What is often referred to as a Hertzian contact can undergo plasticity either at the macroscale, due to an accidental overload, or at an asperity scale, due to the presence of surface defects and/or roughness. An elastic solution does not explicitly consider the surface velocity or loading history, but it is also apparent that a moving (rolling) load will not yield the same residual stress and strain distribution as a purely vertical loading/unloading. Three-dimensional (3D) analysis is also more complex than the two-dimensional (2D) problem because it implies a change in the surface conformity. This paper presents the results of a numerical investigation of frictionless elastic-plastic elliptical point contacts with a moving load, as compared to a purely vertical (indentation) load. In the present analysis, both bodies may behave in an elastic-plastic mode. Both kinematic and isotropic hardening are considered to account for repeated rolling contacts. The contact pressure and the plastic strain are found to be reduced when the two bodies are elastic-plastic, as compared to the case in which one of the bodies remains elastic. Numerical results also indicate that at a given load intensity, the maximum contact pressure and equivalent plastic strain are affected by the contact geometry (circular and elliptical point contacts) and differ significantly when the load is moving as compared to purely vertical indentation. Although the maximum elastic contact pressure (Hertz solution) is often used as a control parameter for rolling contact fatigue analysis, whatever the geometry of the contact (point, elliptical, or line contact), the results presented here show that the effective contact pressure and subsequent residual strains are strongly dependent on the contact geometry in the elastic-plastic regime.

The evolution of static friction and tangential stiffness in presliding of an elastic-plastic sphere in contact with a rigid flat, under full stick contact condition, is analyzed. Empirical dimensionless equations are developed for these parameters.

Elastohydrodynamic lubrication (EHL) is one of the most common types of lubrication, which widely exists in many machine elements such as gears, rolling bearings, cams and followers, metal rolling tools, and continuous variable transmissions. These components often transmit substantial power under heavy loading conditions that may possibly induce plastic deformation of contacting surfaces. Moreover, the roughness of machined surfaces is usually of the same order of magnitude as, or greater than, the average EHL film thickness. Consequently, most components operate in mixed lubrication with considerable asperity contacts, which may result in localized pressure peaks much higher than the Hertzian pressure, causing subsurface stress concentrations possibly exceeding the material yield limit. Plastic deformation, therefore, often takes place, which not only permanently changes the surface profiles and contact geometry, but alters material properties through work-hardening as well. Available mixed EHL models, however, do not consider plastic deformation, often yielding unrealistically high pressure spikes and subsurface stresses around asperity contact locations. Recently, a three-dimensional (3D) plasto-elastohydrodynamic lubrication (PEHL) model has been developed for investigating the effects of plastic deformation and material work-hardening on the EHL characteristics and subsurface stress/strain fields. The present paper is a continuation of the previous work done by Ren et al. (2010, “PEHL in point contacts,” ASME J. Tribol., 132 (3), pp. 031501) that focused on model development and validation, as well as investigation of fundamental PEHL mechanisms in smooth surface contacts. This part of the study is mainly on the PEHL behavior involving simple surface irregularities, such as a single asperity or dent, which can be considered as basic elements of more complicated surface roughness. It is found that considerable plastic deformation may occur due to the pressure peaks caused by the surface irregularity, even though sometimes external loading is not heavy and the irregularity is concave. The plastic deformation may significantly affect contact and lubrication characteristics, resulting in considerable reductions in peak pressure and maximum subsurface stresses.

This paper presents an overview of the hardness differential required for abrasion. Empirically, the abrasive must be at least 1.2 times harder than the worn surface if it is to produce a scratch. This value has been determined theoretically using slip-line field modeling, which assumes rigid-plastic mechanical behavior, an assumption that is inadequate for most abrasive particles. Two approaches using elastic-plastic models and three tribological pairs with similar ratios of abrasive hardness to worn material hardness were tested to gain an understanding of the hardness differential required for abrasion. The analysis showed that the ratios of the property of the abrasive to the property of the worn surface did not change with the model used when the mechanical behavior of the materials was similar. However, when the behavior of the materials was very dissimilar—as is often the case in abrasive processes—the ratios varied greatly depending on the model used, showing that there is a need for models to describe the hardness differential required for abrasion.

Mechanical properties of materials in small-scale applications, such as thin coatings, are often different from those of bulk materials due to the difference in the manufacturing process. Indentation has been a convenient tool to study the mechanical properties in such applications. In this paper, a numerical technique is proposed that can identify the mechanical properties using optimization and evaluate the robustness of identified material properties using sensitivity analysis. First, two response surfaces are constructed for loading and unloading curves from the indentation experiment of a gold film on the silicon substrate. Unessential coefficients of the response surface are then removed based on the test statistics. Unlike the traditional methods of identification, the tip geometry of the indenter is included because its uncertainty significantly affects the results. In order to validate the accuracy and stability of the method, the sensitivity of the identified material properties with respect to each coefficient is analyzed. It turns out that the plastic hardening parameter is the most sensitive to the experimental data. In addition, all material parameters are sensitive to the coefficients of higher-order bases. However, their effects are diminished because the magnitudes of these coefficients are small.

