Effect of Indentation Depth on Friction Coefficient in Adhesive Contacts: Experiment and Simulation.

The quasi-static regime of friction between a rigid steel indenter and a soft elastomer with high adhesion is studied experimentally. An analysis of the formally calculated dependencies of a friction coefficient on an external load (normal force) shows that the friction coefficient monotonically decreases with an increase in the load, following a power law relationship. Over the entire range of contact loads, a friction mode is realized in which constant shear stresses are maintained in the tangential contact, which corresponds to the "adhesive" friction mode. In this mode, Amonton's law is inapplicable, and the friction coefficient loses its original meaning. Some classical works, which show the existence of a transition between "adhesive" and "normal" friction, were analyzed. It is shown that, in fact, there is no such transition. A computer simulation of the indentation process was carried out within the framework of the boundary element method, which confirmed the experimental results.

Indentation and Detachment in Adhesive Contacts between Soft Elastomer and Rigid Indenter at Simultaneous Motion in Normal and Tangential Direction: Experiments and Simulations.

In reported experiments, a steel indenter was pressed into a soft elastomer layer under varying inclination angles and subsequently was detached under various inclination angles too. The processes of indentation and detachment were recorded with a video camera, and the time dependences of the normal and tangential components of the contact force and the contact area, as well as the average contact pressure and average tangential stresses, were measured as functions of the inclination angle. Based on experimental results, a simple theoretical model of the indentation process is proposed, in which tangential and normal contacts are considered independently. Both experimental and theoretical results show that at small indentation angles (when the direction of motion is close to tangential), a mode with elastomer slippage relative to the indenter is observed, which leads to complex dynamic processes-the rearrangement of the contact boundary and the propagation of elastic waves (similar to Schallamach waves). If the angle is close to the normal angle, there is no slipping in the contact plane during the entire indentation (detachment) phase.

Thermal Stability and Melting Dynamics of Bimetallic Au@Pt@Au Core-Shell Nanoparticles.

Thermal stability is an important feature of the materials used as components and parts of sensors and other devices of nanoelectronics. Here we report the results of the computational study of the thermal stability of the triple layered Au@Pt@Au core-shell nanoparticles, which are promising materials for H2O2 bi-directional sensing. A distinct feature of the considered sample is the raspberry-like shape, due to the presence of Au nanoprotuberances on its surface. The thermal stability and melting of the samples were studied within classical molecular dynamics simulations. Interatomic forces were computed within the embedded atom method. To investigate the thermal properties of Au@Pt@Au nanoparticles, structural parameters such as Lindemann indexes, radial distribution functions, linear distributions of concentration, and atomistic configurations were calculated. As the performed simulations showed, the raspberry-like structure of the nanoparticle was preserved up to approximately 600 K, while the general core-shell structure was maintained up to approximately 900 K. At higher temperatures, the destruction of the initial fcc crystal structure and core-shell composition was observed for both considered samples. As Au@Pt@Au nanoparticles demonstrated high sensing performance due to their unique structure, the obtained results may be useful for the further design and fabrication of the nanoelectronic devices that are required to work within a certain range of temperatures.

In silico evaluation of the mechanical stimulation effect on the regenerative rehabilitation for the articular cartilage local defects.

Osteoarthritis is one of the most severe diseases of the human musculoskeletal system, and therefore, for many years, special attention has been paid to the search for effective methods of its treatment. However, even the most modern methods only in a limited number of cases in the early or intermediate stages of osteoarthritis lead to positive treatment results. In the later stages of development, osteoarthritis is practically incurable and most often ends with disability or the need for joint replacement for a large number of people. One of the main reasons hindering the development of osteoarthritis treatment methods is the peculiarities of articular cartilage, in which there is practically no vascular network and tissue homeostasis is carried out mainly due to the diffusion of nutrients present in the synovial fluid. In modern medicine, for the treatment of osteoarthritis, tissue engineering strategies have been developed based on the implantation of scaffolds populated with chondrogenic cells into the area of the defect. In vitro studies have established that these cells are highly mechanosensitive and, under the influence of mechanical stimuli of a certain type and intensity, their ability to proliferate and chondrogenesis increases. This property can be used to improve the efficiency of regenerative rehabilitation technologies based on the synergistic combination of cellular technologies, tissue engineering strategies, and mechanical tissue stimulation. In this work, using a regenerative rehabilitation mathematical model of local articular cartilage defects, numerical experiments were performed, the results of which indicate that the micro-and macro environment of the restored tissue, which changes during mechanical stimulation, has a significant effect on the formation of the extracellular matrix, and, consequently, cartilage tissue generally. The results obtained can be used to plan strategies for mechanical stimulation, based on the analysis of the results of cell proliferation experimental assessment after each stimulation procedure in vivo.

