Method Of Movable Cellular Automata Research Articles

Direct modelling of surface topography development in a micro-contact with the movable cellular automata method

Many aspects of wear are still far from understanding. The paper proposes theoretical approach exploring the mechanisms of friction and wear on the basis of combining micro- and macro-modelling. In a macroscopic phenomenological model processes of wear are considered as stochastic processes in the surface layers of contacting bodies, including spalling of wear microparticles, local stochastic transport due to plastic deformation as well as processes of nano-welding. We show that parameters of this model can be obtained as a result of direct simulation of a microscopic tribological contact. In the paper, the method of movable cellular automata is used for this aim. The results show a stochastic migration of a friction layer in the direction perpendicular to the sliding velocity. Estimation of the effective diffusion coefficient of the friction layer migration for different contacting materials, and construction of corresponding surface power spectra were done. The results help to identify the parameters of the macroscopic model and help to connect the micro- and macro-scales.

Modeling of brake pad-disc interface with emphasis to dynamics and deformation of structures

The frictional behavior at local contacts in an automotive brake system was analysed on the basis of computer simulation by movable cellular automata method. The boundary conditions of the model were adjusted to experimental observations obtained by TEM. The model proved to be adequate for simulating mechanical mixing and velocity accommodation at the pad-disc interface. Dynamics of particle interaction were visualized by showing rotation angles and velocity vectors. The model provided information on the development of plastic deformation for metal-on-metal contacts and on crack formation at graphite lamellae of cast iron disc. Results are in agreement with conventional friction theories.

Spectral analysis of the behavior and properties of solid surface layers. Nanotribospectroscopy

The paper demonstrates the feasibility of spectral analysis of acoustic vibrations and friction resistance force for studying the behavior, structure and properties of surface layers and coatings. Numerical simulation was performed on the nanoscopic scale with the use of the movable cellular automaton method. A method of analysis of elastic waves based on time dependences of velocity components, pressure and stress intensity at a certain point of the counterbody surface was proposed. The main peaks due to eigenfrequencies of the system, geometric and adhesion parameters of the model and the roughness of the interacting surfaces were identified in the obtained spectra. It is shown that the pressure spectra in the model are qualitatively similar to acoustic spectra in actual experiment. The feasibility of tribospectroscopic analysis based on calculation of the friction force for diagnostics of nanoscopic heterogeneities and discontinuities in a surface layer of thickness up to 100 nm is given theoretical grounds. The results of studies demonstrate the possibility of estimating the parameters of nanoscopic discontinuities such as the characteristic spatial period and linear dimensions. The applications of the proposed method as a promising nondestructive technique for studies of the behavior and diagnostics of the structure and damages in coatings and surface layers of nanoscopic thickness are discussed.

A Multi-scale Approach for Dynamical Simulations of the Surface Topography in High-pressure Frictional Contacts: Bridging Simulation Scales

In tribological dry-friction micro-contacts under high pressure the surfaces of both friction partners are subjected to constant change due to severe plastic deformation and wear. Simulations with the method of Movable Cellular Automata (MCA) have shown that a quasi-fluid layer evolves in the contact zone between the friction partners. The simulation length scales are few nanometers. With computational resources available today it is not possible to make simulations on macroscopic length and time scales. In this paper a particle model is presented that includes the basic processes—plastic deformation, mass transfer, and wear—on the micro-scale and allows for simulation and calculation of larger contact areas. With this model it is possible to combine the existing modeling and simulation tools on the micro-scale with simulations and measurements on macroscopic lengths scale. A master equation is developed that contains transition probabilities for particle-like volume-elements. Using the Fokker–Planck-Formalism the result is a stochastic partial differential equation that describes the formation and development of the stochastic surface of one frictional partner. The resulting time-dependent self-affine power spectrum of the surface profile can be used in other macroscopic methods to calculate friction, wear, traction curves, and other macroscopic quantities.

On rotation in the movable cellular automaton method

The paper discusses the problem of rotation in the framework of the particle method. It is shown that taking into account the rotatioi either as an independent degree of freedom or as a rotation of the surrounding allows adequate description of classical continua by th movable cellular automation method. Description of more complex media, for example micropolar media, requires consideration of th rotation by both methods with an independent degree of freedom taken as an independent rotation.

Assessment of nanostructured ceramic coating damage. Nanotribospectroscopy

The applicability of a tribospectral analysis to the detection of nanoscale inhomogeneities and discontinuities at the nanocoating-substrate interface has been substantiated theoretically. The approach put forward in this work is based on the measurement of the counterbody sliding resistance force coupled with an analysis of its frequency spectrum. A theoretical study on the potentialities and limitations of nanotribospectroscopy has been performed with the use of a computer simulation by the method of movable cellular automata. The results of the investigation have shown, among other things, the possibility to estimate a number of parameters of nanoscale discontinuities (characteristic spacing, linear size, etc.). To obtain reliable information on the defect structure and spacing, nanotribospectroscopy must be supplemented by other diagnostic methods. The design of a prototype nanotribospectrometer with spatial resolution up to 8 nm is described. Applications of the examined approach as a promising nondestructive-testing technique for assessment of nanostructured coating and surface layer damage are discussed.

