The calculation of the energy losses in a sliding elastic contact with friction and wear (the plane problem)

The plane problem of the sliding contact of a punch with an elastic foundation when there is friction and wear is considered. Assuming the existence of a steady solution in a moving system of coordinates, relations are derived between the sliding velocity, the wear, the contact stresses and the displacements for an arbitrary dependence of the wear rate on the contact pressure. Taking into account the presence of a deformation component of the friction force, an equation is written for the balance of the mechanical energy for the punch - elastic base system considered. It is shown that the equality of the work of the external force in displacing the punch to the losses due to friction and the change in the shape of the foundation due to wear is satisfied when the work done by the contact stresses on the increments of the boundary displacements is equal to zero, and the frictional losses must be determined taking into account the non-uniformity of the distributions of the shear contact stresses and the sliding velocity in the contact area. Two special cases of the foundation in the form of a wide and narrow strip are considered, for which the total coefficient of friction is calculated, taking into account the deformation component of the friction force.     

Deformation and stress distribution in a layered plastic

The stress distribution over the unidirectionally reinforced layers is investigated in relation to the layer thickness ratio and the direction of loading of a two-way reinforced plastic. An expression is obtained for the modulus of elasticity of the layered plastic in an arbitrary direction relative to the directions of reinforcement. The effect of the geometry of the structure of the layered material on its deformation properties is experimentally illustrated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 563–570, May–June, 1972.     

A differential variational inequality in the study of contact problems with wear

We start with a mathematical model which describes the sliding contact of a viscoelastic body with a moving foundation. The contact is frictional and the wear of the contact surfaces is taken into account. We prove that this model leads to a differential variational inequality in which the unknowns are the displacement field and the wear function. Then, inspired by this model, we consider a general differential variational inequality in reflexive Banach spaces, governed by four parameters. We prove the unique solvability of the inequality as well as the continuous dependence of its solution with respect to the parameters. The proofs are based on arguments of monotonicity, compactness, convex analysis and lower semicontinuity. Then, we apply these abstract results to the mathematical model of contact for which we deduce the existence of a unique solution as well as the existence of optimal control for an associate optimal control problem. We also present the corresponding mechanical interpretations.     

Effect of sliding velocity on area of real contact and on force of friction in high-elastic materials

The velocity dependence of the force of friction and the area of real contact of SKN-18, SKN-26, and SKN-40 rubbers has been simultaneously determined on an optical instrument. In the region of small sliding velocities the area of real contact is virtually independent of the sliding velocity, while the force of friction increases in proportion to the logarithm of the sliding velocity, in accordance with the molecular-kinetic theory of friction. At high sliding velocities a deviation in the velocity dependences of both quantities is observed. The constant of friction has been determined over the entire velocity range and the resulting velocity dependence is examined in molecular terms.Mekhanika Polimerov, Vol. 3, No. 2, pp. 309–311, 1967     

Computation of the contact temperature and wear during braking

We propose a model for determining the surface temperature and wear during braking. We take account of the change of heat flux caused by frictional forces over time. We obtain good agreement with known experimental data.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 108–112.     

Effect of certain technological factors on residual stress formation in stiffened glass-reinforced plastic shells

Conclusions Residual stress formation in stiffened composite shells has a nonmonotonic character determined by the fabrication technology, by the structural geometry and by the relations between the thermophysical and mechanical characteristics of the materials of which the individual elements are composed. For a given temperature regime a residual stress distribution favorable with respect to strength can be obtained by using auxiliary devices with specially selected properties.Moscow Power-Engineering Institute. Translated from Mekhanika Polimerov, No. 1, pp. 34–39, January–February, 1978.     

Dynamic stresses in a compound body with circular crack under sliding contact on an interface

We have considered the three-dimensional problem of harmonic loading of a circular crack in an elastic composite consisting of two dissimilar half-spaces under sliding contact on the surface of their bonding. The defect is situated in one of the half-spaces perpendicularly to the interface of materials. Using the representations of solutions in the form of Helmholtz potentials, we have reduced the problem to a boundary integral equation for the function of dynamic defect opening. Based on the numerical solution of this equation, we have obtained the frequency dependences of mode I stress intensity factor near the crack for different relations between the elastic moduli of components of the composite and the depths of crack location with respect to the interface.     

