Initial stresses in reinforced and filled polymers

The methods of the statistical theory of elasticity are used to calculate the average stresses in the components of uniaxially reinforced and randomly filled polymers arising in the process of fabricating the material as a result of the different linear expansion coefficients of the components and chemical shrinkage of the resin. Expressions are also obtained for the macroscopic characteristics of the media — moduli of elasticity, linear expansion coefficients, and shrinkage coefficients. The results are compared with experimental data and with the results of computations based on the equations proposed by other authors. The relations obtained for the dependence of the stresses in the components on their properties offer a satisfactory explanation for the experimentally established positive correlation between the shrinkage and the compressive strength of a composite based on furan resin.Gomel' State University. Kirov Urals Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 1, pp. 90–96, January–February, 1973.     

Formation of residual stresses in components made out of laminated and fibrous composites during the hardening process

Conclusions The application of the theory of the viscoelasticity of unstable media to the calculation of the residual stresses enables one to reveal effects due to the change in the properties of a solidifying binder under different sets of operating conditions for the technological process. At the same time, it once again confirms that thermal shrinkage makes a significantly larger contribution to the magnitude of the residual stresses than chemical shrinkage. The absolute values of the stresses are in satisfactory agreement with results that were obtained using simpler calculational schemes.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 5, pp. 790–795, September–October, 1976.     

Stresses in various resins cured on glass films

By using Sanzharovskii's method for determining the stresses in lacquer coatings and employing as a model a layer of resin deposited on a glass film, it is possible to simulate the processes that take place in glass-reinforced plastics and determine the stresses that develop in different resins cured under various conditions. The method proposed makes it possible to estimate the effect on the stresses of the shrinkage of the resin, its elasticity, and the difference in the coefficients of thermal expansion of the resin and the glass. Such an investigation is desirable before selecting the composition of the resin, additional organic or mineral fillers and elasticizers, and the optimal curing regime for glass-reinforced plastics.All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 481–486, May–June, 1969.     

Stresses in plastics reinforced with anisotropic fibers and subjected to transverse normal loading

The question of the stress distribution in plastics reinforced with anisotropic fibers and subjected to transverse normal loading is considered. The stresses in the components are determined by the methods of the theory of elasticity using stress functions. The theoretical relations obtained are used to construct diagrams showing the distribution of the tangential, radial, and shear stresses in the composite and the isoclines of the concentration coefficient for a carbon-reinforced plastic. The results obtained for the carbon-reinforced plastic are compared with the analogous results for a glass-reinforced plastic.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 244–252, March–April, 1973.     

Residual stress distribution in different types of adhesion joints

The results of a photoelastic investigation of the distributions of shrinkage and temperature residual stresses in glued joints and coatings are compared. The degree of nonuniformity of the residual stress distribution over the length and thickness is determined as a function of the scale factor. It is shown that the bulk of the residual stresses in metal joints glued with K-115 epoxy adhesive are temperature stresses, which may reach 130 kgf/cm². The shrinkage and temperature residual stress distributions are similar in character.Kucherenko Central Scientific-Research Institute of Building Structures. Translated from Mekhanika Polimerov, No. 4, pp. 738–742, July–August, 1971.     

Variant of the variable-modulus theory of elasticity

A variant of the variable-modulus theory — a generalization of the ideas of the classical theory of elasticity in which the observed difference in the moduli of elasticity in uniaxial tension and compression and homogeneous shear is taken into account — is considered. Quasilinear expressions are proposed for the stresses in terms of the strains and the strains in terms of the stresses.Tula Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 363–365, March–April, 1969.     

Statistical theory of elasticity of reinforced plastics

A method of solving statistical boundary value problems in the stresses is proposed for microinhomogeneous composite media simulating the structure and properties of reinforced plastics. The coefficients of variation of the physical properties of the medium are not assumed small. Numerical examples are presented.Mekhanika Polimerov, Vol. 4, No. 3, pp. 438–444, 1968Presented on 5 June 1967 at a scientific seminar held at the Institute of Polymer Mechanics of the Academy of Sciences of the Latvian SSR.     

