A finite-element analysis of the indentation of an elastic-work hardening layered half-space by an elastic sphere

An elastic–plastic contact problem in elastic-work hardening layered half-space indented by an elastic sphere was solved numerically using the finite element method. The case of a surface layer stiffer than the substrate is considered, and general solutions for the subsurface stresses and deformation fields are presented for a relatively thin elastic layer. Differences between the elastic and elastic–plastic solutions for the contact pressure distribution have been investigated for various layer thicknesses. Crack initiation and decohesion of the layer was also discussed with reference to the growth of the plastic zone.     

金属基/陶瓷复合双涂层的正接触应力分析

以球形压头为模型，采用I—deasCAD／CAE软件对Hertz弹性接触状态下金属基／陶瓷双涂层系统的应力分布情况进行了理论建模，并基于模型计算了在不同的涂层厚度／接触半宽度比和外涂层／过渡层／基体弹性模量比情况下的应力分布情况。双层系统具有相同的厚度和不同的弹性模量。论述了无涂层弹性半空间体的有限元分析结果与经典的Hertz接触力学解析解结果的一致性，计算结果有助于工程中陶瓷涂层的设计与应用。     

The buckling of an orthotropic layer on a half-space

The buckling of an orthotropic layer bonded to an isotropic or orthotropic half-space subjected to compression loading under plane strain is presented. Mechanics of incremental deformation, which considers the effect of the initial stress field on the incremental stress field, is applied to describe the buckling behavior of both the layer and the half-space. The problem is converted to an eigenvalue–eigenvector case, from which the critical buckling strains or stresses are obtained and the effect of orthotropy on buckling is assessed. The results show that the effect of orthotropy becomes more obvious when the modulus ratio, the ratio of longitudinal moduli of the layer to the half-space, is less and that approximating the problem by using isotropic properties for both the layer and the half-space will be unconservative and may cause unexpected failure.     

Simulation of thermal stresses due to grinding

An efficient finite element procedure has been developed to calculate the temperatures and stresses arising due to a moving source of heat. The procedure is applied to calculate the thermal stresses produced in hardened steels during grinding. The thermal load during grinding is modeled as a uniformly or triangularly distributed, 2D heat source moving across the surface of a half-space, which is insulated or subjected to convective cooling. The grinding of elastic and elastic–plastic workpiece materials has been simulated. The calculated transient stresses and temperatures in an elastic solid are found to be in good agreement with prior analytical and numerical results. In an elastic–plastic workpiece material, for which no analytical solution is available for the residual stress distributions, the finite element calculations show that the near surface residual stress is predominantly tensile and that the magnitude of this stress increases with increasing heat flux values. Based on an analysis of the effects of workpiece velocity, heat flux magnitude and convective cooling, on the residual stress distributions in an elastic–plastic solid, it is seen that the calculated thermal stress distributions are consistent with experimentally measured residual stresses on ground surfaces. Furthermore, the results explain often cited observations pertaining to thermally induced grinding stresses in metals.     

The Lamb's problem for a half-space covered with the pre-stretched layer

The Lamb's problem for the half-space covered with the pre-stretching layer is studied within the framework of the piecewise homogeneous body model. The three-dimensional linearized theory of elastic waves in initially stressed bodies is used. It is assumed that a time-harmonic point-located normal force acts on the free face plane of the covering layer. A numerical algorithm is also developed. Numerical results are presented for two cases of material pairs: rubber (layer)+aluminum (half-space); and aluminum (layer)+rubber (half-space). These results involve stresses acting on the interface plane and in the covering layer. The influence of the harmonic force frequency and the pre-stretching of the covering layer on the distribution of stresses is analyzed. In particular, it is established that stresses on the interface plane are decreased as the pre-stretching is increased.     