High-Precision Tribometer for Studies of Adhesive Contacts.

Herein, we describe the design of a laboratory setup operating as a high-precision tribometer. The whole design procedure is presented, starting with a concept, followed by the creation of an exact 3D model and final assembly of all functional parts. The functional idea of the setup is based on a previously designed device that was used to perform more simple tasks. A series of experiments revealed certain disadvantages of the initial setup, for which pertinent solutions were found and implemented. Processing and correction of the data obtained from the device are demonstrated with an example involving backlash and signal drift errors. Correction of both linear and non-linear signal drift errors is considered. We also show that, depending on the research interests, the developed equipment can be further modified by alternating its peripheral parts without changing the main frame of the device.

Preparation of Micro-Pit-Textured PCD Tools and Micro-Turning Experiment on SiCp/Al Composites.

Serious tool wear occurs very often during machining due to the reinforcing phases in the workpiece. In this study, micro-pit-textures were prepared on the surfaces of PCD tools with a nanosecond laser to improve their cutting performance on SiCp/Al composites. The micro-pits were designed with rounded corners to improve the chip flow. The location and size of the texture were determined by analyzing the tool-chip contact area of the non-textured tool. The cutting performance of these textured PCD tools was investigated through orthogonal cutting experiments. It was found that the optimal cutting performance of the textured tools was achieved with the proper distance of the texture from the main cutting edge (35 µm) and the pit spacing (60 µm), aa a result of which the main cutting force reduced by about 14%, and the tool wear and surface adhesion significantly reduced. This texture was then applied in the micro-turning experiments of the PCD tool on the SiCp/Al composites. The cutting force in this experiment reduced by 22%, and the textured tool provided better chip transfer and tool anti-tipping. In this study, the role of SiC particles as a third body between the tool and the chip surface is discussed.

Role of Adhesion Stress in Controlling Transition between Plastic, Grinding and Breakaway Regimes of Adhesive Wear.

A discrete-element based model of elastic-plastic materials with non-ideal plasticity and with an account of both cohesive and adhesive interactions inside the material is developed and verified. Based on this model, a detailed study of factors controlling the modes of adhesive wear is performed. Depending on the material and loading parameters, we observed three main modes of wear: slipping, plastic grinding, cleavage, and breakaway. We find that occurrence of a particular mode is determined by the combination of two dimensionless material parameters: (1) the ratio of the adhesive stress to the pure shear strength of the material, and (2) sensitivity parameter of material shear strength to local pressure. The case study map of asperity wear modes in the space of these parameters has been constructed. Results of this study further develop the findings of the widely discussed studies by the groups of J.-F. Molinari and L. Pastewka.

Dynamic stiction without static friction: The role of friction vector rotation.

In the textbook formulation of dry friction laws, static and dynamic friction (stick and slip) are qualitatively different and sharply separated phenomena. However, accurate measurements of stick-slip motion generally show that static friction is not truly static but characterized by a slow creep that, upon increasing tangential load, smoothly accelerates into bulk sliding. Microscopic, contact-mechanical, and phenomenological models have been previously developed to account for this behavior. In the present work, we show that it may instead be a systemic property of the measurement apparatus. Using a mechanical model that exhibits the characteristics of typical setups of measuring friction forces-which usually have very high transverse stiffness-and assuming a small but nonzero misalignment angle in the contact plane, we observe some fairly counterintuitive behavior: Under increasing longitudinal loading, the system almost immediately starts sliding perpendicularly to the pulling direction. Then the friction force vector begins to rotate in the plane, gradually approaching the pulling direction. When the angle between the two becomes small, bulk sliding sets in quickly. Although the system is sliding the entire time, macroscopic stick-slip behavior is reproduced very well, as is the accelerated creep during the "stick" phase. The misalignment angle is identified as a key parameter governing the stick-to-slip transition. Numerical results and theoretical considerations also reveal the presence of high-frequency transverse oscillations during the "static" phase, which are also transmitted into the longitudinal direction by nonlinear processes. Stability analysis is carried out and suggests dynamic probing methods for the approaching moment of bulk slip and the possibility of suppressing stick-slip instabilities by changing the misalignment angle and other system parameters.