Composite risers for deep-water offshore technology: Problems and prospects. 1. Metal-composite riser

Prospects for the application of advanced composites in the offshore technology of oil production are considered. The use of composites in vertical pipelines-risers seems to be the most efficient. The operating loads are studied and the attendant problems are formulated. A comparative analysis of the characteristics of metal, composite, and metal-composite deep-water risers is presented. A technique is developed for designing multilayered risers, taking into account the action of internal and external pressures, gravity, and the axial tensile force created by tensioners, as well as the residual technological stresses due to the difference in coefficients of thermal expansion, physical-chemical shrinkage, and force winding. Numerical estimations are given for a two-layered riser with an inner metal layer of steel, titanium, or aluminum alloys and a composite layer of glass- or carbon-fiber plastics formed by circumferential winding. It is shown that the technological stresses substantially affect the characteristics of the riser.Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga, LV-1006, Latvia. Trondheim Technical University, Norway. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 577–591, September–October, 1997.     

Stress distribution in layered composites

The mechanism governing the transmission of stresses in layer-like composite materials is analyzed on the basis of the equations of Bolotin's [2, 7] theory of layer-like media. A solution is presented for the plane problem of stress distribution in a medium under the influence of loads at the boundary of one of the reinforcing layers. Some approximate solutions based on various simplifying approximations are presented, and the limits of their applicability are discussed. Simple equations are given for the stress maxima in the binding layers. The results are used in order to discuss the mechanism underlying the transmission of stresses in layered materials.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 2, pp. 319–325, March–April, 1970.     

Shrinkage stresses in bonded plexiglas structures

It is shown by means of photoelasticity that the shrinkage stresses associated with cold polymerization of the adhesive layer in bonded plexiglas structural elements seriously reduce the reliability of the structure. By suitable heat treatment it is possible to reduce the shrinkage stresses by a factor of approximately four without distorting the shape of the element and increase the permissible stresses by a factor of almost three.S. M. Kirov Ural Polytechnical Institute, Sverdlovsk. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 734–736, July–August, 1968.     

Determination of the residual stresses in wound glass-reinforced plastic rings

The stresses that develop during winding in wound glass-reinforced plastic rings change during polymerization, when the modulus of elasticity in the radial direction is reduced by heating. Further changes occur in connection with cooling and removal from the mandrel. The theoretical relations obtained for determining these stresses are found to be confirmed by experiment.Bauman Moscow Higher Technical College. Translated from Mekhanika Polimerov, No. 5, pp. 892–898, September–October, 1969.     

On the stress distribution in a rectangular thick plate of a composite material with curved structure under forced vibration

The stress distribution in a rectangular plate of a multilayer composite material with a periodically curved structure under forced vibration is studied. It is assumed that the plate is hinge supported at opposite sides. The investigation is carried out within the exact three-dimensional linear theory of elasticity. The mechanical relationships of the plate material are described by the continuum theory of Akbarov and Guz'. The numerical results obtained by the finite element method show that even in low-frequency dynamic loading of the plate the extreme values of stresses, which appear as a result of the curving in the plate structure, considerably exceed those in the corresponding static loading.Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 447–454, July–August, 1999.     

Imposing boundary conditions in Sinc method using highest derivative approximation

Sinc approximate methods are often used to solve complex boundary value problems such as problems on unbounded domains or problems with endpoint singularities. A recent implementation of the Sinc method [Li, C. and Wu, X., Numerical solution of differential equations using Sinc method based on the interpolation of the highest derivatives, Applied Mathematical Modeling 31 (1) 2007 1–9] in which Sinc basis functions are used to approximate the highest derivative in the governing equation of the boundary value problem is evaluated for structural mechanics applications in which interlaminar stresses are desired. We suggest an alternative approach for specifying the boundary conditions, and we compare the numerical results for analysis of a laminated composite Timoshenko beam, implementing both Li and Wu’s approach and our alternative approach for applying the boundary conditions. For the Timoshenko beam problem, we obtain accurate results using both approaches, including transverse shear stress by integration of the 3D equilibrium equations of elasticity. The beam results indicate our approach is less dependent on the selection of the Sinc mesh size than Li and Wu’s SIHD. We also apply SIHD to analyze a classical laminated composite plate. For the plate example, we experience difficulty in obtaining a complete system of equations using Li and Wu’s approach. For our approach, we suggest that additional necessary information may be obtained by applying the derivatives of the boundary conditions on each edge. Using this technique, we obtain accurate results for deflection and stresses, including interlaminar stresses by integration of the 3D equilibrium equations of elasticity. Our results for both the beam and the plate problems indicate that this approach is easily implemented, has a high level of accuracy, and good convergence properties.     