The contact area, friction force, and relative displacement evolution at the very early stage of fretting are investigated experimentally. Copper and steel spheres of various diameters are loaded against a hard sapphire flat by a range of normal loads deep into the elastic-plastic regime of deformation. A reciprocating tangential loading is then applied with a maximum loading below the static friction to avoid gross slip. Real-time and in situ direct measurements of the contact area, along with accurate measurements of the friction force and relative displacement, reveal substantial junction growth and energy dissipation mainly in the first loading cycle. The so-called “slip amplitude” is found to be attributed to residual tangential plastic deformation rather than to interfacial slip. Elastic shake-down is observed for the 2.5% hardening steel spheres while plastic shake-down is observed in the case of the elastic perfectly-plastic copper spheres.

Elastic-plastic contact of a smooth sphere and a half-space with a real machined surface is simulated using an integration-based multilevel contact model. The total surface deflection is composed of bulk and asperity deformations. They are calculated at the global and the asperity level, respectively, which are connected through the asperity-supporting load. With this new model, the accurate contact area and contact pressure under a given load are quickly predicted using a relatively coarse grid system. The calculated load-area curve shows good agreement with the experimental data. Finally, the effects of the surface topography, including roughness and the asperity radius, upon the real contact area are analyzed.

Sliding electrical contacts are found in many electromechanical devices, such as relays, switches, and resistance spot welding. Temperature rise due to sliding friction and electrical current may be the major source of sliding electrical contact deterioration. This paper reports the development of a three-dimensional thermo-elasto-plastic contact model of counterformal bodies, which takes into account transient heat flux, temperature-dependent strain hardening behavior, and a realistic heat partition between surfaces. Transient contact simulations induce a significant increase in computational burden. The discrete convolution and fast Fourier transform and the conjugate gradient method are utilized to improve the computation efficiency. The present model is used to study the case of a half-space sliding over a stationary sphere, and both are made of 7075 aluminum alloy; the contact resistance is considered mainly due to the surface oxide film. The simulation results indicate that the transient contact model is able to capture the history of plastic deformation accumulation and the material melting inception.

A set of finite element simulations was performed to analyze the creep behavior of an elastic–perfectly plastic hemisphere in contact with a rigid flat. This study focuses on the time-dependent stress relaxation of a fully plastic asperity. Assuming a Garofalo (hyperbolic sine) type material creep law, the asperity shows two distinct phases of relaxation. In the first phase, the asperity creeps with an accelerated creep rate and shows a contact area increase similar to that of a cylindrical geometry. In the second phase, no contact area change can be measured and the asperity creeps with a slower rate. Empirical evolution laws for the asperity creep behavior are presented, analyzing the influence of both material and geometrical parameters. The results are interpreted in terms of transient friction.

The friction coefficient ( μ ) of a contact surface with elliptical asperities is examined at various values of the plasticity index ( ψ ) , the effective radius ratio ( γ ) , the shear-strength-pressure proportionality constant ( c ) , and the dimensionless limiting interfacial shear strength ( τ ¯ m ) . The results demonstrate that the friction coefficient of the contact system increases with an increasing value of γ but decreases with an increasing value of ψ . Furthermore, it is shown that Amonton’s law is applicable for contact systems with either a low ψ and a high τ ¯ m or a high ψ and a low τ ¯ m . Analyzing the ratio of the nonelastic contact area, it is found that the asperities of a surface characterized by a large γ generally deform elastically at all values of the plasticity index, while those of a surface with a larger c deform plastically, particularly for surfaces with higher values of τ ¯ m and ψ . Finally, an inspection of the critical dimensionless real contact area shows that the contact mode of the surface is determined primarily by the value of the effective radius ratio.

With the increased use of hard disk drives (HDDs) in mobile and consumer applications combined with the requirement of higher areal density, there is enhanced focus on reducing head disk spacing, and consequently there is higher susceptibility of slider/disk impact damage during HDD operation. To investigate this impact process, a dynamic elastic-plastic finite element model of a sphere (representing a slider corner) obliquely impacting a thin-film disk was created to study the effect of the slider corner radius and the impact velocity on critical contact parameters. To characterize the energy losses due to the operational shock impact damage, the coefficient of restitution for oblique elastic-plastic impact was studied using the finite element model. A modification to an existing physics-based elastic-plastic oblique impact coefficient of restitution model was proposed to accurately predict the energy losses for a rigid sphere impacting a half-space. The analytical model results compared favorably to the finite element results for the range from low impact angles (primarily normal impacts) to high impact angles (primarily tangential impacts).

