Influence of vibration on creep in glass-fiber-reinforced plastic in a complex state of stress

The author describes the method and results of tests on tubular specimens of glass-fiber-reinforced plastic for creep under simultaneous torsion (shear in the plane of reinforcement), compression, and vibration in the longitudinal direction. He finds that vibratory creep is not manifested if the amplitudes of the alternating component of the stress are up to 0.1 times the limit of short-term strength and the frequency is 20 kHz.Institute of Mechanics of Polymers, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 358–360, March–April, 1974.     

Winding glass-reinforced plastic rings under programmed tension

The strength, stiffness, and initial stresses of glass-reinforced plastic rings wound under variable tension in accordance with five different programs are considered. The relative thickness of the rings was 0.15–0.20. It is shown that the law of variation of the tension on the tape during winding has an important effect on the investigated parameter.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 361–364, March–April, 1971.     

Shape factor of a specimen in relation to the connection between brittle strength and time

On the basis of the thermal fluctuation theory of brittle fracture of solids an equation is derived for the strength of specimens of various cross-section profile as a function of temperature and time. The theoretical calculations of the shape factor were carried out on a computer.V. I. Lenin Moscow State Pedagogical Institute, Laboratory for Problems in the Physics of Polymers. Translated from Mekhanika Polimerov, No. 1, pp. 157–159, January–February, 1972.     

Diagnostics of the physicomechanical properties of glass textolites in articles of three-layer construction

Possibilities are examined for the diagnostics of some indicators of durability and stiffness of glass textolites in articles of three-layer construction (cemented three-layer combined construction, the two outer layers of which are of glass textolite and the inner layer of which is a foam layer) from a complex of structural parameters and physical characteristics measured directly in the article by nondestructive methods.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 362–364, March–April, 1976.     

Forced Vibration of a Prestretched Two-Layer Slab on a Rigid Foundation

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the forced vibration of a prestretched two-layer slab resting on a rigid foundation is studied. To the upper plane of the slab, a harmonic point force is applied. It is assumed that the layer materials are incompressible, and their elastic properties are characterized by Treloar’s potential. Numerical results are presented for the case where the material stiffness of the lower layer is greater than that of the upper one. The influence of prestretching the layers on the frequency dependences of the normal stresses operating on the interface between the layers and between the slab and the rigid foundation are analyzed.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 335–350, May–June, 2005.     

Rate of resorption of polymeric implants in relation to biological fluid hydrodynamics

The dissociation of water-insoluble macromolecular complexes dissociating with the formation of soluble macromolecules is theoretically examined. The dissociation dynamics in static and open systems are compared (model media and the living organism, respectively). The effect of the rate of metabolic processes and the water-salt balance on the dissociation-association equilibrium in the organism is predicted. The effect of the tension in thread formed from a polycomplex on its life is analyzed for constant and relaxing stress. The use of the theory for predicting the resorption times of polymeric implants (sutures) in the living organism is demonstrated.Paper presented at the First All-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.All-Union Scientific-Research Institute of Medical Polymers, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 740–743, July–August, 1975.     

Scale effect of Young's modulus of highly oriented polymers

The scale effect of the acoustic Young's modulus E of oriented polymer fibers has been experimentally revealed. If the fiber length L is smaller than its critical value L₀, the modulus decreases proportionally to the logarithm of the fiber length. An increasing temperature causes a proportional increase in the slope dE/d(In L). The scale effect is explained by the influence of the specimen volume on the probability of initiation of intense thermal fluctuations, which cause a decline in the Young's modulus.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 839–846, November–December, 1998.     

Ultrasonic determination of the stiffness characteristics of an orthotropic material with imperfect elasticity

The propagation parameters of ultrasonic vibrations in an orthotropic material with imperfect elasticity have been measured. The results of the measurements are used to calculate the complex stiffness characteristics, and the correspondence between the nature of the anisotropy and the adopted model is examined. The anisotropy of the inelastic properties is investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 195–206, March–April, 1973.     

