Structural-statistical analysis of the strain properties of laminated reinforced plastics

Conclusion The structural relations derived here make it possible to analytically predict the main statistical characteristics of the strain properties of an LRP with allowance for the mutual correlation of the random parameters of the structure. Use of the proposed relations is valid for studying combination loading (bending and a plane stress state), as well as when the structure of the composite is unbalanced. We evaluated the scale effect associated with the presence of multiple layers and determined the impact of this effect on the scatter of the strain properties of the LRP for different types of deformation. We also proposed a method of determining the actual statistical characteristics of layers indirectly — on the basis of experimental testing of multilayered unidirectional plastics. One promising prospect is the use of these results to formulate and solve problems involving optimization of the structure of LRP's on the basis of criteria ensuring the composite's reliability and dimensional stability. Finally, the results can also serve as a basis for establishing scientifically substantiated safety factors for stiffness.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 995–1001, November–December, 1990.     

Nonsteady-state damage accumulation processes in composite flanges under cyclic loads

We consider two typical flanges: for a powerplant casing and for the casing of suspensions with a sound-absorbing duct. We model the behavior of flanges under the action of cyclic external loads based on solution of the nonlinear axisymmetric problem of elasticity theory. In order to take into account fatigue fracture of the layers of the structure, we use maximum stress criteria, a tensor damage function, the rule of linear summation of damage, and reduction schemes for the deformation characteristics of the layers, describing different fracture mechanisms. We indicate the possible nature of the development of fracture zones in composite flanges. We have established the spare load-bearing capacity of the flanges after fracture begins.Report presented at the Tenth International Conference on Mechanics of Composite Materials (Riga, April 20–23, 1998).Perm State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 636–643, September–October, 1997.     

Effect of liquid media on the deformation of the surface layers of a polymer-metal pair in sliding friction

The relation between the high-elastic component of polyurethane deformation and the deformation of the surface layers of metals has been investigated for sliding friction in various media. The surface layers of polymer and metal are plastically deformed. There is a certain correlation between the coefficient of friction and the amount of deformation.Kiev Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 1, pp. 147–149, January–February, 1970.     

Effect of interlaminar stiffness and strength of fiber-reinforced materials in plane stress

The distortion of the strains associated with a difference in the influence coefficients of the reinforcing layers is considered. The effect of the compliance of the intermediate resin layers on the average stiffness of composites is estimated. An attempt is made to explain in these terms the experimentally established deformation characteristics of three-dimensionally reinforced materials [12, 13] and laminated plastics loaded at an angle to the direction of reinforcement [11].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 876–883, September–October, 1970.     

Thermal expansion of a polymer composite with an aggregating disperse filler

Conclusion The thermal deformation of HDPE with an aggregating disperse filler was experimentally studied in a wide range of temperatures. The effect of the filler on the characteristics of relaxation transitions in HDPE, determined from dilatometric tests, was analyzed. A method of calculating the effective thermal expansion coefficient of a composite with an aggregating filler was proposed. Satisfactory agreement between the calculated and experimental data was obtained. It was shown that the effect of aggregation results in a significant decrease in the thermal expansion coefficient of the composite.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 70–77, January–February, 1989.     

Formation of the structure and effective properties of composite material in the manufacture of shells with cross-ply reinforcement

Conclusion The proposed model of formation of the reinforcing framework in the manufacture of an axisymmetric shell by the CPW method makes it possible to numerically determine the thicknesses and rates of filling the layers, reinforcement angles as a function of the main parameters of the technological process, geometry of the mandrel, and characteristics of the reinforcing filament. It was established that the thicknesses of the layers, reinforcement rates and angles, and, as a consequence, the effective stiffness characteristics of the composite are substantially variable both along the meridian and over the thickness of the shell.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 609–617, September–October, 1992.The authors thank V. A. Frolov for the experimental results.     

Physicomechanical characteristics of a disperse-filled polytetrafluoroethylene

Composite polymer materials based on PTFE containing ultradisperse -sialon (1–10 wt.%) as the cross-linking agent are studied. It is shown that the injection of small amounts of fillers (1–2 wt.%) increases the degree of composite crystallinity. A correlation between the structure, element distribution on the surface layers of samples, and tribotechnical characteristics of composites is found. The change in the physicomechanical characteristics is associated with the effect of the interstructural plasticization.Ammosov Yakutsk State University, Yakutsk, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 797–806, November–December, 1999.     

Thermal deformation of a composite reinforced with hybrid cloth strips

Conclusion We tested (for mechanical and thermal effects) composites reinforced with hybrid cloth COS and VAI strips; five alternate schemes of material, which differred in terms of the content of VAI layers and layers reinforced with COS, were tested. The elasticity characteristics, tension diagrams, and CLTE of the composites were determined. It was established experimentally that variation in the relative content of the above-indicated layers makes it possible to regulate the thermal expansion of the composite in the longitudinal direction of the reinforcing strips Objectively over significant ranges; in this case, the elastic modulus varies negligibly, while the specific elastic modulus remains virtually unchanged,An alternate scheme for determining the elasticity characteristics and CLTE of laminar polymeric materials reinforced with hybrid cloth strips on the basis of component properties is developed. The model according to which the structural organization of the composite is subdivided into several levels is primarily a computational model. The stress-strain state of the repeating structural elements is evaluated by methods of the strength of materials. The proposed algorithm for computing the physicomechanical characteristics of laminar composites is implemented in the form of a computer program. The experimental elasticity characteristics and CLTE obtained for composites with a different content of COS and VAI layers are compared with those calculated in accordance with the method developed (the computed values correspond to the experimental with an accuracy acceptable for engineering applications).Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 392–401, May–June, 1988.     