As the use of hard disk drives in mobile applications increases, the susceptibility of disk damage due to high velocity slider-disk impact presents a serious challenge. The impact could result in extremely high contact stresses, leading to the failure of the head-disk interface. An elastic-plastic contact-mechanics-based impact model was developed and implemented to study the impact between a slider corner and a disk. The impact model is based on the contact of a rigid sphere on a deformable half-space. The effect of slider corner radii and impact velocities on the contact parameters was initially investigated for a homogeneous disk substrate. To examine the effects of thin-film layers on the disk, the model was extended to a realistic layered disk, where the actual layered mechanical properties were directly measured. At high impact velocities and/or small slider corner radii, the impact was found to be dominated by the substrate and the effect of layers was negligible. At low impact velocities and/or large slider corner radii, the effect of nanometer thick layers could be clearly seen, as these layers are stiffer than the substrate protecting the disk from potential damage at lighter loads. Realistic dynamic impact experiments involving a slider and a spinning thin-film disk were performed using an operational shock tester. The impact damage was characterized in terms of residual penetration depth caused by the impact force of the shock and the impact velocity of the slider. However, the results were inconclusive in correlating with the impact model. To better control the experimental parameters, quasistatic nanoindentation experiments were performed on actual thin-film media and were successfully compared with the model predictions.

This study uses an elastic-plastic, coupled temperature-displacement finite element model to investigate the effect of rail corrugations on the wheel-rail thermal contact stress and temperature distribution during wheel braking. The finite element model assumes that the material properties and the friction coefficient are temperature-dependent. The analysis considers various corrugation wavelengths and amplitudes and is performed over a range of braking speeds. The results indicate that the corrugated rail induces wavelike contact pressure and temperature distributions on the rail surface. The results also show that the variation in the peak contact pressure increases as the corrugation wavelength is reduced or as the corrugation amplitude is increased. Furthermore, it is found that the corrugated rail shifts the location of the peak value of the rail surface temperature toward the leading edge of the contact region. The amplitude of the temperature fluctuations reduces as the corrugation wavelength is increased or as the corrugation amplitude is reduced. Finally, a higher corrugation amplitude or a shorter corrugation wavelength causes the location of the peak maximum shear stress to shift toward the rail surface.

A thermomechanical analysis of elasto-plastic bodies is a necessary step toward the understanding of tribological behaviors of machine components subjected to both mechanical loading and frictional heating. A three-dimensional thermoelastoplastic contact model for counterformal bodies has been developed, which takes into account steady state heat flux, temperature-dependent strain hardening behavior, and interaction of mechanical and thermal loads. The fast Fourier transform and conjugate gradient method are the underlying numerical algorithms used in this model. Sliding of a half-space over a stationary sphere is simulated with this model. The friction-induced heat is partitioned into two bodies based on surface temperature distributions. In the simulation, the sphere is considered to be fully thermoelastoplastic, while the half-space is treated to be thermoelastic. Simulation results include surface pressure, temperature rise, and subsurface stress and plastic strain fields. The paper also studies the influences of sliding speed and thermal softening on contact behaviors for sliding speed ranging three orders of magnitude.

An axisymmetrical hemispherical asperity in contact with a rigid flat is modeled for an elastic perfectly plastic material. The present analysis extends the work (sphere in contact with a flat plate) of Kogut–Etsion Model and Jackson–Green Model and addresses some aspects uncovered in the above models. This paper shows the critical values in the dimensionless interference ratios ( ω ∕ ω c ) for the evolution of the elastic core and the plastic region within the asperity for different Y ∕ E ratios. The present analysis also covers higher interference ratios, and the results are applied to show the difference in the calculation of real contact area for the entire surface with other existing models. The statistical model developed to calculate the real contact area and the contact load for the entire surfaces based on the finite element method (FEM) single asperity model with the elastic perfectly plastic assumption depends on the Y ∕ E ratio of the material.

A model for elastic-plastic nominally flat contacting rough surfaces under combined normal and tangential loading with full stick contact condition is presented. The model incorporates an accurate finite element analysis for contact and sliding inception of a single elastic-plastic asperity in a statistical representation of surface roughness. It includes the effect of junction growth and treats the sliding inception as a failure mechanism, which is characterized by loss of tangential stiffness. A comparison between the present model and a previously published friction model shows that the latter severely underestimates the maximum friction force by up to three orders of magnitude. Strong effects of the normal load, nominal contact area, mechanical properties, and surface roughness on the static friction coefficient are found, in breach of the classical laws of friction. Empirical equations for the maximum friction force, static friction coefficient, real contact area due to the normal load alone and at sliding inception as functions of the normal load, material properties, and surface roughness are presented and compared with some limited available experimental results.

