Calculation and experimental study of a unidirectional rubber-cord composite in tension and compression

Calculation and experimental study of transverse tension and compression of a rubber-cord composite with a unidirectional scheme of reinforcement is presented. The calculation results for components of the composite and for the composite as a whole are compared with the experimental data. The loss of stability of the deformed rubber-cord composite in transverse tension is analyzed.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 325–334, 1999.     

Calculation and experimental investigation of torsion of all-rubber and rubber-cord clutches under large deformations

On the basis of a mathematical model of large deformations of homogeneous and fiber-reinforced bodies of revolution, the deformation of all-rubber and rubber-cord clutches made by using the tire technology is investigated. The results of a theoretical and numerical analysis of torsion of the clutches are compared with experimental data.     

Investigation of Locally Loaded Multilayer Shells by a Mixed Finite-Element Method. 1. Geometrically Linear Statement

The Hu-Washizu functional is constructed for analyzing prestressed multilayer anisotropic Timoshenko-type shells. As unknown functions, six displacements and eleven strains of the faces of the shells are chosen. Based on mixed finite-element approximations, a numerical algorithm is developed for solving linear static problems of prestressed multilayer composite shells. The results of solving the well-known test problem on a cylindrical shell subjected to two opposite point forces and the problem on local loading of a toroidal multilayer rubber-cord shell are presented.     

Investigation of Locally Loaded Multilayer Shells by a Mixed Finite-Element Method. 2. Geometrically Nonlinear Statement

Based on mixed finite-element approximations, a numerical algorithm is developed for solving linear static problems of prestressed multilayer composite shells subjected to large displacements and arbitrarily large rotations. As the sought-for functions, six displacements and eleven strains of the shell faces are chosen, which allows us to use nonlinear deformation relationships exactly representing arbitrarily large displacements of the shell as a rigid body. The stiffness matrix of a shell element has a proper rank and is calculated based on exact analytical integration. The bilinear element developed does not allow false rigid displacements and is not subjected to the membrane, shear, or Poisson locking phenomenon. The results of solving the well-known test problem on a nonsymmetrically fixed circular arch subjected to a concentrated load and the problem on a locally loaded toroidal multilayer rubber-cord shell are presented.     

Statistical characteristics of the mechanical constants of glass-reinforced plastics

The results of statistical treatment of experimental data on the physicomechanical properties of glass-reinforced plastics, based on alkali-free, aluminoborosilicate glass fibers (composition NS-55/6) with paraffin as lubricant and epoxyphenolbutyral composition EFB-4, obtained from tensile tests on flat specimens prepared by "wet" winding on a mandrel, are given. The data can be used for evaluating the effect of the scatter of the mechanical constants of a composite material on the efficiency of a structure and its elements.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1125–1128, November–December, 1972.     

Analysis of the effect of impact damage on the strength characteristics of a composite

Theoretical and experimental investigations into the loss of the static tensile strength of a KMKU-2M.120. E01 composite after low-speed impacts of different energy have been carried out. All calculations are performed by the method of finite elements. The drop in the strength as a function of impact energy is estimated according to two criteria: the criterion of an equivalent hole (the upper limit of loss of strength) and the criterion of concentration (the lower limit of loss of strength). The results obtained agree closely with experimental data and therefore can be recognized as reliable.     

An analysis of moisture diffusion according to Fick’s law and the tensile mechanical behavior of a glass-fabric-reinforced composite

The properties of moisture diffusion parameters and their effect on the tensile mechanical behavior of a fabric composite (glass fiber/epoxy resin) in the warp and weft directions were investigated. The water up take by specimens conditioned in a humid environment under different relative humidities (0, 60, and 96% RH) at a constant temperature of 60°C was evaluated by weight gain measurements. The water absorption followed Fick’s diffusion law in the fabric composite. A comparison between the values obtained for the moisture diffusion coefficient and the equilibrium moisture content at the laboratory and those given by Loos and Springer showed that the parameters depended not only on the nature of materials, but also on environmental conditions. The effect of moisture absorption on tensile characteristics of the composite, which was tested in uniaxial tension in the warp and weft directions at constant imposed displacement rates up to failure, showed a significant reduction in the ultimate tensile strength of the specimens conditioned at 96% RH. Russian translation in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 43, pp. 479-488, May-June, 2009.     

Anchoring and a Load Transfer Technique in Uniaxial Tension of Unidirectional High-Strength Composites

A simplified analytical method for calculating the stress-strain state in uniaxial tension of unidirectional composite specimens with glued wedges is developed. A numerical analysis of the influence of geometry and mechanical parameters of the specimens on the maximum stresses is carried out. The calculations are refined by finite-element modeling. Tests of the specimens have proved the suitability of the suggested technique of anchoring and load transfer in uniaxial tension of unidirectional high-strength composites.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 319–334, May–June, 2005.     

