


Vol 19, No 2 (2016)
- Year: 2016
- Articles: 16
- URL: https://journal-vniispk.ru/1029-9599/issue/view/11977
Article
What does friction really depend on? Robust governing parameters in contact mechanics and friction
Abstract
It is known that the coefficient of friction generally depends on a large number of system and loading parameters. Already Coulomb presented experimental evidence that the static coefficient of friction may depend on time, on normal force, on the contact size, on the nature of contacting materials, and on the presence of intermediate lubricant layers. For the sliding coefficient of friction, he observed the dependence on the sliding velocity as well as the force and size dependencies. Later research has shown that the friction coefficient is very sensitive to the presence of oscillations (including self-excited vibrations). In spite of the practical importance of the problem, no generalized laws of friction or empirical procedures for measuring and representing the law of friction have been developed so far, which included at least the following four parameters: contacting body velocity, normal force, shape (and thus implicitly size), and time. In the present paper, we discuss the question of how the dimension of space of governing parameters can be reduced and if a small set of “robust governing parameters” of friction can be identified. We argue that one of such robust governing parameters is the indentation depth (or relative approach) of contacting bodies and discuss further candidates for the role of robust governing parameters.



Applying the method of dimensionality reduction to calculate the friction force between a rotationally symmetric indenter and a viscoelastic half-space
Abstract
The method of dimensionality reduction is applied to the tangential contact between an elastomer and a rotationally symmetric indenter. The resulting equations are solved analytically, and numerical methods are discussed. The dependence of the normal and tangential force on the indentation depth and velocity is indicated.



Solution to the frictional contact problem via the method of memory diagrams for general 3D loading histories
Abstract
This paper is concerned with the method of memory diagrams developed for solving a problem of frictional elastic contact. Our goal is to establish a link between contact force and displacement for a general plane contact between two arbitrarily-shaped bodies; rolling and torsion are not considered. Description of mechanical interactions between two solids in contact in the presence of friction is a nontrivial task since the desired force-displacement relationships have hysteretic (memory-dependent) character. Arbitrarily changing applied force (or displacement) creates a cumbersome shear stress distribution in the contact zone that has to be adequately parameterized and accounted for. In that regard, it is suggested to consider, instead of complex shear stress distributions, a simpler functional form called memory diagram that contains the same memory information. We have established two integral relationships that link the force and displacement vectors with that internal functional dependency. The integral relationships are supplemented with two other evolution rules for memory diagrams that eventually follow from the Coulomb friction law. The memory diagram is updated with the help of these rules following a given force history. Then the calculated memory diagram is used to update the history of displacement i.e. to produce the desired force-displacement relationship.



Effect of dynamic stress state perturbation on irreversible strain accumulation at interfaces in block-structured media
Abstract
The paper studies how the stress state of the interface between structural elements in a block-structured medium affects its deformation response to dynamic loading. It is shown that the normalized shear stress and mean stress are the major factors that determine the deformation response of the interface. We propose to describe the dependence of the value of induced irreversible displacement at the interface on the normalized shear stress using a logistic function. The central point of this function is the point of transition from the quasi-elastic to quasi-plastic stage of the interface shear deformation. The obtained empirical dependences are important for understanding the mechanism of irreversible strain accumulation in fault zone fragments and, particularly, for the development of an earlier proposed approach to estimate the characteristic level of active shear stresses in separate tectonic fault regions.



Friction and wear of a spherical indenter under influence of out-of-plane ultrasonic oscillations
Abstract
This paper presents an experimental and theoretical investigation of friction and wear of a spherical indenter. With the pin-on-disc-tribometer the out-of-plane oscillations are applied to the sliding indenter. Oscillations lead to a decrease of the coefficient of friction, and this effect is also related to the sliding velocity and oscillation amplitude. During the sliding movement, the contact area of indenter increases due to the wear of material. This radius of the worn spherical cap is measured after each sliding period. It is found that the radius of the wear flat increases with sliding distance according to a power law with the power 1/4 and is independent of the sliding velocity. It further is practically insensitive to the presence of oscillations. A theoretical analysis and a numerical simulation based on the method of dimensionality reduction are carried out, both describing the experimental data very well.



Normal contact problem between a cylindrical indenter and a half-space with long-range adhesion: Study with the method of dimensionality reduction
Abstract
Adhesive contact with exponential adhesive interaction is simulated with the use of the method of dimensionality reduction. The developed procedure is illustrated with an example of adhesion of a cylindrical punch and an elastic half space. However, it is general and can be used for any form of interaction potential and any form of indenter.



