Elastic constants of glass-reinforced plastics with anisotropic structure

The macroscopic elastic constants of plastics reinforced in one direction are calculated by solving the statistical boundary value problem of the theory of elasticity. The results obtained and the method proposed in [15] are used to compute the macromoduli of GRP with an anisotropic layered structure created by an orthogonal arrangement of unidirectional tapes and to compute the moduli of elasticity of a unidirectional layered material with random deviations of the layers from the direction of preferred orientation.V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR, Sverdlovsk Branch. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 631–637, July–August, 1968.     

Effect of the arrangement of the reinforcement on the stability of circular,cylindrically orthotropic plates with low shear strength

The Bubnov-Galerkin method is used to find the critical loads for cylindrically orthotropic circular continuous and annular plates with different edge conditions in axisymmetric buckling. The effect of the ratio of the Young moduli in the circumferential (E) and radial (E_r) directions and the ratio of E to the interlaminar shear modulus G_rz is investigated. The results are in qualitative agreement with the experimental data of [13].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 275–283, March–April, 1971.     

Composites reinforced with a system of three straight mutually orthogonal fibers

The effectiveness of reinforcement in direction 3 has been estimated by investigating the mechanical characteristics of two types of three-dimensionally reinforced materials differing with respect to the arrangement of the reinforcement and the fiber content in each direction. The superior transverse stiffness, shear strength, and transverse tensile strength of three-dimensionally reinforced composites based on a system of three mutually orthogonal fibers, as compared with laminated materials, is demonstrated. The theoretical values of the elastic constants, calculated from the relations of [5], are compared with the experimental data.For communication 1 see [5].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1011–1018, November–December, 1973.     

Determination of the elastic moduli of reinforced materials

A method is proposed for determining the elastic moduli of reinforced materials at arbitrary concentrations of the components. The method is based on the successive symmetrization of the frequency function of the moduli of the component elements of a two-component material with subsequent application of the correlation theory [1]. Algorithms are constructed for determining the elastic moduli of layered, fibrous, and granular materials and typical calculations are presented.Mekhanika Polimerov, Vol. 4, No. 1, pp. 78–85, 1968     

Bending of prestressed glass-reinforced plastic beams

Initial waviness of the fibers and prestressing are investigated in relation to their effect on flexural stiffness and strength for beams with low shear strength. It is shown that prestressing the reinforcement increases the flexural stiffness but at the same time adds to the shear correction as a result of an increase in the modulus of elasticity E_x in the direction of reinforcement and the insensitivity of the shear modulus G_xz to prestress. It is established that prestressing increases the shear strength and the degree of anisotropy . Materials of two types are investigated: unidirectional (AG-4S) and cloth-reinforced (SKT-11).Mekhanika Polimerov, Vol. 3, No. 5, pp. 888–893, 1967     

Structural characteristics of materials reinforced with high-modulus fibers

Research on the mechanics of boron and carbon-reinforced plastics is briefly reviewed. The design and testing characteristics of these materials associated with the high degree of anisotropy of their elastic properties, as compared with those of glass-reinforced plastics, are discussed. Problems relating to testing at an angle to the direction of the reinforcement, the effect of misorientation and distortion of the fibers, and the consequences of the low shear strength are considered. Experimental confirmation has been obtained by testing unidirectional (1 : 0), orthogonally reinforced (1 : 1 and 2 : 1), and tridirectional (1 : 1 : 1 in the 0°, +60°, and –60° directions) boron and carbon-reinforced plastics.DeceasedInstitute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 676–685, July–August, 1971.     

Numerical model of one possibility of determining the tensor of elastic constants of an anisotropic body

An algorithm for a digital computer is presented which permits calculating the tensor of the elastic constants of a material with any given symmetry on the basis of experimentally measured Young moduli and Poisson ratios for several specimens oriented in unequivalent crystallographic directions. The results of determining the components of the tensor of elastic constants by means of it for a modification of orthotropic reinforced plastic are also given.Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 436–442, May–June, 1973.     

Carrying capacity of rings formed by winding composites with high-modulus anisotropic fiber reinforcement

The characteristics of composites associated with the essential anisotropy of the reinforcing fibers are studied. The effect of distortion and pretensioning of the reinforcement on the axisymmetricity of the strain field, the moduli of elasticity, and the strength in the direction of the fibers under external and internal pressure are investigated with allowance for the high compliance of the material in the transverse direction. Numerical estimates are obtained for the moduli of elasticity E and E_r, expansion coefficient and _r, and initial temperature stresses _r ⁰ and ⁰ for a model material. The dependence of the bursting pressure on the thickness of the rings is described and strength criteria are formulated. In all the problems considered it is necessary to make allowance for the high compliance of the composites in the transverse direction.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 673–683, July–August, 1973.     

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 reinforcement on the stress relaxation and creep ofelasto-hereditary materials

The elastic moduli of a reinforced material are calculated. The reinforcing fibers are assumed to be elastic and isotropic and the polymer matrix isotropic and elasticoviscous. It is further assumed that in the latter case the hereditary properties are described by a linear integral shear modulus operator with a fractional-exponential kernel. The changes in the relaxation and retardation times due to the correlations between inhomogeneities are estimated.Moscow Institute of Electronics Engineering. Translated from Mekhanika Polimerov, No. 3, pp. 470–474, May–June, 1969.     

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.     

