Sinusoidal Asperity Research Articles

A Novel Fractal Model for Contact Resistance Based on Axisymmetric Sinusoidal Asperity

In this paper, a novel fractal model for the contact resistance based on axisymmetric sinusoidal asperity is proposed, which focuses on the resistance characteristics of the rough interface at a microscopic scale. By introducing the unique geometric shape of axisymmetric sinusoidal asperity, and combining it with a three-dimensional fractal theory, the micro-morphology characteristics of the rough interface can be characterized more precisely. Subsequently, by conducting a theoretical analysis and numerically solving the deformation mechanisms of asperities on the rough interface, a refined model for contact resistance is constructed. This research comprehensively employs theoretical analysis, numerical simulation, and experimental testing methods to deeply explore the current transmission mechanisms during the contact process of the rough interface. The findings suggest that the proposed model is capable of precisely capturing the intricate interplay of various factors, including contact area, contact load, and material properties, with the contact resistance. Compared to the existing models, the presented model demonstrates significant advantages in terms of prediction accuracy and practicality. This research provides an important theoretical basis and design guidance for optimizing the electrical performance of the rough interface, which has great significance for engineering applications.

Modeling and characterization of contact behavior of asperities with irregular shapes

This paper introduces a model for characterizing the contact behavior of irregular asperities, transforming it into a superposition of sinusoidal asperity contact behaviors. A new sinusoidal asperity model is developed for bilinear hardening under plane strain conditions. Empirical equations are proposed, considering geometric shapes, tangent modulus, and Young’s modulus. The frequency of asperity height is extracted through Fourier transform for irregular asperities. Contact area and pressure are predicted using the sinusoidal asperity model, and the behavior of irregular asperities is obtained by superimposing those with the first three frequencies. Experimental validation is conducted with milling and knurling-formed asperities, showing good alignment between the model and experimental results. In rough surface models, the proposed irregular asperity model exhibits greater accuracy in predicting contact behavior than a single sinusoidal asperity when interference exceeds 10% of the amplitude.

On the origin of plasticity-induced microstructure change under sliding contacts

Discrete dislocation plasticity (DDP) calculations are carried out to investigate the response of a single crystal contacted by a rigid sinusoidal asperity under sliding loading conditions to look for causes of microstructure change in the dislocation structure. The mechanistic driver is identified as the development of lattice rotations and stored energy in the subsurface, which can be quantitatively correlated to recent tribological experimental observations. Maps of surface slip initiation and substrate permanent deformation obtained from DDP calculations for varying contact size and normal load suggest ways of optimally tailoring the interface and microstructural material properties for various frictional loads.

On the Origin of Plastic Deformation and Surface Evolution in Nano-Fretting: A Discrete Dislocation Plasticity Analysis

Discrete dislocation plasticity (DDP) calculations were carried out to investigate a single-crystal response when subjected to nano-fretting loading conditions in its interaction with a rigid sinusoidal asperity. The effects of the contact size and preceding indentation on the surface stress and profile evolution due to nano-fretting were extensively investigated, with the aim to unravel the deformation mechanisms governing the response of materials subjected to nano-motion. The mechanistic drivers for the material’s permanent deformations and surface modifications were shown to be the dislocations’ collective motion and piling up underneath the contact. The analysis of surface and subsurface stresses and the profile evolution during sliding provides useful insight into damage and failure mechanisms of crystalline materials subject to nano-fretting; this can lead to improved strategies for the optimisation of material properties for better surface resistance under micro- and nano-scale contacts.

Influences of Morphology Parameters on the Contact Behavior of a Steel Interface

The surface roughness induced by geometric irregularities (asperities) has substantial influence on the contact stiffness, which further affects the working performance and service life of mechanical equipment. In this study, an elastic–plastic contact law between a sinusoidal asperity and a rigid smooth flat is first studied, which is then applied on a statistical model to simulate the contact behavior of a pair of 18CrMo4 steel surfaces to investigate the influences of morphology parameters on the contact stiffness. The analysis shows that smaller shape ratios [Formula: see text] and larger wavelengths [Formula: see text] induce larger normal contact stiffness [Formula: see text] for surfaces with identical roughness, wherein the roughness is defined by the mean value of asperity heights [Formula: see text] and the standard deviation of asperity heights [Formula: see text]. The normal contact stiffness increases as [Formula: see text] decreases under the same loading conditions, while the normal contact stiffness increases as [Formula: see text] decreases for surfaces with a fixed [Formula: see text]. Besides, the normal pressure and normal contact stiffness derived from the proposed contact model are validated. The results demonstrate the potential of the proposed model in contact design due to its ability of establishing the relations between the normal contact stiffness and surface morphology parameters.

