Elastic-plastic Contact Research Articles

The correlation of theoretical contact models for normal elastic-plastic impacts

In this study, eighteen elastic-plastic theoretical contact models are selected to investigate the spherical particle impacting on a half-space, where deformations occur on both objects. The analytical results of the selected theoretical contact models by using a spring-mass model are compared with the numerical results by using finite element analysis. The differences and correlations of the contact models are identified comprehensively by comparing the variations of the impact force, the indentation and the velocity of the particle during impact. Large discrepancies are found for the predictions of the loading and unloading impact behaviours by using different contact models. For different impact behaviours, including the maximum impact force, the maximum indentation, the impact duration, the permanent indentation and the coefficient of restitution, the analyses provide the corresponding matchable contact models both for indentation contact and flattening contact compared with finite element analysis results. Further analyses of the predicted impact behaviours by different contact models, especially analyses of the impact duration and the permanent indentation, reveal that the definition of the yield condition during loading phase as well as the effective radius of curvatures during unloading phase are important for contact models in predicting accurate local impact behaviours.

Influence of distribution parameters of rough surface asperities on the contact fatigue life of gears

The influence of the distribution parameters of asperities, i.e. mean radius of curvature of asperities β, density of asperities η, and standard deviation of asperity heights σ, on the contact fatigue life of gears is first studied in this paper. Based on the elastic–plastic contact model of asperities, the surface contact pressure and subsurface stress field during the gear meshing process are calculated by the iterative calculation method. According to the multi-axis fatigue life model, the calculation method of fatigue life under different distribution parameters of asperities in the gear meshing process is obtained. The quantitative calculation results of fatigue life and measured distribution parameters of asperities are analyzed. The relationship between the fatigue life and the distribution parameters of asperities on the measured gear surface is calculated and analyzed quantitatively. The following conclusions are drawn: (1) when the roughness value Ra is less than 0.3 µm, the contact fatigue life of gears with rough surfaces is close to that of smooth surfaces; (2) when the roughness value Ra ranges from 0.5 µm to 0.9 µm, the contact fatigue failure occurs near the surface (micro-pitting); (3) under the same roughness value Ra, the contact fatigue life of the gear decreases with the decrease of the density of the asperity and the mean curvature radius of the asperity. The mean radius of curvature of the asperity has a greater influence on the contact fatigue life than the density of the asperity.

A Three-Dimensional Elastic-Plastic Contact Analysis of Vickers Indenter on a Deep Drawing Quality Steel Sheet.

Three-dimensional finite element-based numerical analysis of Vickers indenter hardness test was conducted to investigate the effect of frictional conditions and material anisotropy on indentation results of deep drawing quality steel sheets. The strain hardening properties and Lankford’s coefficient were determined through the uniaxial tensile tests. The numerical computations were carried out using ABAQUS nonlinear finite element (FE) analysis software. Numerical simulations taken into account anisotropy of material described by Hill (1948) yield a criterion. The stress and strain distributions and loading–unloading characteristics were considered to study the response of the material. It was found that the hardness values seemed to be influenced by the value of the friction coefficient due to the pile-up phenomenon observed. The increasing of the friction coefficient led to a decrease of the pile-up value. Moreover, the width of the pile-ups differed from each other in the two perpendicular directions of measurement. Frictional conditions did not significantly affect the maximum force and the character of load–displacement curves. Frictional regime between the indenter and workpiece caused that the region of maximum residual stresses to be located in the subsurface.

A prediction method for wheel tread wear

PurposeThe increasing demands of high-speed railway transportation aggravate the wheel and rail surface wear. It is of great significance to repair the worn wheel timely by predicting the wheel and rail surface wear, which will improve both the service life of the wheel and rail and the safe operation of the train. The purpose of this study is to propose a new prediction method of wheel tread wear, which can provide some reference for selecting proper re-profiling period of wheel.Design/methodology/approachThe standard and worn wheel profiles were first matched with the standard 60N rail profile, and then the wheel/rail finite element models (FEMs) were established for elastic-plastic contact calculation. A calculation method of the friction work was proposed based on contact analysis. Afterwards, a simplified method for calculating wheel tread wear was presented and the wear with different running mileages was predicted.FindingsThe wheel tread wear increased the relative displacement and friction of contact spots. There was obvious fluctuation in the wheel tread friction work curve of the worn model. The wear patterns predicted in the present study were in accordance with the actual situation, especially in the worn model.Originality/valueIn summary, the simplified method based on FEM presented in this paper could effectively calculate wheel tread wear and predict the wear patterns. It would provide valuable clews for the wheel repair work.

