The influence of original imperfections on the equilibrium states of physically nonlinear panels

The influence of original imperfections, curvature of the panels, and the level of growth of plastic deformations on the equilibrium states of longitudinally compressed cylindrical panels have been studied. The physical relationships were established on the basis of the theory of localized deformations. It has been found that original imperfections substantially lower the upper critical stresses in the zone of elastic and slowly growing plastic deformations, depending on the curvature parametera/R. In a zone of growing plastic deformations, the solution according to nonlinear shell theory approximates the solution according to linear shell theory, and change of curvature of the panels does not cause a sharp increase of the upper critical stress as occurs in a zone of plastic deformations.Institute for Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 345–351, March–April, 1970.     

Normal stresses in non-Newtonian polymer flows

The calculation of the normal stresses from the flow curve is considered on the basis of the method of correlation of the frequency and stationary characteristics of flowing polymer systems. Simple expressions are given for finding the initial normal stress coefficient and the high-elastic modulus from the point corresponding to the beginning of non-Newtonian flow. A necessary condition for the appearance of normal stresses is a viscosity anomaly. It is shown that for a bounded value of the initial normal stress coefficient to exist the derivative of the effective viscosity with respect to shear rate must be zero at the initial point.Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 506–514, May–June, 1971.     

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.     

Nonlinear physical stress - strain relationship of cellular polymers and glass plastics under conditions of attenuating creep

The coupling equations of hard cellular polymers and glass plastics based on these are analyzed. The material is considered as an elastically relaxing medium for the case of small deformations. The physical relationship between the rubber-elastic stresses and strains is derived in explicit form for the case of attenuating creep and a uniform three-dimensional stressed state. The total deformations are described by the one-dimensional rheological model of a "typical body" with a reduced stress and an instantaneous elastic modulus, having the appropriately chosen viscosity of a non-Newtonian liquid.Institute of Technical Mechanics, Bulgarian Academy of Sciences, Sofia. Translated from Mekhanika Polimerov, No. 2, pp. 231–235, March–April, 1972.     

Uniaxial extension of polystyrene with a constant true stress

A apparatus designed for the extension (stretching) of yielding polymers at a constant true stress is described. The changes taking place in the general, rubber-elastic, and irreversible deformations aredetermined, together with the corresponding rates of deformation, as well as the viscosity and relaxation characteristics, during the extension (tensile strain) of block polystyrene at various constant true stresses and a temperatore of 130°C.All-Union Scientific-Research Institute of Synthetic Fiber, Kalinin. Translated from Mekhanika Polimerov, No. 6, pp. 1104–1109, November–December, 1972.     

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.     

Investigation of the causes of crack formation in punches for hot upsetting of components

It is shown that tangential stresses due to inconsistent thermal deformations is responsible for the formation of radial cracks in punches used in hot upsetting.Fiftieth Anniversary of the USSR Bus Factory, L'vov.Translated from Matematicheskie Metody i Fiziko-mekhanicheskie Polya, No. 26, pp. 64–68, 1987.     

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.     

Statistical derivation of the equations of viscoelasticity of rubbery polymers for homogeneous finite deformations

The statistical derivation of the equations of linear viscoelasticity [1, 2] is extended to the slow finite homogeneous deformations of rubbery polymers. It is shown with reference to a Gaussian subchain network model that the time correlation functions of the momentum fluxes (relaxation moduli) in the deformed and undeformed states are the same. The relations previously proposed on the basis of purely phenomenological considerations [15] are obtained for the viscous stresses in uniaxial tension. Comparison with experiment has shown that the proposed relations approximately describe the existing data on the stretching of elastomers in a certain region of finite strains.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 980–986, November–December, 1969.     

Viscoelastic deformations of a thick-walled cylinder under prolonged exposure to gravitational stresses

A method is presented for the calculation of the stress-deformed state of an infinitely long viscoelastic thick-walled cylinder, enclosed in an elastic casing and exposed to gravitational stress in equilibrium with a system of concentrated forces, applied to the casing. The problem is solved by analyzing the flat deformation of the annular region under the influence of mass forces and unknown reactions on the outer surface, and by determining the stress-deformed state of the casing ring exposed to distributed normal and tangential loads, and to a system of concentrated forces. The solutions are then compared on the basis of compatibility of the deformations and equality of the stresses. Integral transformations are used in the calculations and an example is cited.S. Ordzhonikidze Aviation Institute, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 846–853, September–October, 1972.     

Mathematical model of muscular contraction with a ccount of excitability

A model of muscular contraetion has been developed which establishes the relationship between normal stresses and longitudinal deformations of the muscle tissue and takes into account its excitability. A transfer function has been proposed for the equation describing the behavior of the muscle as a dynamic system which is controlled by synegisms. The validity of the model has been tested experimentally. The model has been used to develop type-II Lagrange equations for the solution of the basic task of biomechanics for some movements of the human body.Paper presented at the FirstAll-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.P. F. Lesgaft State Institute of Physical Culture, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 608–612, July–August, 1975.     