Elastic and elastic-perfectly plastic analysis of an axisymmetric sinusoidal surface asperity contact

ABSTRACTClosed-form finite-element empirical models are available for elastic and elastic–plastic spherical and sinusoidal contact. However, some of these models do not consider the effect of interaction with adjacent asperities or require extensive numerical resources because they employ a full 3-D model. Therefore this work has analysed and quantified the behaviour of an elastic and elastic- perfectly plastic axisymmetric sinusoidal surface in contact with a rigid flat for a wide range of material properties and different values of the amplitude to wavelength ratio from initial to complete contact (high load). The numerical results agreed well with the Hertz model and the Jackson–Green elastic–plastic spherical contact model at low loads. Empirical equations for elastic and also elastic-perfectly plastic cases are formulated for the contact pressure, contact area and surface separation. From the current analysis, it is found that it is not any single parameter, but different combinations of material properties and surface roughness that govern the whole contact behaviour. The critical value of the amplitude of the sinusoidal asperity below which it will deform completely elastically from initial to complete contact is established. At low values of amplitude normalized by the critical amplitude, it was found that the contact behaved similar to a spherical contact, with the average pressure (hardness) always remaining lower than three times the yield strength. However, at higher values the average pressure increased toward a value as high as six times the yield strength at complete contact. All of these equations should be useful in rough surface contact modelling, lubrication analysis, electrical contact modelling and in many other applications.

Discrete Greenwood–Williamson Modeling of Rough Surface Contact Accounting for Three-Dimensional Sinusoidal Asperities and Asperity Interaction

Abstract The Greenwood–Williamson (GW) model has been one of the commonly used contact models to study rough surface contact problems during the past decades. While this has been a successful model, it still has a number of restrictions: (i) surface asperities are spheres; (ii) the overall deformation must be assumed to be small enough, such that there is no interaction between asperities, i.e., they are independent of each other; and (iii) asperity deformation remains elastic. This renders the GW model unrealistic in many situations. In the present work, we resolve above restrictions in a discrete version of the GW model: instead of spherical asperities, we assumed that the surface consists of three-dimensional sinusoidal asperities which appear more similar to asperities on a rough surface. For single asperity mechanical response, we propose a Hertz-like analytical solution for purely elastic deformation and a semi-analytical solution based on finite element method (FEM) for elastic–plastic deformation. The asperity interaction is accounted for by discretely utilizing a modified Boussinesq solution without consideration of asperity merger. It is seen that the asperity interaction effect is more than just the delay of contact as shown in the statistical model, it also contributes to the loss of linearity between the contact force and the contact area. Our model also shows that: for elastic contact, using spherical asperities results in a larger average contact pressure than using sinusoids; when plasticity is taken into account, using a sphere to represent asperities results in a softer response as compared with using sinusoids. It is also confirmed that sinusoidal asperities are a much better description than spheres, by comparison with fully resolved FEM simulation results for computer-generated rough surfaces.

Temperature rise of diamond-like carbon during sliding: Consideration of the real contact area

Abstract The real contact area based on modified Hertzian theory derived from sinusoidal asperity model is introduced and the measurement method for the real contact area is proposed. The real contact approach is compared with the Greenwood-Williamson theory showing good agreement between the two methods. The separation between the contact surfaces is estimated by taking into account the surface roughness. The temperature rise at the sliding interface between the DLC coating and E52100 steel is evaluated experimentally by the thermal indicator paint method, and the real contact area ratio is estimated from the temperature simulation data. The temperature rise is discussed from the entropy balance point of view induced from the real contact area and the frictional energy.

Research on Contact Behavior of Single Asperity on Work Roll Surface in Mixed Lubrication

The present paper focuses on asperity contact during cold rolling at a microscopic level. As analyses of such a contact are not practical with experimental facilities, a three-dimensional finite element method (FEM) is adopted to simulate the indentation and furrow behaviors of a single asperity on work roll surface in mixed lubrication. The effects of the tensile stress, the hydrodynamic pressure and the plastic deformation of steel strip are considered comprehensively. Most calculations are done for parabolic asperities, but for comparison purposes, some results are presented for sinusoidal and elliptical asperities. The indentation behaviors including uplift height of edges and plastic deformations of strip steel are calculated and analyzed. The friction during furrow behaviors is also considered. It reveals that the reduction and lubrication condition has a significant effect on the uplift height of strip steel edges around the asperity. Furthermore, long-term repeated effects of mixed lubrication contact are liable to spark asperity wear and decrease the roughness of rolls and even cause the failure of rolls in strip rolling mills.