Variant of the variable-modulus theory of elasticity

A variant of the variable-modulus theory — a generalization of the ideas of the classical theory of elasticity in which the observed difference in the moduli of elasticity in uniaxial tension and compression and homogeneous shear is taken into account — is considered. Quasilinear expressions are proposed for the stresses in terms of the strains and the strains in terms of the stresses.Tula Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 363–365, March–April, 1969.     

Statistical theory of defect buildup in composite materials and the scale-factor effect in reliability

A statistical theory of fracture based on the concept of defect buildup is applied to composite materials with a definite fiber orientation. On the premise that the concentration of defects that precede a fracture is sufficiently low, asymptotic distributions of defectiveness are established and asymptotic expressions for the reliability function are derived. It appears feasible to use this theory for predicting the reliability and the scale-factor effect for structures made of oriented composite materials.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 2, pp. 247–255, March–April, 1976.     

Calculation of thin-wall closed profiles of composite materials under a complex loading

Uniclosed caisson structures with deformable perimeters, which are asymmetric in terms of geometry and stiffness and which are subjected to a complex loading (bending in two planes and torsion with respect to the longitudinal axis) are examined in terms of a cylindrical coordinate system Z, S. The possibility of partitioning the general problem of the stress and strain state into elementary problems by fulfilling conditions of orthogonality is demonstrated. The coordinates of the center of rotation are determined. The need for consideration of the deformation of the cross-sectional perimeter, which defines the warping function and normal bitorque stresses under torsion is indicated. The law governing the distribution of tangential stresses, which contains both a constant component that corresponds to Bredt's theory, and also a part corresponding to Vlasov's theory, is derived.Moscow State Aviation Institute (Technical University), Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 349–359, May–June, 1997.     

Small finite deformations of an amorphous polymer material

Small finite deformations of a polymer material are considered. It is assumed that the volume of the specimen is conserved during deformation and that the strains are affine; furthermore, the equilibrium distance between network nodes is not equal to zero in the specimen, and the unit cell of the network is cubic. Various types of deformation are considered. The expressions obtained are compared with the results of the theory of high elasticity and the experimental data.Branch Institute of Chemical Physics, AS USSR, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 997–1001, November–December, 1968.     

Application of number theory in mathematical statistics

Elementary number theory (divisibility theory) is used to prove that, in the case of repeated sampling, when the k-th generalized sample moment is independent of the sample mean then the sampling is normal if the volume of the sample is large and k is a square-free integer which, if it is even, is not of the form 2(2^s +1)).Translated from Matematicheskie Zametki, Vol. 7, No. 4, pp. 383–388, April, 1970.     

Flexible composites, strength, deformation, and fracture processes. 1. Reinforcement structures and tensile strength

Fiber-reinforced flexible composites are extensively used for different kinds of applications, for example, tubes, drive belts, tires, and coated fabrics. Typical for these materials are matrix materials allowing large strain deformation and reinforcement structures allowing bending. Apart from the tensile strength and limited bending stiffness, damage resistance and ductile-brittle transition characteristics are discussed. The tensile strength usually follows the rule of mixture. The mode of fracture and damage resistance, however, strongly depend on penetration of the matrix into the fiber bundles, textile structure, and internal friction. Models for the work of fracture and the ductile-to-brittle fracture transition are discussed.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 747–760, November–December, 1998.     

A method for determining the dynamic Young's modulus of curvilinear specimens

On the basis of a numerical solution of the problem of the natural frequencies of a rod shaped as the are of a circle, the authors suggest a method for determining the dynamic Young's modulus of a curvilinear specimen. They derive an approximate expression suitable for practical use. The results agree well with experiment.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 335–339, March–April, 1974.     

