Effect of curvature of the reinforcement on the mechanical and thermophysical properties of a composite

The elastic constants and thermal expansion coefficients of a composite consisting of a matrix with low elastic properties and exceptionally stiff fibers have been experimentally determined. The curvature of the reinforcement in the specimens has been investigated. The results of the experiments are compared with the corresponding theoretical characteristics. The calculations are based on a model with an ideal arrangement of the fibers [4] and a model that takes the curvature of the reinforcement into account [5, 6].Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1036–1039. November–December, 1971.     

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 curvature of the reinforcing fibers on the moduli of elasticity and strength of composites

The curvature of the reinforcing fibers of a composite material is taken into account by determination of the change in wave amplitude due to radial forces. Three ideal cases of unidirectional fiber distribution and two cases of two-way fabric reinforcement are considered.Mekhanika Polimerov, Vol. 4, No. 2, pp. 314–321, 1968     

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.     

Effect of curvature of the fibers on the elastic properties of unidirectionally reinforced plastics

An approximate method is proposed for determining the reduced elastic constants of reinforced plastics (glass-reinforced plastics) with allowance for the curvature of the reinforcing fibers. All the conclusions relate to plane stress. The results of model tests are presented as confirmation of the theoretical conclusions.Mekhanika Polimerov, Vol. 3, No. 5, pp. 858–863, 1967     

The Harnack Estimate for the Yamabe Flow on CR Manifolds of Dimension 3

We deform the contact form by the amount of the Tanaka–Webstercurvature on a closed spherical CR three-manifold.We show that if a contact form evolves with free torsion from initial datawith positive Tanaka–Webster curvature, then a certainHarnack inequality for the Tanaka–Webster curvature holds.     

Effect of temperature on the mechanical properties of boron fibers

The effect of exposure to temperatures on the interval 20–600°C for up to 1000 h on the physicomechanical properties of boron fibers at room temperature has been investigated. Prolonged exposure to temperatures up to 200°C does not have much effect on the mechanical characteristics of the fibers, whereas heating for one hour at 300–350°C increases the strength of the fibers by 10–12%.All-Union Scientific Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 329–332, March–April, 1971.     

A Cartan–Hadamard Theorem for Banach–Finsler Manifolds

In this paper we study Banach–Finsler manifolds endowed with a spray which have seminegative curvature in the sense that the corresponding exponential function has a surjective expansive differential in every point. In this context we generalize the classical theorem of Cartan–Hadamard, saying that the exponential function is a covering map. We apply this to symmetric spaces and thus obtain criteria for Banach–Lie groups with an involution to have a polar decomposition. Typical examples of symmetric Finsler manifolds with seminegative curvature are bounded symmetric domains and symmetric cones endowed with their natural Finsler structure which in general is not Riemannian.     

Effect of residual stresses on the strength of oriented glass-reinforced plastics

The effect of structural residual stresses on the strength of a glass-reinforced plastic loaded along and across the fibers is investigated. It is established that the residual stresses lead to an increase in the strength of the glass-reinforced plastic across the fibers and to cracking of the polymer matrix in tension along the fibers, but have practically no effect on the combined deformation of the matrix and the fibers in compression.Moscow Ordzhonikidze Aviation Institute. Translated from Mekhanika Polimerov, No. 3, pp. 475–480, May–June, 1969.     

The Yamabe Problem and Applications on Noncompact Complete Riemannian Manifolds

We let (M,g) be a noncompact complete Riemannian manifold of dimension n 3 whose scalar curvature S(x) is positive for all x in M. With an assumption on the Ricci curvature and scalar curvature at infinity, we study the behavior of solutions of the Yamabe equation on –u+[(n–2)/(4(n–1))]Su=qu ^{(n+2)/(n–2)} on (M,g). This study finds restrictions on the existence of an injective conformal immersion of (M,g) into any compact Riemannian n -manifold. We also show the existence of a complete conformal metric with constant positive scalar curvature on (M,g) with some conditions at infinity.     

Riemannian Geometry of Conical Singular Sets

In this paper, we study a class of singular Riemannian manifolds. The singular set itself is a smooth manifold with a cone-like neighborhood. By imposing a reasonable convergence condition on the metric, we can determine the local geometrical structure near the singular set. In general, the curvature near the singular set is unbounded. We prove that a bounded curvature assumption would have a strong implication on the geometrical and topological structures near the singular set. We also establish the Gauss–Bonnet–Chern formula, which can be applied to the study of singular Eistein 4-manifolds.     

Hyperbolic Manifolds, Harmonic Forms, and Seiberg–Witten Invariants

New estimates are derived concerning the behavior of self-dual harmonic 2-forms on a compact Riemannian 4-manifold with nontrivial Seiberg–Witten invariants. Applications include a vanishing theorem for certain Seiberg–Witten invariants on compact 4-manifolds of constant negative sectional curvature.     