Static friction of sinusoidal surfaces: a discrete dislocation plasticity analysis

Discrete dislocation plasticity simulations are carried out to investigate the static frictional response of sinusoidal asperities with (sub)-microscale wavelength. The surfaces are first flattened and then sheared by a perfectly adhesive platen. Both bodies are explicitly modelled, and the external loading is applied on the top surface of the platen. Plastic deformation by dislocation glide is the only dissipation mechanism active. The tangential force obtained at the contact when displacing the platen horizontally first increases with applied displacement, then reaches a constant value. This constant is here taken to be the friction force. In agreement with several experiments and continuum simulation studies, the friction coefficient is found to decrease with the applied normal load. However, at odds with continuum simulations, the friction force is also found to decrease with the normal load. The decrease is caused by an increased availability of dislocations to initiate and sustain plastic flow during shearing. Again in contrast to continuum studies, the friction coefficient is found to vary stochastically across the contact surface, and to reach locally values up to several times the average friction coefficient. Moreover, the friction force and the friction coefficient are found to be size-dependent.

Elastic–Plastic Sinusoidal Waviness Contact Under Combined Normal and Tangential Loading

The behavior of an elastic plastic contact between a deformable three-dimensional sinusoidal asperity and a rigid flat under combined normal and tangential loading is investigated using the finite element method. The sliding inception is determined by the maximum shear stress criterion. The resulting junction growth and static friction coefficient are investigated. It is found that for a general case, at the low dimensionless contact pressures, the static friction coefficient decreases sharply with increasing contact pressure. However, at the medium contact pressures, the static friction coefficient nearly approaches a constant value (around 0.23). Nevertheless, as the contact pressure further increases, the static friction coefficient keeps on reducing at a linear rate. The effects of material properties, geometric properties and critical shear strength on the static friction coefficient are also studied. An empirical expression for the static friction coefficient is provided.

Finite Element Analysis of the Effects of Thermally Grown Oxide Thickness and Interface Asperity on the Cracking Behavior Between the Thermally Grown Oxide and the Bond Coat

Finite element simulations based on an interface cohesive zone model (CZM) have been developed to mimic the interfacial cracking behavior between the α−Al2O3 thermally grown oxide (TGO) and the aluminum-rich Pt–Al metallic bond coat (BC) during cooling from high temperature to ambient temperature. A two-dimensional half-periodic sinusoidal geometry corresponding to interface undulation is modeled. The effects of TGO thickness and interface asperity on the stress distribution and the cracking behavior are examined by parametric studies. The simulation results show that cracking behavior due to residual stress and interface asperity during cooling process leads to stress redistribution around the rough interface. The TGO thickness has strong influence on the maximum tensile stress of TGO and the interfacial crack development. For the sinusoidal asperities, there exists a critical amplitude above which the interfacial cracking is energetically favored. For any specific TGO thickness, crack initiation is dominated by the amplitude while crack propagation is restricted to the combine actions of the wavelength and the amplitude of the sinusoidal asperity.

Finite element analysis of contact deformation regimes of an elastic-power plastic hardening sinusoidal asperity

A series of finite element simulations of frictionless contact deformation between an elastic-power plastic sinusoidal asperity and a rigid flat are carried out to explore the influence of the ratio of yield stress to elastic modulus on the evolution of contact deformation regime. The deformation behavior comprises five regimes with four transitional states corresponding to four critical events determined by curve-fitting of simulation results. The transitional boundaries between neighboring deformation regimes are: (1) initiation of plastic deformation; (2) plastic deformation just reaches the top surface; (3) the whole contact surface just experiences plastic deformation; (4) the attainment of maximum mean contact pressure. It is found the mean contact pressures at transitional events are closely associated with yield stress and characteristic stress, which can be used as normalization parameters.

Strain gradient plasticity analysis of elasto-plastic contact between rough surfaces

From a microscopic point of view, the real contact area between two rough surfaces is the sum of the areas of contact between facing asperities. Since the real contact area is a fraction of the nominal contact area, the real contact pressure is much higher than the nominal contact pressure, which results in plastic deformation of asperities. As plasticity is size dependent at size scales below tens of micrometers, with the general trend of smaller being harder, macroscopic plasticity is not suitable to describe plastic deformation of small asperities and thus fails to capture the real contact area and pressure accurately. Here we adopt conventional mechanism-based strain gradient plasticity (CMSGP) to analyze the contact between a rigid platen and an elasto-plastic solid with a rough surface. Flattening of a single sinusoidal asperity is analyzed first to highlight the difference between CMSGP and J2 isotropic plasticity. For the rough surface contact, besides CMSGP, pure elastic and J2 isotropic plasticity analysis is also carried out for comparison. In all cases, the contact area A rises linearly with the applied load, but with a different slope which implies that the mean contact pressures are different. CMSGP produces qualitative changes in the distributions of local contact pressures compared with pure elastic and J2 isotropic plasticity analysis, furthermore, bounded by the two.