Numerical modeling of processes of mass transfer in tribological contacts by the method of movable cellular automata

Wear is viewed as a stochastic process in the surface layers of contacting bodies; it comprises the processes of spalling of wear particles and their stochastic transportation and nanobonding. These processes can be described within the framework of the macroscopic phenomenological theory [1]; however, the parameters of the macroscopic theory can be found only by microscopic modeling of the tribological interface. In the present paper, the dynamic processes are modeled by means of the method of movable cellular automata in the interface of a tribological couple. The results allow us to identify the parameters of the macroscopic model based on the modeling of processes at the nanolevel; this enables us to extrapolate from the nano- to the macrolevel.

A multilevel computer simulation of friction and wear by numerical methods of discrete mechanics and a phenomenological theory

A procedure for a multilevel computer simulation of friction and wear is proposed where numerical calculations at local contact scales by the method of movable cellular automata and a macroscopic phenomenological friction theory are chained together within a unified concept. For a mesoscopic simulation, use is made of the method of movable cellular automata in combination with numerical methods of continuum mechanics. Results obtained from a simulation of local contacts in contacting pairs of heterogeneous friction materials are reported. The effect of the initial surface microroughness on a quasi-fluid layer in the contact zone of plastic materials is examined. The macroscopic phenomenological model for friction describes spalling, reintegration of wear debris into the wear surfaces and mass transfer from one contacting body to the other, using stochastic differential equations. The parameters of the phenomenological equations are found solely by means of microscopic models for processes involved in a tribological contact. It is suggested that a simulation by the method of movable cellular automata be used to this end. The procedure developed enables the effective diffusion coefficient of the friction layer to be estimated. Identification of the parameters of the macroscopic model is made possible by simulating the processes operative at the nanoscale level thus bridging nano- and macroscale levels.

Numerical Simulation of Mechanically Mixed Layer Formation at Local Contacts of an Automotive Brake System

Processes taking place at local contacts in an automotive brake system are analyzed on the basis of computer simulation with the method of movable cellular automata. The conditions of a mechanically mixed layer (MML) formation on the tribosurfaces and the influence of the layer on the friction coefficient are investigated. The results show that the MML formation leads to the stabilization of the coefficient of friction at a convenient range (0.3–0.4) for brake application. The presence of graphite particles in the MML decreases the critical value of local normal stress for switching from stick-slip to smooth relative motion with MML formation.

Analytical approach for wear prediction of metallic and ceramic materials in tribological applications

Wear mechanisms, as adhesion, abrasion, fatigue and tribochemical wear, are complex in their physical and chemical nature. A theoretical description and prediction of wear are in most cases still far from reality. It is, therefore, important to use test rigs before a practical application of a given material combination under tribological loading. On the other hand, model equations can be helpful for wear description, if a single wear mechanism is dominant. Under oscillating and continuous sliding contact conditions, equations for wear calculation are presented to describe running-in and stationary wear behaviour of metals and ceramics. By using shear energy density, real area of contact, flash temperature, activation energy and numerical simulations with the method of movable cellular automata (MCA), wear data were calculated and compared to experimental laboratory results.

Development of surface topography for the rail–wheel contact

We investigate the development of surface topography of two solids in a high-pressure frictional contact, like the rail–wheel contact. The friction process is simulated with the method of Movable Cellular Automata. It is shown that a quasi-fluid layer develops that influences the change of the surface topography and shows stochastic vertical migration. The resulting surfaces are analysed and the corresponding power spectra calculated. We further present a model that describes the basic processes in the quasi-fluid layer, like plastic deformation, detachment of wear particles and their reintegration and calculate the resulting time-dependent power spectra numerically and analytically.

Computer modeling of local tribological contacts by the example of the automotive brake friction pair

In the paper the method of discrete modeling (movable cellular automata method) and combined discrete-continuous description of the simulated medium are used to analyze processes occurring in the local contact of the automotive brake system. The characteristic size of the considered region is 1.5 μm. The following contact situation is simulated: steel fiber coated by an iron oxide film as the brake pad and pearlitic steel also coated by an iron oxide layer as the disc. On the assumption of oxide layer wearing we simulate the iron oxide - iron oxide, iron oxide - metal and metal - metal contacts. The calculation results for the friction coefficient for various contact situations give quite adequate values. For example, for the oxide - oxide system the calculated coefficient is approximately equal to 0.4, while for the metal - metal contact the obtained value varies from 0.7 to 0.9. Analysis of a set of the obtained results allows concluding that oxide is formed more rapidly than the sliding layer, which in turn makes the friction coefficient value stabilized.

Fracture Toughness Calculation by Movable Cellular Automata Method

Fracture toughness calculation by Movable Cellular Automata (MCA) method is demonstrated in this study in order to verify the validity of application of MCA method to the fracture problems. Two different geometries: edge-cracked strip and center cracked plate tension specimen have been considered to simulate numerically, which make place in real experiments. Soda-Lime silica glass for brittle material, AISI 1040 Steel and Aluminum Alloy 2024 for ductile materials were used, respectively. Fulfillment of basic principles of fracture mechanics has been checked. In MCA method, special fracture criterion is used to describe the process of crack propagation and critical stress and displacement was obtained, which are used as input data for evaluating the fracture toughness. In comparisons with table data, the results showed the sufficient agreement, which states the facility of the MCA method in application to the fracture problems.

