Viscous and high-elasticity properties of solutions of monodispersed polybutadienes in the region of critical concentrations

It is shown that there is a critical concentration corresponding to the formation of a compact, fluctuating network, which results in a sharp change in the concentration dependence of the viscosity, first difference of normal stresses and high-elasticity deformations. It is found that at concentrations below the critical concentration high-elasticity deformations do not develop, although normal stresses exist. In consequence, the relationship whereby the modulus of high elasticity is equivalent to the ratio between the square of the viscosity and the coefficient of normal stress is fulfilled only for concentrations higher than the critical.A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 896–902, September–October, 1972.     

Normal stresses associated with the flow of non-Newtonian polymer systems

It has been experimentally confirmed that the method of calculating the shear rate dependence of the normal stresses from the flow curve, proposed in [1], gives good results consistent with the experimental data. A series of simple relations proposed for estimating the initial normal stress coefficient are compared with the experimental results and it is shown that there is good agreement between calculation and experiment. In the linear region the Lodge relation, which equates the high-elastic strains to half the ratio of the normal to the shear stresses is satisfied.For communication 1 see [1].Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 714–721, July–August, 1971.     

Theory of flow of concentrated polymer solutions and melts

Starting from the concept of a polymer system as a collection of macromolecules forming an effective network, an expression is obtained for the stress tensor of a flowing concentrated polymer solution or melt. It is shown that the variation of the effective viscosity of polymer systems is associated with the orientation of the macromolecules and changes in the equilibrium number of nodes during flow. A system of equations describing the flow of polymer systems characterized by a gradient dependence of the effective viscosity and normal stresses in shear is written in the single relaxation time approximation.Institute of Chemical Physics, Moscow Region, Academy of Sciences of the USSR. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 724–730, July–August, 1968.     

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.     

A refined model for three-point bending of sandwich panels. 1. Deflections and bending stresses

Design formulas for the flexural characteristics of sandwich panels under three-point loading by point forces, taking into account local effects, have been derived. Transverse deformation of the normal in the modified model is deduced in terms of the difference between deflections of face layers. It is considered that the rotation of the normal depends also on shear of the filler. The deflections, local curvatures, and bending stresses, dependent on the face-layer thicknesses and transverse characteristics of the filler, are studied. The danger of initial failure caused by the local moment stresses at the central panel section is shown. Comparative estimates refining the conventional designs are established.Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 747–767, November–December, 1997.     

Effect of a uniaxial load on moisture absorption by an epoxy binder

Conclusion The above-developed method of studying the effect of uniaxial compressive and tensile loads on moisture absorption in polymers was tested on epoxy binder EDT-10. It was established experimentally for this material that tensile stresses up to 50 MPa significantly increase the equilibrium moisture content (up to 20% of the initial value). There is a corresponding increase in the rate of moisture absorption during the initial stage of the sorption process — up to 80% of the initial value. No changes in the diffusion coefficient were seen in this case. The application of compressive stresses of up to 40 MPa also had no effect on the kinetics of moisture absorption.Deceased.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 1, pp. 110–115, January–February, 1993.     

Determination of contact stresses in problems on bending of a package of transversely isotropic bars

A mechanomathematical model for bending of packages of transversely isotropic bars of rectangular cross section is proposed. Adhesion, slippage, and separation zones between the bars are considered. The resolving equations for deflections and tangential displacements are supplemented with a system of linear differential equations for determining the normal and tangential contact stresses, and boundary conditions are formulated. A scheme for analytical solution of two contact problems—a package under the action of a distributed load and a round stamp—is considered. For these packages, a transition is performed from the initial system of differential equations for determining the contact stresses, where the unknown functions are interrelated by recurrent relationships, to one linear differential equation of fourth order and then to a system of linear algebraic equations. This transition allows us to integrate the initial system and get expressions for the contact stresses.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 761–778, November–December, 2004.     