Failure by deformation in the lateral contact between sinusoidal asperities

This article presents a study about the lateral force which produces the failure by deformation between asperities with the sine profile. This study begins with obtaining this force with experimental tests and numerical simulations by the finite element method, which shows good correspondence. The formulation of an analytical procedure to calculate the lateral force is also presented. This formulation is based on the theory of Hertz, which considers lateral contact between asperities, which causes deformation and eventually the failure. The results obtained by this method are compared to the results from tests and simulations using materials with different values of elasto-plasticity. The analysis of results shows the differences between analytical formulation and experimental data, according to which an empirical equation is formulated, whose results improve the approximation to the experimental data. The simplicity of the empirical equation formulated and adequate representation by the results of this, in tests and simulations, make it a numerical model useful for studies of surface wear.

Finite element analysis of large contact deformation of an elastic–plastic sinusoidal asperity and a rigid flat

Normal contact deformation of an asperity and a rigid flat is studied within an axisymmetric finite element model. The asperity features a sinusoidal profile and is elastic–plastic with linear strain hardening. Influences of geometrical (asperity height and width) and loading (the maximum interference) parameters on frictionless contact responses are explored for both loading and unloading. Dimensionless expressions for contact size and pressures covering a large range of interference and asperity ratio values are obtained in power-law forms. Results show the mean contact pressure after fully-plastic contact reaches a plateau only for small asperity ratios, while it continues increasing for large asperity ratios. The residual depth is found to be associated with plastically dissipated energy.

Finite element analysis of frictionless contact between a sinusoidal asperity and a rigid plane: Elastic and initially plastic deformations

A series of finite element simulations of frictionless contact deformations between a sinusoidal asperity and a rigid flat are presented. Explicit expressions of critical variables at plastic inception including interference, contact radius, depth of first yielding, and pressures are obtained from curve fitting of simulation results as a function of material and geometrical parameters. It is found Hertz solution is not applicable to the critical contact variables at plastic inception for sinusoidal contact, although contact responses of initially plastic deformation follow the same trend as that of purely elastic deformation. The contact pressure at incipient plasticity, which is defined as yield strength, is dependent on Poisson’s ratio, yield stress, and geometrical parameters, but independent of elastic modulus. It is not yield stress, but yield strength that correlates with indentation hardness. The results yield the insight into the specification of material properties to realize elastic contact. A larger ratio of yield stress to elastic modulus is beneficial to sustain a larger load before plastic deformation.

An electro-mechanical contact analysis of a three-dimensional sinusoidal surface against a rigid flat

Abstract All engineering surfaces have roughness that obstructs the flow of electrical current between two contacting surfaces. The peaks of roughness on the surface are modeled using the single asperity concept. In this work a semi-analytical model is developed for a sinusoidal asperity in contact and conducting electrical current. Also to verify the accuracy of the semi-analytical model, a finite element electro-mechanical three-dimensional perfectly elastic sinusoidal asperity in contact with rigid body is modeled. These results could be used in rough surface contact models that are based on sinusoidal shaped asperities.

Dynamic rupture at a frictional interface between dissimilar materials with asperities

A numerical investigation dealing with dynamic rupture at a frictional interface between dissimilar materials is proposed. The numerical Finite Element model is comprised of two homogeneous and isotropic elastic solids which are brought into contact with friction by remote normal compression and shear traction. The applied shear traction is less than the required one to produce overall sliding of the two solids. The rupture is nucleated by decreasing instantaneously the friction coefficient to zero at the nucleation area. A “rupture” is considered when an initially sticking zone of the interface becomes in sliding state; after nucleation two propagating ruptures appeared. The properties (velocity, generated waves, interface state …) of the obtained ruptures are here analyzed for a flat interface between dissimilar materials in function of the nucleation energy; then, the analysis of the effect of the interface roughness (sinusoidal asperities) is developed. The differentiated rupture inside the asperity and the conditions for coupling or uncoupling between the waves radiating in the two bodies, in function of the asperity dimensions, have been investigated. The aim of this work is to present the results from the non-linear finite element analysis in large transformations of the dynamic rupture at the interface with contact friction between two deformable bodies with and without roughness.

Size effects in single asperity frictional contacts

Two sets of indentation and sliding discrete dislocation plasticity analyses are carried out to investigate the initiation of frictional sliding between a rigid asperity and a single crystal film. Most calculations are carried out for sinusoidal asperities, but for comparison purposes some results are presented for wedge-shaped asperities. In one set of calculations the friction coefficient is evaluated from separate indentation and sliding calculations while in another set the indentation and sliding processes are carried out sequentially. Both sets of friction calculations predict a similar friction stress versus contact size relation with the friction stress dominated by adhesion at small contact sizes, being plasticity governed at large contact sizes and being strongly size dependent at intermediate values of the contact size. Remarkably, the predicted values of the friction coefficient are similar for both sets of calculations even though the predicted deformation fields and dislocation structures differ significantly.