Numerical simulation of competing mechanism between pitting and micro-pitting of a wind turbine gear considering surface roughness

Gear rolling contact fatigue displays itself with many failure modes such as micro-pitting, pitting or tooth flank fracture. Competing mechanism exists between these failure modes. Tooth surface micro-topography plays an important role in contact behavior and contact fatigue performance of gears. In particular, the root of mean square (RMS) of surface roughness is extensively characterized as one of the main parameters influencing the service performance. In this work an elastic-plastic finite element contact fatigue model is proposed in which the surface roughness is explicitly measured through an optical profiler. The relationship between the dimensionless normal loads and the contact area ratio is plotted. The critical planes and the characteristic shear strain amplitudes are captured at each material point within the contact area. Then the Brown-Miller multi-axial fatigue criterion is applied to evaluate the fatigue life of rough surface contacts. Results reveal that the surface roughness significantly influences the contact fatigue life of gears, and the competing mechanism between the micro-pitting from near-surface area and pitting from sub-surface area. When the RMS value of surface roughness is considerably small, the pitting failure risk and the micro-pitting risk coexist since the minimum fatigue life appears both at the near-surface area and the sub-surface area.

Estimation of Service Life of Mechanical Engineering Components

The paper is aimed to the methodology for estimation of service life of mechanical engineering components in the case of elastic-plastic contact of surfaces. Well-known calculation methods depending on physics, theory of probability, the analysis of friction pair’ shape and fit include a number of parameters that are difficult or even impossible to be technologically controlled in the manufacturing of mechanical engineering components. The new approach for wear rate estimation using surface texture parameters as well as physical-mechanical properties and geometric parameters of components is proposed. The theoretical part of the calculations is based on the 3D surface texture principles, the basics of material fatigue theory, the theory of elasticity and the contact mechanics of surfaces. It is possible to calculate the service time of the machine, but the process of running-in of the components is relatively short (less than 5%), therefore, the service time is mainly determined by a normal operating period, which also was used to evaluate this period. The calculated input parameters are technologically and metrologically available and new method for calculating the service time can be used in the design process of the equipment. The results of approbation of the method for estimation service time of mechanical engineering, which prove the applicability of mentioned method, are offered as well.

A numerical elastic–plastic contact model for a half-space with inhomogeneous inclusions and cracks

The elastic–plastic contact problem plays an important role in predicting the mechanical properties of materials. In this paper, a semi-analytic solution is developed to investigate the plastic behaviors of a half-space with inhomogeneous inclusions and cracks under contact loading. In this solution, the plastic zones are determined based on the stress field equations and the von Mises yield criterion. The contact area and surface pressure distribution are obtained by solving a set of governing equations via a modified conjugate gradient method. The inhomogeneous inclusions are modeled as homogeneous inclusions with the initial eigenstrains plus unknown equivalent eigenstrains according to the Eshelby’s equivalent inclusion method. The cracks are treated as a collection of distributions of unknown dislocation densities according to the distributed dislocation technique. The case studies of a cylinder loaded against a half-space with inhomogeneous inclusions and vertical or horizontal cracks are conducted to explore the effects of the Young’s moduli and positions of the inhomogeneous inclusions on the plastic behavior of materials.

Characteristics analysis of rotor model with support–foundation looseness fault considering elastic–plastic contact

In this paper, the nonlinear response characteristics of a single degree of freedom lumped mass model with a new support looseness fault are analyzed. In this model, a new nonlinear contact stiffness model between the support and foundation is considered, which considers the elastic–plastic deformation of the contact parts. The nonlinear response of the system is obtained by numerical integration methods. The nonlinear results are compared with an asymmetric model and a piece-wise contact model. By comparing three different looseness fault models, the mechanism of generating multi-frequencies and fractional frequencies is analyzed. The result shows that plastic deformation makes the displacement amplitude increase rapidly; odd harmonics appear in symmetric stiffness model due to the modulation of symmetric shock forces; however, harmonic response appears in asymmetric stiffness model; when the contact number is odd, the frequency components contain odd or even order fractional frequencies at supercritical speeds due to the incompatibility of contacts on the upper and lower surfaces; when the contact number is even, multiple frequency components appear at subcritical frequencies.