Numerical simulation of typical contact situations of brake friction materials

In the paper, a model typical for contact situations of automotive brakes is established based on the method of movable cellular automata. The processes taking place at local contacts in an automotive brake system are analysed. Based on microscopic and micro-analytical observations, the following contact situations were simulated: (i) a couple of ferritic steel against pearlitic steel, both covered by an oxide layer mixed with graphite nanoparticles and (ii) the same situation but without oxide layers. The results of calculated mean coefficients of friction of the oxide-on-oxide contact correspond well to expected values for a real braking system, whereas steel-on-steel contact are twice as high. This allows one to make some conclusions; for example, oxide formation will take place more quickly than friction layer elimination, and finally this is responsible for the stabilisation of the coefficient of friction.

Towards a better understanding of brake friction materials

This work focuses on surface changes induced by repeated brake applications and tries to provide explanations, how such material modifications might affect friction and wear properties of automotive disc brakes. Surface films were investigated locally by transmission electron microscopy (TEM) after having prepared thin cross-sections with a focused ion beam instrument (FIB). Since the observed friction layers revealed a nanocrystalline structure, modelling with the method of movable cellular automata (MCA) was performed by assuming an array of linked nanometer-sized particles. In spite of complicated material combinations at the pad surface, two very characteristic features were always observed at both the pad and disc surface, namely a steel constituent—either ferritic (pad) or pearlitic (disc), partly covered with patches of nanocrystalline iron oxide, on a zone of severe plastic deformation with fragmented grain structure. When using an automata size of 10 nm, reasonable values for the mean coefficient of friction (COF) were obtained, namely 0.35 and 0.85 for oxide-on-oxide and metal-on-metal contacts, respectively. Immediately after brake application mass-mixing and bond-breaking was observed within a narrow zone at both surfaces.

Simulation of mechanical behavior of calcium-phosphate coatings with different calcium content under shear loading based on the movable cellular automaton method

The discrete movable cellular automaton method (MCA-method) is used to develop a technique for determining shear components of the stress and strain tensor in an arbitrary elementary volume of the specimen. We perform calculations for different calcium distributions through the coating thickness, which correspond to different methods of calcium distribution or different time of its being in the organism. The calculation results allow us to evaluate elastic properties as well as shear strains and stresses depending on the distribution of elements in the coating. For the chosen coating compositions we determine calcium distributions at which the shear stress and strain values in the coating are maximum and minimum.

Quasi-viscous fracture of brittle media with stochastic pore distribution

The development of deformation and fracture under uniaxial loading conditions in porous ceramic materials with the pore space having regular and stochastic structures of various types has been studied by method of movable cellular automata. The influence of the porous structure on the dynamics of damage nucle- ation and development is been analyzed, and a correlation between the effective stiffness of porous samples and the rate of damage accumulation is found. It is concluded that brittle materials can exhibit quasi-viscous frac- ture determined entirely by the pore space structure.

Multiscale simulation of dry friction in wheel/rail contact

Friction is a phenomenon involving elastic interactions, plastic deformation and failure processes at different length scales. The friction coefficient is one of the most relevant parameters for the rolling contact of railway wheels and rails. A model of dry friction is established based on the method of movable cellular automata (MCA). The influence of pressure and sliding velocity has been investigated by means of a large number of numerical simulations. A general qualitative conclusion is the fact that dynamic processes of plastic deformation and fracture at the nanolevel are of great importance. Within this model, the contact temperature can also be considered by its influence on the strength of materials. The new friction law is applied to the calculation of stresses, deformations and tractive forces in wheel/rail contact with rough surfaces. Thus, the understanding for the physical background of dry friction in engineering applications can be considerably improved.

Numerical simulation methods in tribology

We presented a general structure of a possible reduced description of classical macroscopic tribological systems, which should make it possible to simulate the friction and wear of real systems, taking into account a large variety of relevant processes and space scales, including the contact mechanics and hydrodynamics at macro and meso scales as well as inelastic processes, detachment of particles and their reintegration into the surfaces at the nanoscale. The main features of this reduced description are reduction in the dimensionality of the elastic contact problem from three to one and substitution of the complete hydrodynamics by distance- and velocity-depending surface forces as well as simulation of inelastic surface processes as stochastic deposition and diffusion along the surface. The processes on the nanoscale are simulated with the method of Movable Cellular Automata.

Macroscopic isotropy of two- and three-dimensional elastic lattice models

Particle methods such as the meso-particle method or the method of movable cellular automata provide new possibilities for the simulation of wear, mass-transfer, plastic deformation and melting processes. One crucial point, however, is to ensure that in the continuum limit macroscopic isotropy is guaranteed. We show how this can be done in two- and three-dimensional lattices.