State of stress of flexible plastic shells with an opening

The state of stress of flat flexible shells with an opening is investigated with allowance for the viscoelastic properties of the material. The equilibrium equations and boundary conditions are written in finite-difference form. A nonlinear system of algebraic equations is solved by successive approximations. A method of accelerating the convergence of slowly converging iteration processes is proposed. The effect of the viscoelastic properties of the shell material on its state of stress is investigated with reference to the example of a polymethyl methacrylate shell. The variations of the ring moment and ring forces at the free edge of the shell are plotted for various moments of time, load values, and flatness parameters. It is shown that as soon as the viscosity factor begins to take effect, the state of stress and strain of the shell changes sharply; the concentration of forces and moments increases in the flexible viscoelastic (as compared with the elastic) shell.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1071–1075, November–December, 1973.     

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.     

Effect of loading rate on polymer wear

The effect of loading rate on polymer wear in metal-polymer friction pairs is considered. Investigations show that at low loading rates the wear resistance of the polymer specimens increases, evidently owing to orientation of the elements of the molecular structure in the surface layer. This finding applies both to dry friction and friction with lubricants.Mekhanika Polimerov, Vol. 2, No. 6, pp. 862–866, 1966     

Two classes of sub-optimal shapes for one dimensional slider bearings with couple stress lubricants

Shape optimization of slider bearings operating with couple stress lubricants is performed here for the first time by using a novel direct optimal control approach, which defines the gradient of the film height as a control. The bearing load is maximized. One dimensional Reynolds and energy equations are used. Several constraints are taken into consideration. They avoid the occurrence of cavitation and ensure the validity of the Reynolds equation. The model is validated against a known analytical solution (the Rayleigh step bearing). Two simple design rules are inferred, which yield two different classes of sub-optimal shapes: the multi-stepped bearings and the multi-sloped bearings, respectively. Multi-stepped bearings consist of several steps and the couple stress parameter may affect the constant value of the film height between steps. Multi-sloped bearings consist of several inclined regions and the couple stress fluid parameter may affect the constant value of the film height between regions. The slider bearings operation under variable load is stable. A sensitivity analysis identified the design parameters which have the highest impact on bearing performance. The optimal slider bearing shapes obtained for Newtonian lubricants do not change when most common couple stress fluids are used. Isothermal models may be used successfully at lower values of the couple stress parameter.     

Effect of prestress on the strength of metal shells reinforced with a glass-reinforced plastic

The effect of prestress on the strength of metal glass-reinforced plastic shells has been investigated. A method of calculation is described, and experimental results showing the role of the tensile stress in the reinforcement of reinforced metal shells are presented.Mekhanika Polimerov, Vol. 2, No. 2, pp. 285–289, 1966     

Effect of mechanical factors on rubber wear in aggressive media

The effect of mechanical factors on rubber wear in aggressive slurries has been investigated. As the mechanical action becomes more intense, the effect of the aggressive medium increases. Rubber wear in an abrasive flow is a two-stage process: the aggressive medium modifies the surface layer, which is then worn away by the abrasive.Mekhanika Polimerov, Vol. 4, No. 3, pp. 499–503, 1968     

Effect of internal stresses on the wear resistance of epoxy coatings

The results of wear tests on ED-5 epoxy coatings are used to derive a relation between internal stresses, modulus of elasticity, and wear resistance. During wear the internal tensile stresses diminish, the rate of decrease depending on the initial stress state, the material of the abrading body, and the test conditions. The thickness of the coating affects wear resistance up to a certain value; for ED-5 the limiting thickness is 500 microns.Mekhanika Polimerov, Vol. 1, No. 2, pp. 123–128, 1965     

Effect of ultrasound on the properties of a glass-reinforced plastic

It is shown that removing paraffin size from the glass strands by means of ultrasound has little effect on their strength, improves the structure of the material, and raises the mechanical strength of the GRP by 11–12%. An ultrasonic strand cleaner employing focusing piezoelectric ceramic transducers is described.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 3, pp. 546–548, May–June, 1969.     

On the propagation of stress waves in a rate sensitive plastic medium

Zusammenfassung Es wird für gewisse elastisch-viskoplastische Materalien, deren Stoffgleichungen der Verfasser in früheren Arbeiten diskutiert hat, die Ausbreitung von Kompressions- und Distorsionswellen verschiedener Art untersucht.