Frictional shakedown and ratcheting of an oscillating cylindrical, elastic contact with coulomb friction
Abstract
We examine frictional shakedown of an elastic contact of a cylinder pressed on a flat substrate. Slight oscillatory rolling of the cylinder varies the pressure distribution and the contact region. Together with the tangential load, this rocking motion causes incremental sliding processes and a macroscopic rigid body motion. In case that the oscillation amplitude is sufficiently small, the slip ceases after the first few periods and a safe shakedown occurs: the residual force in the contact withstands the tangential load. Otherwise ratcheting occurs: one side of the contact alternately sticks, while the other slips. This leads to a continuing rigid body motion. By derivation of the tangential stress distribution and use of the Boussinesq and Cerruti potential functions, we find approximations for the shakedown limits for the tangential load and the oscillation amplitude. This allows the accurate prediction of the displacement and the reduced tangential load capacity in the shakedown state. The results show strong agreement with numerical and experimental data.



A wear-reduced nanodrive based on oscillating rolling
Abstract
In this article we introduce a promising new concept for a high precision actuator. It is based on inertia effects and oscillating rolling. A sphere acts as the drive and is pressed on a movable substrate that acts as the runner. A combination of oscillating translation and rotation of the sphere induces motion of the runner. A varying normal force leads to varying indentation depth and contact area. This asymmetry together with the inertia of the runner enables accurate control of its displacement. As slip is completely omitted here, in theory the actuator works principally wearless. We use the method of dimensionality reduction to conduct a quasistatic numerical simulation of the system. In addition we derive analytical expressions for the steady working points of the system that are in perfect agreement with the simulation results.



Simulation of frictional energy dissipation in a fiber contact subjected to normal and tangential oscillation
Abstract
This paper presents a numerical study on the frictional contact between two crossed fibers subject to both normal and tangential oscillation. The results from simulation using the method of dimensionality reduction show that the frictional energy dissipation increases firstly with coefficient of friction, and then almost symmetrically decreases to a constant. The fiber aspect ratio has an important effect on the energy dissipation and this effect becomes more significant for larger coefficient of friction. The simulation results for very large coefficient of friction show a good agreement with the analytical solution for the case of infinite coefficient of friction.



Relaxation damping in contacts under superimposed normal and torsional oscillation
Abstract
It was recently shown that if a contact of two purely elastic bodies with no sliding is subjected to oscillations in normal and tangential directions, a kind of damping occurs due to relaxation of tangential stress in areas of intermittent contact, despite the absence of sliding and corresponding frictional work. In the present paper we show that the same mechanism acts in contacts with superimposed normal and torsional oscillations. A closed-form solution for the torsional and combined (torsional/tangential) relaxation dissipation for a contact of arbitrary bodies of revolution is presented.



Influence of the size and concentration of soft-phase inclusion agglomerates on ceramic specimen strength
Abstract
The paper is a theoretical study into the influence of the content and distribution of soft-phase inclusion agglomerates in the matrix of a ceramic composite specimen on its strength and deformation properties. The movable cellular automata method was used to simulate uniaxial compression of two-dimensional composite material specimens with an aspect ratio of 1:1. It is found that the strength and deformation properties of the generated composites decrease nonlinearly with the growing volume fraction of inclusions. The average size of inclusion agglomerates at the same volume fraction of the soft-phase particles slightly affects the strength and deformation properties of the simulated specimens. The obtained theoretical results can be used to develop new ceramic materials, such as composite ceramics with dimensions preserved at varying temperature.



Experimental study of different modes of block sliding along interface. Part 1. Laboratory experiments
Abstract
This paper is the first part of an experimental work on studying the formation of different deformation modes of rock discontinuities under laboratory and field conditions. The formation conditions of different sliding modes were studied under laboratory conditions for several types of discontinuities, such as rigid surface contact and cracks filled with quartz sand, talc, and clay. A wide range of shear deformation modes were experimentally reproduced—from dynamic slip with a maximum velocity of tens of mm/s to stable sliding with a velocity of 1 µm/s. The behavior of a crack with a clay-containing gouge drastically changes after its wetting. The larger is the content of clay, the longer is the slip duration. The motion of a block consists of a long phase (~100 s) in which displacement velocity smoothly increases, and a retardation phase of almost the same duration in which displacement velocity decreases down to a few tens of µm/s. The used sensors detected no acoustic emission prior to the beginning of block sliding as well as on all stages of block motion until its full stop. It is shown that slow slip events have all stages typical for stick-slip motion: acceleration, long sliding, retardation, arrest, and quiescence. The conducted laboratory experiments substantiate the earlier statement that all types of deformation processes in the Earth’s crust produce a common range of phenomena.



