An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. The model provides dimensionless expressions for the contact load, contact area, and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone. Comparison with previous elastic-plastic models that were based on some arbitrary assumptions is made showing large differences. ©2002 ASME

Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat

A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses

This work presents a finite element study of elasto-plastic hemispherical contact. The results are normalized such that they are valid for macro contacts (e.g., rolling element bearings) and micro contacts (e.g., asperity contact), although micro-scale surface characteristics such as grain boundaries are not considered. The material is modeled as elastic-perfectly plastic. The numerical results are compared to other existing models of spherical contact, including the fully plastic truncation model (often attributed to Abbott and Firestone) and the perfectly elastic case (known as the Hertz contact). This work finds that the fully plastic average contact pressure, or hardness, commonly approximated to be a constant factor of about three times the yield strength, actually varies with the deformed contact geometry, which in turn is dependent upon the material properties (e.g., yield strength). The current work expands on previous works by including these effects and explaining them theoretically. Experimental and analytical results have also been shown to compare well with the current work. The results are fit by empirical formulations for a wide range of interferences (displacements which cause normal contact between the sphere and rigid flat) and materials for use in other applications.

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A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat

An elastic-plastic model for contacting rough surfaces that is based on accurate Finite Element Analysis (FEA) of an elastic-plastic single asperity contact is presented. The plasticity index π is ...

A Finite Element Based Elastic-Plastic Model for the Contact of Rough Surfaces ©

The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Green's, function for the cases with known Green's functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC- FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.

Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm

Analyzing the contact between rough surfaces plays a key role in studying friction, wear, and lubrication in tribological systems. A proper description of the lubrication state and thermal condition also relies on a thorough understanding of the contact phenomena. The existing models for simulating the contact between rough surfaces are reviewed in this paper in three aspects: descriptions of rough surface profiles, expressions of the relations between the contact pressure and the surface displacement, and techniques used to solve the contact equations for the contact pressure and the surface displacements. Recent advancements in contact-models development are also briefly introduced. Presented at the 53rd Annual Meeting in Detroit, Michigan May 17–21, 1998

A Survey of Current Models for Simulating the Contact between Rough Surfaces

The rough surface contact in a tribological process involves frictional heating and thermoelastic deformations. A three-dimensional thermal-mechanical asperity contact model has been developed, which takes into account steady-state heat transfer, asperity distortion due to thermal and elastic deformations, and material yield. The finite-element method (FEM), fast Fourier transform (FFT), and conjugate gradient method (CGM) are employed as the solution methods. The model is used to analyze the thermal-mechanical contact of typical rough surfaces and investigate the importance of thermal effects on the contact performance of surface asperities.

A Three-Dimensional Thermal-Mechanical Asperity Contact Model for Two Nominally Flat Surfaces in Contact

One of the important issues in mixed lubrication is the contact problem involving frictional heating in the interface of contacting bodies. Due to contact and rubbing, temperature in the solid media varies, causing the contact conditions to change as a consequence of thermal distortion. A thermoelastic model for rough surfaces is developed for asperity contact subject to steady-state heat transfer. In this model, asperity distortion due to thermal and elastic-plastic deformations is considered. The thermal deformation is related to the contact pressure through a thermal influence function. Matrices for thermal and elastic influence functions are solved with the finite element method and the contact problem is computed with a mathematical programming method. Numerical analyses on the thermoelastic contact involving a rough surface reveal that asperity thermal distortion affects the contact pressure and surface separation at high frictional heat and deep asperity penetration. Presented at the 54th Annual Me...

A Thermoelastic Asperity Contact Model Considering Steady-State Heat Transfer

A thermoelastic asperity contact model has been developed for two-dimensional problems. This model takes into account a steady-state heat transfer and the asperity distortion due to thermoelastic deformations. The work reported in this paper further refines the thermoelastic model to include the shear traction effect on the thermoelastic stress distributions and derives semi-empirical relations for the contact pressure, temperature, asperity separation, and contact area, as functions of friction, asperity properties, and material properties. A method of boundary constraint coefficients is developed to facilitate the stress analyses of a half space using a finite computation domain.

Geng Liu

Papers

A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses

A Survey of Current Models for Simulating the Contact between Rough Surfaces

A Three-Dimensional Thermal-Mechanical Asperity Contact Model for Two Nominally Flat Surfaces in Contact

A Thermoelastic Asperity Contact Model Considering Steady-State Heat Transfer

Thermoelastic asperity contacts, frictional shear, and parameter correlations