Elastic Plastic Spherical Contact Research Articles

Model for an elastic-plastic spherical contact with the DMT adhesion

This paper studied the elastic-plastic spherical contact with the DMT adhesion, and presented an improved smooth formula for the local separation outside the elastic-plastic contact area on the KE empirical formula. The elastic-plastic local separation was equal to the elastic local separation with the same contact area and a equivalent elastic contact displacement. When the contact entered the elastic deformation regime, due to zero residual plastic contact displacement, the present formula for the elastic-plastic local separation could reduce to that for the elastic local separation naturally. Utilizing the present formula for the local separation, a unified adhesion model suitable for between the elastic and elastic-plastic spherical contact with the DMT adhesion was presented. In comparison with the KE adhesion model, the present adhesion model had higher fitting accuracy and could approach the Bradley’s value as the contact displacement approached zero well, which was a good approximation to the complete integration calculation. The present adhesion model could be used for the study of the elastic and elastic-plastic spherical contact with adhesion.

Evolution of adhesive wear and friction in elastic-plastic spherical contact

A finite element (FE) model is presented for the evolution of fracture and friction in elastic-plastic adhesive spherical contact. The model is based on a realistic criterion of ductile fracture in a three-dimensional contact problem and the failed elements are deleted. Full stick contact condition is used at the contact interface to model a strong adhesion there. Fracture evolution is presented allowing the process of material removal in the form of a wear particle. The evolution of friction with increasing tangential loading as well as sliding inception are presented. Predicted wear coefficient and static and dynamic friction coefficients are compared with experimental results and possible reasons for discrepancies between the predicted and experimental results are discussed.

A Coupled Eulerian–Lagrangian Model for Sliding Inception of Elastic–Plastic Spherical Contact

AbstractCurrently existing finite element (FE) Lagrangian models of elastic–plastic spherical contact are costly in terms of computing time to reach vanishing tangential stiffness at sliding inception. A coupled Eulerian–Lagrangian (CEL) model with explicit dynamic analysis and power-law hardening is proposed to resolve this problem. The CEL model also avoids convergence problem caused by excessive distortion of elements in Lagrangian models. Static friction coefficient at sliding inception is investigated and compared with available experimental results. It is found that the proposed new CEL model is more efficient and accurate compared to previously published results of Lagrangian models.

Model for the static friction coefficient of spherical contact with a soft metal coating

An elastic–plastic spherical contact with soft metallic coating under combined normal and tangential loading is studied by finite element analysis. Full-stick contact condition is assumed and sliding inception is related to vanishing tangential stiffness of the contact junction. Previously observed, both experimentally and theoretically, effects of increasing coating thickness on static friction coefficient that were published in the literature are thoroughly explained here, to the authors’ best knowledge, for the first time. These effects include initial sharp drop of friction as soon as a thinnest coating film is applied, followed by a transitional behavior from decrease to increase of friction when the coating thickness is continuously increased. An intensive parametric study is performed and the effects of substrate and coating material properties on the static friction coefficient are revealed and thoroughly explained. An empirical expression for the static friction coefficient is derived along with the values for optimum coating thickness that provides the minimum friction coefficient.

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.

Cyclic tangential loading of a power-law hardening elastic–plastic spherical contact in pre-sliding stage

The cyclic tangential loading of the contact between a power-law hardening elastic–plastic sphere and a rigid flat under full stick condition is studied. The contact behavior in pre-sliding stage is investigated with a developed finite element model, and the contact parameters are obtained. Under the same maximum load in the cyclic tangential loading process, the tangential load–displacement relation is significantly affected by hardening exponents. Meanwhile, the dissipated energy obtained from the tangential load–displacement loops is larger for the smaller hardening exponent cases because the plastic deformation is more severe for these cases. The contact area increases mainly during the first tangential load cycle, and the increase is larger for materials with smaller hardening exponents.

