Optimal reinforcement of a material in a known state of stress

The problem of minimizing the total reinforcement of a material in a known state of stress is considered. In the proposed geometric formulation the problem reduces to the determination in normal stress space of the shortest path from a point representing the state of stress to the region of strength. Examples of the determination of the relative area of reinforcement in three-dimensional and plane states of stress are given for characteristic regions of strength: for plane stress and plane strain the calculations lead to expressions that permit the relative areas of reinforcement to be determined directly.Kucherenko Central Scientific-Research Institute of Building Structures, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 922–930, September–October, 1971.     

Deformation of teflon in linear and plane states of stress

Teflon specimens have been deformed in accordance with various laws of variation of stress and strain with time under plane stress conditions. Fairly simple expressions describing the relation between the stresses and large (up to 60% relative to the initial dimensions) strains are constructed for a broad class of loading regimes.Scientific-Research Institute of Mathematics and Mechanics, A. A. Zhdanov Leningrad State University. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 742–746, July–August.     

Experimental evaluation of the strength anisotropy of a unidirectionally reinforced organic fiber-reinforced plastic

Conclusions The strength of a unidirectional organic fiber-reinforced plastic has been experimentally determined in various special cases of plane stress. An analysis of the data obtained shows that it is possible to describe the strength of the material in plane stress by means of a second-order surface equation containing linear and quadratic terms. The dependence of the strength in tension and compression on the angle between the directions of loading and reinforcement has been predicted and experimentally confirmed using the values found for the components of the strength surface tensors. The results of the study can be used to estimate the strength of multilayer organic fiber-reinforced plastics in cases where a unidirectionally reinforced layer can be taken as the basic structural element of the material.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 799–803, September–October, 1979.     

Experimental investigation of the strength of glass-reinforced plastics in biaxial compression in three planes of symmetry

Glass-reinforced plastics (GRP) with fiber (wound) and fabric (hot-molded textolites) reinforcement have been investigated in biaxial compression in the three planes of symmetry. The high strength in biaxial compression in the transverse plane, observed for all the GRP investigated, is explained. A method of investigating the tensile strength of the fiber components of the GRP from the results of testing a unidirectional composite in biaxial compression in the transverse plane is proposed. The possibility of a nondestructive estimation of the strength of GRP in biaxial compression at an arbitrary stress ratio is demonstrated.Translated from Mekhanika Polimerov, No. 1, pp. 63–72, January–February, 1976.     

Calculation of elasticity parameters of a material with defects

Conclusions 1. With the aid of averaging integrals, it is possible to arrive at various approximations for the elastic parameters of a material with microdefects in the form of plane cracks.2. These approximations differ appreciably in the case of high crack concentrations, with the use of a self-consistent field in both the Reiss model and the Voigt model yielding different results.3. In the absence of information about the microdefect structure in a material, the defectiveness parameters must be determined from a macrotest under conditions of a plane state of stress. The expressions derived on this basis will then yield predictions as to changes in the mechanical properties under other conditions of stress and loading.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 838–845, September–October, 1977.     

Statistical laws of fracture and statistical estimation of the static strength of structural elements made from polymeric composites

The basis of the statistical estimation of the strength of structural elements made from fibrous composites is considered; the statistical characteristics of the strength of these materials are described and the limit states are formulated. Special attention is given to the resistance to debonding. The conditions of fracture of this class of materials in plane stress are subjected to a statistical analysis.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.Aviation Engineering Institute, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 466–482, May–June, 1972.     

Load transmission in layered materials

Load transmission in reinforced plastic heterogeneous media is investigated on the basis of the equations of the theory proposed in [1–3]. The stress distribution problem is solved for a layered half-space with loads applied to one of the "hard" layers in the plane of that layer. Simplified stress formulas are presented. The corresponding error is estimated by working a numerical example. The results are compared with the corresponding problem of the theory of elasticity for a homogeneous orthotropic body.Mekhanika Polimerov, Vol. 4, No. 2, pp. 322–327, 1968     

Temperature dependence of the strength of a woven composite in a plane state of stress

Conclusions On the basis of an analysis of test results obtained by typical patterns of simple momentary quasistatic loading at various temperatures within the 20–150°C range, we have found a family of strength surfaces for a woven organic plastic material in a plane state of stress in the reinforcement plane. These experimentally found strength surfaces can be approximated by the equation of a second-degree surface. It has been established that the range of safe states of stress in the stress space narrows nonuniformly with rising temperature; namely, this narrowing is accompanied by a shift of the center and a reorientation of the axes of the strength ellipsoid. We have revealed and described the temperature dependence of the components of the strength surface tensors involved in the strength criterion. The data can be used for predicting the strength of a composite material under consideration when the latter is subject to simple quasistatic loading patterns in the three-dimensional (₁₁, ₂₂, ₁₂) stress space in the reinforcement plane within a given test range of temperatures.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 452–457, May–June, 1978.     

Static and vibrational creep of a fabric-reinforced plastic in shear in the plane of the reinforcement

The results of a comparative experimental investigation of the short-term static and vibrational creep of a fabric-reinforced plastic in shear in the plane of the reinforcement are presented. The experimental procedure is described in detail. It is shown that on the investigated ranges of temperature, stress, and amplitude-frequency parameters the effect of an additional vibrational load on the creep process is unimportant.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 605–610, July–August, 1971.     

