Physico-mechanical properties of polymer materials and the friction problem

Aspects of the friction behavior of polymer materials associated with their molecular structure and responsible for the relatively small value of the modulus of elasticity as compared with the ultimate strength are examined. It is shown that, in view of the important influence of hydrostatic pressure on the mechanical properties of polymer materials, the mechanical characteristics obtained from uniaxial testing cannot be used in calculating the contact area and the forces of friction. Formulas are presented for calculating the mechanical characteristics under these conditions. The results of indentation experiments designed to simulate contact processes are discussed. It is shown that the resistance to deformation of the asperities on the surface of polymer materials is of the order of the yield stress, and not two or three times greater, as with metals. The results of contact creep studies are described and evaluated. The results of investigations of the mechanical and antifriction properties of filled polymer materials show that the forces of friction are inversely proportional to the modulus of elasticity, while the thermophysical characteristics are a function not only of the thermophysical characteristics of the filler and the base, but also depend to a great extent on the shape of the filler particles; thus, when a fibrous filler with a low coefficient of linear expansion is used, the thermal stability of the friction material can be considerably improved. The results of a study of the adhesion interaction of polymer materials under conditions of omnidirectional nonuniform compression and simultaneous deformation are presented. It is shown that the adhesion interaction is strong even at room temperature. Aspects of the mechanical properties of lubricants that determine their effectiveness in polymer friction are considered.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 303–314, March–April, 1969.     

Influence of friction in material characterization in microindentation measurement

A comprehensive computational study is undertaken to identify the influence of friction in material characterization by indentation measurement based on elasto- plastic solids. The impacts of friction on load versus indentation depth curve, and the values of calculated hardness and Young’s modulus in conical and spherical indentations are shown in this paper. The results clearly demonstrate that, for some elasto-plastic materials, the curves of load versus indentation depth obtained either by spherical or conical indenters with different friction coefficients, cannot be distinguished. However, if utilizing the parameter β (see text for details), to quantify the deformation of piling-up or sinking-in, it is easy to find that the influence of friction on piling-up or sinking-in in indentation is significant. Therefore, the material parameters which are related to the projected area will also have a large error caused by the influence of friction. The maximum differences on hardness and Young’s modulus can reach 14.59% and 6.78%, respectively, for some elastic materials shown in this paper. These results do not agree with those from researchers who stated that the instrumented indentation experiments are not significantly affected by friction.     

Nature and mechanism of friction of rubberlike polymers in different physical states

We have investigated the frictional properties of crosslinked butadiene-nitrile and butadiene-styrene copolymers and natural rubber in friction against polished steel under vacuum conditions in the temperature interval from –200 to +150° C, which embraces the glassy and high-elastic states, as well as the transition region between them. The temperature dependence of polymer friction is characterized by two maxima, a principal and a low-temperature maximum. The principal maximum, observed in the glass transition region, is not associated with the mechanical loss maximum observed in the polymers themselves. The temperature dependence of the force of friction is composed of three parts. In the high-elastic region there is an increase in the force of friction with fall in temperature, in accordance with the molecular-kinetic theory of friction of rubberlike polymers. In this region the nature of friction is associated with mechanical losses in the surface layer of polymer. The mechanical losses inside the polymer itself are unimportant. The deviation from the theoretical curve and the fall in the force of friction below a certain temperature in the transition region are chiefly associated with a decrease in the actual area of contact as the polymer passes into the glassy state. In the glassy region the friction is significantly determined by the mechanical losses in the polymer itself associated with the repeated elastic and forced-elastic deformation of the asperities in the layer of polymer in contact with the rigid surface. Therefore the low-temperature maximum is closely related to the mechanical loss maximum observed in the same temperature region in dynamic tests. Apart from this, the friction maximum is also associated with the increase in the forces of adhesion and the reduction of the actual area of contact at temperatures at which a forced-elastic mechanism of compression of the polymer asperities is not realized.Mekhanika Polimerov, Vol. 3, No. 1, pp. 123–135, 1967     

Flow of viscoplastic materials through converging channels

Many classical rigid perfectly/plastic solutions cannot be extended to more complicated rigid plastic materials, such as rigid plastic hardening materials and rigid viscoplastic materials. The present paper reveals sources of this difficulty in the case of flow of rigid viscoplastic material through infinite converging rough wedge-shaped and axisymmetric channels. Two types of viscoplastic models without strain hardening are considered, with and with no saturation stress. The maximum friction law is adopted at the friction surface. Qualitative features of the solutions are compared to those occurring in compression of a rigid plastic layer between rough, parallel plates. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical modeling and comparison of air standard Dual and Dual-Atkinson cycles with friction,heat transfer and variable specific-heats of the working fluid

Based on finite-time thermodynamics, a comparative performance analysis of air standard Dual and Dual-Atkinson cycles with heat-transfer loss, friction like term losses and variable specific-heats of the working fluid have been performed. Also the effects of heat loss, as characterized by a percentage of the fuel’s energy, friction and variable specific-heats of the working fluid, on performance of the mentioned irreversible cycles are analyzed. Moreover, detailed numerical examples show the relations between the power output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between the power output and the thermal efficiency of cycles. Results show the importance of consideration of heat loss effects on the both cycles’ performance. Also performance comparison of two cycles show that heat efficiency and power output of a Dual-Atkinson cycle are higher than a Dual cycle’s ones. The results obtained from this paper will provide guidance for the design of Dual-Atkinson engines.     