Modeling contact of indenter with elastic half-space with adhesive attraction assigned in arbitrary form

A model of the contact of an elastic indenter with an elastic half-space with adhesive attraction has been proposed. The adhesive attraction has been specified as an arbitrary dependence of the adhesive pressure that acts outside the contact zone on the gap between the indenter and the half-space. The shape of the indenter has been described by a power function with an arbitrary exponent. The constructed model has been used to study the applicability of a model with the single-step adhesive potential (the Maugis–Dugdale model). The results of calculations carried out using the Lennard-Jones potential have been compared to the results obtained using linear and exponential potentials.     

The depth of propagation of elastic deformation in rough bodies under frictional contact

The problem of the depth of propagation of the perturbations of the stress-deformed state in an elastic half-space produced when a periodic sinusoidal indenter slides along the surface to model the roughness has been studied by using the solution of the periodic contact problem of elasticity theory. Equations are derived for the stresses and deformations on the axes of symmetry at the centre of the contacting area and between the projections of the rough surface. Calculations indicate that roughness and friction forces only affect the thin near-surface layer of the elastic half-space and the effects rapidly decrease with distance from the surface. The thickness of this perturbed layer is independent of the friction forces, the radius of curvature and heights of the roughnesses and the elasticity properties. It depends only on the distance between the roughnesses. At a depth equal to a factor of 1.5 of the distance between the projections the deflection of the stressed state does not exceed 0.4% and the deformation is 1%. This has been shown to be characteristic for roughnesses in general. The results of the calculations are presented as graphs.     

Contact Problem for a Viscoelastic Half-Space and a Rough Rigid Cylinder under the Conditions of Hydrodynamic Lubrication

A model has been proposed for use in studying the combined effect of the roughness of a rigid punch and the viscous properties of a base separated by a thin lubricant layer exerted on the characteristics of contact interactions and the sliding friction force. The problem of the motion of a thin a lubricant layer between a fixed rigid cylinder with a regular relief, as well as the surface of a moving viscoelastic half-space, the rheological properties of which are described by an integral operator with an exponential creep kernel, has been considered. The pressure and thickness of the lubricating layer, as well as the deformation component of the frictional force depending on the sliding velocity, have been analyzed. A comparison of the results of solutions of contact problems for viscoelastic and elastic rough bodies in the presence of a lubricant has been presented.     

Plastic deformation in rough surface line contacts—a finite element study

The paper describes an elastic-plastic finite element (EPFE) analysis of line contact between a cylinder and rigid plane using commercial software. The range of loading demonstrates the transition from purely elastic to fully plastic contact behaviour, revealing the residual deformations and stress fields upon unloading. A multiple contact configuration was analysed in the form of sinusoidal roughness. Results obtained under elastic conditions were validated by comparison with theoretical solutions. This model was extended by replacing the sinusoidal surface with a real roughness profile. Modelling multiple contacts indicates the influence of adjacent surface “asperities” on contact pressure and residual stress distributions.     

Elastic Sinusoidal Wavy Surface Contact Under Full Stick Conditions

A purely normal contact problem of an elastic half-space with a three-dimensional periodic sinusoidal wavy surface and a rigid flat under the full stick condition is studied. The contacting points from mating surfaces have zero relative tangential displacement under the full stick condition. The scope of this study is restricted to a special case where the entire contact interface is in contact (referred to as complete contact) under the full stick condition. Complete contact is defined as when there are no gaps remaining between the surfaces. The corresponding state of stress of the half-space is derived analytically. According to the state of stress, we find (1) an analytical solution for the average pressure required to cause complete contact, (2) the location of the global maxima of the von Mises stress and (3) the critical magnitude of the waviness amplitude below which the plastic yielding of the half-space will never occur before the initiation of complete contact. The results are also compared with the solution under the perfect slip condition. We find that the location of the maximum von Mises stress may occur either on the contact interface or beneath it depending on the value of Poisson’s ratio.     

