Influence of temperature on frictional properties of highly elastic materials in vacuum under high normal pressures

Experimental results obtained by the rubbing of cross-linked rubbers against smooth steel surfaces in vacuum under volume compression conditions at high normal pressures are examined. The influence of volume compression on the frictional properties of highly elastic materials at various temperatures is explained. Basic rules of temperature functions of specific frictional force at high normal pressures in vacuum and in atmosphere are established.V. I. Lenin Moscow State Pedagogical Institute, Problem Laboratory for Polymer Physics. Translated from Mekhanika Polimerov, No. 1, pp. 91–97, January–February, 1972.     

An illustration of sliding contact at any constant speed on highly elastic half-spaces

A rigid smooth indentor slides at a constant speed on a compressibleisotropic neo-Hookean half-space that is subjected to pre-stressaligned with the surface and sliding direction. A dynamic steady-slidingsituation of plane strain is treated as the superposition ofcontact-triggered infinitesimal deformations superposed uponfinite deformations due to pre-stress. The neo-Hookean materialbehaves for small strains as a linear elastic solid with Poisson'sratio 1 : 4. Exact solutions are presented for both deformationsand, for a range of acceptable pre-stress values, the infinitesimalcomponent exhibits the typical non-isotropy induced by pre-stress,and several critical speeds. In view of the unilateral constraintsof contact, these speeds serve to define the sliding speed rangesfor which physically acceptable solutions arise. A Rayleighspeed is the upper bound for subsonic sliding, and transonicsliding can occur only at a single speed. For the generic parabolicindentor, contact zone traction continuity is lost at the zoneleading edge for trans- and supersonic sliding. For pre-stresslevels that fall outside the acceptable range, either a negativePoisson effect occurs, or a Rayleigh speed does not exist andthe unilateral constraints cannot be satisfied for any subsonicsliding speed. Received 15 March 2000. Revised 22 November 2000.     

Investigation of the thermophysical properties of polymethyl methacrylate at high hydrostatic pressures

Conclusions 1. The experimentally observed course of heat capacity is explained by competition of contributions from the lattice and defects, on one hand, and from retarded rotators, on the other.2. An equation is proposed which describes the dependence of the thermal conductivity of polymers on pressure and which agrees with experimental data to an accuracy of ±1%.Moscow Chemical Engineering Institute. Translated from Mekhanika Polimerov, No. 5, pp. 845–851, September–October, 1976.     

Procedure for measuring the thermophysical properties of polymers at high hydrostatic pressures

A procedure is suggested for determining the thermophysical properties of solids under hydrostatic pressure conditions by the instantaneous cylindrical heat source method without allowance for heat exchange at the sample-liquid boundary. A calculation performed showed that the temperature field of a cylinder of finite radius is identical to the temperature field of an infinite body up to Fo=0.05–0.07 with an accuracy far better than 0.5%. It is shown that the sample dimensions can be small thereupon at measurement times sufficient for performing the measurements on a standard apparatus of the order of 40–70 sec.Moscow Chemical Engineering Institute. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 568–570, May–June, 1973.     

Effective elastic properties of particulate-reinforced compossite materials

A numerical approach for determination of the effective properties of particulate composite materials has been developed. A representative volume element (RVE) of the composite material is analyzed with help of the finite-element method. Uniform boundary displacements or tractions are applied on the boundaries of the RVE for introducing the known average strain in the RVE. Local stress and strain distributions in the RVE are calculated using the finite-element method. Different effective elastic constants can be calculated by averaging the local fields corresponding to different sets of boundary conditions. The present approach allows us to determine the effective properties of particle-reinforced composites with acceptable accuracy. The calculated effective properties of the composite are between the upper and lower Hashin—Shtrikman bounds. The results based on the present approach lead to higher stiffness of composites in comparison with analytical approaches.Institute fur Werkstoffwissenschaften, Fachberech Werkseoffwissenschaften, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 450–459, July–August, 1997.     

Numerical analysis of a bilateral frictional contact problem for linearly elastic materials

We consider a mathematical model which describes the contactbetween a linearly elastic body and an obstacle, the so-calledfoundation. The process is quasistatic and the contact is bilateral,i.e. there is no loss of contact during the process. The frictionis modelled with Tresca's law. The variational formulation ofthe problem is a nonlinear evolutionary inequality for the displacementfield which has a unique solution under certain assumptionson the given data. We study spatially semi-discrete and fullydiscrete schemes for the problem with finite-difference discretizationin time and finite-element discretization in space. The numericalschemes have unique solutions. We show the convergence of thescheme under the basic solution regularity. Under appropriateregularity assumptions on the solution, we derive optimal ordererror estimates. Finally, we present numerical results in thestudy of two-dimensional test problems.     