Ratchetting–multiaxial fatigue damage analysis in gear rolling contact considering tooth surface roughness

Under the combined effect of the tooth surface roughness and heavy load condition, gear materials might experience both the fatigue damage and the ratchetting damage. An elastic-plastic finite element contact fatigue model is proposed considering the optically measured tooth surface roughness and the gear contact geometry. The kinematic hardening constitutive equation and the Jiang and Sehitoglu ratchetting-multiaxial fatigue model are applied, and the contribution of the ratchetting-fatigue damage in the mechanism of gear contact fatigue problems is discussed. Results reveal that the surface roughness can promote the emergence of ratchetting behavior within a very shallow area near surface. Furthermore, the effect of the normal load condition on the ratchetting-fatigue damage is also discussed.

A statistical model of elastic-plastic contact between rough surfaces

In a mechanical interface, the contact surface topography has an important influence on the contact stiffness. In the contact processes of asperities, elastic-plastic change can lead to discontinuity and lack of smoothness at a critical contact point. The result is a large difference between the elastic-plastic deformation and the actual asperity deformation. Based on Hertz contact theory, the heights of asperities on a rough surface obey a Gaussian distribution. To take into consideration the continuity of elastic-plastic asperity deformation, we divide the elastic-plastic deformation into three stages: pre-elastic-plastic, mid-elastic-plastic, and post-elastic-plastic deformation. This establishes an elastic-plastic contact model of asperity at a continuous critical point. The contact model of a single asperity fits well with the Kogut–Etsion model and the Zhao–Maietta–Chang model, and the variation trend is consistent. At a lower plastic index, the present model coincides with classical models of contact area and contact load. At a higher plastic index, the simulation results of the present model differ from the Greenwood–Williamson model and the Chang–Etsion–Bogy model but are similar to results from the Kogut–Etsion and Zhao–Maietta–Chang models. This study provides a more accurate microscopic contact model for rough surfaces and a theoretical framework for interface design and analysis.

The elastic-plastic contact behavior of rough surfaces with hard coatings

Abstract An elastic-plastic coated rough surface contact model is presented, which incorporates existing single coated asperity contact models in a GW-based statistical multi-coated-asperity surface model. Effects of the coating thickness and its material properties as well as the substrate surface roughness on the mode of the coated surface contact deformation and its contact behavior are investigated through a qualitative parametric analysis. An equivalent plasticity index for the coated surface contact is defined to determine the mode of the coated surface contact deformation, which mainly depends on the coating material properties and the substrate surface roughness. It is found that a coated surface with a thicker, stiffer, harder coating and a rougher substrate has a higher separation and smaller real contact area under a given load.

Cycles of triply coupled mechanical contact, current, and thermal conduction phenomena during resistance spot welding

The characteristics of the cycles of coupled phenomena that occur among elastic-plastic contact deformation, current distribution, heat generation, and thermal conduction during resistance spot welding are examined using coupled finite element analyses. The current density peak that appears at the center of the interface moves outward along the interface to the high-contact resistance region, then the peaks in the current density, contact resistance, Joule heat generation, and temperature migrate outward with the contact edge followed by the melting zone during the welding process. The influence of welding parameters on the cycles of coupled phenomena is also examined. When the weld current is increased, the current density within the contact surface does not increase but enlarges the high-temperature region instead of heating the central part of the interface. When a small electrode force is applied, the nugget formation is initially enhanced not due to the increased contact resistance but rather because of the increase in the current density through the interface with a reduced contact area.

Effect of Interlayer on the Elastic-Plastic Deformation of Coating Systems

ABSTRACTThe finite element method (FEM) was used to study the elastic-plastic contact in the coating systems with interlayer. The results reveal that with the increase of interlayer thickness, the maximum shear stress of coating/interlayer and interlayer/substrate interfaces decreases. Moreover, the sharply changed shear stress between the interfaces of coating/interlayer and interlayer/substrate decreases too. There is no further decrease when interlayer thickness increase to 0.04 mm and above. With the increasing of interlayer elastic modulus, the shear stress of coating/interlayer interface decreases while the shear stress of interlayer/substrate interface increases. Meanwhile, the higher elastic modulus leads to the intensive tensile stress concentration on the interface of coating/interlayer. Hence, the interlayer with appropriate elastic modulus not only reduces the shear stress of coating/interlayer and interlayer/substrate interfaces but also decreases the tensile stress of coating/interlayer interface. The mechanical properties of coating systems were investigated with different interlayer yield strength. The effective hardness and elastic modulus increase with the increase of interlayer yield strength, which is good to protect the substrate from the deformation. In addition, higher indentation load can lead to the decrease of effective hardness and elastic modulus.