Frictional Energy Dissipation in Spherical Contacts Under Presliding: Effect of Elastic Mismatch, Plasticity and Phase Difference in Loading

Behavior of friction at material interfaces is inherently nonlinear causing variations and uncertainties in interfacial energy dissipation. A finite element model (FEM) of an elastic–plastic spherical contact subjected to periodic normal and tangential loads is developed to study fundamental mechanisms contributing to the frictional energy dissipation. Particular attention is devoted to three mechanisms: the elastic mismatch between contacting pairs, plastic deformations, and phase difference between the normal and tangential fluctuations in loading. Small tangential loads simulating mild vibrational environments are applied to the model and resulting friction (hysteresis) loops are used to estimate the energy loss per loading cycle. The energy losses are then correlated against the maximum tangential load as a power-law where the exponents show the degree of nonlinearity. Exponents increase significantly with in-phase loading and increasing plasticity. Although increasing elastic mismatch facilitates more dissipation during normal load fluctuations, it has negligible influence on the power-law exponents in tangential loading. Among all the configurations considered, out-of-phase loading with minimal mismatch and no plasticity lead to the smallest power-law exponents; promising linear frictional dissipation. The duration the contact remains stuck during a loading cycle is found to have a predominant influence on the power-law exponents. Thus, controlling that duration enables tunable degree of nonlinearity and magnitude in frictional energy dissipation.

On the tangential contact behavior at elastic–plastic spherical contact problems

The problem of tangential contact between an elastic–plastic sphere and a rigid plane is studied analytically and numerically with the specific aim to derive force–displacement relations to be used in numerical simulations of granular materials. The simulations are performed for both ideal-plastic and strain hardening materials with different yield stresses and including large deformation effects in order to draw general conclusions. The results are correlated using normalized quantities pertinent to the correlation of indentation testing experiments leading to a general description of the tangential contact problem. Explicit formulas for the normal and tangential forces are presented as a function of the tangential displacement using data that are easily available from axi-symmetric analyses of spherical contact. The proposed model shows very good agreement when compared with the FE-simulations.

An Elastic-Plastic Spherical Contact Model Under Combined Normal and Tangential Loading

Spherical contact under combined normal and tangential loading has been investigated by many researchers, and some physically based criteria were proposed to capture the sliding inception, e.g., the local yielding criterion of the Kogut-Etsion (KE) model and the tangential stiffness criterion of the Brizmer-Kligerman-Etsion (BKE) model. In this work, by utilizing the maximum frictional shear stress criterion for the sliding inception, a finite element model for obliquely loaded spherical contact has been developed, which realized a friction transition from the KE model to the BKE model, with an increasing normal approach. The stress, strain, tangential force, normal force, and contact area during tangential loading are investigated using different models. It was found that with an elastic normal displacement preload, material failure is initiated on the surface, while with an elastic-plastic normal displacement preload the failure is initiated under the surface and then extends to the surface with the increasing tangential load. With an elastic-plastic normal displacement preload, there is an obvious normal force release during tangential loading. Different from the full stick model, both the Coulomb friction model and the proposed model are partial slip models in nature. However, the Coulomb friction is more empirically determined with some arbitrary friction coefficient, whereas the proposed model is based on physics parameters. Furthermore, both the Coulomb friction model and the proposed model predict a lower tangential force at the same tangential displacement, a slower growth of the contact area under elastic normal displacement preload, and a faster growth of the contact area under an elastic-plastic normal displacement preload compared to the full stick model.

The Evolution of Static Friction for Elastic-Plastic Spherical Contact in Pre-sliding

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.

Elastic–plastic spherical contact under cyclic tangential loading in pre-sliding

Abstract An elastic–plastic spherical contact under cyclic tangential loading in pre-sliding is numerically analyzed assuming full stick contact condition. Both isotropic and kinematic strain hardening laws are studied. It is found that the slip index and the dissipated energy, calculated from numerically obtained friction–displacement loops, are qualitatively similar to corresponding recently published experimental results. An empirical expression to predict dissipated energy is derived, showing good agreement with the numerical model prediction.

Analysis on elastic–plastic spherical contact and its deformation regimes, the one parameter regime and two parameter regime, by finite element simulation

In this paper the contact problem of a rigid sphere against an elastic–plastic sphere and a spherical elastic–plastic cavity is studied by means of finite element simulation for a wide range of radius ratios. Our results indicate that the deformation range naturally divides into two regimes, i.e. a one parameter regime (covering the elastic, small elastic–plastic and similarity deformation) and a two parameter regime (covering the finite deformation). In these two regimes average contact pressures (as well as contact area) versus indentation depth can be described respectively by the single parameter, i.e. indentation depth h/ R e, and the two parameters, i.e. h/ R e and radius ratio R 1/ R 2. Moreover, the variation trends of average contact pressure with the increase of indentation depth differ markedly in different deformation regimes. The numerical evolution of pressure distribution indicates that with increase of indentation depth the pressure distribution becomes more peaked at the center of the contact area meanwhile the maximum contact pressure, limited by the flow stress, increases slightly. Therefore in the two parameter regime, the average pressure would stop growing and get lower rather than continuously higher as it does in the one parameter regime.