Structural damage accumulation and stable postcritical deformation of composite materials

The macroscopic failure of composite materials is preceded by complex multilevel processes accompanied by accumulation and localization of damaged centers and formation of a failure cluster. Therefore, the study of these mechanisms is one of the basic problems for the mechanics of modern composite materials used in aerospace engineering. The formation of a theory of the stable postcritical deformation of the work-softening media is considered. The pseudo-plastic deformation affected by structural damage of granular composites is investigated within the framework of the considered two-level structurally phenomenological model of heterogeneous media. The stable evolution of the interconnected processes is accompanied by stress redistributions, partial or complete unloading, and strain or damage localization that are one of the main causes of implementation of the postcritical deformation stage. The numerical calculation results of inelastic deformation and failure of the periodic unidirectional fiber-reinforced composites are presented under conditions of the displacement-controlled transverse proportional loading mode. The main mechanisms of the work-softening behavior for the indicated type of materials are described in the macro-homogeneous stress-strain states. Macroscopically, the failure of heterogeneous media as a result of postcritical deformation and the loss of stability of damage accumulation depends on the stiffness of the loading system. When a deformable body is fixed on the closed surface with sufficiently but not infinitely large coefficients of stiffness, it is possible to observe the equilibrium development of the localized volumes of work-softening and damage. The constitutive equations for the work-softening isotropic, transverse isotropic, and orthotropic media are presented. The effect of the loading system on the stability of deformation, damage accumulation, and failure under monotone and nonmonotone triaxial loading was studied. The growth of failure strains with increase in stiffness of the loading system and unequal resistance of heterogeneous body are registered and investigated. A preventive unloading method is offered for the mathematical modeling of the damage accumulation during the testing of the materials on the servo-controlled systems. The displacement-controlled mode is simulated by a series of soft loading and unloading cycles. The detected phenomenon of failure where the unloading leads to stress-strain diagrams with a negative slope of the descending branch was not found either in the displacement or stress-controlled monotone loading mode.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 234–250, March–April, 1998.     

The nature of polymer friction

The evolution of views on the nature of friction in polymers is examined, commencing at 1940 with the publications of Kragel'skii, Tirion, Tabor, Tanaka Kunichiro, Schallamach. The Bartenev molecular-kinetic theory of friction is analyzed in more detail, and the results obtained by its adherents are also presented. Studies on the mechanochemical changes taking place at the frictional contact are discussed. The deduction of formulas is shown for calculating the mechanical and molecular components of the frictional force. To account for the molecular component the concepts of Frenkel as well as Glasstone, Eyring and Polyani have been enlisted.Presented at the Second All-Union Conference on the Mechanics of Polymers, Riga, November, 1971.State Scientific-Research Institute of Mechanical Engineering, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 797–808, September–October, 1972.     

Effect of plasticization on the activation energy of failure of nitrocellulose

The authors investigate the temperature-force dependence of the service life of plasticized nitrocellulose under uniaxial tension. They show that when the plasticizer content of the polymer is sufficiently high, the activation energy U₀ of mechanical breakage is higher than the value for the same polymer without plasticizer. The authors propose the hypothesis that when the plasticizer content of the polymer is increased, an increasingly important part in the development of breakage is played by rupture of the intermolecular bonds and by mutual slippage of the segments of the macromolecules, while the part played by chemical bond rupture decreases.Presented at the Sixth Symposium on the Rheology of Polymers, Moscow, May 1971.D. I. Mendeleev Moscow Chemical Technology Institute. A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 355–358, March–April, 1974.     

Fundamentals of the statistical mechanics of composite systems

Conclusions The proposed variant of the statistical theory of composite media makes it possible to derive relations between the effective parameters of the medium and the dispersion characteristics of the structure, and also to account for the effect of specimen shape and variable structural heterogeneity on these parameters. In the limiting case of an infinitely large specimen, all relationships comply with the results of the traditional theory of composite systems.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 21–30, January–February, 1988.     

Nonstatic solutions of Kazner type in the relativistic theory of gravitation

A nonstatic solution of Kazner type to the system of equations (1)–(2) satisfying all requirements of the relativistic theory of gravitation is constructed.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 173–176, April, 1992.