W. Wayne Chen

Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces

This paper presents a three-dimensional numerical elasto-plastic model for the contact of nominally flat surfaces based on the periodic expandability of surface topography. This model is built on two algorithms: the continuous convolution and Fourier transform (CC-FT) and discrete convolution and fast Fourier transform (DC-FFT), modified with duplicated padding. This model considers the effect of asperity interactions and gives a detailed description of subsurface stress and strain fields caused by the contact of elasto-plastic solids with rough surfaces. Formulas of the frequency response functions (FRF) for elastic/plastic stresses and residual displacement are given in this paper. The model is verified by comparing the numerical results to several analytical solutions. The model is utilized to simulate the contacts involving a two-dimensional wavy surface and an engineering rough surface in order to examine its capability of evaluating the elasto-plastic contact behaviors of nominally flat surfaces.

Thermomechanical Analysis of Elastoplastic Bodies in a Sliding Spherical Contact and the Effects of Sliding Speed, Heat Partition, and Thermal Softening

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.

Three-Dimensional Repeated Elasto-Plastic Point Contacts, Rolling, and Sliding

Accumulative plastic deformation due to repeated loading is crucial to the lives of many mechanical components, such as gears, stamping dies, and rails in rail-wheel contacts. This paper presents a three-dimensional numerical model for simulating the repeated rolling or sliding contact of a rigid sphere over an elasto-plastic half-space. This model is a semi-analytical model based on the discrete convolution and fast Fourier transform algorithm. The half-space behaves either elastic-perfectly plastically or kinematic plastically. The analyses using this model result in histories of stress, strain, residual displacement, and plastic strain volume integral (PV) in the half-space. The model is examined through comparisons of the current results with those from the finite element method for a simple indentation test. The results of rolling contact obtained from four different hardening laws are presented when the load exceeds the theoretical shakedown limit. Shakedown and ratchetting behaviors are discussed in terms of the PV variation. The effect of friction coefficient on material responses to repeated sliding contacts is also investigated.

A multilevel model for elastic-plastic contact between a sphere and a flat rough surface

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.

A Numerical Static Friction Model for Spherical Contacts of Rough Surfaces, Influence of Load, Material, and Roughness

The relative motion between two surfaces under a normal load is impeded by friction. Interfacial junctions are formed between surfaces of asperities, and sliding inception occurs when shear tractions in the entire contact area reach the shear strength of the weaker material and junctions are about to be separated. Such a process is known as a static friction mechanism. The numerical contact model of dissimilar materials developed by the authors is extended to evaluate the maximum tangential force (in terms of the static friction coefficient) that can be sustained by a rough surface contact. This model is based on the Boussinesq-Cerruti integral equations, which relate surface tractions to displacements. The materials are assumed to respond elastic perfectly plastically for simplicity, and the localized hardness and shear strength are set as the upper limits of contact pressure and shear traction, respectively. Comparisons of the numerical analysis results with published experimental data provide a validation of this model. Static friction coefficients are predicted for various material pairs in contact first, and then the behaviors of static friction involving rough surfaces are extensively investigated.

Plasto-Elastohydrodynamic Lubrication (PEHL) in Point Contacts

Elastohydrodynamic lubrication (EHL) is an important branch of the lubrication theory, describing lubrication mechanisms in nonconformal contacts widely found in many mechanical components such as various gears, rolling bearings, cams and followers, metal-rolling tools, traction drives, and continuous variable transmissions. These components. often transmit substantial power under heavy loading conditions. Also, the roughness of machined surfaces is usually of the same order of magnitude as, or greater than, the estimated average EHL film thickness. Consequently, most components operate in mixed lubrication regime with significant asperity contacts. Due to very high pressure concentrated in small areas, resulted from either heavy external loading or severe asperity contacts, or often a combination of both, subsurface stresses may exceed the material yield limit, causing considerable plastic deformation, which may not only permanently change the surface profiles and contact geometry but also alter material properties through work hardening as well. In the present study, a three-dimensional plasto-elastohydrodynamic lubrication (PEHL) model has been developed by taking into account plastic deformation and material work-hardening. The effects of surface/subsurface plastic deformation on lubricant film thickness, surface pressure distribution, and subsurface stress field have been investigated. This paper briefly describes the newly developed PEHL model and presents preliminary results and observed basic behavior of the PEHL in smooth-surface point contacts, in comparison with those from corresponding EHL solutions under the same conditions. The results indicate that plastic deformation may greatly affect contact and lubrication characteristics, resulting in significant reductions in lubricant film thickness, peak surface pressure and maximum subsurface stresses.

An elastohydrodynamic lubrication model for coated surfaces in point contacts

An elastohydrodynamic lubrication (EHL) model for coated surfaces in point contacts has been developed by combining the elastic deformation formulation for the coated surfaces with an EHL model. Inverse fast Fourier transform (IFFT) is employed first to obtain the influence coefficients (ICs) from the frequency response function (FRF). The subsequent calculation of elastic deformation is performed using the efficient algorithm of discrete convolution and fast Fourier transform (DC-FFT). The coating EHL model is verified by the comparison to available numerical results. The effects of coating on lubrication under various loads, speeds, rheological models, and pressure-viscosity behaviors are numerically investigated. Similar to the observations from dry contact, stiffer coatings in EHL tend to reduce the nominal contact radius but increase the maximum contact pressure, and vice versa for more compliant coatings. However, as coating thickness increases, the influence of coatings on film thickness, including the central and the minimum film thicknesses, does not follow a monotonic variation, and therefore, cannot be predicted by any simple film thickness equation. The reason for that is the pressure viscosity effect which tends to counterbalance the effect of coating. The average friction coefficient in lubricant film increases in stiff coating cases but decreases for compliant coating cases. Furthermore, two possible approaches to improving the minimum film thickness thus reducing friction and wear in mixed lubrication are indicated: a thin stiff coating for conventional EHL and a thick compliant coating for soft EHL.

Transient Thermomechanical Analysis of Sliding Electrical Contacts of Elastoplastic Bodies, Thermal Softening, and Melting Inception

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.

Elasto-Plastic Analysis of a Contact Under Normal and Torque Loading

A spinning rigid sphere pressed against an elasto-plastic half space under combined normal and torque loading is presented. The elastic results based on present method are compared with an analytical solution to validate the current model. Stresses, strains, and residual displacements are investigated. The effects of friction coefficient on the spinning and half space contacts are studied. The surface pressure, subsurface stress, von Misses stress, the first yield point, plastic strain fields and evolution of the plastic region are further analyzed. Results show that the application of the torque shifts the maximum von Mises stress and plastic region in the half space closer to the surface; the whole plastic region also moves near the surface. Moreover, the position of the first yield points becomes closer to the surface as well; the evolution of the plastic region shows more complex shapes than those only under a normal load condition.Copyright

Transient Thermo-Elasto-Plastic Spherical Contact Analyses Considering Effects of Thermal Softening and Heat Partition

Frictional heating leads to the temperature rise, thermal expansion, and the thermo-elasto-plastic deformation, which may be responsible for the failure of components under contact and relative motion. This paper reports the development of a three-dimensional thermo-elasto-plastic contact model of counterformal bodies, which account for the transient heat transfer, temperature-dependent strain hardening behavior of materials, and realistic heat partition between surfaces. An extensive study on the contact of a sliding half-space over a stationary ball is conducted using this model.Copyright