Analysis of the tensile deformation of glass-reinforced plastics

The deformation of an orthotropic glass-reinforced plastic is considered with allowance for the failure of the resin in the transverse layers.Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 1, pp. 144–147, January–February, 1970.     

Second-approximation shear theory for shallow layered shells and plates

Analysis of a second-approximation refined shear model for shallow layered composite shells and plates with a substantially inhomogeneous structure over the thickness is presented. The tangential displacements and corresponding normal stresses are expressed in the form of a polynomial of the fith degree in the transverse coordinate and contain squared rigidity characteristics. In this way, the accuracy of results and practical coincidence with the 3D solutions is ensured. Based on the refined model, a theory of shallow layered shells is developed. A system of resolving equations of sixteenth power together with appropriate boundary conditions was obtained and solved analytically. It is shown that the area of application of the formed model is extended as compared with the model of the first approximation. The model proposed allows us to examine the stress-strain state of layered composite structures of substantially different thickness and physical-mechanical characteristics of the layers, including the possibility of simulating relatively large shear deformations of rigid layers separated by a low-modulus thin interlayer pliable to transverse shear.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian Transport University, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 363–370, May–June, 1998.     

Optimization of reinforced cylindrical shells with nonuniform thickness

An optimum multilayer shell is designed whose stack of elementary layers has a nonuniform thickness. This optimization problem is solved numerically for the special cases of three-layer cylindrical shells with dynamic and static stability. The optimum variants of layer distribution in this model are compared with the optimum solutions in [1].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 298–303, March–April, 1976.     

Mechanical properties of a composite with a carbonized matrix

The effect of reinforcement schemes that differ in the magnitude of the disorientation angle of neighboring filler layers on the mechanical properties of a "carbon-carbon" composite under extension, compression, or bending is shown.Translated from Mekhanika Polimerov, No. 2, pp. 235–240, March–April, 1976.     

Numerical modeling of nonlinear deformation and buckling of composite plate-shell structures under pulsed loading

Nonlinear three-dimensional problems of dynamic deformation, buckling, and posteritical behavior of composite shell structures under pulsed loads are analyzed. The structure is assumed to be made of rigidly joined plates and shells of revolution along the lines coinciding with the coordinate directions of the joined elements. Individual structural elements can be made of both composite and conventional isotropic materials. The kinematic model of deformation of the structural elements is based on Timoshenko-type hypotheses. This approach is oriented to the calculation of nonstationary deformation processes in composite structures under small deformations but large displacements and rotation angles, and is implemented in the context of a simplified version of the geometrically nonlinear theory of shells. The physical relations in the composite structural elements are based on the theory of effective moduli for individual layers or for the package as a whole, whereas in the metallic elements this is done in the framework of the theory of plastic flow. The equations of motion of a composite shell structure are derived based on the principle of virtual displacements with some additional conditions allowing for the joint operation of structural elements. To solve the initial boundary-value problem formulated, an efficient numerical method is developed based on the finite-difference discretization of variational equations of motion in space variables and an explicit second-order time-integration scheme. The permissible time-integration step is determined using Neumann's spectral criterion. The above method is especially efficient in calculating thin-walled shells, as well as in the case of local loads acting on the structural element, when the discretization grid has to be condensed in the zones of rapidly changing solutions in space variables. The results of analyzing the nonstationary deformation processes and critical loads are presented for composite and isotropic cylindrical shells reinforced with a set of discrete ribs in the case of pulsed axial compression and external pressure.Scientific Research Institute of Mechanics, Lobachevskii Nizhegorodsk State University, N. Novgorod, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 757–776, November–December, 1999.     

Deformation and strength of hybrid composites reinforced with unidirectional fibers. 1. Numerical models

The hybrid composite consists of n(n > 2) jointly working phases. We define the thermomechanical characteristics and strength of composites by filling and reinforcing materials thermomechanical characteristics and strength basing on the suggestion that thin and strong fibre reinforced composite is quasiuniform, and there is a continuous contact between the filling medium and reinforcing fibers. The development of a mathematical model of the design under consideration has been based on following assumptions: 1) for irreversible processes, the classical thermodynamic postulates are valid, and they are introduced as functions of state of internal energy and entropy; 2) for a solitary volume of materials, internal energy is assumed to be proportional to the volume fraction of the j-th phase v_j; 3) for the material pressure limit conditions just before the essential damage, it is suggested that: a) the whole composite as well as the components are steady, i.e. Drukker's postulate is valid; b) the deformation law associated with the corresponding strength surface is valid, and c) small values of increases in plastic deformation play the leading role. The strength of unidirectionally reinforced hybrid monolayers is predicted by using a linear programming code.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 186–192, March–April, 1995.The studies were carried out with financial support of the International Scientific Fund founded by G. Soros.     

