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.     

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.     

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.     

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 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.     

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.     

Effect of fiber curvature on the modulus of elasticity for unidirectional glass-reinforced plastics in tension

The effect of curvature of the fibers on the modulus of elasticity of unidirectional glass-reinforced plastics (GRP) in tension has been investigated on the basis of the theory of layered reinforced media with random initial irregularities [1,2]. It is shown experimentally that relatively minor distortion of the fibers during manufacture may result in important changes in the modulus of elasticity. A model is proposed for determining the effect of fiber curvature on Young's modulus; experiments on specimens with a given regular fiber curvature indicate good agreement with the theory. The effect of prestressing the fibers on the modulus of elasticity has been studied using commercial AG-4S material and the optimum prestress has been established.Mekhanika Polimerov, Vol. 3, No. 2, pp. 243–249, 1967     

Effect of orientation and molecular weight on the modulus of elasticity of polymer materials

The modulus of elasticity of a perfectly crystalline polymer is calculated as a function of the orientation of the crystallites. The calculations are based on the mechanics of a micro-inhomogeneous continuum. The dependence of the modulus of elasticity on crystallite orientation and molecular weight is calculated with reference to the example of crystalline kapron.Moscow-Lenin Pedagogical Institute. Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1002–1007, November–December, 1968.     

Vibration using for the longitudinal elasticity modulus determination

Longitudinal elasticity modulus, E, is a material specific feature, which,. in general, is establish on the pieces by longitudinal stress. This procedure is possible to apply to the compact material but not to the sintered power parts (or porous material test pieces). For sintered parts, the establishing of Young's modulus, in this paper, it is proposed by transmition of mechanical vibrations along to the test pieces. The test pieces of compact or porous material were strained at longitudinal vibrations. It was establish the linkage between vibration and density, respective between the density and the value of the longitudinal elasticity modulus. Using the test pieces of compact material we realized the methodology to obtain the longitudinal elasticity modulus regarding the compact material, and in this way can be establish the possibility to measure with a good result the longitudinal elasticity modulus for the pieces of sintered powders or of porous material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

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.     

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.     

Stability of the physicomechanical properties of carbon filaments (fibers)

The relationship between the tensile strength and cross-sectional area of high-modulus carbon fibers is examined. An equation is given for the strength of these promising fillers of composite materials; it is shown that the stability of their tensile strength is determined by the average defectiveness of the surface and degree and stretch, as well as variations in these quantities over any particular group of fibers. The elastic modulus and strength of the carbon fibers are related to the degree of stretch.     

Evolution of the Fiber Density in Biological Tissues

An important challenge in the field of biomechanics is to understand and to model the properties of fibrous tissues. We consider a matrix-fiber composite for which the matrix microstructure and its mechanical properties are taken to be constant. The initial fiber distribution is assumed to be unstructured and the mechanical properties of the fibers evolve during deformation. Further we assume that the fiber creation rate is constant while the fiber degeneration is stretch-dependent. In particular, this study investigates the change of the fiber orientation density when a sudden simple shear is applied to the material. The fiber orientation density depends on the current deformation, the history of the deformation, and the deformation state of the fibers at the time of their creation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multifractal Parametrization of the Structure of Deformed Carbon Fibers

Deformed carbon fibers are investigated, and their failure model is proposed based on the Sierpinski set and the hypothesis of two — brittle and viscous — fracture modes, whose existence is confirmed by examples of a correlation between the mechanical strength and elastic modulus of the fibers. For the first time, a multifractal diagram is obtained, which allows one to justify the classification of carbon fibers into brittle and inelastic ones.     

Asymptotic expansion of the solution to the system of elasticity equations with a concentrated pulse force

For the linear system of elasticity equations, we consider the problem of wave excitation by a concentrated pulse force of arbitrary orientation. On assuming that the medium is isotropic and its density and elastic moduli are infinitely differentiable functions constant in some neighborhood of the source point, we write down an asymptotic series for the solution. The coefficients of the series determine the singular component of the solution, as well as the jumps, of the solution and its derivatives, as the characteristic cones are crossed, corresponding to longitudinal and transverse waves.     

Determination of some dynamic characteristics of forming bone callus by the induced vibration method

Conclusions 1. Upon maturation, bone callus not only goes through a series of morphological chantes but also changes in mechanical properties. This is true primarily for an increase in the elasticity modulus.2. The specific energy of dispersion and loss modulus have maxima which occur after 25 to 30 days. This behavior is apparently related to the fact that bone callus at this period has the nature of spongy bone tissue. For compact bone tissue, on the other hand, these values are equal to zero.3. The area of the hysteresis loop is almost completely independent of the frequency upon cyclic stressing.4. The elasticity modulus is proportional to the x-ray density of the samples, which thus may serve as an objective criterion of the degree of maturity of callus.Smolensk State Medical Institute. Translated from Mekhanika Polimerov, No. 5, pp. 896–900, September–October, 1977.     

Small deformations of oriented polymers

On the basis of a phenomenological analysis of the temperature dependence of the modulus of instantaneous elasticity and the stress relaxation process, it is suggested that in the region of small deformations there are no breakages of the macromolecules that might affect the elasto-relaxational behavior of highly oriented polymers (fibers) as in the region of large deformations. To judge from the values obtained for the energy constants, these properties are determined by the number of intermolecular bonds in the amorphous regions (modulus of instantaneous elasticity) and the physical events associated with the reorganization of these bonds and hindered rotation of the chain units (relaxation process).S. M. Kirov Leningrad Institute of Textiles and Light Industry. Translated from Mekhanika Polimerov, No. 6, pp. 976–980, November–December, 1971.     

Computation of the Coupled Dynamics of Fibers in a Spray

The PUR-fiber-spray molding technology is a manufacturing process which produces polyurethane-based (PUR) composites by spraying the matrix together with reinforcing fibers in a tool form or on a substrate. Thereby chopped fibers are laterally (sidewise) injected in the polyurethane-air spray cone for wetting before the entire composite is spread on the substrate, where it starts curing. To investigate and compute the fiber orientation and density distribution in the final composites manufactured by this process, a new approach simplifying the multiply coupled interaction of the three phases is presented in this paper. Hereby it is presumed that the final position and orientation of a fiber on a substrate results from its dynamics and coupled interactions with air, PUR-droplets and other fibers within the spray cone. Thus, a model of the process is built, that computes the transient behavior of the air-liquid droplets mixture by the CFD code ANSYS Fluent and its influence on the dynamics of the fibers by an extra code called FIDYST. For this multiphase problem two approaches are presented for the droplet-fiber coupling using a concept called “homogenization” of the liquid phase (droplets in the continuous phase). (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)