Cold flow and melting of plastics under severe friction conditions

Dry friction of a series of crystalline polymers (polypropylene, nylon, PTFE) against steel over a wide range of sliding velocities (4.4–4.4×10^–4 cm/sec) and loads (P=7.5–360 kg) with almost complete mutual overlap of the friction surfaces is studied. It is shown that friction of polymer materials against steel may be accompanied by melting of the crystalline polymer (at high velocities) or cold flow (at low velocities) in the surface layers associated with an orientation effect and the appearance of anisotropy.Mekhanika Polimerov, Vol. 1, No. 5, pp. 95–100, 1965     

A variational inequality and applications to quasistatic problems with Coulomb friction

The aim of this paper is to study an evolution variational inequality that generalizes some contact problems with Coulomb friction in small deformation elasticity. Using an incremental procedure, appropriate estimates and convergence properties of the discrete solutions, the existence of a continuous solution is proved. This abstract result is applied to quasistatic contact problems with a local Coulomb friction law for nonlinear Hencky and also for linearly elastic materials.     

A penalty approximation for a unilateral contact problem in non-linear elasticity

Using Ball's approach to non-linear elasticity, and in particular his concept of polyconvexity, we treat a unilateral three-dimensional contact problem for a hyperelastic body under volume and surface forces. Here the unilateral constraint is described by a sublinear function which can model the contact with a rigid convex cone. We obtain a solution to this generally non-convex, semicoercive Signorinin problem as a limit of solutions of related energy minimization problems involving friction normal to the contact surface where the friction coefficient goes to infinity. Thus we extend an approximation result of Duvaut and Lions for linear-elastic unilateral contact problems to finite deformations and to a class of non-linear elastic materials including the material models of Ogden and of Mooney-Rivlin for rubberlike materials. Moreover, the underlying penalty method is shown to be exact, that is a sufficiently large friction coefficient in the auxiliary energy minimization problems suffices to produce a solution of the original unilateral problem, provided a Lagrange multiplier to the unilateral constraint exists.     

Study of the strength and coefficients of friction of metal-containing polymers based on heteropolyacids

The strength and coefficients of friction of new heat-resistant composite materials consisting of metallopolymers of iron and cobalt based on molybdosilicic and tungstosilicic heteropolyacids have been studied. It has been established that the use of a lubricant in the frication of metallopolymers over steel brings about a sharper deerease in the coefficients of friction than in the case of the friction of the compact material; this is due to the ability of the metallopolymers to absorb the lubricant material.Kiev Automobile-Road Institute. Translated from Mekhanika Polimerov, No. 5, pp. 931–933, September–October, 1973.     

Friction and wear of polymer-based composites

Polymeric materials containing different fillers and/or reinforcements are frequently used for applications in which friction and wear are critical issues. This overview describes how to design high temperature-resistant thermoplastics, e.g., filled with carbon fibers and internal lubricants, for operation under low friction and wear at elevated temperatures as sliding elements in, e.g., textile drying machines. Further information will be given on the systematic development of continuous fiber/polymer composites with high wear resistance, and on attempts for the prediction of their load-bearing capacity using a finite element approach. Finally, the application of such composites in thermoplastic filament-wound journal-bearings is discussed.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Institute of Composite Materials (IVW), University of Kaiserslautern, D-67663 Kaiserslautern, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 717–732, November–December, 1998.     

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)     

Crankshaft-bearing evolution indexes investigation and asperity contact identification based on neural network

The dynamic and lubrication characteristic analyses of the crankshaft–bearing system is quite a complex problem, and it is important to avoid asperity contact which may lead to bearing wear and increase of friction loss significantly in dynamic lubrication condition. In this paper, the dynamic characteristic that has an essential impact on lubrication was investigated over an inline six-cylinder engine. Multi-body dynamics method, tribology, finite element method (FEM), finite difference method (FDM) and component mode synthesis method (CMS) were combined to analyze the dynamic characteristic of crankshaft, oil leakage, oil film pressure, asperity contact pressure and friction loss. Then the orthogonal experiment that included 5 levels and 6 factors was conducted to obtain the training sample sets for neural network, and the probabilistic neural network (PNN) was employed to identify weather the asperity contact happened or not according to its nonlinear characteristic. The analyses which can provide the guidance for the design of main bearing, and avoid the asperity contact in the lubrication are significant to the design of the bearing at the development stage of the engine.     