Strength of reinforced plastics under static loading

The question of the static fatigue of reinforced plastics is considered for plane stress. Relations that predict the static fatigue are given for very simple types of loading. Experimental data are presented for thin-walled tubes of SVAM (5:1) glass-reinforced plastic subjected to long-time tests at constant internal pressure.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 265–273, March–April, 1969.     

Yield surfaces in local strain theory

The initial yield surfaces for biaxial tension and combined tension and torsion are determined on the basis of the local strain theory. The limit surfaces of the resultant stress on a local plane in tension (torsion) are obtained. A plastic strain probability factor is introduced and its values are calculated for various loading paths.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 594–598, July–August, 1971.     

Influence of vibration on creep in glass-fiber-reinforced plastic in a complex state of stress

The author describes the method and results of tests on tubular specimens of glass-fiber-reinforced plastic for creep under simultaneous torsion (shear in the plane of reinforcement), compression, and vibration in the longitudinal direction. He finds that vibratory creep is not manifested if the amplitudes of the alternating component of the stress are up to 0.1 times the limit of short-term strength and the frequency is 20 kHz.Institute of Mechanics of Polymers, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 358–360, March–April, 1974.     

Propagation of longitudinal viscoelastic waves in a three-layer medium

The nonstationary problem of propagation of a longitudinal plane one-dimensional stress wave through a plane-parallel viscoelastic layer of finite thickness separating two linear elastic half-spaces with different properties is solved in the linear formulation. A plane wave traveling in one of the half-spaces is normally incident on the boundary of the layer (one-dimensional problem). The field in the other elastic half-space, excited as a result of the multiple reflection of the fronts from the boundaries of the layer, is investigated. Graphs of the small displacements at a given point of the elastic half-space are presented. The solution of the problem is based on the dynamic correspondence principle formulated by Bland [3].Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 151–156, January–February, 1971.     

On the statistical mechanics of deformable media

Random stress and strain fields are examined in relation to machine parts made of materials of the randomly reinforced fiberglass type subjected to random external loads. The conditions of existence of the principal axes of the fourth-order tensor representing the second-order central moments of a plane random stress or strain field are determined. A method of determining the principal axes and principal values is described. A numerical example is worked.V. A. Steklov Mathematical Institute, Sverdlovsk Branch, Academy of Sciences of the USSR. S. M. Kirov Ural Polytechnic Institute, Sverdlovsk. Translated from Mechanika Polimerov, Vol. 4, No. 4, pp. 618–623, July–August, 1968.     

Calculation of rubber engineering components for average deformations

The calculation of rubber engineering components is simplified for average deformations to avoid certain mathematical difficulties and to employ approximate methods. The plane stress and strain problem for a rubber-metal shock absorber is solved as an example.Mekhanika Polimerov, Vol. 4, No. 2, pp. 271–275, 1968     

Bending of a nonlinear orthotropic cantilever beam

The method of elastic solutions is employed to investigate the plane problem of the deformation of a cantilever beam of orthotropic glass-reinforced plastic under a concentrated load with allowance for the non-linear properties of the material. The first approximation of the stress function is given and the stress distribution over the cross section is calculated for a specific GRP.Mekhanika Polimerov, Vol. 2, No. 5, pp. 773–778, 1966     

Nonlinear creep in high-density polyethylene under time-dependent stresses

The authors have performed experiments on the creep of specimens of high-density poly-ethylene in states of plane stress which vary linearly with time. The theoretical curves are calculated from equations of two types, namely the cubic and principal cubic theories of viscoelasticity [3]. The parameters of the material are taken from a previous paper [1].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 796–803, September–October, 1973.     

Anisotropic ring stretched by rigid half-disks

A theoretical basis is provided for the experimental method of determining the elastic and strength properties of materials by stretching ring specimens with a pair of rigid half-disks. The equilibrium equations of the plane problem for an anisotropic ring with mixed boundary conditions are solved by means of an expansion in Fourier series with respect to the circumferential coordinate. Numerical results obtained on a computer are analyzed. The dependence of the circumferential stress concentration coefficient on various parameters is investigated.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1113–1116, November–December, 1970.     

Estimation of the anisotropy of the short-time and long-time strengths of glass-reinforced plastics

A linear correlation between the tensile stress and the logarithm of the lifetime of a glass-reinforced plastic in various directions in the plane of the sheet has been experimentally established. The parametric introduction of the time factor into the criterion of the short-time strength of anisotropic materials is proposed as a first approximation. The Gol'denblat-Kopnov criterion is used to derive a simple relation describing the strength properties of glass-reinforced plastics in the uniaxial state of stress.Moscow Institute of Chemical Machine-Building. Scientific-Research Institute of Mechanics, Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 243–249, March–April, 1969.     

Structural theory of the strength of reinforced plastics

Conclusions In the present study, we developed structural criteria that make it possible to predict at the component level (polymer binder, fibers) and interface level the long-term strength of laminated reinforced plastics in a plane stress state. The proposed relations make it possible to evaluate the effect of the rheological properties of the components, their volume fractions, and the geometry of the structure of the laminated packet on the long-term strength of reinforced plastics. The relations also permit resolution of the inverse problem: efficiently design the structure of such materials for specific loading conditions.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 833–839, September–October, 1989.