Multicritical phenomena in flow of viscoelastic liquids. 3. Liquid-crystalline polymers. The Akay-Leslie anisotropic liquid. Viscometric functions

The advances in determination of the rheological material functions of liquid-crystalline polymers (LCP) in a wide range of concentrations or temperatures are briefly examined. Special attention is focused on a discussion of the concentration region of the existence of liquid-crystalline order and textures initiated by shear flow. The phenomenological rheological equation for an anisotropic liquid proposed by Akay and Leslie (A-L model) was selected for describing the flow resistance of LCP, and the problem of simple shear flow of a liquid was solved. It was shown that the A-L model can describe all of the basic characteristics of the viscometric functions of LCP, including the phenomenon of negative values of the first normal stress difference for some range of concentrations and shear rates. The available data on the initial viscosity of lyotropic LCP were classified based on the types of cohesion (dimensionality) of the system, characterized by the exponent of the concentration dependence of the viscosity. It was found that each type of cohesion has its own kind of viscometric functions and that the A-L rheological model can reflect their basic characteristics. It was shown that by varying the initial ordering parameter of the A-L model, linear (or almost linear) functions N₁(q) and ₁₂(q) can be described in the region of low shear rates. It was hypothesized that region 1 of the flow curve (Onogi and Asada) inevitably exists in the continuous liquid crystalline phase, which could be outside of the region of measurements accessible to rheometry.See [23] for Communication 2.Institute of Polymer Mechanics. Riga. LV-1047 Latvia. Translated from Mekhanika Kompozitnykh Materialov. No. 6. pp. 821–839. November–December, 1997.     

A refined model for three-point bending of sandwich panels 2. Transverse stresses

According to the relationships derived in [1], transverse normal and tangential stresses in a sandwich panel have been analyzed. Asymptotic formulas for the stress concentration area in the vicinity of point forces are derived. Analytical estimates of a normal stress at the central and end sections of the panel are deduced. The Saint-Venant effect of the degeneration of a panel of finite length into an infinite strip is studied. For the estimation of the concentration of the transverse tangential stress, the possibility of a superposition of the solution of the slippage problem of the face layers and the classical solution allowing for shear is substantiated. It is shown that the local Reissner-type effects are specified by reducing the concentration of the tangential stress in the face layers along the longitudinal coordinate and transition to the steady tangential stress state in the filler layer. The concentration coefficients of the tangential stress are derived as functions of the dimensional parameters of the panel section.Institute of Polymer Mechanics. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 1, pp. 66–93, January–February, 1998.     

Effect of fillers on the viscosity and viscoelasticity of low-density polyethylene melts. Communication 1

An investigation of low-density polyethylenes filled with up to 30% by volume dispersed particles, has shown that for both the matrix and the composites the apparent viscous flow activation energy does not depend on the shear stresses and increases starting from a certain filler concentration at which the conformation range in the matrix is depleted. The dependence of the relative viscosity of the compositions on the volume filler content is satisfactorily described by an equation that contains the reduced filler concentration, defined as the ratio of the nominal filler concentration to the limiting concentration at which the adsorption layers on the particles extend throughout the matrix. The thickness of the polymer layer adsorbed on the particles must be determined from the specific exterior particle surface, with allowance for the volume of the polymer in the sorption space of the porous filler.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 478–486, May–June, 1976.     

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.     

Stress on the interatomic bonds near the surface of a polymer

The stresses on the interatomic bonds in the interior and at the surface of polyethylene terephthalate film in uniaxial tension have been determined by means of infrared transmission and reflection spectroscopy. The stresses are found using the shift in the frequency of the atomic vibrations produced by the application of a mechanical load. It is shown that the stresses on some bonds in the specimen reach 700 kgf/mm², i.e., approach their theoretical strength. The concentration of these bonds in a surface layer 1 µ thick is approximately an order greater than the concentration in the interior of the specimen.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 512–514, May–June, 1976.     

Second-approximation shear theory for shallow layered shells and plates

Analysis of a second-approximation refined shear model for shallow layered composite shells and plates with a substantially inhomogeneous structure over the thickness is presented. The tangential displacements and corresponding normal stresses are expressed in the form of a polynomial of the fith degree in the transverse coordinate and contain squared rigidity characteristics. In this way, the accuracy of results and practical coincidence with the 3D solutions is ensured. Based on the refined model, a theory of shallow layered shells is developed. A system of resolving equations of sixteenth power together with appropriate boundary conditions was obtained and solved analytically. It is shown that the area of application of the formed model is extended as compared with the model of the first approximation. The model proposed allows us to examine the stress-strain state of layered composite structures of substantially different thickness and physical-mechanical characteristics of the layers, including the possibility of simulating relatively large shear deformations of rigid layers separated by a low-modulus thin interlayer pliable to transverse shear.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 363–370, May–June, 1998.     

Prediction of the bearing capacity of composite flanges for aircraft-engine casing parts

Computed results of the stress-strain state of four different composite flanges for aircraft engines are presented for assigned external-load parameters, and their most heavily loaded regions are defined. The static strength of the structures is found from the stresses in the layers using the maximum-stress criterion and Hill's modified criterion. It is established that transverse tensile stresses are most critical. The service life of the flanges is estimated on the basis of the fatigue-failure criterion of the weakest link.Perm' State Technical University. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 360–369, May–June, 1997.     

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.     

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.