Determination of the modulus of elasticity of the amorphous regions of chemical fibers

A method of calculating the orientation index and modulus of elasticity of the elements of a two-phase fiber model is presented. The effect of orientational drawing on the variation of these characteristics has been investigated for nylon [capron] fibers.Mekhanika Polimerov, Vol. 3, No. 3, pp. 409–412, 1967     

Investigation of the stability of the physicomechanical properties of carbon fibers 1. Dependence of Young's modulus on the cross-sectional area of the fiber

The modulus of elasticity in tension and the density of various carbon fibers (re-inforcement for high-modulus carbon-reinforced plastics) have been studied. There is an experimentally confirmed dependence of the modulus of elasticity on the orientation and density of the monofilament which explains the variation of this characteristic in a fiber bundle. It is shown that the principal factor determining the modulus of elasticity and its stability in a bundle of carbon fibers is the orientation and its variation for the individual fibers.     

Non-uniformly scaled buckling modes of reinforcing elements in fiber reinforced plastic

We consider a problem about non-uniformly scaled buckling modes of isolated fiber (without accounting of interaction with the surrounding epoxy) or bundle of fibers, which are structural elements of fiber reinforced plastics under the transverse tension (compression) and shear stresses in prebuckling state. Such initial state is formed in fibers and bundles of fibers at tension-compression tests of flat specimens from cross ply composites with unidirectional fibers. For problem statement we use equations recently constructed by reduction of consistent version of geometrically nonlinear equations of theory of elasticity to one dimensional equations of rectilinear beams. Equations are based on refined shear S. P. Timoshenko model with accounting of tension-compression stresses in transverse directions. We give theoretical explanation of developed phenomenon as reducing shear modulus of elasticity of fiber reinforced plastic during the increasing of shear strains. We show that under the loading process of specimens under review uninterruptedly structure reconstruction of composite trough implementation and uninterruptedly changing of internal buckling modes at changing wave parameter is feasible.     

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.     

Effect of thermal treatment temperature on the structure and properties of carbon fibers

Conclusions 1. It has been shown that the presence of a maximum in the dependence of strength on Young's modulus for carbon fibers made from PAN fiber may be explained by an effect of the process of temperature stress accumulation which takes place under the conditions of isometric heating. The start of this process, which causes a rearrangement of the internal structure of the high-modulus fiber, coincides with the start of the anomalous rise in fiber density.2. The interconnection between surface and internal defects and the elastic-strength properties of carbon fibers made in the temperature treatment range 600–3000°C has been studied.3. Original data on the elastic-strength properties of borided carbon fibers have been obtained; the structure of these is marked by a high degree of perfection. It has been shown that in boriding, which facilitates graphitization of the carbon, the process of regular reduction in fiber strength which is reached in the precrystallization stage is somewhat retarded.All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1036–1042, November–December, 1976.     

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.     

Effectiveness of using hollow fibers to improve the rigidity of glass-reinforced plastics

Calculated and experimental relations between the modulus of elasticity and rigidity of unidirectional glass-reinforced plastics (GRP) and the capillarity coefficient of the hollow fiber reinforcement are presented. It is established that in calculating the flexural rigidity ratio of hollow- and solid-fiber GRP specimens of equal weight it is not permissible to neglect the mass and modulus of elasticity of the resin. The potentialities of hollow fibers as reinforcement for GRP shells subjected to external pressure are demonstrated.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fibers, Moscow Region. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 672–676, July–August, 1968.     

Investigation of the modulus of elasticity of carbon fibers

A simplified analysis of the dependence of the elastic properties and electrical conductivity of a carbon fiber on its orientation index is presented. The experimentally confirmed inverse correlation between the electrical resistivity and the speed of sound makes it possible to calculate the modulus of elasticity of carbon fibers from data on the bulk resistivity.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 5, pp. 846–850, September–October, 1971.     

Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 433–448, July–August, 2005.     

Stress Distribution in an Elastic Body with a Periodically Curved Row of Fibers

Within the framework of a piecewise homogeneous body model, with the use of exact three-dimensional equations of elasticity theory for anisotropic bodies, a method is developed for investigating the stress distribution in an infinite elastic matrix containing a periodically curved row of cophasal fibers. It is assumed that fiber materials are the same and fiber midlines lie in the same plane. The self-balanced stresses arising in the interphase in uniaxial loading the composite along the fibers are investigated. The influences of problem parameters on these stresses are analyzed. The corresponding numerical results are presented.     

Investigation of the dynamic characteristics of composites

The dynamic characteristics E and G and the damping capacity δ* of polymeric resins and composites based on glass, carbon, and boron fibers have been investigated. It is shown that the mechanical losses are correlated with the modulus of elasticity and the shear modulus of the resin and composites with different types of reinforcement. The vibrational strength of various structural materials is estimated.     

Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli

The model of the equations of generalized magneto-thermoelasticity with two relaxation times in an isotropic elastic medium under the effect of reference temperature on the modulus of elasticity is established. The modulus of elasticity is taken as a linear function of reference temperature. Reflection of magneto-thermoelastic waves under generalized thermoelasticity theory is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid in a vacuum. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained. Similarly, the reflection coefficients ratios variations with the angle of incident under different conditions are shown graphically. A comparison is made with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature.     

Structural changes in a cotton fiber under load

Mechanical tests and x-ray studies have shown that a shift of the meridional reflection towards smaller angles signifies the stretching of the crystallite lattice in the meridional direction. The shift has been used to determine the modulus of elasticity of the crystal lattice of cotton. The microdeformation (of the crystal lattice) and the macrodeformation (extension of the specimen as a whole) are compared. The modulus of elasticity of the crystal lattice is an order greater than that of the fiber itself.V. I. Lenin Tadzhik State University, Dushanbe. Translated from Mekhanika Polimerov, No. 4, pp. 594–598, July–August, 1973.     

Compression tests on composite tubes

The possibility of determining the modulus of elasticity, Poisson's ratio, and compressive strength across the fibers of a unidirectional composite by means of compression tests on cross-wound tubes is examined. By analyzing the Leknitskii [3] solution for the case of a transversely isotropic cylinder it is shown that only the modulus of elasticity can be reliably determined in this way. The conclusions are confirmed by experimental data obtained by testing glass-reinforced plastic tubes.     

Elastic characteristics of graphitoplastics and impregnated graphites

The effect of aging on the moduli of elasticity of graphitoplastics and resin-impregnated graphites has been directly investigated. The dependence of the modulus of elasticity in tension and compression on the normal stress in the specimen cross section has been studied for the same materials.Novocherkassk Sergo Ordzhonikidze Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1127–1130, November–December, 1970.     

Influence of the Interaction between Two Neighboring Periodically Curved Fibers on the Stress Distribution in a Composite Material

A method is developed for a stress analysis in an infinite elastic body containing two neighboring periodically cophasaly curved fibers located along two parallel lines. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. The investigation is carried out within the framework of a piecewise homogeneous body model with the use of exact three-dimensional equations of elasticity theory. Numerical results related to the stress distribution considered and the influence of interaction between the fibers on this distribution are given.     

Possibilities of a nondestructive one-parameter method of checking the strength of anisotropic glass-reinforced plastics in uniaxial compression

A nondestructive method of checking the strength of glass-reinforced plastics (GRP) in finished products is proposed. This method is based on the correlation, investigated by the authors, between the modulus of elasticity and the compressive strength determined by a standard method. Various orientations in the plane of reinforcement of glass-reinforced plastics with different ratios of the orthogonally arranged fibers are investigated. It is proposed to determine the modulus of elasticity from the propagation velocity of an ultrasonic pulse measured under conditions of one-sided access to the surface of the product."Ritm" Research-Production Association, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 909–919, September–October, 1974.     

Transverse compression of PPTA fibers

Results of single transverse compression testing of PPTA and PIPD fibers, using a novel test device, are presented and discussed. In the tests, short lengths of single fibers are compressed between two parallel, stiff platens. The fiber elastic deformation is analyzed as a Hertzian contact problem. The inelastic deformation is analyzed by elastic-plastic FE simulation and by laser-scanning confocal microscopy of the compressed fibers ex post facto. The results obtained are compared to those in the literature and to the theoretical predictions of PPTA fiber transverse elasticity based on PPTA crystal elasticity.Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).3TEX, Inc. 109, MacKenan Drive, Cary, North Carolina 27511, USA. Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 533–544, March–April, 2000.     

Experimental evaluation of the effect of prestressing the fibers in two directions on certain elastic characteristic of woven-glass reinforced plastics

The effect of prestressing the reinforcing fibers in either of two mutually perpendicular directions on the elastic characteristics of woven-glass reinforced plastics has been experimentally investigated. It is shown that an increase in the elastic characteristics in the prestress direction is accompanied by a decrease in the direction at right angles. Applying the same prestress in both directions considerably improves the moduli of elasticity (E_x, E_y). The possibility of using Bolotin's theory [1] and the relations proposed in [4, 6] to estimate the effect of regular distortions of the fibers on the elastic moduli of woven-glass reinforced materials is examined.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 859–863, September–October, 1968.     

Stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers in a composite material

In the present paper, within the framework of a piecewise homogenous body model, with the use of the exact three-dimensional equations of elasticity theory, a method proposed earlier is developed for investigating the stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers located along two parallel planes in an infinite elastic body. The body is loaded at infinity by uniformly distributed normal forces in the direction of fiber location. The self-equilibrated normal and shear stresses caused by the curved fibers are analyzed, and the influences of interaction between the fibers and of the geometric nonlinearity on the distribution of these stresses are studied. Numerical results for this interaction are obtained.