Spectra of pressure relaxation times of polymer and copolymer melts and their practical use

The possibility of using pressure relaxation of melted polymers for the investigation of the structure of three types of polymers and their compositions and the analysis of the change of their molecular characteristics during aging is shown.Kazan State Technological University, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 531–538, July–August, 1998.     

High-temperature destruction of composite materials during intense heat and gasdynamical action

High-temperature destruction of polymer composite materials during interaction with gas flows has been investigated experimentally. The braking pressure of the flow varied from 5 to 25 MPa. The basic laws of the destruction under high pressure were established. The condition of thermomechanical destruction of the materials studied under a pressure of 15 to 25 MPa was determined. A physical model of the high-temperature destruction of polymer composite materials subjected to intense heat and gasdynamical action was developed.Scientific Research Institute of Applied Mathematics and Mechanics, Tomsk State University, Tomsk, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 1, pp. 107–115, January–February, 1998.     

Nonsteady-state damage accumulation processes in composite flanges under cyclic loads

We consider two typical flanges: for a powerplant casing and for the casing of suspensions with a sound-absorbing duct. We model the behavior of flanges under the action of cyclic external loads based on solution of the nonlinear axisymmetric problem of elasticity theory. In order to take into account fatigue fracture of the layers of the structure, we use maximum stress criteria, a tensor damage function, the rule of linear summation of damage, and reduction schemes for the deformation characteristics of the layers, describing different fracture mechanisms. We indicate the possible nature of the development of fracture zones in composite flanges. We have established the spare load-bearing capacity of the flanges after fracture begins.Report presented at the Tenth International Conference on Mechanics of Composite Materials (Riga, April 20–23, 1998).Perm State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 636–643, September–October, 1997.     

Synthesis of averaging methods in stochastic boundary-value problems of the mechanics of microheterogeneous solids

The method of periodic components is further developed, which allows us, on unified positions, to predict the effective characteristics and structural strain fields in partially or fully disordered composites. The stochastic boundary-value problem of elasticity theory for microheterogeneous solids with a statistically homogeneous structure is treated. The heterogeneous solid is considered to be macroscopically homogeneous and macroanisotropic (or quasi-isotropic) with geometric form and properties of the structural components determined and given. The structural elements are assumed to have perfect interfaces, i.e., the displacements and tractions are continuous across the interface. The boundary-value problem was solved by the method of local approximation. Numerical results were obtained for composites with a stochastic structure.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 3–12, January–February, 1999.     

Initial stresses in reinforced and filled polymers

The methods of the statistical theory of elasticity are used to calculate the average stresses in the components of uniaxially reinforced and randomly filled polymers arising in the process of fabricating the material as a result of the different linear expansion coefficients of the components and chemical shrinkage of the resin. Expressions are also obtained for the macroscopic characteristics of the media — moduli of elasticity, linear expansion coefficients, and shrinkage coefficients. The results are compared with experimental data and with the results of computations based on the equations proposed by other authors. The relations obtained for the dependence of the stresses in the components on their properties offer a satisfactory explanation for the experimentally established positive correlation between the shrinkage and the compressive strength of a composite based on furan resin.Gomel' State University. Kirov Urals Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 1, pp. 90–96, January–February, 1973.     

A molecular model of creep and stress relaxation in crystalline polymers

A possible model of defect formation in a polymer crystal lattice is considered. The results of an investigation of creep and stress relaxation in crystalline polymers are interpreted on the basis of the model proposed.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 6, pp. 969–975, November–December, 1971.     

Relaxation phenomena in rubber-like polymers with small deformation above the glass transition temperature

In the temperature region in which rubber-like polymers have a high elasticity, a high-temperature subregion has been observed which is characterized by the presence on the extension curve of a critical strain at a small deformation (1–2%). The rigidity of the polymer below and above the critical value is different. The relaxation character of this phenomenon is considered.V. I. Lenin Moscow State Pedagogical Institute. Laboratory of Polymer Physics Problems. Translated from Mekhanika Polimerov, No. 3, pp. 544–546, May–June, 1970.     