In a recent paper ( 2004, “Elasto-Plastic Normal Contact of Three-Dimensional Fractal Surfaces Using Halfspace Theory,” J. Tribol., 126, pp. 28–33 ) the author developed a halfspace model for the elasto-plastic normal contact of rough surfaces. This model is now used to study the influence of intrinsic surface parameters on constitutive contact laws, such as load-gap relation and load-area relation, for a specific type of surface topography known as fractal-regular surfaces. Numerical investigations show that the fractal dimension has only minor influence on the load-gap relationship, which is mostly determined by the dimensionless ratio between the transition length and the rms values of the height data. Due to the fractal nature of the surfaces at the small wavelength limit, initial deformation will always be in the plastic range. The load-area relation becomes then completely independent of the geometric surface parameters and is determined by material properties alone, at least if the predicted plastic deformation occurs at a length scale larger than the atomic scale.

The determination of the elastoplastic deformation regime arising at the microcontact of a deformable ellipsoid and a rigid smooth flat was the main purpose of this study. One-eighth of an ellipsoid and a flat plate were taken as the contact bodies in the finite element analysis, and a mesh scheme of multisize elements was applied. Two observed phenomena regarding the contact pressures and the equivalent von Mises stresses formed at the contact area are given in order to identify the inception of the fully plastic deformation regime of an ellipsoid with an ellipticity k e . If the ellipticity ( k ) of an elliptical contact area is defined as the length ratio of the minor axis to the major axis, it is asymptotic to the k e value when the interference is sufficiently increased, irrespective of the k e value. The dimensionless interference regime associated with the elastoplastic deformation regime is narrowed by increasing the ellipticity of the ellipsoid ( k e ) . Significant differences in the microcontact parameters such as the contact pressure, the contact area, and the contact load were found to be a function of the interference and the k e parameter of an ellipsoid. The interferences corresponding to the inceptions of the elastoplastic and fully plastic deformation regimes are both increased if the k e value is lowered. The interference, the contact area, and the contact load predicted by the present model for the behavior demonstrated at the inception of the elastoplastic deformation regime are lower than those obtained from the Horng model ( Horng, J. H., 1998, “An Elliptical Elastic-Plastic Asperity Microcontact Model for Rough Surfaces,” ASME J. Tribol., 120, pp. 82–88 ) and the Jeng-Wang model ( Jeng, Y. R., and Wang, P. Y., 2003, “An Elliptical Microcontact Model Considering Elastic, Elastoplastic, and Plastic Deformation,” ASME J. Tribol., 125, pp. 232–240 ). Big differences in the results of the average contact pressure, the contact area, and the contact load among the above microcontact models are discussed. The discrepancies are also explained from the developments of these models and boundary conditions set for the elastoplastic deformation regime.

The paper presents a numerical analysis of the rolling contact between an elastic ellipsoid and an elastic-plastic flat. Numerical simulations have been performed with the help of a contact solver called Plast-Kid®, with an algorithm based on an integral formulation or semi-analytical method. The application of both the conjugate gradient method and the discrete convolution and fast Fourier transform technique allows keeping the computing time reasonable when performing transient 3D simulations while solving the contact problem and calculating the subsurface stress and strain states. The effects of the ellipticity ratio k —ranging from 1 to 16—and of the normal load—from 4.2 GPa to 8 GPa—are investigated. The reference simulation corresponds to the rolling of a ceramic ball on a steel plate made of an AISI 52100 bearing steel under a load of 5.7 GPa. The results that are presented are, first, the permanent deformation of the surface and, second, the contact pressure distribution, the von Mises stress field, the hydrostatic pressure, and the equivalent plastic strain state within the elastic-plastic body. A comparison with an experimental surface deformation profile is also given to validate the theoretical background and the numerical procedure.

In this paper, a theoretical and experimental investigation is presented to study the contact behavior of the plastic contact of deterministic rough surfaces. Analyses exclude bulk deformation of the rough surface and concentrate to the contact on asperity level. Surface asperities are modeled by an array of elliptic paraboloids where the unit event of a single contact is analyzed using an elastic-plastic elliptical contact model. A new method to determine the surface topography change due to plastic deformation is presented. Results show that the theoretical model developed predicts the contact area and the deformed geometry of the rough surface very well.