Daniel Nelias

Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code

A three-dimensional elastic-plastic contact code based on semi-analytical method is presented and validated. The contact is solved within a Hertz framework. The reciprocal theorem with initial strains is then introduced, to express the surface geometry as a function of contact pressure and plastic strains. The irreversible nature of plasticity leads to an incremental formulation of the elastic-plastic contact problem, and an algorithm to solve this problem is set up. Closed form expression, which give residual stresses and surface displacements from plastic strains, are obtained by integration of the reciprocal theorem. The resolution of the elastic-plastic contact using the finite element (FE) method is discussed, and the semi-analytical code presented in this paper is validated by comparing results with experimental data from the nano-indentation test. Finally, the resolution of the rolling elastic-plastic contact is presented for smooth and dented surfaces and for a vertical or rolling loading. The main advantage of this code over classical FE codes is that the calculation time makes the transient analysis of three-dimensional contact problems affordable, including when a fine mesh is required. @DOI: 10.1115/1.1467920#

Role of Inclusions, Surface Roughness and Operating Conditions on Rolling Contact Fatigue

Tests have been performed on a two-disk machine in order to evaluate the role of inclusions, surface roughness and operating conditions on rolling contact fatigue of AISI 52100 and M50 bearing steels. Important parameters-such as nature and location of inclusions, small and large wavelengths of surface roughness, normal loading or sliding conditions-on crack initiation and propagation stages have been identified. The operating conditions have been selected to encompass typical jet engine applications. Tests have been carried out up to 4.2 GPa, for two different surface finishes. Surface distress and sub-surface damage which could result in catastrophic failure have been observed. Indeed, surface initiated deep spalling (observed at 3.5 GPa for unpolished surfaces and under rolling plus sliding conditions) as well as sub-surface initiated deep spalling (at 4.2 GPa for polished specimens) have been observed. Sub-surface micro-cracks were detected early and followed during some interrupted tests by the means of an ultrasonic echographic device. Results of our experiments are analyzed and discussed in relation to the rolling contact fatigue theories.

Elastic-Plastic Contact Between Rough Surfaces: Proposal for a Wear or Running-In Model

A semi-analytical thermo-elastic-plastic contact model has been recently developed and presented in a companion paper. The main advantage of this approach over the classical finite element method (FEM) is the treatment of transient problems with the use of fine meshing and the possibility of studying the effect of a surface defect on the surface deflection as well as on subsurface stress state. A return-mapping algorithm with an elastic predictor/plastic corrector scheme and a von Mises criterion is now used, which improves the plasticity loop. This improvement in the numerical algorithm increases the computing speed significantly and shows a much better convergence and accuracy. The contact model is validated through a comparison with the FEM results of Kogut and Etsion (2002, J. Appl. Mech., 69, pp. 657–662) which correspond to the axisymmetric contact between an elastic-perfectly plastic sphere and a rigid flat. A model for wear prediction based on the material removal during cyclic loading is then proposed. Results are presented, first, for initially smooth surfaces and, second, for rough surfaces. The effects of surface shear stress and hardening law are underlined.

Contact analyses for bodies with frictional heating and plastic behavior

The stress field within machine components is an important indicator for contact failures. Since both thermal stresses due to frictional heating and plasticity are significant in engineering application, it is critical to predict the total stress field. In this work, the steady-state thermal effect is considered and a thermo-elastic-plastic contact model is developed. The model is applicable for rolling and/or sliding contact problem, as far as small equivalent plastic strain hypothesis is respected. Influence coefficients for surface normal displacement, temperature, and strain and stress tensors are used with the discrete convolution and fast Fourier transform algorithm. The single-loop conjugate gradient iteration scheme is also applied to achieve fast convergence speed. Simulations are presented for several academic examples ranging from elastic to thermo-elastic-plastic. The thermo-elastic-plastic analyses show that the heat factor in a contact situation has significant effect not only on the critical Hertzian pressure and on the pressure distribution, but also on the magnitude and depth of the maximum von Mises stress during loading and the residual ones found after unloading.

Modeling of the rolling and sliding contact between two asperities

A semi-analytical method for the tridimensional elastic-plastic contact between two hemispherical asperities is proposed. The first part of the paper describes the algorithm used to deal with the normal contact, which can be either load-driven or displacement-driven (dd). Both formulations use the conjugate gradient method and the discrete convolution and fast Fourier transform (DC-FFT) technique. A validation of the code is made in the case of the displacement-driven formulation for an elastic-plastic body in contact with a rigid punch, simulating a nano-indentation test. Another new feature is the treatment of the contact between two elastic-plastic bodies. The model is first validated through comparison with the finite element method. The contact pressure distribution, the hydrostatic pressure and the equivalent plastic strain state below the contacting surfaces are also found to be strongly modified in comparison to the case of an elastic-plastic body in contact with a purely elastic body. The way to consider rolling and sliding motion of the contacting bodies consists of solving the elastic-plastic contact at each time step while upgrading the geometries as well as the hardening state along the moving directions. The derivations concerning the interference calculation at each step of the sliding process are then shown, and an application to the tugging between two spherical asperities in simple sliding (dd formulation) is made. The way to project the forces in the global reference is outlined, considering the macro-projection due to the angle between the plane of contact and the sliding direction, and the micro-projection due to the pile-up induced by the permanent deformation of the bodies due to their relative motion. Finally, a load ratio is introduced and results are presented in terms of forces, displacements, and energy loss in the contact.