Strength of boron fibers

The tensile and flexural strength and elastic properties of continuous boron fibers 95–105 µ in diameter obtained by depositing boron on a tungsten filament 10–12 µ in diameter have been investigated. The strength properties are primarily determined by the defects present at the boron sheath-core interface and for the fibers investigated have a limit of approximately 400 kgf/mm². Coarse surface or internal defects are capable of reducing the strength of the fibers to 200–250 kfg/mm².All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1126–1127, November–December, 1970.     

The Topoligical Sphere Theorem for Complete Submanifolds

A topological sphere theorem is obtained from the point of view of submanifold geometry. An important scalar is defined by the mean curvature and the squared norm of the second fundamental form of an oriented complete submanifold Mn in a space form of nonnegative sectional curvature. If the infimum of this scalar is negative, we then prove that the Ricci curvature of Mn has a positive lower bound. Making use of the Lawson–Simons formula for the nonexistence of stable k-currents, we eliminate Hk (Mn, Z) for all 1 ` k ` n – 1.We then observe that the fundamental group of Mn is trivial. It should be emphasized that our result is optimal.     

Superrigidity for homomorphisms into isometry groups of CAT(−1) spaces

CAT(–1) spaces are generalizations of manifolds with negative curvature. In this paper, we prove three types of rigidity results related to CAT(–1) spaces, namely the rigidity of the isometric actions on CAT(–1) spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles. The main idea for our approach relies on a study of the boundary theory we established for the general CAT(–1) spaces.     

Low-frequency internal friction in complex composite strands

Conclusion A method was proposed which makes it possible to study the low-frequency internal friction of complex fibers. This method was used to study the internal friction of complex composite fibers based on PCA and PE. We observed a relaxation process which is typical of the composite and is absent in the pure materials.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 11–15, January–February, 1989.     

Riemannian manifolds with a generalized axiom of planes

This paper introduces a class of Riemannian manifolds satisfying the axiom of (l, s)-planes that is a generalization of Cartan's axiom of p-planes. The structure of the curvature and Riemannian metric of a manifold with the axiom of (n – 2, n – 1)-planes is established.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 103–110, 1992.     

Realization of the mechanical properties of fibers in high-modulus polymer composites

The effect of scatter in the strength and deformation properties of the high-modulus fibers, the degree of twist, and the presence of pores in the polymeric matrix on the degree of realization of the potential possibilities of these fibers in composite materials is briefly considered.All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1123–1125, November–December, 1972.     

Regulation of the mechanical properties of thermoplastic carbon fiber-reinforced plastics by changing their production conditions and surface treatment of the fibers

The effect of technological parameters of processing and surface treatment of carbon fibers on the mechanical properties of carbon fiber-reinforced plastics (CFRPs) was investigated. The copolymer of 1,3,5-trioxane with 1,3-dioxolane was used as the polymer matrix, and medium-modulus hydrated cellulose Ural LO-24 carbon fibers served as the reinforcing filler. The polymer matrix was mixed with the carbon fibers by the method of combined extrusion. The dependence of the mechanical properties of CFRPs on the technological parameters of screw-disk extrusion was studied. It was found that the properties of the composites were greatly affected by the size of the working disk gap, the disk rotation rate, and the temperature in the zone of normal stresses. The surface of the carbon fibers was activated with atmospheric oxygen in the temperature range of 450–600°C, with mass loss of the fibers no greater than 3–4%. A 30–40% increase in the mechanical properties of the CFRPs was achieved. A decrease in the melt index of the 1,3,5-trioxane copolymer with 1,3-dioxolane reinforced with oxidized carbon fibers was observed, which should be taken into account in processing the composites into products. Introduction of carbon fibers in the 1,3,5-trioxane copolymer with 1,3-dioxolane allows us to increase the wear resistance and decrease the friction coefficient, which makes it possibile to use these materials in the friction units of machines and mechanisms, such as plain bearings, gears, and flange packings.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian State University of Chemical Technology, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 673–682, September–October, 1998.     

Choice of optimal structure of glass laminates with random reinforcement. I

The effect of structural parameters — length, diameter, and distribution of the reinforcing elements — on the mechanical characteristics of glass-reinforced plastics is investigated with reference to the case of glass laminates with randomly distributed, straight, uncut glass fibers in parallel planes. It is shown that the reduced strength of these laminates as compared with unidirectional material is associated with the redistribution of the load between the fibers and the resin and the relative reduction in the number of fibers in the cross section. A formula is proposed for estimating the strength of glass-reinforced plastics with a random distribution of the fibers in parallel planes.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow Region. Moscow Bauman Higher Technical College. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1043–1050, November–December, 1968.