Moduli of elasticity of polymer melts

The physical significance of the so-called initial modulus, determined in measuring the rheological properties of thermoplastic melts from the initial slope of the time dependence of the stresses at given constant shear rate, is considered. It is shown that this quantity is related with the ratio of the shear and normal stresses.Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 534–538, May–June, 1969.     

stresses and reversible deformations during shear flow of polymer solutions and melts

The influence of the accumulated elastic energy on the relationships between tangential stresses, the first difference between the normal stresses and the reversible deformations during isothermal shearing steady-state flow of polymer solutions and melts, is analyzed. It is shown that the reversible deformation in the non-Newtonian flow region is related to the tangential and normal stresses by Lodge's formula, if the thixotropic disruption of the structural flow units is accompanied by the dissipation of the elastic energy accumulated in them; the conservation of the elastic energy accumulated during the flow causes exceeding of the reversible deformation values as compared with the values calculated by Lodge's formula.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 886–895, September–October, 1972.     

Continual mechanics of monodisperse suspensions. rheological equations of state for suspensions of moderate concentration : PMM vol. 37, n6, 1973, pp. 1059–1077

Rheological relationships linking mean and moment stresses and, also, the force and moment of interphase reaction in a macroscopic flow of small solid sphere suspension with the kinematic characteristics of the flow are derived. This makes it possible to close the system of equations of suspension hydrodynamics. Coefficients of viscosity and of moment viscosity of a suspension are obtained and calculated.The equations of conservation of mass, momentum and moment of momentum of suspension and of its phases, considered (from the macroscopic point of view) to be coexistent continuous media, were formulated in a general form in [1]. These equations contain unknown vectors and tensors which define the interaction between the considered continuous media and, also, stresses and moment stresses appearing when these are in motion. To close the equations of conservation it is necessary to express all these quantities in terms of unknown variables of these equations (mean concentration of suspension, pressure in the fluid phases, and phase velocities). This problem is the second of the fundamental problems of hydromechanics of suspensions indicated in [1].Here this problem is solved with the use of a kind of self-consistent field theory, which is essentially an extension and generalization of methods developed in [2 – 7]. Expressions for all of the quantities mentioned above are derived. They can be considered to be rheological equations of state for suspensions. Expressions for the various coefficients of these equations and their dependence on parameters of phases and on the flow frequency spectrum are also considered.     

Influence of an electric field on the rheological behavior of a dilute suspension of dipolar dumbbells in a viscoelastic oldroyd liquid

Conclusions 1. Rheological equations of state of a dilute suspension of dipolar dumbbels in a viscoelastic Oldroyd liquid have been obtained for a stationary orientation of suspended particles in steady flows and electric fields.2. Study of the rheological properties of such a medium in simple shear flow in the presence of an electric field, the intensity vector of which lies in the shear plane and is perpendicular to the velocity vector, has shown that the medium examined conducts itself as a viscoelastic liquid. This is the result of both the viscoelastic properties of the dispersion medium and the orientation of the suspended particles under the action of frictional forces and the electric field. The effective viscosity of the suspension and difference in normal stresses resulting from the presence of the suspended particles are greater if one does not take the elastic properties of the dispersion medium into account.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 3, pp. 519–524, May–June, 1978.     

Stresses in plastics reinforced with anisotropic fibers and subjected to transverse normal loading

The question of the stress distribution in plastics reinforced with anisotropic fibers and subjected to transverse normal loading is considered. The stresses in the components are determined by the methods of the theory of elasticity using stress functions. The theoretical relations obtained are used to construct diagrams showing the distribution of the tangential, radial, and shear stresses in the composite and the isoclines of the concentration coefficient for a carbon-reinforced plastic. The results obtained for the carbon-reinforced plastic are compared with the analogous results for a glass-reinforced plastic.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 244–252, March–April, 1973.     