Singular approximation of the method of periodic components in statistical mechanics of composite materials

A quasi-periodic model is developed for random structures of composites, when the locations of inclusions are given in terms of random deviations from nodes of an ideal periodic lattice. Solution of the stochastic boundary problem of the theory of elasticity is examined for a quasi-periodic component by the method of periodic components, which is reduced to determination of the field of deviations from the known solution for a corresponding periodic composite. The solution is presented for the tensor of effective elastic properties of a quasi-periodic composite in singular approximation of the method of periodic components in terms of familiar solutions for tensors of the effective elastic properties of composites with periodic and chaotic structures and the parameters of the quasi-periodic structure: the coefficient of periodicity and the tensor of the anisotropy of inclusion disorder. A numerical calculation is performed for the effective transversally isotropic elastic properties of unidirectional fibrous composites with different degrees of fiber disorder.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 460–473, July–August, 1997.     

Vibrations of isotropic viscoelastic shells

It is shown that the boundary value problems for viscoelastic and elastic shells coincide. The natural and forced vibrations of shells are investigated by the averaging method.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 157–163, January–February, 1971.     

Methods of finite element analysis of arbitrary buckling forms of sandwich plates and shells

Two statements of the problem of arbitrary buckling forms (BFs) (including synphasic, antiphasic, mixed flexural, flexural-shear, and shear forms in the tangential directions) of general-form sandwich shells and two schemes of its solution by the FEM are given. The first of the schemes is based on the use of refined linear equations for determination of the precritical stress-strain state and linearized equations of neutral equilibrium with all parametric addends necessary to determine the critical loads and reveal the possible BFs. The second one uses the general geometrically nonlinear relations of elasticity theory for investigation of the whole deformation process up to buckling in terms of a modified incremental (stepwise) statement of the problem. Examples of solution of particular problems are given.Center for Study of Dynamics and Stability, Tupolev Kazan' State Technical University, Kazan', Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 473–486, July–August, 2000.     

Investigation of the deformation of a rubbery network polymer (SKN-40) in various types of states of stress

From the experimental data on equilibrium uniaxial and nonsymmetrical and symmetrical biaxial tension and pure and mixed shear it follows that the deformation behavior of SKN-40 crosslinked butadiene-nitrile copolymer is more accurately described by the Bartenev-Khazanovich high-elastic potential. The potential of the classical statistical theory of high elasticity of network polymers does not describe different types of states of stress with the same value of the material constant.Lenin Moscow State Pedagogical Institute, Laboratory for Problems in Polymer Physics. Leningrad Branch of the Scientific-Research Institute of the Rubber Industry. Translated from Mekhanika Polimerov, No. 5, pp. 840–845, September–October, 1971.     

3Development of methods of solving nonlinear boundary problems of stability of viscoelastic thin-walled elements

A new numerical method of solving nonlinear boundary problems based on collocational-type approximations is developed with examples of one- and two-dimensional stability problems for a viscoelastic shell. The method allows us to simplify significantly the arithmetization procedure of differential expressions with subsequent efficient computer implementation of the algorithm. A high degree of calculation accuracy is provided. The estimation of the efficiency of the new numerical scheme is obtained by comparing the results with data where the system was modeled using the method of finite differences and the Galerkin method.Rostov State University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 51–58, January–February, 1999.     

Multicritical phenomena in flow of viscoelastic liquids. 1. Zaremba-Fromm-De Witt liquid

It has been shown that multicritical phenomena caused by nonlinearity of viscosity and high elasticity, and forced anisotropy at finite shear rates take place during flow of viscoelastic polymer melts which are isotropic in the resting state. The sign of the low-frequency asymptotic values of the dynamic viscosity and elasticity measured during steady flow is a criterion of the appearance of instability. These arguments are illustrated by the solution and analysis of the complex reaction to low-amplitude, periodic shear of a steady-flowing, very simple viscoelastic liquid — ZFD liquid. It was shown that the instability of viscoelastic liquids for a given steady shear rate is due to the effect of perturbations lasting for no less than some limiting value and its manifestations are caused by superposition of different types of instability — multicritical phenomena.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 555–572, July–August, 1995.The study was conducted based on Topic 93,177 of the Latvian Science Council.     