Concurrence of mass and energy density for conservative and dissipative systems
Abstract
The falling body velocity is 00000 when mass and energy are interdependent. The overestimated 00000 prevails when mass and energy are separately independent. The falling time is found to be greater by a factor of 00000. A consistent account of the laws of motion from Galileo to Newton is made possible by using E = mv2 for conservative and dissipative systems. By the same token, the equivalence of energy and mass can be used for the mathematical assessment of gravitational waves at any velocities and not just at the speed of light. The personalized units should be replaced by the “energy density unit” to avoid ambiguities. The key step is the application of the Hookean “force” in conjunction with the work done as energy. The equivalence of mass and energy at any velocity were derived by using Ideomechanics, which is a mathematized verion of I-Ching. Gravitational waves are intimately related to the entanglement of multi-atom space-time.



Elastic-plastic fracture analysis of notched Al 7075-T6 plates by means of the local energy combined with the equivalent material concept
Abstract
The main goal of the present research is to analyze tensile fracture in Al 7075-T6 thin plates weakened by blunt V-notches. For this purpose, first, 27 fracture tests are carried out on rectangular plates containing a central rhombic hole with two blunt V-shaped corners horizontally located. The experimental observations indicated that a plastic region initiates from the notch tip and grows as the tensile load monotonically increases, and finally, fracture happens suddenly with a significant opening of the notch tip. By showing significant plastic deformations around the notch tip and also inclined fracture planes, the specimens after fracture confirm well the ductile rupture in V-notched Al 7075-T6 plates. As the main experimental result, the load-carrying capacity of the notched plates corresponding to the onset of crack initiation from the notch tip is recorded. To theoretically predict the experimental results, the equivalent material concept is utilized together with the well-known brittle fracture criterion, namely the averaged strain energy density criterion. Without requiring elastic-plastic finite element analysis, it is shown that the combination of the averaged strain energy density and equivalent material concept is successful in predicting the load-carrying capacity of the V-notched Al 7075-T6 plates that fail by moderate-scale yielding regime.



Physical meaning of nonholonomic strain measure
Abstract
The paper overviews the main approaches to the introduction of strain measures. It has been concluded that the physical meaning of certain measures is insufficiently clear. Problems concerning the definition of the physical meaning of the nonholonomic asymmetric strain measure introduced in the framework of a multiscale model, which is based on the physical theory of plasticity, are discussed. This measure is calculated using the corotational integration of the asymmetric and frame-independent strain rate measure equal to the relative velocity gradient. The integration is carried in terms of the corotational coordinate system whose instantaneous motion is determined by averaging the spins of mesoscale elements. It is shown that if elastic distortions are neglected, the introduced mesoscale strain measure is equal to the sum (over all slip systems of the crystallite) of products of accumulated shear multiplied by the basis dyads of the slip systems. The averaging reveals that additional contribution to the value of the macroscale strain measure is attributed, along with elastic distortions, to corotational terms that appear due to different rotation rates of the introduced macroscale corotational frame and crystallite lattices. In view of the absence of analytical expressions for the meso- and macroscale spins, the physical meaning of the macroscale nonholonomic measure is defined in numerical experiments for several strain paths. Calculations have shown that contributions of the elastic and corotational components to the macroscale nonholonomic strain measure are negligible for strain paths of different complexity.



Bulk strain energy density in randomly reinforced polymer composites with antifriction dispersed additives
Abstract
Bulk strain energy density was numerically simulated for epoxy-phenol-based composites randomly reinforced with short polyimide fibers, with antifriction dispersed polytetrafluoroethylene (PTFE) additives. A mathematical model was constructed using the notion of a stress concentration operator (fourth-rank tensor) that relates volume averaged, or external, stresses within a heterogeneous material with their local values within an individual heterogeneity. The simulation was based on a generalized singular approximation of random field theory used to solve a stochastic differential equation of equilibrium of an elastic medium. This approximation yields an explicit expression for stress concentration in a composite material. The explicit expression allows one to analyze the distribution of bulk strain energy density depending on the composition, structure, volume and mass fraction of heterogeneities, and on the type and value of applied load. We studied how the considered energy characteristic depends on the type of external mechanical loading and concentration of isotropic components in the model composites. It is shown that with the increasing concentration of polyimide fibers at a fixed concentration of PTFE inclusions, the bulk strain energy density values of all components decrease and approach each other independently of the type of external loading. The form of these dependences is nonlinear. A change in the mass fraction of dispersed PTFE inclusions in the model composites exerts little effect on local energy values of all components under any of the considered applied external loads.


