An analysis of three-dimensional elasto-plastic sinusoidal contact

Researchers have developed many models to simulate the elasto-plastic contact of spheres. However, there does not appear to exist a closed-form analytical model for elasto-plastic three-dimensional sinusoidal contact. This work uses a finite element model (FEM) to characterize elasto-plastic sinusoidal contact. Although at initial contact the sphere and sinusoidal case are very similar and can both be described by the classic elastic Hertz contact case, once the contact is pressed past a certain range of deformation the two cases are very different. The model produces equations which can be used to approximately relate the area of contact to the contact pressure for elasto-plastic sinusoidal contact. The equations are fit to the FEM results and existing elastic solutions of sinusoidal contact. An empirical expression for the average pressure which causes complete contact between elasto-plastic sinusoidal contacts is also provided.     

Analysis of wheel and rail adhesion under wet condition by using elastic–plastic microcontact model

This paper presents a numerical model to investigate the adhesion characteristics of the wheel/rail contact with consideration of surface roughness under wet conditions. The elastohydrodynamic lubrication theory is used to obtain the load carried by water, and the statistical elastic–plastic microcontact model presented by Zhao–Maietta–Chang is applied to calculate the load carried by asperities contact. Meanwhile, the thermal influencing reduction factor is used to consider the inlet heating effects on the film thickness, and the change of water viscosity is also taken into consideration due to the flash temperature generated by the moving rough surfaces. Furthermore, the present work investigates the dependence of the wheel/rail adhesion coefficient on train speed, surface roughness amplitude, the initial temperature, the plasticity index and the maximum contact pressure under wet condition. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

表面粗糙度对油套管特殊螺纹密封面性能的影响

以往对油套管特殊螺纹密封的数值模拟都是在光滑平面的基础上展开的，不能真实反映油管连接时载荷接触状况。运用蒙特卡洛法建立考虑粗糙度的油管密封面接触模型，分析表面粗糙度、接头母扣球面半径、内压载荷对油管密封面性能的影响。结果表明：同一过盈量下，密封面粗糙度越小，平均接触压力越小；母扣球面半径越大，密封面接触长度越长，贴合度越高；随着内压的增加，由于公扣密封接触面上的微凸体与锥面的接触次数逐渐增多，并且在相互接触的情况下，其弹性变形程度逐渐降低，而塑性变形增大，此时因接触长度增大，密封表面具有较好的密封性能。     

Three-dimensional modeling of elasto-plastic sinusoidal contact under time dependent deformation due to stress relaxation

In the current work, the effect of stress relaxation in contact between sinusoidal surfaces is studied using FE simulations. There are a few works on the elastic and elasto-plastic contact between sinusoidal surfaces, but the transient effects such as creep and stress relaxation are not considered in these works. Stress relaxation causes significant change in the contact area and pressure between the contacting surfaces. The Garofalo formula is used to model the transient behavior of stress relaxation. The results for the contact area and contact pressure are presented and discussed. Empirical equations are developed to predict contact area and pressure by fitting to the FEM results. The equations are dependent on the initial surface separation, aspect ratio, and the Garofalo constants.     

A new roughness parameter to evaluate the near-surface deformation in dry rolling/sliding contact

Within this work, a two-dimensional finite element model for rolling contact of a wheel on a rail is presented that accounts for the roughness of the contact surfaces. The rail material is modeled with elastic–plastic behavior. The maximum of the plastic shear strain is concentrated close to the surface of the rail and is mainly influenced by the surface roughness. A concept is proposed that demonstrates one crucial parameter of the roughness determines surface deformation (based on results of a sinusoidal roughness model). This roughness parameter depicts the ratio between asperity height and width. Numerical validation is achieved for predicting plastic shear strains in rough surfaces. The plastic shear strain is associated with surface damage, such as cracks and wear.     

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.     

点接触弹流动压性能的多网格法分析

点接触问题主要研究在一定载荷作用下,运动球体间的接触力学性能,涉及物体的弹性变形和流体动压的相互作用。本文应用多网格重积分方法,在给定的物体几何结构、载荷、速度、流体性质条件下,对运动球体的弹性变形、流体膜的厚度分布、流体膜的压力分布等参数的性能及其关系做了研究。分析结果反映出这类问题的基本特征和参数之间相互作用的规律。这一分析技术为相关结构和参数的设计及进一步分析提供了一个强有力的手段。     

Plastic flattening of a sinusoidal metal surface: A discrete dislocation plasticity study