Analysis of elastomeric composites based on fiber-reinforced systems. 2. Unidirectional composites

The elastic properties of unidirectionally reinforced composite materials under large deformations are studied. The applied model for deformation of materials is based on the structural macroscopic theory of stiff and soft composites, including micro- and macromechanical levels of analysis of composite media. The properties of unidirectional elastomeric composites are studied in tension and shear in the plane of reinforcement. The microscopic fields in the structural components of composites having poorly compressible and compressible matrices are also analyzed. Changes in the parameters of macroscopic deformation of the composites are examined as functions of the loading parameters and initial conditions of the structure. The evolution of the structural changes in deformed composite materials is described.State Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 29–50, January–February, 1999.     

Influence of edge effects on the state of stress and strength of carbon composites in tension

Conclusions A difference has been found between the theoretical and experimental strength values. The theoretical strength of flat strips with straight edges, obtained on the basis of the two-dimensional solution within the elastic range for a composite with fiber angle < 30°, is higher than the actual strength. The difference is due to the failure to take account of interlaminar shear. The strength tensor is applied to a monolayer with respect to which the internal state of stress and the nature of the interrelationship between the layers are not taken into account. In this connection, it is desirable to supplement the given criterion with a condition which would take account of the difference between the stresses _xy in adjacent layers. If the directions of reinforcement > 30°, then the agreement between the theoretical strength of flat strips of variable width, obtained on the basis of the two-dimensional solution within the elastic range using the tensor strength criterion, is in good agreement with the actual strength obtained experimentally. The big differences between the actual and theoretical strengths for the three-dimensional solution are attributable to the physical and geometric nonlinearity in the boundary zone between the elementary layers of the composite.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 263–270, March–April, 1985.     

A refined model for three-point bending of sandwich panels. 1. Deflections and bending stresses

Design formulas for the flexural characteristics of sandwich panels under three-point loading by point forces, taking into account local effects, have been derived. Transverse deformation of the normal in the modified model is deduced in terms of the difference between deflections of face layers. It is considered that the rotation of the normal depends also on shear of the filler. The deflections, local curvatures, and bending stresses, dependent on the face-layer thicknesses and transverse characteristics of the filler, are studied. The danger of initial failure caused by the local moment stresses at the central panel section is shown. Comparative estimates refining the conventional designs are established.Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 747–767, November–December, 1997.     

Rheological characteristics of orthotropically reinforced polymeric materials

It is proposed to calculate the rheological characteristics of orthotropically reinforced polymeric materials using a model in accordance with which the composite is assumed to consist of layered blocks, the planes of the layers having one of three possible orientations with given probabilities. The effective rheological characteristics of each block are exactly determined, while those of the composite as a whole are determined in the Voight or Reuss approximations. The first scheme is convenient for calcuating the shear modulus operators, the second for calculating the Young's modulus and Poisson's ratio operators. A numerical computer analysis has been made for the Young's moduli. It is shown that for the anisotropic composites in question each of the technical elastic moduli is characterized by two resolvent Q* operators of real or complex argument. The conditions under which one of the Q* operators can be neglected are determined. The integral representation of the kernel of the Q* operator of complex argument is given in the case where the latter is fractional-exponential with fractional index =–1/2 and the corresponding curves are presented.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 276–283, March–April, 1972.     

Bending features of a sandwich panel with asymmetric structure under local loads

The bending characteristics of a composite panel with asymmetric layered structure under local surface loads are obtained. A refined version of the applied theory is developed using the analytical solution of the bending problem of a sandwich plate with arbitrary asymmetric structure under a point load. Local effects are investigated within the limits of a discrete model allowing for the specific character of elastic properties of a soft filler. The advantages of the solution are expressions of bending characteristics — layer curvatures, displacements, and stresses — in a closed form. It is shown that these characteristics can vary several times depending on the asymmetry parameters of the structure. Degeneration peculiarities of the solution, stemming from the slipping of layers or, otherwise, their rigid linking by the Kirchoff—Love hypothesis, as well as from account of the transverse shear and compression of the normal, are examined in line with the degeneration of geometric and physical parameters of the discrete model adopted. The results obtained are illustrated by curves and surfaces for the characteristics studied.Submitted for the 11th International Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).Institute of Polymer Mechanics, Latvian University, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 717–742, November–December, 1999.     

Deformation of polymers under friction loading

A study has been made of the laws of distribution of elastic and residual deformations in the surface layers of polymers subjected to friction. The dependence of these deformations on normal pressure, sliding velocity, and duration of loading has been determined. A relation between deformation and antifriction characteristics has been established, and the relative effect of normal and tangential loads on surface-layer deformation determined.Mekhanika Polimerov, Vol. 3, No. 3, pp. 539–543, 1967