given periodic loading from known creep curves recorded at constant stress. In deriving the theoretical relation certain simplifying assumptions are made (the creep strain accumulated in 1–2 cycles is small, no vibration [4–6]). An experimental check shows that the proposed method can be used to predict the behavior of a material under periodic loading with an accuracy sufficient for practical purposes.Mekhanika Polimerov, Vol. 2, No. 3, pp. 330–336, 1966     

Determination of the rheological characteristics of polymer materials from the static σ-ε curves and creep and relaxation curves

A method is proposed for determining the rheological characteristics of polymer materials from the experimental - curves and the creep and relaxation curves, when the behavior of the material is described exactly and approximately by the equation of a standard solid, together with a method of determining the conditional rheological characteristics when only a certain section of these curves is approximately described by the equation of a standard solid. The proposed method makes it possible to eliminate the ambiguity in the determination of the rheological characteristics due to difficulties in the exact determination of the coordinates of the beginning and end of the static curves. The use of conditional rheological characteristics makes it possible to describe the behavior of polymer materials over a broad time interval under static loading conditions by means of the equation of a standard solid without resorting to the use of complex spectral functions. A relation is established between the spectral viscoelastic functions and the conditional rheological characteristics.Mekhanika Polimerov, Vol. 3, No. 6, pp. 977–988, 1967     

Express determination of polymer composite porosity

Results are given for an experimental and theoretical study of a rapid method for determining the porosity of polymer composites by measuring the limiting moisture content in the material. The limiting moisture content was calculated using Fick 's equation solved for a plane parallel plate. The necessary parameters required for solving Fick 's equation were determined experimentally in the initial stage of the kinetic curve for water absorption. The porosity calculation was carried out using constants of a control material previously determined for pilot samples. This method is sufficiently accurate for engineering purposes and does not require special equipment.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6, pp. 824–827. November–December, 1995.     

Thermal-fluctuation model of a thixotropic rubbery liquid

The isothermal deformation of a viscoelastic liquid, whose structural elements are simulated by the Maxwell elements of the relaxation spectrum, is considered. It is assumed that in the presence of temperature fluctuations the elements of the spectrum can be destroyed and restored. A comparison is made with experiment. A procedure for calculating the relaxation spectrum from the results of shear and normal stress measurements in the steady-state shear flow regime is proposed.Presented at the Symposium on Polymer Rheology, Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow, May, 1970.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 307–317, March–April, 1971.     

Some new static charged spheres

We present new exact solutions for the Einstein–Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the system in a closed form. For specific parameter values it is possible to find new exact models for the Einstein–Maxwell system in terms of elementary functions. Our model includes a particular charged solution found previously; this suggests that our generalized solution could be used to describe a relativistic compact sphere. A physical analysis indicates that the solutions describe realistic matter distributions.     

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     

Prediction of the relaxation properties of materials based on heat-resisting polymers

Conclusions The PB0, P0D, and PI materials were used to show the possibilities of simulating the long-term relaxation processes for a new group of polymer materials using the time analogies in the linear and nonlinear regions of the viscoelastic properties. The results show that the generalized dependences of compliance and relaxation modulus widen the time range of lead of the relaxation processes by approximately six to seven decimal orders. Satisfactory results were obtained in comparing the generalized dependences with the results of the long-term reference experiment carried out in the same basic conditions.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 778–783, September–October, 1984.     

The Coordinate of the Singular Point of Generating Functions of Clusters in the High-Temperature Dynamics of Spin Lattice Systems with Axially Symmetric Interaction

We investigate generating functions for equipped trees composed of double bonds of two sorts on a hypercubic lattice of dimension d with built-in fragments. Rules for constructing these clusters are chosen to ensure the estimate for coefficients of power series in time for the longitudinal and transverse autocorrelation functions of the spin system with axially symmetric interaction. We derive a system of two equations for the tree-generating functions and an equation for the generating functions of chains leading from the root to a fragment in a tree using the Bethe approximation and under the condition that mainly bonds of one sort are taken into account. For the face-centered hypercubic lattice, we find the first terms of the 1/d expansion for the coordinate of the singular point of the generating function in both the anisotropic and the isotropic cases taking fragments in the forms of a triangle from four bonds and a four-fold bound pair into account. The obtained result is written in terms of ratios of lattice sums and is generalized to nuclear spin systems with dipole–dipole interaction. The theoretical value of the singular-point coordinate agrees well with the experimental value calculated from the tail of the absorption spectrum of the nuclear magnetic resonance in a barium fluoride monocrystal.