Energy Loss in the Impact of Elastic Spheres on a Rigid Half-Space in Presence of Adhesion

Adhesion can cause energy losses in asperities or particles coming into dynamic contact resulting in frictional dissipation, even if the deformation occurring is purely elastic. Such losses are of special significance in impact of nanoparticles and friction between surfaces under low contact pressure to hardness ratio. The objective of this work is to study the effect of adhesion during the normal impact of elastic spheres on a rigid half-space, with an emphasis on understanding the mechanism of energy loss. We use finite element method for modeling the impact phenomenon, with the adhesion due to van der Waals force and the short-range repulsion included as body forces distributed over the volume of the sphere. This approach, in contrast with commonly used surface force approximation, helps to model the interactions in a more precise way. We find that the energy loss in impact of elastic spheres is negligible unless there are adhesion-induced instabilities. Significant energy loss through elastic stress waves occurs due to jump-to-contact and jump-out-of-contact instabilities and can even result in capture of the elastic sphere on the half-space.     

Frictional heating of a half-space with cracks. I. Single or periodic system of subsurface cracks

The paper deals with the two-dimensional problem of frictional heating for an elastic half-space containing one or a system of periodic subsurface cracks. The generation of frictional heating in the region of contact is estimated by the use of sliding speed, frictional coefficient and contact pressure. The problem is reduced to a pair of singular integral equations which are solved numerically. The influence of the location of cracks on the stress intensity factor is investigated.     

Analysis of contact between transversely isotropic coated surfaces: development of stress and displacement relationships using FEM

The problem of an elastic cylinder in normal contact between transversely isotropic layered substrate surfaces is investigated using the finite element method (FEM). A two-dimensional finite element model is developed which accurately determines the normal stress, contact length, and approach distance of layered surfaces. Numerical results, which are initially verified using Hertzian theory, are obtained at 756 distinct conditions by varying coating material, coating thickness, normal load, cylinder radius, and cylinder material. The numerical results are normalized with respect to Hertzian contact theory and a dimensionless anisotropic coating material parameter, ζ, is introduced. Numerical expressions for the normalized maximum normal stress, contact length, and approach distance are subsequently determined by curve-fitting the results of the 756 simulations performed. The relevance of such expressions are ascertained and discussed by comparing predicted results to isotropic layer theory presented by Gupta and Walowit [P.K. Gupta, J.A. Walowit. Contact stresses between an elastic cylinder and a layered elastic solid, ASME J. Lubrication Technol., Vol. 94 (1974) pp. 250–274.]     

Contact Problems for Rolling with Slip for Viscoelastic Solids

The three-dimensional contact problem for rolling of a rigid sphere over a base, which consists of viscoelastic layer bonded to a rigid half-space has been considered. The thin viscoelastic layer simulates the action of a friction modifier. The Kelvin model has been used to describe the layer properties. The method of calculating the distribution of normal and shear stresses within the contact interaction area has been presented, the boundaries of traction have been determined, and the slip subareas have been studied. In addition, the influence of the viscoelastic layer properties on the distributions of contact stresses has been analyzed.     

A numerical investigation of the sinusoidal model for elastic layers in line contact

Distributions of normal stresses and surface deformations, induced when an elastic layer of finite thickness is indented by a frictionless rough rigid flat or cylindrical indenter, are calculated numerically. It is assumed that the punch has a sinusoidal roughness superimposed on its nominal profile. Two cases will be examined, namely when the elastic layer is either bonded to a rigid backing or resting on a frictionless rigid backing (unbonded). Chebyshev polynomials of the first kind T_n(x) are utilized to model both the unknown pressure and the given deformation over the contact area. The governing elasticity equation is thereby reduced to a finite set of linear equations and hence a complete solution is found. The present numerical method is simple, accurate and valid in the full range of Poisson's ratio 0 v 0.5. Moreover, a set of semi-analytical solutions for the contact pressure is obtained for both thin unbonded and bonded elastic layers. The numerical results compared favourably with the asymptotic solutions. The effects of the layer thickness, layer compressibility and roughness amplitude parameters on the contact stresses and deformations are considered.     