Fracture of fiber-reinforced materials

The fracture behaviour of fiber-reinforced materials is studied in this paper. Using a simple shear lag model, which includes friction at the debonded interface and the Poisson contraction of the fiber, the fiber-matrix debonding problem is solved. This gives the relationship between debonding load and debonded length. Interfacial friction is shown to have a significant effect on the debonding load. The fracture toughness of fiber-reinforced materials due to fiber debonding, frictional dissipation at fibre-matrix interface following debonding and other micro-fracture mechanisms is discussed with reference to strong and weak fibres. Finally, the strength and toughness of short fibre-reinforced materials are given.On leave from Harbin Shipbuilding Engineering Institute, Harbin, China     

Certain aspects of friction between natural polymers and metal

It is shown, on the basis of test data, that one of the most likely processes responsible for the adhesive characteristics of a friction contact between metal and wood is the formation of compounds containing the metal, namely, compounds between metal oxides and active groups within the lignocarbon complex in wood (hydroxyl groups, for example) with an electropositive hydrogen atom. The correlation established here between the molecular component of the friction coefficient, the change in OH groups, and the moisture absorption level in wood yields criteria for selecting the filler materials which will ensure, during friction, that the positive gradients of resistance to shear become localized and that stable boundary layers form within the contact zone.     

Friction of polymeric materials

The dry friction between a polymeric and a metallic surface is considered on the assumption that the friction power is such that heating of the surfaces can be neglected. The effect of the dimensionless specific load (ratio of nominal stress to elastic hardness of the polymer) on the friction process of elastomers and rigid polymers is analyzed and expressions are given for calculating the coefficients of friction of these materials at large values of the nominal stress.

     

A distributed friction model for energy dissipation in carbon nanotube-based composites

Being lighter and stiffer than traditional metallic materials, nanocomposites have great potential to be used as structural damping materials for a variety of applications. Studies of friction damping in the nanocomposites are largely experimental, and there has been a lack of understanding of the damping mechanism in nanocomposites. A new friction contact model is developed to study the energy dissipation of carbon nanotube (CNT)-based composites under dynamic loading. The model incorporates the spatially-distributed nature of the CNT in order to capture the stick/slip phenomenon at the interface and treats the total slip force in a statistical sense. The effects of several parameters on energy dissipation are investigated, including the excitation’s amplitude, the interaction between CNT’s ends and matrix, the orientation, concentration, and diameter distribution of the CNTs inside the matrix. The results are in good agreement with experimental observations in the literature.     

Explicit solution of the frictional contact problem of anisotropic materials indented by a moving stamp with a triangular or parabolic profile

The frictional contact problem of anisotropic materials under a moving rigid stamp is solved exactly. Inside the contact region, the Coulomb friction law is applied. Both Galilean transformation and Fourier transform are employed to get the appropriate fundamental solutions, which can lead to real solutions of physical quantities no matter whether the eigenvalues are real or complex. The complicated mixed boundary value problem is converted to singular integral equations of the second kind, which are solved analytically in terms of elementary functions for either a triangular or a parabolic stamp. Explicit formulae of surface stresses are obtained. Numerical analyses are performed in detail to reveal the surface damage mechanism. It is also found that in the frictionally moving contact problem, the friction coefficient has a more important role than the moving velocity.     

An asymptotic analysis of the solution in the neighbourhood of the corner point of a crack along the kinked interface of two media

The asymptotic behaviour of an elastic field in the neighbourhood of the corner point of a crack at the interface of different materials is investigated within the framework of plane elasticity, taking into account the contact of its surfaces and the possibility of their mutual slippage with dry friction. The problem is solved by the method of complex Kolosov-Muskhelishvili potentials. The results obtained enable one to estimate the angular range of existence of contact zones and the singularity of the stresses close to the corner point of the crack. It is shown that the formation of contact zones, taking into account the friction forces accompanying slippage, depends essentially on the magnitude of the angle of the interface kinking the elasticity moduli of the materials and the friction coefficient. Numerical calculations are carried out and the stress and displacement distributions in the neighbourhood of the corner point are obtained.     

Temperature dependence of the actual contact area and friction force of high-elasticity materials

An investigation of the temperature dependence of the actual contact area (under static conditions and during friction at a given sliding speed) of materials based on butadienenitrile rubber in a wide temperature interval is described. Measurements of the friction force were also made. It was established that the temperature dependence of the contact area is associated with corresponding changes in the elasticity modulus (nonequilibrium static modulus for contacts at rest and dynamic modulus for nonstationary contacts). The friction constant c decreases linearly with rising temperature and does not depend on the applied load.Mekhanika Polimerov, Vol. 3, No. 4, pp. 726–729, 1967