Effect of elastic grading on fretting wear.

We consider fretting wear in elastic frictional contact under influence of oscillations of small amplitude and investigate the question, how wear damage can be influenced by the introduction of material gradients. To achieve a general understanding we restrict our consideration to media with a power-law dependency of the elastic modulus on depth. In this case, a complete analytical solution can be found for the final worn shape. In the limiting case of small fretting oscillations we obtain a simple, closed-form asymptotic solution of the problem. We find that the optimum grading depends on the oscillation amplitude: for large amplitudes, the use of materials with a positive exponent decreases the wear volume whilst for very small amplitudes the use of graded materials with slightly negative exponent is beneficial. Especially interesting is the case of the Gibson-medium which may help avoiding both fretting wear and fretting fatigue.

Heterogeneity of material structure determines the stationary surface topography and friction.

The character of surface roughness and the force of friction in the stationary state after a sufficiently long run-in process are of key importance for numerous applications, e.g. for friction between road and tire. In the present paper, we study theoretically and experimentally the asymptotic worn state of a bi-phasic material that is arbitrarily heterogeneous in the contact plane, but homogeneous in the direction of the surface normal. Under the assumption of Archard's wear law in its local formulation, the asymptotic shape is found in the closed integral form. Given the surface profile, the coefficient of friction can be estimated, since the coefficient of friction is known to be strongly correlated with the mean square root value of the surface slope. The limiting surface profiles and the corresponding coefficient of friction are determined as functions of size, relative concentration and wear ratio of the phases. The results of numerical calculations are compared to and validated by experiments carried out on simplified model systems. The main conclusion is that the rms value of the surface slope is not influenced by the characteristic linear size of inclusions and depends solely on the relative concentration of phases, as well as the ratio of their wear coefficients.

Adhesive contact of rough brushes.

The adhesive contact between a rough brush-like structure and an elastic half-space is numerically simulated using the fast Fourier transform (FFT)-based boundary element method and the mesh-dependent detachment criterion of Pohrt and Popov. The problem is of interest in light of the discussion of the role of contact splitting in the adhesion strength of gecko feet and structured biomimetic materials. For rigid brushes, the contact splitting does not enhance adhesion even if all pillars of the brush are positioned at the same height. Introducing statistical scatter of height leads to a further decrease of the maximum adhesive strength. At the same time, the pull-off force becomes dependent on the previously applied compression force and disappears completely at some critical roughness. For roughness with a subcritical value, the pressure dependence of the pull-off force qualitatively follows the known theory of Fuller and Tabor with moderate modification due to finite size effect of the brush.

Stick-slip boundary friction mode as a second-order phase transition with an inhomogeneous distribution of elastic stress in the contact area.

This article presents an investigation of the dynamical contact between two atomically flat surfaces separated by an ultrathin lubricant film. Using a thermodynamic approach we describe the second-order phase transition between two structural states of the lubricant which leads to the stick-slip mode of boundary friction. An analytical description and numerical simulation with radial distributions of the order parameter, stress and strain were performed to investigate the spatial inhomogeneity. It is shown that in the case when the driving device is connected to the upper part of the friction block through an elastic spring, the frequency of the melting/solidification phase transitions increases with time.

Influence of tangential displacement on the adhesion strength of a contact between a parabolic profile and an elastic half-space.

The adhesion strength of a contact between a rotationally symmetric indenter and an elastic half-space is analysed analytically and numerically using an extension of the method of dimensionality reduction for superimposed normal/tangential adhesive contacts. In particular, the dependence of the critical adhesion force on the simultaneously applied tangential force is obtained and the relevant dimensionless parameters of the problem are identified. The fracture criterion used coincides with that suggested by Johnson. In this paper, it is used to develop a method that is applicable straightforwardly to adhesive contacts of arbitrary bodies of revolution with compact contact area.

Effect of stress nonhomogeneity on the shear melting of a thin boundary lubrication layer.