Elastic–Plastic Spherical Contact Modeling Including Roughness Effects

The effect of material properties and surface roughness on the contribution of asperities and sphere bulk displacements to the total displacement of a rough spherical contact is investigated. A dimensionless transition load, above which the contribution of the bulk displacement exceeds the contribution of the asperities displacement, is found as a function of the plasticity index and dimensionless critical interference of the sphere bulk. A criterion is proposed for evaluating the importance of surface roughness in calculating the displacement of a rough spherical contact. Some experimental results with a spherical micro-contact are presented to verify the model.

Unloading of an elastic–plastic spherical contact under stick contact condition

The unloading process of an elastic–plastic spherical contact under stick contact condition is analyzed for various material properties. The evolution of normal and shear stress distribution at the contact area as well as the residual profile of the sphere and residual von Mises stresses inside the sphere are presented. Empirical expressions for the residual interference and for the evolution of the interference and contact area during the unloading are provided. Good agreement with experimental results is shown.

Junction Growth and Energy Dissipation at the Very Early Stage of Elastic-Plastic Spherical Contact Fretting

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.

The Effect of Surface Roughness on Static Friction and Junction Growth of an Elastic-Plastic Spherical Contact

A model for elastic-plastic spherical contact of rough surfaces under combined normal and tangential loadings, with full stick contact condition, is presented. The model allows evaluation of the effect of surface roughness on the real contact area, static friction and junction growth under small normal loads. It is shown that as the normal load approaches a certain threshold value, which depends on the plasticity index, the results of the present rough surface model approach these of previous corresponding models for smooth sphere and a rigid flat. At normal load values below the threshold load, the correlation of the present results and published experimental results is much better in comparison with the results of the smooth surface models.

Cyclic loading of an elastic-plastic adhesive spherical microcontact

A previous study of a single load-unload cycle of an adhesive contact between an elastic-plastic microscopic sphere and a rigid flat is extended here for several load-unload cycles. The interacting forces between the sphere and the flat obey the Lennard–Jones potential. Kinematic hardening is assumed for the sphere material to account for possible plastic shakedown, and the difference between kinematic and isotropic hardenings is discussed. The main goal of the current work is to investigate the evolution of the load-approach curves for the elastic-plastic spherical contact during its cyclic loading-unloading. These curves are presented for different physical conditions, represented by three main dimensionless parameters, which affect the behavior of the elastic-plastic adhesive contact. A transition value of the Tabor parameter is found, below which the load-approach curves are always continuous and jump-in and jump-out instabilities are not expected.

In situ investigation of the contact area in elastic–plastic spherical contact during loading–unloading

The real contact area between a sphere and a flat during loading, unloading, and cyclic loading–unloading in the elastic–plastic regime of deformations was investigated experimentally. A direct optical technique was used to observe in situ the evolution of the contact area. The experimental results obtained with copper and stainless steel spheres of different diameters that were pressed against a sapphire flat were compared with existing theoretical models, and whenever possible, with previous experimental works. These models are based on the assumption of either perfect slip (i.e., frictionless) or full stick contact condition. Good agreement was found between the experimental and theoretical results for the contact area and mean contact pressure. The existing models for the unloading process fail to accurately predict the residual radius of curvature of fully unloaded spheres, and the irreversibility of multiple loading unloading cycles at least for the several initial cycles. Some recommendations to improve the models are provided.

Elastic–plastic spherical contact under combined normal and tangential loading in full stick

The behavior of an elastic–plastic contact between a deformable sphere and a rigid flat under combined normal and tangential loading with full stick contact condition is investigated theoretically. Sliding inception is treated as a plastic yield failure mechanism, which allows static friction modeling under highly adhesive conditions. Several contact parameters such as: junction tangential stiffness, static friction force and static friction coefficient are extensively investigated. The phenomenon of junction growth and the evolution of the plastic zone in the contact region are briefly described. It is found that at low normal dimensionless loads the static friction coefficient decreases sharply with increasing normal load, in breach with the classical laws of friction. As the normal load further increases the static friction coefficient approaches a constant value that is about 0.3 for many material properties combinations.

The effect of contact conditions and material properties on elastic-plastic spherical contact

The effect of contact conditions and material properties on elastic-plastic spherical contact