The plastic flattening of a sinusoidal metal surface is studied by performing plane strain dislocation dynamics simulations. Plasticity arises from the collective motion of discrete dislocations of edge character. Their dynamics is incorporated through constitutive rules for nucleation, glide, pinning and annihilation. By analyzing surfaces with constant amplitude we found that the mean contact pressure is inversely proportional to the wavelength. For small wavelengths, due to interaction between plastic zones of neighboring contacts, the mean contact pressure can reach values that are about 1/10 of the theoretical strength of the material, thus significantly higher than what is predicted by simulations that do not account for size dependent plasticity. Surfaces with the same amplitude to period ratio have a size dependent response, such that if we interpret each period of the sinusoidal wave as the asperity of a rough surface, smaller asperities are harder to be flattened than large ones. The difference between the limiting situations of sticking and frictionless contacts is found to be negligible.     

微观随机粗糙表面接触有限元模型的构建与接触分析

基于相关文献提出粗糙表面模拟方法,通过软件工具在ANSYS中建立微观粗糙表面接触有限元模型,利用该模型分析载荷对弹塑性变形和接触面积的影响。结果表明:随着正压力的增大,粗糙表面上不断地有微凸峰与平面发生弹性接触变形,接触斑点(或接触斑点群)的数目逐渐增加,斑点中心区域的弹性变形很快达到最大,微凸峰负荷变形的同时也使斑点四周区域受到挤压;初始接触时,轮廓高度较大的微凸峰率先发生弹性变形,随着压力的增大,金属材料所受应力达到屈服极限同时粗糙表面的弹性变形和塑性变形的集中区域不断增加,真实接触面积不断增大;接触区数目的增多和接触区面积的增加都可以导致接触面上真实接触面积增加;随着压力的增大,真实接触面积的增大并不是由于接触区数目的增多,而是微观接触区面积的增大。     

一种套管悬挂器金属密封结构设计与研究

针对高温高压下悬挂器橡胶密封件的失效问题,采用316L软金属,设计线型、正弦、椭圆、抛物线4种不同的密封结构,采用ANSYS软件分析套管悬重及不同顶丝压力下的接触压力和接触宽度的变化规律。结果表明:随顶丝压力的增加,线型密封各接触面处的平均接触压力增幅较小,正弦和抛物线型密封各接触面处的平均接触压力起伏式增加,椭圆密封各接触面处的平均接触压力平稳增加,表明采用椭圆型接触面有利于密封的稳定。实验结果表明,该全金属多级等锥椭圆曲面密封结构可靠,能满足油田井口装置140 MPa极限工况的密封要求。     

Investigation into the Normal Contact Stiffness of Rough Surface in Line Contact Mixed Elastohydrodynamic Lubrication

In this work, the statistical asperity microcontact models in combination with the acoustic spring model and the load sharing concept are utilized to study the interfacial normal contact stiffness for a rough surface in line contact elastohydrodynamic lubrication (EHL). Two different statistical microcontact models of Greenwood and Williamson (GW) and Kogut and Etsion (KE) are employed to derive the normal contact stiffness expressions for a dry rough line contact considering the purely elastic contact and the multiple regimes elastic–elastoplastic–fully plastic contact, respectively. The liquid film stiffness is calculated based on the relationship between film thickness and bulk modulus of the lubricant. The lubricant film thickness equations are employed in conjunction with the load sharing concept and the empirical formulas for the maximum contact pressure in a dry rough contact are fitted for the GW model and the KE model, to evaluate the relationship between film thickness and motion velocity for the purely elastic GW microcontact model and the multiregime KE microcontact model, respectively. The comparison with experimental results shows that the KE model predicts closer total contact stiffness results than the GW model. The stiffness contributions from the solid asperity contact and lubricant film are obtained and effects of surface roughness, applied load, motion velocity, and type of lubricant on the normal contact stiffness are analyzed.     

机械结合面法向动态接触刚度理论模型与试验研究

机械结合面经常可能在动态条件下工作,使得结合面的接触状态偏离静态工作状态,导致接触刚度发生改变。为了揭示动态接触刚度的变化规律,考虑两个粗糙结合表面上单个微凸体由弹性变形向弹塑性变形以至最终向完全塑性变形转化的接触过程,建立一个振动周期内各变形阶段微凸体的平均接触刚度模型;在此基础上,基于高斯分布假设,建立整个粗糙结合表面的动态接触刚度解析模型。该模型揭示了接触面压、振动频率和相对位移振幅对动态接触刚度的影响规律,并与试验结果和静态接触刚度计算结果进行了比较。研究表明:法向动态接触刚度和静态接触刚度与接触面压之间的关系基本一致,但有一定偏离。这种偏离程度随动态位移幅值和振动频率的增加而分别呈线性和非线性增大。     