Numerical investigation of the deformation characteristics and heat generation in pneumatic aircraft tires Part II. Thermal modeling

A numerical procedure to determine the temperature rise in aircraft tires under free rolling conditions is presented in this article. Energy dissipation from cyclic inelastic deformation is considered the main heat generation source. This modeling considers the deformation process of the tire to be a steady-state problem, where all concurrent cycles are assumed to be the same as the first. The inelastic energy is determined by imposing a phase lag between the strain and the stress fields. The phase lag is assumed to be frequency independent in the range of interest, in keeping with the experimental observations in aircraft tire materials. It is further assumed that the inelastic energy is completely converted into volumetric heat input for a transient thermal conduction analysis. A conduction model is described and results are compared against thermocouple data recorded by Clark and Dodge [1].     

Results of an experimental investigation of the residual stresses in wound glass-reinforced plastics

The results of an experimental investigation of the residual stresses in wound glass-reinforced plastic rings are presented. The residual stresses were determined by the Davidenkov method. The dependence of the maximum tensile and compressive circumferential stresses on ring thickness and polymerization temperature is investigated. The experimental data are compared with the results of calculations based on the theory proposed in [1, 2].Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1116–1119, November–December, 1970.     

Analysis of extension propagation process of interface crack between belts of a radial tire using a finite element method

A radial tire is a very complex structure made from rubber elastomers and fiber–rubber composite materials. During its use, extension propagation of interface crack between belts can occur, which obviously affects its durability and life. In the present paper, a new mathematical model of extension propagation of interface crack in complex composite structures is presented. The model can reveal the extension propagation dependence of interface crack on the relative size of energy release rates at the left and right crack tips and on the interfacial material properties. The extension propagation model of interface crack, Irwin’s virtual crack close technique and the finite element analysis method are used together in simulating numerically the extension propagation process of a interface crack between belts of a radial tire. The present study numerical results show that the extension propagation model of interface crack proposed in this paper can more realistically characterize the complexity of the extension propagation process of interface crack in complex composite structures.     

Large deformations of bodies of revolution made of elastic homogeneous and fiber-reinforced materials 2. Toroidal bodies under the action of centrifugal forces and torsion

A technique of numerical solution of boundary-value problems is expounded for elastic homogeneous fiber-reinforced bodies of revolution, which is based on equations obtained previously and employs the methods of finite differences and continuation of solutions with respect to loading parameters of the bodies. Results for the torsion of highly elastic toroidal clutches with a semiannular profile are presented. The paper continues the investigation on large deformations of all-rubber and rubber-cord clutches initiated in its first part. The deformations are caused by centrifugal forces in their rotation around the symmetry axis and by the rotary movement in a combination with torsion caused by a relative rotation of their butt-end sections around the axis. The effect of imposition sequence of butt-end torsion and rotary movement on the deformational behavior of the clutches is evaluated.     

Multiscale simulation for description of rubber friction

The interaction between tire and road generates the transferable forces, which are necessary for driving dynamics and safety. These forces are based on friction between rubber material and pavement surface and depend on the roughness of the pavement, the slip velocity, the contact pressure and the temperature. Based on the finite element method, the friction coefficient is calculated by numerical simulation. The roughness of the pavement surface is described by the height difference correlation function (HDCF), which allows partitioning into different length scales. This multiscale approach is suitable to understand and to evaluate friction phenomena. These phenomena are hysteresis friction based on dissipation inside the rubber material and adhesion friction, which describes the direct bonding between two materials. Given, that the material parameters of rubber highly depend on temperature and the frictional dissipation leads to a warming of the rubber, the provision for these effects is necessary for a realistic desciption of friction. The method allows an understanding of friction phenomena on the micro-scale like the real contact area or the microscopic contact pressure. Also, the temperature distribution inside the tire cross-section can be illustrated. The resulting coefficient of friction is validated by experimental data based on linear friction tests and compared to analytical solutions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic rolling process of tires as layered structures

Due to inner pressure the tire is a prestressed system of cord layers. The cord layers are covered by rubber layers. The whole structure is coated by a wear-resistive thread and a soft side wall coating. Serving as a boundary condition at the cord ends is a steel ring at both sides of the wheel rim. To stiffen the thread the structure has a steel cord belt with a ply angle of ±20° to the circumferential direction. The rolling system works like a spring with changing contact forces, and to compute the car dynamics it is necessary to take into account a high frequency and nonlinear varying contact. The forces between tire and road are limited by friction which gives rise to high frequency friction oscillations. Also the structural dynamics of the tire is nonconservative and self-excited, and an appropriate damping of cords and rubber is needed to stabilize the system dynamically. The computing static equilibrium and equations of motion of a continuum mechanics membrane model are treated, and the discretization to a multi-masspoint model is shown. The resulting nonlinear system of Newtonian equations is solved by using the predictor-corrector integration method in time. The time step of integration is due to the highest frequency of the system, and it is ten times shorter than the minimum of oscillation time in the system. All the nonlinearities, the hysteretic damping, and small bending moments of the rubber layers are taken into account to compute the nonstationary rolling with slip and spin on uneven roads or soft ground.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Berlin Technical University, Berlin, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 824–834, November–December, 1996.     