Comparative analysis of two algorithms for numerical solution of nonlinear static problems for multilayer anisotropic shells of revolution. 1. Account of transverse shear

The discussion focuses on two numerical algorithms for solving the nonlinear static problems of multilayer composite shells of revolution, namely the algorithm based on the discrete orthogonalization method and the algorithm based on the finite element method with a local linear approximation in the meridian direction. The material of each layer of the shell is assumed to be linearly elastic and anisotropic (nonorthotropic). A feature of this approach is that the displacements of the face surfaces of the shell are chosen as unknown functions, i.e., the functions which allows us to formulate the kinematic boundary conditions on these surfaces. As an example, a cross-ply cylindrical shell subjected to uniform axisymmetric tension is considered. It is shown that the algorithms elaborated correctly describe the local distribution of the stress tensor over the shell thickness without an expensive software based on the 3D anisotropic theory of elasticity.Tambov State Technical University, Tambov, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 347–358, May–June, 1999.     

Some laws of the elastic properties of oriented fibrous polymers and fibers

The author considers the results of calculations of the limiting values of the elastic properties (modulus of elasticity and load-extension diagram) of the main types of chemical fibers, using a model with "ideal orientation" of the molecules and the derived laws of deformation of polymer chains. A method is proposed for calculating the elastic properties of "ideally oriented" polymers from the velocity of propagation of an elastic deformation pulse and the effective density of the "skeletons" of the polymer chains. Values of the moduli of elasticity of the amorphous regions of the structure of oriented polymers are calculated. The calculated results are compared with experimental data on the elastic properties of fibers.Mekhanika Polimerov, Vol. 2, No. 1, pp. 34–42, 1966Paper read at the XIV All-Union Conference on High-Molecular Compounds, Oriented State.     

Fundamental theories and methods of polymer mechanics

The fundamental theories and methods of polymer mechanics are analyzed in the light of modern ideas about the structure and mechanical properties of polymers.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 3–13, January–February, 1969.     

Theory of filled polymers and the problem of modifying the structure and properties of polymers with fillers

An attempt is made to explain the effect of fillers on the structure and properties of polymers. The effect of fillers on the state of thermodynamic equilibrium and the stability of polymer structure and properties is also considered.Kiev Shevchenko State University. Translated from Mekhanika Polimerov, No. 6, pp. 1031–1041, November–December, 1970.     

Correspondence principle and the method of approximations for certain nonlinear hereditary media

Problems for two classes of nonlinear hereditary media are reduced by integral transforms to problems of the nonlinear theory of elasticity. An approximation of the elastic solution that makes it possible to solve the formulated problems for nonlinear hereditary materials is demonstrated in the case when the viscoelastic problems reduce to problems of the theory of small elastoplastic strains with active loading.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 66–73, January–February, 1971.     

Sudden buckling of the outer layer of a noncentrally compressed triple-layer rod

The stability of the outer nonmetallic layer of a triple-layer rod with foam core was studied both experimentally and theoretically by the energy balance method. The buckling of the outer layer occurs by a sudden transition to a nonadjacent equilibrium form and this process should be seen in regard to a set of deformational factors.Moscow State University for Ecology and Environmental Studies, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 525–530, July–August, 1996.     

Failure of composite tubes in the Chinese lantern mode under a weight-type load

The failure of unidirectional composite tubes in the Chinese lantern mode is analyzed in the case of a tube compressed by a weight type load, which retains its magnitude after splitting of the tube. Calculation formulas are derived for predicting the critical load. The main regularities of the solution obtained are illustrated with specific examples. It is shown that the nature of the acting load must be considered in the analysis of unidirectional composite tubular bars with axial reinforcement.Bauman Moscow State Technical University, Russia. Scientific Research Institute of Mechanical Engineering, Moscow, Russia. Translated from Mekhanika Komspozitnykh Materialov, Vol. 35, No. 3, pp. 319–324, May–June, 1999.