Asymptotic behaviour of contact problems between two elastic materials through a fractal interface

Two linear elastic materials are brought into contact along a fractal interface Σ. We suppose that the contact is perfect on small zones disposed on Σ. Using Γ-convergence arguments, we establish the possible limit contact laws which appear when letting the common size of these zones tend to 0. We also generalise these results to the case of more general obstacle problems on this fractal interface.     

Friction of polymeric materials

The case of contact of polymer and metallic surface has been examined. A formula is proposed for calculating the contact area as a function of time of holding the compression surface under load and for calculating the coefficient of friction, the dependence of Young's modulus and shear strength on temperature, deformation rate, and average force on the contact surface being taken into account. The nature of deformation of irregularities on the surfaces of polymeric materials under the action of normal and tangential loading has been examined.See [1] for Communication 1.Institute for Polymer Mechanics, Academy of Sciences of the Latvian SSSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 809–815, September–October, 1972.     

Description of the elastic deformation and degradation of elastic properties of dispersedly failing isotropic materials

A model is put forward for describing the elastic deformation of a quasi-homogeneous isotropic material capable of accumulating scattered microdamages during loading, which eventually leads to its total failure. The degree of damage of the material at a point is characterized by a centrosymmetric scalar function on the unit sphere, named the damage function, whose values depend on a dimensionless equivalent stress. This function is approximated by a fourth-rank tensor, which is used to construct a constitutive relation between stresses and strains in a differential form. By way of example, the elastic deformation of concrete and the degradation of its linearly elastic properties are described, and the basic three-dimensional sections of the corresponding strength surface are constructed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 193–208, March–April, 2006.     

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.

     

Iterative method of designing uniform and laminated shells of revolution made of highly elastic materials

Conclusion An iterative method was proposed for numerical solution of problems concerning the axisymmetric deformation of uniform and laminated shells of revolution made of highly elastic materials. Calculations performed for rubber, rubber-fiber, and rubber-layered shells demonstrate the reliability and effectiveness of the method.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 109–116, January–February, 1990.     

Phases of elastic materials

Zusammenfassung Es wird eine Methode beschrieben für die Charakterisierung von Stoff-Phasen durch Angabe der Symmetrie-Gruppe als Funktion der Deformation und Temperatur. Wenn in einem elastischen Stoff die Phase durch Dichte und Temperatur bestimmt wird, dann gelten die meisten der üblichen Resultate für die Gesamt-Symmetrie-Gruppe auch für die Gruppe, die einer gegebenen Phase entspricht.     

A dynamic contact problem for an elastic half-plane in the case of high frequency oscillations

Harmonic high frequency oscillations of a rigid stamp coupled without friction tc an elastic half-plane are considered. The main difficulty in constructing the high-frequency asymptotic forms is that of carrying out the effective factorization of the kernel of the basic integral equation. A function is proposed, which takes into account all properties of the kernel, enables it to be uniformly approximated and is easily factorized. Such a solution of the problem of approximate factorization makes it possible to write, in a simple explicit form, the principal term of the asymptotic expression of the solution. The nature of the distribution of contact stresses under the stamp is studied, as well as the compliance of the foundation and phase shift between the applied force and the displacement of the stamp.     

Control of the elastic properties of a shell working at stability

This examines a shell with elastic properties varying across the coordinates, which are prescribed by means of scalar functions of the invariants of the elasticity tensor. The basis of the arrangement of the tensor for the elasticity consists of q linear-independent tensors of the fourth range (q is the number of linear-independent components of the elasticity tensor) which are obtained by multiplying and turning the first tensor of the surface and the tensor characterizing the class of symmetry of the medium. The invariants of the elasticity tensor present in the stability equation and their derivatives are taken to be the equations and parameters for the state of the system (shell), and the problem is thus reduced to a problem of optimum equations. As an example we shall examine an orthotropic cylindrical shell with a model varying over the length under the action of external pressure.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 93–100, January–February, 1974.     

Investigation of the contact area of a rigid spherical indenter and a polymeric surface at various pressures,temperatures, and contact times

The effect of temperature and normal load on the variation with time of the indentation depth of a rigid spherical indenter in polymeric materials has been investigated with the object of obtaining the dependence of the contact area on the principal parameters of the process. Plexiglas, PVC and polyformaldehyde were selected for study. It is shown that at a given temperature the ratio _m/(a/R)^n–2=A is a function of time only and almost independent of the applied load. It is established that the time-temperature superposition principle can be used for investigating metal-thermoplastic contact phenomena. An expression is obtained for calculating the contact area at various temperatures and loading times.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 457–464, May–June, 1971.