Shear thinning in non-Brownian suspensions explained by variable friction between particles

We propose to explain shear-thinning behaviour observed in most concentrated non-Brownian suspensions by variable friction between particles. Considering the low magnitude of the forces experienced by the particles of suspensions under shear flow, it is first argued that rough particles come into solid contact through one or a few asperities. In such a few-asperity elastic–plastic contact, the friction coefficient is expected not to be constant but to decrease with increasing normal load. Simulations based on the force coupling method and including such a load-dependent friction coefficient are performed for various particle volume fractions. The results of the numerical simulations are compared to viscosity measurements carried out on suspensions of polystyrene particles ($40~\unicode[STIX]{x03BC}\text{m}$in diameter) dispersed in a Newtonian silicon oil. The agreement is shown to be satisfactory. Furthermore, the comparison between the simulations conducted either with a constant or a load-dependent friction coefficient provides a model for the shear-thinning viscosity. In this model the effective friction coefficient$\unicode[STIX]{x1D707}^{eff}$is specified by the effective normal contact force which is simply proportional to the bulk shear stress. As the shear stress increases,$\unicode[STIX]{x1D707}^{eff}$decreases and the jamming volume fraction increases, leading to the reduction of the viscosity. Finally, using this model, we show that it is possible to evaluate the microscopic friction coefficient for each applied shear stress from the rheometric measurements.

Fractal modeling of normal contact stiffness for rough surface contact considering the elastic–plastic deformation

In this work, a new formulation of elastic–plastic contact model for the normal contact between rough surfaces is proposed based on the fractal theory. The surface topography is described using the modified one-variable Weierstrass–Mandelbrot fractal function. A new elastoplastic asperity contact model is developed based on the contact mechanics combined with the continuity and smoothness of mean contact pressure and contact load across different deformation regimes from elastic to elastoplastic, and from elastoplastic to fully plastic. The contact stiffness of a single asperity in the three deformation regimes of fully plastic, elastoplastic and elastic is derived, which changes smoothly at transit points between different deformation modes and overcomes the shortcoming of discontinuity derived from previous model. The contact stiffness and contact load of the whole surface in the three deformation regimes are formulated by integrating the micro-asperity contact. The difference between contact stiffness calculated from the plastic–elastoplastic–elastic three contact regimes and plastic–elastic two contact regimes is not obvious for surface with rougher topograph; however, for surface with smoother topograph, the two contact regimes predict a much smaller contact stiffness. The relationship of the normal contact stiffness and the normal contact force follows a power law function for the fractal surface contact considering three deformation regimes. The power exponent is nonlinearly dependent on the fractal dimension, which is different from the linear relationship for the purely elastic contact.

Weakly anisotropic residual contact stress in silicon demonstrated by electron backscatter diffraction and expanding cavity models

The residual stress field surrounding an elastic-plastic spherical indentation contact in Si is determined by electron backscatter diffraction (EBSD)-based experimental measurements and expanding hemispherical cavity-based models. The experiments provide support for indentations as test vehicles for assessment of EBSD as a two-dimensional deformation mapping method but make clear that selection of coordinate axes is critical to determining the correct representation of a stress field. The use of principal stress coordinates rather than the conventional Cartesian coordinates is required in cases in which the direction of the stress field is not aligned with Cartesian axes. In particular, the use of principal coordinates in the analysis of a spherical indentation stress field in Si removed misleading artefacts from the Cartesian-based field and revealed only a weak effect of Si crystalline elastic anisotropy. The experimental results are supported by isotropic and anisotropic finite element analysis models.

Evaluation of contact fatigue life of a wind turbine carburized gear considering gradients of mechanical properties

Case hardening processes such as carburizing are extensively applied in heavy-duty gears used in wind turbines, ships, high-speed rails, etc. Contact fatigue failure occurs commonly in engineering practice, thus reduces reliabilities of those machines. Rolling contact fatigue life of a carburized gear is influenced by factors such as the gradients of mechanical properties and profile of initial residual stress. In this regard, the study of contact fatigue life of carburized gears should be conducted with the consideration of those aspects. In this study, a finite element elastic–plastic contact model of a carburized gear is developed which takes the gradients of hardness and initial residual stress into account. Initial residual stress distribution and the hardness profile along the depth are obtained through experimental measurements. The effect of the hardness gradient is reflected by the gradients of yield strength and fatigue parameters. The modified Fatemi–Socie strain-life criterion is used to estimate the rolling contact fatigue life of the heavy-duty carburized gear. Numerical results reveal that according to the Fatemi–Socie fatigue life criterion, rolling contact fatigue failure of the carburized gear will first initiate at subsurface rather than surface. Compared with the un-carburized gear, the rolling contact fatigue lives of the carburized gear under all load conditions are significantly improved. Under heavy load conditions, the carburized layer significantly reduces the fatigue damage mainly due to the benefit to inhibit the accumulation of plasticity. Influence of the residual stress is also investigated. Under the nominal load condition, compared with the residual stress-free case, the existence of the tensile residual stress causes remarkable deterioration of the rolling contact fatigue life while the compressive residual stress with the same magnitude leads to a moderate growth of the rolling contact fatigue life. As the load becomes heavier when plasticity becomes notable, the influence of the initial residual stress on the life is somewhat weakened.

