Calendering mechanics of viscoelastic materials (communication 1)

The kinematics and dynamics of the deformation of a viscoelastic material (rubber mix) between the rolls of a calender are considered. Approximate calculations are presented for the elastic recovery of the sheet after it passes through the nip in terms of the calendering speed, the geometry of the deformation zone, and the rheological properties of the rubber mix. Equations are also given for estimating the vertical thrust and torque.Scientific-Research Institute of the Tire Industry, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 539–545, May–June, 1969.     

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.     

Iterative method of designing uniform and laminated shells of revolution made of highly elastic materials

Conclusion An iterative method was proposed for numerical solution of problems concerning the axisymmetric deformation of uniform and laminated shells of revolution made of highly elastic materials. Calculations performed for rubber, rubber-fiber, and rubber-layered shells demonstrate the reliability and effectiveness of the method.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 109–116, January–February, 1990.     

A Theoretical Model and Experimental Investigation of a Nonlinear Constitutive Equation for Elastic Porous Metal Rubbers

Starting from the theory of porous materials, the nonlinear theory of dry friction, and the model of a bent slender beam, a nonlinear constitutive equation for elastic porous metal rubbers is constructed. Static compressive experiments were carried out on hollow cylinders of such a rubber, from which relations between all coefficients of the constitutive equation and the material density were determined. Based on the data obtained, the constitutive equation of the material was predicted successfully. The effect of density of the metal rubber on its stiffness and on the nonlinear constitutive equation was revealed by experiments.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 449–460, July–August, 2005.     

Nondestructive investigation of the thixotropic recovery of unvulcanized heavily filled rubber

A dynamic method has been used to estimate the thixotropic change in the viscoelastic properties of materials. The thixotropic recovery of the structure of a heavily filled rubber, destroyed by processing under stationary conditions, has been investigated. It is found that the relaxation spectrum changes during the recovery process.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 561–564, May–June, 1969.     

Torsional stability of a glass-reinforced plastic cylindrical shell with an elastic core

The problem of the stability of a glass-reinforced plastic cylindrical shell with an elastic core subjected to twisting moments applied to the edges of the shell is considered. As in various other studies [4–6], the glass-reinforced plastic is treated as an elastically orthotropic material. The core is treated as an isotropic elastic cylinder, whose outer surface is bonded to the shell. Expressions for the critical stresses are obtained for an infinitely long shell and a shell of finite length.Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1082–1086, November–December, 1970.     

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.     

Variation of the instantaneous modulus of elasticity of certain types of plastics under long-time static loads

The variation of the elastic characteristics of polymeric materials tested to destruction under long-time static loads has been investigated. Experiments on polymethyl methacrylate, KAST-V glass laminate, and Soviet and Finnish polyester glass-reinforced plastics under constant and intermittent (with "recovery") static tensile loads have shown that their elastic characteristics vary with the loading regime, the type of material, and the stress level. In a number of cases the value of the modulus of elasticity falls by 25–35%. This is attributed to the reduction of the effective cross section of the specimen as a result of damage accumulation.All-Union Correspondence Structural Engineering Institute, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 430–435, May–June, 1971.     

Flow of a viscous fluid in a deformable valved tube in the presence of gravity

The problem of the flow of a viscous incompressible fluid in a tube of finite length with valves at the ends is solved numerically with allowance for gravity and elastic wall properties that vary periodically with time.Paper presented at the First All-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 4, pp. 756–760, July–August, 1975.     

Stability of orthotropic cylindrical shells under variable pressure

A method of determining the critical stresses is developed for elastic orthotropic cylindrical shells subjected to nonuniform pressure. It is assumed that the external pressure varies over the cross section and is constant along the length of the cylinder. A shell stability analysis is given for the case of a weakly varying load.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 897–902, September–October, 1970.     

Liquid flow in a tube with deforming walls in the presence of valves

A numerical solution is presented for the flow of a viscous liquid in a tube of finite length with valves at the ends and elastic properties of the tube walls periodically changing with time. Such conditions may be encountered in the flow of blood through veins equipped with valves to prevent reverse flow.Scientific-Research Institute of Mechanics. M. V. Lomonosov State University, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 903–908, September–October, 1972.     

Relative stiffness of irregularly perforated plates

Approximation of the average field is used in order to calculate the relative elastic properties of plates irregularly perforated with a large number of different hole. Relative properties are calculated for a plate perforated with a different kind of elliptical hole. It is shown that the Young's modulus and shear modulus of a plate perforated with identical round holes calculated in this approximation have values similar to those calculated accurately for the case of a regularly perforated plate.Translated from Dinamicheskie Sistemy, No. 5, pp. 3–11, 1986.     

Quasistatic anti-plane motion in the simplest theory of nonlinear viscoelasticity

We consider a very simple model in the framework of differential viscoelastic materials which are isotropic and incompressible. In this model the Cauchy stress tensor is split in an elastic part and a dissipative part. The elastic part is derived from a strain-energy density function only of the first invariant of the Cauchy–Green strain tensor. The dissipative part is like the Navier–Stokes equations: linear in the stretching tensor with a constant viscosity parameter. For this model we provide some time and spatial estimates in the quasistatic approximations for the equations governing anti-plane shear motions. Several explicit examples for specific form of the strain energy are produced. Our results impose analytical restrictions on the mathematical properties of the strain energy to ensure a physical behavior in the creep and recovery experiments. Moreover, we show polynomial decay for the spatial behavior in the class of stress-hardening (or strain-stiffening) materials. For stress-softening materials a Phragmen–Lindelof alternative is proved.     