Combined bending and compression of circular cylindrically orthotropic plates with low shear strength

Equations are derived for the combined bending and compression of cylindrically orthotropic plates with allowance for shear and without postulating a shear distribution lawf/it(z). Solutions of the equations obtained are given for various boundary conditions. The error introduced by postulating the distribution lawf/it(z) is estimated. The effect of the ratio of the Young's moduli in the circumferential and radial directions E/E_r and the ratio of the Young's modulus E_r and the shear modulus G on the deflection w and the critical load T_cr is investigated. It is shown that for plates made of materials such as oriented glass-reinforced plastics the shear correction is very important. It is noted that buckling (due to shear) can occur even when the Young's moduli of the material are infinite.Mekhanika Polimerov, Vol. 4, No. 1, pp. 116–123, 1968     

Elastic constants of randomly reinforced plastics

A previously developed [4] general method of solving the nonlinear (in the statistical sense) boundary value problem of the theory of elasticity is used to determine the macroscopic moduli of elasticity of randomly reinforced plastics whose structure is simulated by a two-phase microinhomogeneous medium. The macroscopic modulus is represented in the form of a series composed of the sum of the mean value of the modulus and a sequence of corrections that take into account the central moments of the distribution of elastic constants. The limits of convergence of this series are established. The values of the macroscopic moduli for a glass-reinforced plastic obtained by calculation are compared with the experimental data.Mekhanika Polimerov, Vol. 3, No. 2, pp. 259–265, 1967     

Deformative characteristics of plastics reinforced with high-modulus anisotropic fibers

The independent elastic constants of plastics unidirectionally reinforced with transversely isotropic fibers have been determined. It has been assumed that the distribution of reinforcement in a transverse section of the plastic is regularly rectangular or hexagonal. To determine the transverse elastic modulus and the shear modulus in the plane of reinforcement, a constancy-of-plane-sections hypothesis was used. Values of deformative characteristics determined by the assumed calculational dependences have been compared with the experimental ones for plastics reinforced with graphite fibers.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 631–639, July–August, 1972.     

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.     

Anisotropy of the elastic and strength properties of reinforced plastics

The method and results of experimental investigation of anisotropy of the elastic and strength properties of reinforced plastics are discussed. A method of determining the mechanical characteristics in different directions on tubular test pieces is proposed. A special testing machine is described. It is shown that determining the strength and elastic properties of reinforced materials in directions other than the directions of reinforcing on flat test pieces cut mechanically leads to distorted results.Mekhanika Polimerov, Vol. 3, No. 3, pp. 461–466, 1967     

Rational structures for spherofibrous composites. 2. 4Dm models

A method of calculating elastic moduli from component properties is proposed for a 4D composite. It is established that when subject to shear, composites with such a structure cannot be described by Hooke's law for anisotropic bodies. It has been found that 4D₀ and 0m composites with a fixed bulk content of components possess nearly equivalent normal-elasticity indicators. The latter makes it possible to use these less expensive materials.See [1] for report 1.A. A. Blagonravov Machine Science Institute, Russian Academy of Sciences, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 370–376, May–June, 1997.     

Numerical realization of the asymptotic averaging method for thermoelastic multidirectional composites

A zero approximation of the asymptotic averaging method is applied to investigate the structural stresses in the structures of spatially reinforced composite materials subjected to mechanical loading and high-temperature heating. A carbon-carbon composite material reinforced with anisotropic fibers in three mutually orthogonal directions in the ratio 111 is considered. According to the averaging method, the local functions, namely the components of the tensors of elastic moduli and thermoelasticity in a zero approximation, must be determined by solving a set of problems for a periodicity cell. The effective thermoelastic constants of the composite are found by averaging the local functions obtained over the periodicity cell. To calculate the structural stresses in constructions, the periodic local functions and the field of macrostrains, which is obtained from the solution of the averaged boundary value problem, must be known. The problems posed for the periodicity cell are solved by the method of finite elements. The average values of the local functions and the measures of deviation from them are examined for various temperatures and volume fractions of fibers of two different cross section shapes.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 455–464, July–August, 1999.     

Theory of a reinforced layered medium with random initial irregularities

The author examines an elastic medium reinforced with slightly distorted elastic layers. The basic equations are obtained by the method proposed in [1,2]. It is assumed that the functions describing the initial distortions of the reinforcing layers form a random field. With the help of the method of canonical expansions [3], expressions are derived for the statistical characteristics of the stresses, strains and displacements in the reinforced medium. The theory is used to account for the known experimental fact of the reduction in the moduli of elasticity of layered glass-reinforced plastics as compared with the values calculated for an ideal reinforced medium. In particular, it is shown that this reduction may be considerable even when the initial irregularities are relatively small.Mekhanika Polimerov, Vol. 2, No. 1, pp. 11–19, 1966     

Determination of elastic characteristics of flexible cables on basis of model of helically anisotropic solid

Conclusions A model of a flexible cable as a helically anisotropic solid with three elastic constants is constructed within the framework of the continual approach. An experimental-analytic method of determining the cable moduli and evaluating the correctness of use of the model of a helically anisotropic solid is developed. Also developed is an algorithm for computing the elastic constants of the cable, which is based on analysis of errors of moduli determination and minimization of the functionalf(E₁, G) in preset intervals . Computations indicate that the equality ₁₁ E₁ is fulfilled with a high degree of accuracy for flexible cables.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 136–141, January–February, 1984.