Strain Hardening From Elastic–Perfectly Plastic to Perfectly Elastic Flattening Single Asperity Contact

For elastic contact, an exact analytical solution for the stresses and strains within two contacting bodies has been known since the 1880s. Despite this, there is no similar solution for elastic–plastic contact due to the integral nature of plastic deformations, and the few models that do exist develop approximate solutions for the elastic–perfectly plastic material model. In this work, the full transition from elastic–perfectly plastic to elastic materials in contact is studied using a bilinear material model in a finite element environment for a frictionless dry flattening contact. Even though the contact is considered flattening, elastic deformations are allowed to happen on the flat. The real contact radius is found to converge to the elastic contact limit at a tangent modulus of elasticity around 20%. For the contact force, the results show a different trend in which there is a continual variation in forces across the entire range of material models studied. A new formulation has been developed based on the finite element results to predict the deformations, real contact area, and contact force. A second approach has been introduced to calculate the contact force based on the approximation of the Hertzian solution for the elastic deformations on the flat. The proposed formulation is verified for five different materials sets.

Effect of the residual stress on contact fatigue of a wind turbine carburized gear with multiaxial fatigue criteria

Carburized gears are extensively applied in heavy duty machines such as wind turbines. The variations of hardness and residual stress introduced by carburizing and quenching processes remarkably affect the rolling contact fatigue (RCF) during repeated gear meshing. The present work attempts to study the effect of the residual stress on rolling contact fatigue and predict the rolling contact fatigue life of a wind turbine carburized gear based on multiaxial fatigue criteria. A finite element elastic-plastic contact model is developed which takes the gradients of hardness and initial residual stress into account. Initial residual stress distribution is obtained through experimental measurements. The stabilized stress strain field is carried out by considering the shakedown state under the heavy load conditions. The Fatemi–Socie and the Brown–Miller criteria are used to estimate the contact fatigue damage of the carburized gear. Numerical results reveal that the effect of the initial residual stress on the contact fatigue failure can be reflected by the Fatemi–Socie criterion whereas it is not reflected by the Brown–Miller criterion since the two strain parameters appeared in the criterion are not influenced by residual stress. In terms of the Fatemi-Socie criterion, under modest load conditions where elastic response occur, a considerable compressive residual stress would alter the plane orientations of crack initiation, while under extremely heavy load conditions where plasticity occur, the influence of the initial residual stress on contact fatigue damage is limited within the near-surface non-plastic zone. The effect of the initial residual stress on contact fatigue life represents a bilinear curve. As the magnitude of the tensile residual stress increases, the RCF life decreases linearly. As the magnitude of the compressive residual stress exceeds a certain value, the RCF life does not increase anymore.

Shakedown analysis of a wind turbine gear considering strain-hardening and the initial residual stress

Under some heavy-duty conditions, the shakedown state may occur on gears such as those used in a megawatt wind turbine gearbox. The plastic deformation and the residual stress formed within the shakedown process further influence the contact behavior and the service life of the gear. The initial residual stress caused by the heat treatment of the case-hardening gear, together with the strain-hardening constitutive behavior of the material, have a combined effect on the shakedown state. A two-dimensional elastic-plastic contact numerical model was developed for a case-hardened wind turbine gear to study effects of the initial residual stress and the strain-hardening properties. Plastic strain and residual stress are calculated at each loading cycle without the consideration of the tooth friction. The initial yield limit and the hardening modulus of the material were obtained through a tension test on a universal tensile test machine. The initial residual stress distribution was measured with the X ray diffraction method and then embedded in the finite element model. The results show that strain-hardening behavior can significantly improve the shakedown performance, and the larger the hardening modulus is, the less the maximum plastic strain is at the final shakedown state. Initial residual compressive stress is helpful to improve the shakedown performance, while initial residual tensile stress has negative influence on the shakedown performance. As the normal load increases, the influence of the initial residual stress on the shakedown state becomes weakened.