Prediction and Measurement of Residual Strains for a Composite Bonded Joint

A quasi-isotropic composite laminate/adherend of IM6/3501-6 and a composite bonded specimen were manufactured and tested. The bonded specimen was fabricated by postbonding composite adherends together using a 177°C adhesive resin. Predictions for the residual curing strains in the composite adherends and the adhesively bonded composite specimen were performed using a thermomechanical linearly elastic analysis. The analysis was performed using a computer program based on a polynomial spline displacement approximation method [1]. The residual strains of the specimens were measured using the moiré interferometry technique. Diffraction gratings were replicated at room temperature onto the edges of polished laminated adherends and on the edge of a fully cured adhesively bonded specimen. The specimens were cut through their entire thickness in the middle of the diffraction grating area, resulting in a redistribution of the residual curing stresses, with corresponding changes in the strain field at the edges of the cut. A full-field deformation pattern was obtained in the grating area by analyzing the recorded fringe patterns. The deformation field induced by the cut in the laminated adherends and the adhesive bondline were estimated by the linear thermomechanical analysis. A good agreement between the analysis and the experimental results was obtained.     

Stability of axially compressed cylindrical composite shells in the presence of nonstationary heating

The problem of smooth cylindrical composite shells uniformly compressed in the axial direction and subjected to nonstationary heating is solved in the linear quasi-static formulation. Expressions are obtained for the critical loads and their regions of application are determined. The calculations are compared with experimental data obtained by linearly heating the outer surface of axially compressed smooth cylindrical shells of glass-reinforced plastic based on phenol-formaldehyde resin.Zhukovskii Central Aerohydrodynamic Institute, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 289–297, March–April, 1973.     

Resonance methods for determining the complex shear moduli of orthotropic composites

A survey of various methods for determining the complex elasticity and shear moduli from the resonant frequencies of flexural and torsional vibrations of rectangular rods cut out from a plate of an orthotropic composite is presented. The errors in the computed values of dynamic shear moduli caused by inaccuracies in the experimental determination of resonance frequencies are examined. A new variant of the resonance method is developed, which permits one to find three complex shear moduli of a composite from the resonant frequencies and the damping of torsional vibrations of three rods oriented along three symmetry axes of the material. For computing the moduli in the case of an overdetermined system, an algorithm of nonlinear optimization based on the least-squares method is recommended. From the results obtained it follows that, for determining the interlaminar shear moduli with a necessary accuracy, the rods must be sufficiently thick. It is shown that a good agreement alone between calculated and experimental frequencies of flexural and torsional vibrations of rods does not ensure a reliable determination of the moduli of interlaminar shear if experiments are carried out on wide test specimens cut out from a thin plate. Recommendations are given for the choice of geometrical sizes of test specimens for resonance experiments. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 721–744, November–December, 2007.     

Damage and Failure of Metal/Fibre-Reinforced Polymer Tensile Specimens with Inelastic Interface

Hybrid specimens of metal and fibre-reinforced polymer are applied in automotive and aerospace industry. The simulation and analysis of damage of such engineering structures is the focus of this research. The investigation includes a computation of the extension of single lap tensile specimen, produced by ultrasonic metal welding. The specimen is manufactured from CF-PA66 - fibre-reinforced polymer and AlMg3 (AA5754), which is used as a metallic joining partner. The aluminium substrate is treated as an elastoplastic material. The polymer composite generally shows an orthotropic elastic behaviour. The interface material has been numerically modeled as an elastoplastic material with linear hardening, coupled with Lemaitre-type damage. The finite element method is used for the investigation of so-called interface elements. The geometry of the interface is a consequence of the welding sonotrode geometry. The behaviour of specimens with square and ring interface geometry are analysed. The influence of the interface geometry on the mechanical properties of the joint is shown. The increase of the damage parameter and the development of failure are described for both cases. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of anisometry of a platelike nanofiller on the elastic constants of a transversely isotropic composite

Analysis results for the elastic properties of a composite with a small amount of coplanarly arranged platelike filler particles are presented. The geometrical form of the particles is described by an oblate ellipsoid of revolution. The calculations are performed by formulas obtained by using the Eshelby approach for media with a low concentration of inclusions. The effect of anisometry of the ellipsoidal particles and of the ratio between the elastic moduli of the filler and matrix on the effective elastic constants of the composite is discussed. Calculation results are compared with experimental data for the elastic moduli of a nanocomposite containing completely exfoliated particles of an unmodified montmorillonite. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 493–504, July–August, 2008.