A Three-Dimensional Semianalytical Model for Elastic-Plastic Sliding Contacts

A three-dimensional numerical model based on a semianalytical method in the framework of small strains and small displacements is presented for solving an elastic-plastic contact with surface traction. A Coulombs law is assumed for the friction, as commonly used for sliding contacts. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces are derived from Betti s reciprocal theorem with initial strain. The main advantage of this approach over the classical finite element method (FEM) is the computing time, which is reduced by several orders of magnitude. The contact problem, which is one of the most time-consuming procedures in the elastic-plastic algorithm, is obtained using a method based on the variational principle and accelerated by means of the discrete convolution fast Fourier transform (FFT) and conjugate gradient methods. The FFT technique is also involved in the calculation of internal strains and stresses. A return-mapping algorithm with an elastic predictor/plastic corrector scheme and a von Mises criterion is used in the plasticity loop. The model is first validated by comparison with results obtained by the FEM. The effect of the friction coefficient on the contact pressure distribution, subsurface stress field, and residual strains is also presented and discussed.

An Experimental Study on the Concentration and Shape of Dents Caused by Spherical Metallic Particles in EHL Contacts

An experimental study of metallic contaminant effects on surface indentation in EHL contacts is presented. Particles are initially spherical and are composed of M50 high-carbon steel powder. Their diameter ranges from 32 to 40 μm. An original lubrication system with a controlled level of contamination was built. The contaminant distribution and concentration are measured on-line by an automatic particle counter. Tests are conducted on a two-disk machine with different operating conditions. Particles may travel through the EHL contact only one time, the lubricant flow being used only once. The oil is a synthetic one qualified under the MIL-L-23699 specification. An optical profilometer is used to describe the indent topography and a CCD video camera to count the number of dents. The test bench is described and the experimental procedure is presented. Specific tests were performed to quality the contamination bench. The combined effects of particles concentration and test duration on dent distribution were ...

Modeling of Fretting Wear Under Gross Slip and Partial Slip Conditions

The paper presents a numerical model to investigate fretting wear either under partial or gross slip conditions. An efficient three-dimensional elastic-static contact model to solve both the normal contact problem and the tangential contact problem is presented. The contact model is validated with analytical solutions for a sphere on flat geometry. A wear law issued from the literature and based on the friction energy is used to simulate surface wear. Numerical friction logs are obtained and the wear rate evolution is found to be highly dependent on the tangential displacement.

A Comprehensive Method to Predict Wear and to Define the Optimum Geometry of Fretting Surfaces

This paper presents a fast and robust three-dimensional contact computation tool taking into account the effect of cyclic wear induced from fretting solicitations under the gross slip regime. The wear prediction is established on a friction-dissipated energy criteria. The material response is assumed elastic. The contact solver is based on the half-space assumption and the algorithm core is similar to the one originally proposed by Kalker (1990, Three Dimensional Elastic Bodies in Rolling Contact, Kluwer, Dordrecht) for normal loading. In the numerical procedure the center of pressure may be imposed. The effect of surface shear stress is considered through a Coulomb friction coefficient. The conjugate gradient scheme presented by Polonsky and Keer (1999, Wear, 231, pp. 206-219) and an improved fast Fourier transform (FFT) acceleration technique similar to the one developed by Liu et al. (2000, Wear, 243, pp. 101-111) are used. Results for elementary geometries in the gross slip regime are presented. It is shown that the surface geometry influences the contact pressure and surface shear stress distributions found after each loading cycle. It is also shown that wear tends to be uniformly distributed. This process continuously modifies the micro- and macrogeometry of the rubbing surfaces, leading after a given number of cycles to (i) an optimum or ideal contact geometry and (ii) a prediction of wear.

Experimental and Theoretical Investigation on Rolling Contact Fatigue of 52100 and M50 Steels Under EHL or Micro-EHL Conditions

The purpose of this investigation is to clarify the role of roughness on rolling contact fatigue. Tests have been carried out on a two-disk machine, for two rolling bearing steels (52100 and M50), two surface roughnesses corresponding to EHL and micro-EHL conditions (two different surface finishing), three normal loadings (1.5, 2.5 and 3.5 GPa), and under pure rolling or rolling plus sliding conditions. No surface damage has been observed up to 50 10 6 cycles for tests with smooth specimens. Tests with rough specimens have produced a typical surface damage, called here surface distress, made of a large population of asperity-scale micro-cracks and micro-spalls. The paper describes the surface distress observed, such as micro-cracks and micro-spalls. Surface damages obtained are different for tests under pure rolling conditions and tests under rolling plus sliding conditions. Therefore, the role of the friction direction is underlined. A link is made between our experimental observations and calculations that have been carried out using a transient EHL model. The influence of an indent in a line contact, simulating a micro-spall, is studied. Surface pressure and associated sub-surface stress field are analyzed versus the sliding direction.