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.     

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.     

Analysis of stresses in an infinite elastic body with a locally curved covered nanofiber

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional geometrically nonlinear exact equations of the theory of elasticity, the method developed for determining the stress distribution in nanocomposites with unidirectional locally curved covered nanofibers is used to investigate the normal stresses acting along nanofibers. The investigation is carried out for an infinite elastic body containing a single locally curved covered nanofiber in the case where there exists a bond covering cylinder of constant thickness between the nanofiber and the matrix material. It is assumed that the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. Upon formulation and mathematical solution of the boundary value problem, the boundary form perturbation method is used. Numerical results for the stress distribution in the body and the influence of geometrical nonlinearity on this distribution are presented and interpreted.     

Natural vibrations of a strip made of a composite material with a locally curved structure

The possibility of using the finite-element method for investigating two-dimensional problems on natural vibrations in the mechanics of composite materials with curved structures is considered. With the example of a hinge-supported strip made of a composite material with a locally curved structure, the influence of geometrical and mechanical parameters of the strip on its eigenfrequencies is examined. It is established that the presence of local curving in the structure of strip material decreases the magnitude of eigenfrequencies.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 71–78, January–February, 2005.     

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.     

Stress distribution in an infinite elastic body containing two neighboring locally curved fibers

A method is developed for analyzing the stresses in an infinite elastic body containing two neighboring inphase locally curved fibers located along two parallel lines. The body is loaded at infinity by uniformly distributed nor mal forces in the direction of fibers. The investigation is carried out within the frame work of a piecewise homogeneous body model with the use of the three-dimensional ex act equations of the elasticity theory. Numerical results for stress distributions in the body and for the influence of interaction between fibers on these distributions are given. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 457-478, May-June, 2009.     

Investigation of the fiber packing density in a unidirectional composite

Recommendations are made for designing a unidirectional composite with an optimal arrangement of the fibers. The effect of the fiber diameter distribution law on the packing density is investigated.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow. Moscow Institute of Electronic Machine-Building. Translated from Mekhanika Polimerov, No. 3, pp. 538–541, May–June, 1976.     

Effect of the structure of a fibrous layer on its permeability for a nonlinearly viscous fluid

The solution of the problem of the percolation of a nonlinearly viscous (with a power flow law) fluid through unit cells is used to find the dependence of the permeability coefficient of a unidirectional layer of fibers on fiber concentration, parameters characterizing the location of the fibers, and the parameters of the fluid (the exponent in the flow law) for random and regular fiber configurations in the transverse plane. It is established that the degree of nonuniformity of the pore space of the layer has a significant effect on its permeability and that this effect increases with an increase in the nonlinearity of the fluid. Data from a model experiment and computer simulation are used to describe the mechanism of transformation of the pore space by the fluid front. It is shown that consolidation of the layer also affects its permeability.Belarus State Technological University (Minsk, Belarus). Translated from Mekhanik Kompozitnykh Materialov, Vol. 33, No. 4, pp. 554–563, July–August, 1997.     

Propagation of acoustic waves in a fibrous fluid-filled material

The homogenization method is used for the analysis of acoustic wave propagation in a unidirectional fibrous material for the acoustic control of the fiber arrangement in manufacturing composites. Acoustic equations for a rigid periodic structure filled by a nonviscous fluid are obtained by two-dimensional asymptotic expansions. A regular square and triangular arrangement of the fibers with a round cross-section are considered. The analysis reveals that the velocity of acoustic waves is significantly affected by both the volume content and the fiber arrangement.Moscow State Academy of Chemical Engineering, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 651–655 September–October, 1997.     

Stress distribution in an infinite elastic body with a covered periodically curved fiber

Within the frame work of a piecewise homogeneous body model, with the use of the three-dimensional geometrically nonlinear exact equations of elasticity theory, a method is developed for determining the stress distribution in unidirectional fibrous composites with periodically curved fibers. The distribution of the normal and shear stresses acting on interfaces for the case where there exists a bond covering cylinder of constant thickness between the fiber and matrix is considered. The concentration of fibers in the composite is assumed to be low, and the interaction between them is neglected. Numerous numerical results related to the stress distribution in the body considered are obtained, and the influence of geometrical nonlinearity on this distribution is analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 269-288, March-April, 2009.     

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.     

Determination of adhesive strength in a thermoplastic-resin-thin-fiber system

Conclusion A method was developed for determining adhesive strength in thermoplastic-material—thin-fiber systems formed from a melt. Values of _o were determined for joints between PSF and PC On the one hand and high-modulus organic fibers on the other hand. We studied the dependence of the bond strength on the temperature at which the contact is formed, the area of the contact, and the condition of the surface. The adhesion of PC and PSF to organic polyamide fibers is good enough to make it unnecessary to develop adhesives or specially modify the fiber surfaces for the production of organic-fiber-reinforced plastics. The low shear strength of laminated plastics based on thermoplastic resins is evidently due to the small area of actual contact, which is in turn a consequence of the poor wetting and impregnation of the fiber filler by the melt.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 9–12, January–February, 1990.     