Design of orthotropic parts of complex shape by the method of nonplanar sections

Procedures based on the hypothesis of nonplanar sections are used to derive equations for determining the normal stresses at an arbitrary point of a body of complex shape in tension and bending. The anisotropy of the material properties is taken into account by introducing a variable modulus of elasticity. The theoretical results have been checked experimentally.Gor'kii Zhadanov Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 351–354, March–April, 1969.     

Bending of a thin cantilevered orthotropic plate with a concentrated load at the free edge

The problem of a thin rectangular cantilevered plate of constant thickness with a concentrated load in the center of the free edge is considered. The plate is assumed to be orthotropic, the fixed edge coinciding with the principal direction of elasticity. An equation is obtained for the normal stresses at an arbitrary point on the plate. The theoretical results are compared with experiment.A. A. Zhdanov Gor'kii Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 739–741, July–August, 1968.     

Strong law of large numbers for the interface in ballistic deposition

We prove a hydrodynamic limit for ballistic deposition on a multidimensional integer lattice. In this growth model particles rain down at random and stick to the growing cluster at the first point of contact. The theorem is that if the initial random interface converges to a deterministic macroscopic function, then at later times the height of the scaled interface converges to the viscosity solution of a Hamilton–Jacobi equation. The proof idea is to decompose the interface into the shapes that grow from individual seeds of the initial interface. This decomposition converges to a variational formula that defines viscosity solutions of the macrosopic equation. The technical side of the proof involves subadditive methods and large deviation bounds for related first-passage percolation processes.     

Identification of a free boundary in Norton–Hoff flows with thermal effects

This work deals with a free boundary identification problem in a steady viscoplastic flow. We provide a novel identification model based on a non-linear optimization. The fluid motion is governed by the incompressible Norton–Hoff model coupled with the heat equation. The viscosity of the fluid is modeled by the non-linear Arrhenius law. Our point of view is to treat the problem as a shape sensitivity of a cost functional formulated on the free boundary and governed by the normal component of the velocity of the flow. We analyze the mathematical statement of the forward problem. The equations related to the free boundary are simplified. Various properties of this optimization are proved. Since the state of Norton–Hoff model is not regular enough we introduce a parameter penalization. The shape gradient of the considered cost functional is given in the strong sense up to the parameter of penalization. We supply the expression of the shape gradient in a weak sense.     

Initial stresses in filament-wound reinforced-plastic rings

Methods of experimentally determining the initial stresses in filament-wound GRP rings are examined and the effect of winding tension is investigated. It is shown that by varying the winding tension it is possible to exercise a considerable degree of control over the magnitude and distribution of the initial stresses.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 505–511, May–June, 1969.     

Correlation of the effective and complex dynamic viscosities of viscose

The results of comparative measurements of viscosity of viscose in the steady-state flow and harmonic vibration regimes are presented. It is shown that in order to describe the dependence of the effective viscosity on the velocity gradients in the steady-state flow regime it is possible to employ the mathematical apparatus of the phenomenological theory used in dynamic investigations. The operating regimes of automatic viscometers intended for measuring the maximum Newtonian viscosity of viscose are determined.All-Union Scientific-Research Institute of Synthetic Fiber, Moscow Region. Translated from Mekhanika Polimerov, No. 4, pp. 756–759, July–August, 1973.     

Variation of certain transverse characteristics over the thickness of wound glass-reinforced plastic rings

The variation of certain transverse characteristics over the thickness of wound glass-reinforced plastic rings has been experimentally determined under normal conditions and at the polymerization temperature of the material investigated. The characteristics in question are used in investigating the state of stress of the ring and the initial fabrication stresses.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 165–167, January–February, 1970.     

Residual stresses in glass-reinforced plastics parts

The determination of the residual stresses in glass-reinforced plastics elements is considered. It is shown that these stresses reach appreciable values and should be taken into account in strength calculations. Quantitative data are supplied for a series of materials. At normal operating temperatures the residual stresses are stable.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1117–1119, November–December, 1969.