Water absorption and its effect on rubber strength

The effect of the swelling of rubbers in water and their recovery on the tear strength of the material has been investigated and a mechanism of water absorption is proposed. It is shown that there is a fundamental difference between the mechanism of water absorption and swelling in solvents. The strength of a rubber dried after being kept in water is anomalously high. This effect is explained in terms of the proposed polymer-nonsolvent interaction mechanism.É. A. Ter-Gazaryan State Scientific-Research and Design Institute of Polymer Adhesives, Kirovakan. Moscow Technological Institute of the Meat and Dairy Industry. Translated from Mekhanika Polimerov, No. 1, pp. 136–138, January–February, 1970.     

Applicability of the superposition principle to periodically loaded polyethylene

The lifetime of isotropic specimens of high-density polyethylene subjected to periodic tensile loading and "recovery" has been investigated. The lifetime determined without allowance for the time for "recovery" of the polymer is greater than the lifetime under constant load; under periodic application of a constant stress the lifetime increases exponentially with increase in the length of the "recovery" interval; at the same "recovery" time the life-time decreases exponentially with increase in the time under load during each cycle.Higher Chemical Engineering Institute, Sofia. Translated from Mekhanika Polimerov, No. 6, pp. 1009–1013, November–December, 1970.     

Statistical aspects of the failure of organic-fiber-reinforced plastics

Conclusions Dispersion of the strength of filaments and of the Weibull coefficient leads to a drop in strength of a strand compared with the strength of the components when the adhesion by gluing together does not amount to 2–5%. The drop in strength is determined by the dispersion of strength which depends on the length of the tested specimens.Gluing together of the fibers in filaments changes the nature of the load diagrams - of a filament when its length exceeds ₀. A consequence is that the mechanism of rupture of the strand changes, and this leads to an additional drop of its strength. When specimens are 500 mm long, the drop in strength of the strand compared with the mean strength of the filaments amounts to 10%.Because of the dispersion of the Weibull coefficient, the strength of filaments does not correspond exactly to the strength of the microplastic obtained from these filaments. When there is dispersion of the strength of the filaments, failure of the plastic proceeds by failure of the microplastics as a whole.Gluing together of fibers has a double effect on the strength of the material: increased degree of gluing together of the fibers reduces the noneffective length from ₀ to 0.4–0.5 mm, and this leads to an increase of approximately 50% of the strength of the microplastic; increased gluing together leads to a change in the mechanism of failure of the strand and of the organic-fiber-plastic made from it if there is dispersion of the strength of the component filaments, and this reduces the strength of the material in accordance with (3) (by 12–14% in our case). The longitudinal instability of the properties of the filament leads to an additional drop in strength of the material by 4.5%.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1011–1017, November, 1984.     

Basic equations of the theory of reinforced media

The author derives the basic equations of the theory of composite elastic media obtained by reinforcing some elastic medium with a large number of linear or planar elastic elements with high strength and deformation resistance. The argument is based on macrostructural considerations. The stress-strain state of each of the reinforcing elements is considered with allowance for interaction with the matrix material. In addition, the "smoothing" principle introduced in [1–3] is applied. This corresponds to approximating the reinforced medium with some equivalent quasi-homogeneous anisotropic medium.The case of a fibrous medium in which the reinforcing elements are rods or filaments [4] is discussed in detail. Allowance for moment effects leads to equations analogous to the equations of the Voight-Cosserat moment theory and its later generalizations. Similar equations are obtained for the case of laminated media, where the reinforcing elements are membranes or plates. On the basis of the viscoelastic analogy [7], the equations of the theory of reinforced media are extended to include the case in which the matrix and/or reinforcing materials are linear viscoelastic.Mekhanika Polimerov, Vol 1, No. 2, pp. 27–37, 1965     

Effect of loading on the roughness set in run-in metal - rubber surfaces

A study has been made on the effect of loading on the roughness set of a metal surface run-in with rubber containing an SKN-18 + SKN-26 nitrile rubber blend in conditions of friction without lubrication. The experimental results are compared with those calculated.State Scientific-Research Institute of Mechanical Engineering, Moscow. Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 737–740, July–August, 1972.     

Fatigue of glass laminates subjected to repetitive impact loading

Fatigue characteristics obtained for repetitive impact tensile loading in a DSO impact tester are presented for a glass-reinforced Textolite. There are differences in the fatigue life, temperature rise, and the variation of the elastic properties as compared with the case of repetitive sinusoidal stress cycles. The effect of the geometry of the test piece gage length on the measured parameters is examined and methods of predicting fatigue life are discussed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 751–754, July–August, 1969.     

Effect of parameters of the distribution of the length and orientation of short fibers on characteristics of the dynamic viscoelasticity of a polymer composite

Conclusion An algorithm for calculating the dynamic viscoelastic characteristics of a composite reinforced with short fibers was developed and realized in the form of a computer program. An analysis was made of the dependence of the characteristics of the composite on the volume content and length of its fibers, as well as on statistical distributions of fiber length and orientation in the material. It was shown that a change in the parameters of the statistical distributions has a significant effect on both the elastic and the dissi-pative properties of the composite. It was found that ignoring the statistical fiber-length distribution might lead to overestimation of the real component of the complex modulus and underestimation of the mechanical loss tangent.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 13–17, January–February, 1990.