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.     

Strength and deformability of reinforced polymers in tension normal to the fibers

The strength and deformability of reinforced polymers in tension across the fibers is investigated. It is assumed that the polymer deforms as an ideal elastoplastic body. Relations are obtained for the nature of the deformation of the polymer between the fibers and the strength and deformability of the composite with allowance for the structural distribution of the components. Theoretical stress-strain diagrams are presented for composites with different reinforcement densities and resin elasticities. The theoretical values of the strength and deformation of reinforced polymers with the load applied across the fibers are compared with the results of experiments on model specimens of epoxy-Thiokol polymers.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 4, pp. 682–687, July–August, 1970.     

A note on the characteristic classes of non-positively curved manifolds

In this expository note, we give a simple conceptual proof of the Hirzebruch proportionality principle for Pontrjagin numbers of non-positively curved locally symmetric spaces. We also establish (non)-vanishing results for Stiefel–Whitney and Pontrjagin numbers of (finite covers of) the Gromov–Thurston examples of compact negatively curved manifolds. A byproduct of our argument gives a constructive proof of a well-known result of Rohlin: every closed orientable 3-manifold bounds orientably. We mention some geometric corollaries: a lower bound for degrees of covers having tangential maps to the non-negatively curved duals and estimates for the complexity of some representations of certain uniform lattices.     

Effect of fiber length on the strength and fracture properties of a fiber-filled silicone composite

The mechanism by which fillers strengthen polymers is discussed, and the effect of fiber length on static and impact bending strength and on the area of the fracture surface is studied with reference to the example of a silicone composite. A correlation is established between the strength properties and the area of the fracture surface. On the basis of the data obtained it is shown that, as the fiber length increases, the fracture mechanism changes from extraction of the ends of the fibers along the fracture path to breakage of the fibers.Moscow Lomonosov Institute of Fine Chemical Technology. Ter-Gazaryan State Scientific-Research Planning Institute of Polymer Adhesives, Kirovakan. Translated from Mekhanika Polimerov, No. 3, pp. 445–449, May–June, 1971.     

Stress analysis for a rectangular thick plate of a composite material with a spatially locally curved structure under forced vibration

Natural and forced vibrations of a thick rectangular plate fabricated from a composite material with a spatially locally curved structure are investigated with the use of exact three-dimensional equations of motion of the theory of elastic anisotropic bodies. The investigations are carried out within the framework of the continuum approach developed by Akbarov and Guz. It is supposed that the plate is clamped at all its edges and is loaded on the upper face with uniformly distributed normal forces periodically changing with time. The influence of the parameters of local curving on the fundamental frequency of the plate and on the distribution of the normal stress acting in the thickness direction under forced vibration is studied. The corresponding boundary-value problems are solved numerically by employing the three-dimensional FEM modelling.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 779–790, November–December, 2004.     

Thermoelastic expansion of spherical fiber composites

A refined solution is constructed for thermoelastic expansion of spherical fiber composites with a three-dimensional structure on the basis of existing hypotheses about the longitudinal state of fibers in a matrix strengthened with spherical inclusions. Relationships defining the dependence in explicit form of thermoelastic coefficients on structural parameters are obtained in analytical form. Thermal expansion coefficients for composites with cubic symmetry are discussed in detail.Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 251–257, March–April, 1997.     

Comparative analysis of the structural order and defectiveness of reinforcing fibers on the basis of normalized values of mechanical properties

Experimental data on mechanical properties referred to their limiting values for a flawless polymer crystal with long molecular chains is used in a comparative analysis of the degree of ordering of the structure (crystallinity, orientation) and the defectiveness of the reinforcing fibers. The actual elastic moduli and limiting (theoretical) elastic modulus are used to obtain coefficients that characterize the overall order of the structure of the fibers but are independent of their defectiveness. Values of true strength in tension and the limitingly attainable or theoretical strength are used to calculate conditional coefficients that depend both on the overall order and the defectiveness of the fiber structure. The difference in the coefficients makes it possible to detect dangerous local defects that lead to fiber failure. Results are presented from calculations for more than 20 types of reinforcing fibers. Despite the approximate nature of these representations, the data that is obtained permits comparisons of different types of fibers, characterization of their quality, and evaluation of the degree of perfection of the fiber production technology.Paper presented at the IX International Conference on the Mechanics of Composite Materials, Riga, October, 1995.St. Petersburg State University for Technology and design, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 444–453, July–August, 1996.     

Variation in angles between fibers in forming articles from unhardened composite materials

Conclusion The Gaussian curvature of the surface and the geodesic curvatures of the reference filaments of the fabric exerts a significant influence on the interfilament angles of the base fabric of composites formed to a surface. It is demonstrated that the lines of constant grid angle in the coordinates of the plane fabric are close to hyperbolas, while the optimum layout of the base fabric of the composite material in the sense of least fiber disorientation is that layout for which the lines of the seams intersect the fibers of the fabric at an angle of 45 °.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 138–142, January–February, 1991.