We consider the dynamical properties of boundary lubrication in contact between two atomically smooth solid surfaces separated by an ultrathin layer of lubricant. In contrast to previous works on this topic, we explicitly consider the heterogeneity of tangential stresses, which arises in a contact of elastic bodies that are moved tangentially relative to each other. To describe phase transitions between structural states of the lubricant we use an approach based on the field theory of phase transitions. It is assumed that the lubricant layer, when stressed, can undergo a shear-melting transition of first or second order. While solutions for the homogeneous system can be easily obtained analytically, the kinetics of the phase transitions in the spatially heterogeneous system can only be studied numerically. In our numerical experiments melting of the lubricant layer starts from the outer boundary of contact and propagates to its center. The melting wave is followed by a wave of solidification. This process repeats itself periodically, following the stick-slip pattern that is characteristic of such systems. Depending on the thermodynamic and kinetic parameters of the model, different modes of sliding with almost complete or only partial intermediate solidification are possible.

Johnson-Kendall-Roberts adhesive contact for a toroidal indenter.

The unilateral axisymmetric frictionless adhesive contact problem for a toroidal indenter and an elastic half-space is considered in the framework of the Johnson-Kendall-Roberts theory. In the case of a semi-fixed annular contact area, when one of the contact radii is fixed, while the other varies during indentation, we obtain the asymptotic solution of the adhesive contact problem based on the solution of the corresponding unilateral non-adhesive contact problem. In particular, the adhesive contact problem for Barber's concave indenter is considered in detail. In the case when both contact radii are variable, we construct the leading-order asymptotic solution for a narrow annular contact area. It is found that for a v-shaped generalized toroidal indenter, the pull-off force is independent of the elastic properties of the indented solid.

Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids.

We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P-wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat et al., Phys. Rev. Lett. 92, 085502 (2004)10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru et al., Phys. Rev. E 64, 036128 (2001)10.1103/PhysRevE.64.036128].

Universal limiting shape of worn profile under multiple-mode fretting conditions: theory and experimental evidence.

We consider multiple-mode fretting wear in a frictional contact of elastic bodies subjected to a small-amplitude oscillation, which may include in-plane and out-of-plane translation, torsion and tilting ("periodic rolling"). While the detailed kinetics of wear depends on the particular loading history and wear mechanism, the final worn shape, under some additional conditions, occurs to be universal for all types and loading and wear mechanisms. This universal form is determined solely by the radius of the permanent stick region and the maximum indentation depth during the loading cycle. We provide experimental evidence for the correctness of the theoretically predicted limiting shape. The existence of the universal limiting shape can be used for designing joints which are resistant to fretting wear.

Key role of elastic vortices in the initiation of intersonic shear cracks.

Using the particle-based method of movable cellular automata, we analyze the initiation and propagation of intersonic mode II cracks along a weak interface. We show that the stress concentration in front of the crack tip, which is believed to be the mechanism of acceleration of the crack beyond the speed of shear waves, is due to the formation of an elastic vortex. The vortex develops in front of the crack during the short initial period of crack propagation. It expands and moves away from the crack tip and finally detaches from it. Maximum stress concentration in the vortex is achieved at the moment of detachment of the vortex. The crack can accelerate towards the longitudinal wave speed if the magnitude of shear stresses in the elastic vortex reaches the material shear strength before vortex detachment. We have found that for given material parameters, the condition for the unstable accelerated crack propagation depends only on the ratio of the initial crack length to its width (e.g., due to surface roughness).

On the role of scales in contact mechanics and friction between elastomers and randomly rough self-affine surfaces.

The paper is devoted to a qualitative analysis of friction of elastomers from the point of view of scales contributing to the force of friction. We argue that--contrary to widespread opinion--friction between a randomly rough self-affine fractal surface and an elastomer is not a multiscale phenomenon, but is governed mostly by the interplay of only two scales--as a rule the largest and the smallest scales of roughness of the contacting bodies. The hypothesis of two-scale character of elastomer friction is illustrated by computer simulations in the framework of the paradigm of Greenwood, Tabor and Grosch using a simplified one-dimensional model.

The functional significance of density and distribution of outgrowths on co-opted contact pairs in biological arresting systems.

Microstructures responsible for temporary arresting of contacting surfaces are widely distributed on surfaces in different organisms. Recent morphological studies show that these structures have different density of outgrowths and not ideal distribution pattern on both complementary parts of the contact. One can suggest that this difference is optimized by natural selection to get stronger mechanical arrest within the system. In this paper, we simulate such a system numerically, both in the frames of continuous contact and discrete dynamical models to prove this hypothesis and elucidate other aspects of optimization of such mechanical adhesive systems.