Finite element analysis of a subsurface penny-shaped crack with crack-face contact and friction under a moving compressive load

A three-dimensional subsurface penny-shaped crack in an elastic half-space subjected to a compressive moving load is analyzed using the finite element method. The compressive load is applied through a spherical asperity, which moves from left to right on the top surface of the half-space. Normal contact between the crack faces of the penny-shaped crack is modeled using the classical Lagrange multiplier method for constraint enforcement; the tangential contact between the crack faces is assumed to exhibit frictional behavior. Therefore, although the present analysis is limited to a purely linear elastic quasistatic approach, the analysis results show the loading path dependence caused by the frictional contact. Based on linear elastic fracture mechanics, stress intensity factors along the crack front of the penny-shaped crack are evaluated as functions of the crack-front angle, frictional coefficient, normalized load position, and the ratio of the crack depth to the crack length. Finite element analysis shows that shearing-mode failure rather than tearing-mode failure is the dominant cracking mechanism of the penny-shaped crack. This shearing-mode failure tends to occur in the direction of the loading path.     

软弹滚体线接触的边界元分析

软弹滚体的接触是关于表面附有一层软弹性材料的滚体间的弹流动压润滑问题,它涉及滚体表面的弹性变形与流体压力之间的相互作用。考虑到表面易于出现较大变形和两滚体间的压入啮合量,用普通的模拟方法来研究这种接触问题,在技术上存在着很大的困难。本文应用边界元方法,将流体的动压控制方程和表层弹性变形方程分别转化为边界积分方程,并对这些方程施行迭代运算,从而获得收敛解,对这类接触问题做了研究。研究结果将为结构设计、选择参数值提供指导性的依据,表明这种方法是对这类接触问题进一步研究的一种有效的方法。     

Numerical Investigation on the Effects of Machining-Induced White Layer during Rolling Contact

It is well known that a thin phase-transformed white layer can be formed on component surfaces produced by hard machining. However, it is not clear as to how the white layer affects component performance, for example, in rolling contact fatigue. This study aims to determine the effects of white layer and associated residual stress on rolling contact stresses and strains. It is nearly impossible for an experimental study to identify the effects of white layer alone on rolling contact. Furthermore, small-scale contact stresses and strains (less than 30 μm) of the phase-transformed region are difficult to measure using the current experimental techniques. Therefore, a finite element analysis simulation model of rolling contact incorporating machining-induced surface integrity has been developed in this study. Three cases were investigated to decouple the effects of surface integrity factors: surface with white layer only, surface with residual stress only, and surface with white layer and residual stress. The simulation results show that distinct material properties of the white layer significantly influence the magnitudes and distributions of near-surface stresses and strains instead of those in the subsurface. Furthermore, it can be inferred that the white layer would affect near-surface fatigue damage instead of subsurface fatigue damage. The simulated near-surface fatigue damage mechanisms have been substantiated by the fatigue test data.     

Fretting fatigue in elastic contacts due to tangential micro-motion

Stress analysis of two elastic bodies in contact, when one of them is subjected to an alternating stress, was carried out in this study. Surface and effective stresses for different values of applied alternating stress were determined within the area of contact. Critical zones where fretting fatigue cracks may initiate were found at the edge of contact where stresses reach a maximum. Displacement distribution due to various types of stresses was determined and was found to increase with increasing the applied alternating stress and the distance from the centre of contact. An expression to predict fatigue failure under fretting conditions was proposed. This expression includes most parameters which contribute to failure, such as: contact pressure, applied stresses, friction coefficient, displacement amplitude and elastic properties of both contacting materials. Initial predictions of the suggested expression provide good correlation with test results, and the expression could thus be adopted as an analytical tool for predicting strength under fretting conditions.     

Contact problem for elastic layer and rigid cylinder with friction forces

The contact problem for the elastic layer of an arbitrary thickness and the rigid cylinder with friction forces acting in the contact area is solved and the solution is analyzed. Domains of applicability of the widely used solutions, i.e. the solution for a rigid cylinder and elastic half-space and the solution for a thin elastic layer, are determined for the contact under consideration. It is shown that for coatings from composite materials with a low elastic modulus both solutions can result in a significant error. Typical modes of the elastic displacement of the layer surface are given for different contact area width, Poisson’s ratio, and friction coefficient. The example of the calculation of the particular contact for the layer of the polymer composite with a low elastic modulus is presented.