Calculation of thermal stresses in an orthotropic cylinder

The present article describes the determination of thermal stresses in an orthotropic cylinder with an axially symmetric temperature field taking into account the change in the elasticity constants over the cylinder radius. A closed solution is given for constant elasticity coefficients.P. I. Baranov Central Institute of Aircraft-Engine Building, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 310–314, March–April, 1972.     

Effect of technological factors on the mechanical reliability of structures made from composites

Research on the effect of technological factors on the strength of reinforced-plastics structures is reviewed. Attention is concentrated on structures in the form of bodies of revolution fabricated by the winding technique. The influence of the winding parameters and the curing regime on the residual stresses is discussed. Data on the variation of the mechanical properties of the resin in the course of the curing process are examined. The contributions of chemical and thermal shrinkage to residual stress formation are compared. Methods of reducing the residual stresses are considered.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 3, pp. 529–540, May–June, 1972.     

Methods of exploiting natural internal stresses to strengthen composites

A method of strengthening nonuniformly reinforced composites is proposed. A rational scheme for coordinating the external stress field, the resistance field, and the internal stress field is examined in relation to the case when the internal stresses are caused by shrinkage of the resin.Ural Kirov Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 5, pp. 870–875, September–October, 1970.     

Effect of a filler on the strength properties of thermosets

The effect of a filler on the strength properties of polymers in tension is investigated. The thermostructural stresses that develop in the composite during cure are taken into account. Relations are given for the strength of the filled polymer as a function of the percentage filler content. In the process of analyzing the thermostructural stresses an analytic expression is obtained for the linear expansion coefficient of the composite with allowance for the structural distribution of the components. Calculated values of the strength and thermostructural stresses are presented for composites with different filler contents. The theoretical determination of the strength of filled polymers is compared with the results of experimental investigations of composites based on epoxy resin filled with quartz dust.Leningrad Mechanical Institute. Translated from Mekhanika Polimerov, No. 1, pp. 97–101, January–February, 1973.     

Design of orthotropic parts of complex shape by the method of nonplanar sections

Procedures based on the hypothesis of nonplanar sections are used to derive equations for determining the normal stresses at an arbitrary point of a body of complex shape in tension and bending. The anisotropy of the material properties is taken into account by introducing a variable modulus of elasticity. The theoretical results have been checked experimentally.Gor'kii Zhadanov Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 351–354, March–April, 1969.     

Viscous and high-elasticity properties of solutions of monodispersed polybutadienes in the region of critical concentrations

It is shown that there is a critical concentration corresponding to the formation of a compact, fluctuating network, which results in a sharp change in the concentration dependence of the viscosity, first difference of normal stresses and high-elasticity deformations. It is found that at concentrations below the critical concentration high-elasticity deformations do not develop, although normal stresses exist. In consequence, the relationship whereby the modulus of high elasticity is equivalent to the ratio between the square of the viscosity and the coefficient of normal stress is fulfilled only for concentrations higher than the critical.A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 896–902, September–October, 1972.     

Bending of a thin cantilevered orthotropic plate with a concentrated load at the free edge

The problem of a thin rectangular cantilevered plate of constant thickness with a concentrated load in the center of the free edge is considered. The plate is assumed to be orthotropic, the fixed edge coinciding with the principal direction of elasticity. An equation is obtained for the normal stresses at an arbitrary point on the plate. The theoretical results are compared with experiment.A. A. Zhdanov Gor'kii Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 739–741, July–August, 1968.