Modeling of fretting wear evolution in rough circular contacts in partial slip

This paper presents a numerical model that maps the evolution of contact pressure and surface profile of Hertzian rough contacting bodies in fretting wear under partial slip conditions. The model was used to determine the sliding distance of the contacting surface asperities for one cycle of tangential load. The contact pressure and sliding distance were used with Archard's wear law to determine local wear at each surface asperity. Subsequently, the contact surface profile was updated due to wear. The approach developed in this study allows for implementation of simulated and/or measured real rough surfaces and study the effects of various statistical surface properties on fretting wear. The results from this investigation indicate that an elastic–perfectly plastic material model is superior to a completely elastic material model. Surface roughness of even small magnitudes is a major factor in wear calculations and cannot be neglected.     

渗氮钢粗糙表面的弹塑性接触研究

利用弹塑性有限元和单纯形法求解弹塑性接触模型，分别模拟了屈服强度呈梯度变化的渗氮钢、未经处理的匀质材料和硬涂层材料粗糙表面的弹塑性接触行为。与未经处理的匀质材料相比，渗氮钢可承受更大接触载荷。在相同载荷作用下，渗氮钢表面粗糙峰接触面积较小，平均间距较大，接触体内材料不易发生屈服，从而显著提高接触性能。和硬涂层材料相比，渗氮钢接触体内等效von Mises应力分布平缓，没有应力突变。最后讨论了渗氮层和硬涂层的厚度对粗糙表面接触特性的影响。     

Basic principles of rough surface contact analysis using numerical methods

A detailed account of the principles involved in using numerical elastic contact techniques on digitized measurements from rough surfaces is presented in relation to two- and three-dimensional topography data. The main results of such analyses are shown to include the detailed interface geometry and the subsequent contact pressure distribution involved. Methods of defining the resulting sub-surface stresses created by this contact pressure distribution are also presented for static normal loading, and for the case of a normal load in the presence of a frictional surface shear. The problems posed in dealing with plastic asperity contacts are also discussed, together with an outline of how the numerical methods described have been modified further to allow analysis of rough layered bodies of dissimilar materials, thus offering a very useful design tool for surface coatings.     

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.     

The behavior of an elastic-perfectly plastic sinusoidal surface under contact loading

The goal of this paper is to provide the foundation for an analysis of contact between elastic-plastic solids, whose surface roughness is idealized with a Weierstrass profile. To this end, we conduct a parametric study of the plastic deformation and residual stress developed by the two-dimensional contact between a flat, rigid platen and an elastic-perfectly plastic solid with a sinusoidal surface. Our analysis shows that the general characteristics of the deformation can be characterized approximately by two parameters: α = a/λ, where a is the half-width of the contact and λ is the period of the surface waviness; ψ = E^*g/σ_Yλ, where E^* and σ_Y are the effective modulus and yield stress of the substrate, respectively, and g is the amplitude of the surface roughness. Depending on the values of these parameters, we identify eight general types of behavior for the asperity contacts: (a) elastic, elastic-plastic or fully plastic isolated Hertz type contacts; (b) elastic, or elastic-plastic non-Hertzian isolated contacts; and (c) elastic, elastic-plastic or fully plastic, interacting contacts. Relationships between contact pressure, contact size, effective indentation depth and residual stress are explored in detail in each regime of behavior. Implications on rough surface contacts are discussed.     

含涂层真实粗糙表面的弹塑性接触特性研究

运用有限元法、线性规划法和塑性增量理论对含涂层真实粗糙表面的弹塑性接触问题进行了分析。通过改变涂层材料的弹性模量、屈服极限及涂层厚度，研究了不同条件下接触面积与接触压力、平均间隙与接触压力的关系及变化规律，给出了3种数值方法的解与弹性解的比较，分析了各主要因素对接触压力、接触面积及平均间隙的影响。     

The contact of elastic regular wavy surfaces

A complete solution in closed form to the elastic contact of a one-dimensional sinusoidal surface with a flat surface was presented by Westergaard in 1939. This paper is concerned with the elastic contact of a two-dimensional sinusoidal surface with a flat. In this case the stress distribution within the elastic solids is three-dimensional. As the load is increased the contact areas change in shape from being circular to square and finally leave a circular region of no contact when the waves are almost squashed flat. The problem is solved in general using a numerical method due to Kalker, but asymptotic solutions in closed form have been found for light loads and also for heavy loads at which contact is almost complete. The variation of the mean separation with load, which determines the volume of the space trapped between the two surfaces, is also found.