Micro-plasticity of surface steps under adhesive contact: Part I—Surface yielding controlled by single-dislocation nucleation

Mechanics of nano- and meso-scale contacts of rough surfaces is of fundamental importance in understanding deformation and failure mechanisms of a solid surface, and in engineering fabrication and reliability of small surface structures. We present a micro-mechanical dislocation model of contact-induced deformation of a surface step or ledge, as a unit process model to construct a meso-scale model of plastic deformations near and at a rough surface. This paper (Part I) considers onset of contact-induced surface yielding controlled by single-dislocation nucleation from a surface step. The Stroh formalism of anisotropic elasticity and conservation integrals are used to evaluate the driving force on the dislocation. The driving force together with a dislocation nucleation criterion is used to construct a contact-strength map of a surface step in terms of contact pressure, step height, surface adhesion and lattice resistance. Atomistic simulations of atomic surface-step indentation on a gold (1 0 0) surface have been also carried out with the embedded atom method. As predicted by the continuum dislocation model, the atomistic simulations also indicate that surface adhesion plays a significant role in dislocation nucleation processes. Instabilities due to adhesion and dislocation nucleation are evident. The atomistic simulation is used to calibrate the continuum dislocation nucleation criterion, while the continuum dislocation modeling captures the dislocation energetics in the inhomogeneous stress field of the surface-step under contact loading. Results show that dislocations in certain slip planes can be easily nucleated but will stay in equilibrium positions very close to the surface step, while dislocations in some other slip planes easily move away from the surface into the bulk. This phenomenon is called contact-induced near-surface dislocation segregation. As a consequence, we predict the existence of a thin tensile-stress sub-layer adjacent to the surface within the boundary layer of near-surface plastic deformation. In the companion paper (Part II), we analyze the surface hardening behavior caused by multiple dislocations.     

微/纳尺度接触问题计算方法研究进展

接触问题广泛存在于现实生活的众多领域,近来随着微/纳米技术的不断发展,接触力学在基础理论和研究方法上面临许多新的挑战.本文在摩擦学的范畴内,对近年发展的若干求解微/纳尺度接触问题的计算方法及理论进行了综述.按发展先后及所解决问题的尺度范围划分,主要有3类评估微/纳尺度接触性能的计算方法:(1)连续介质力学方法;(2)分子动力学模拟; (3)多尺度方法.介绍了这3类计算方法的典型理论和主要数学描述,给出了这些方法对解决若干微/纳观接触问题如黏着效应、粗糙表面描述、表面摩擦及润滑、表面热效应、生物接触等的主要应用.最后, 探讨了微/纳尺度接触问题计算方法可能的发展方向及应用领域.      

Micro-plasticity of surface steps under adhesive contact: Part II—Multiple-dislocation mediated contact hardening

The study of micro-plastic behavior of rough surface contacts is the critical link towards a fundamental understanding of contact, friction, adhesion, and surface failures at small length scales. In the companion paper (Yu, H.H., Shrotriya, P., Gao, Y.F., Kim, K.-S., 2007. Micro-plasticity of surface steps under adhesive contact. Part I. Surface yielding controlled by single-dislocation nucleation. J. Mech. Phys. Solids 55, 489–516), we have studied the onset of surface yielding due to single-dislocation nucleation from a stepped surface under adhesive contact. Here we analyze the contact hardening behavior due to multiple dislocations in a two-dimensional dislocation model. Continuum micro-mechanical analyses are used to derive the configurational force on the dislocation, while a modified Rice–Thomson criterion is used to model dislocation nucleation. Dislocations nucleated from the surface step are stabilized and pile up as a result of the balance between the resolved driving force and the non-zero lattice resistance in the solid. The dislocation pileup will exert a strong back stress to prevent further dislocation nucleation and thus lead to the contact hardening behavior, the degree of which depends on the slip-plane orientation. Particularly, we find that dislocation interactions between two slip planes can make the contact loading order-of-magnitude easy to nucleate multiple dislocations, which is thus named “latent softening”. A mechanistic explanation shows that the latent softening is closely related to the stress-concentration mode mixity at the surface step. Dislocation nucleation will modify the geometric characteristics of the surface step, so that the contact-induced stress state near the step, as described by the mode mixity, changes, which influences the subsequent dislocation nucleation. Our calculations show that the dislocation pileup on one slip plane can even cause the spontaneous dislocation nucleation on the other slip plane without further increase of the contact load. Furthermore, it is found that rough surface contacts at small length scale can lead to the dislocation segregation and the formation of a surface tensile sub-layer. The discrete-dislocation model presented here and in the companion paper provides novel insights in bridging the atomistic simulations and continuum plastic flow analysis of surface asperity contact.     

An adhesive wear model of fractal surfaces in normal contact

A generalized adhesive wear analysis that takes into account the effect of interfacial adhesion on the total load was developed for three-dimensional fractal surfaces in normal contact. A wear criterion based on the critical contact area for fully-plastic deformation of the asperity contacts was used to model the removal of material from the contact interface. The fraction of fully-plastic asperity contacts, wear rate, and wear coefficient are expressed in terms of the total normal load (global interference), fractal (topography) parameters, elastic–plastic material properties, surface energy, material compatibility, and interfacial adhesion characteristics controlled by the environment of the interacting surfaces. Numerical results are presented for representative ceramic–ceramic, ceramic–metallic, and metal–metal contact systems to illustrate the dependence of asperity plastic deformation, wear rate, and wear coefficient on global interference, surface roughness, material properties, and work of adhesion (affected by the material compatibility and the environment of the contacting surfaces). The analysis yields insight into the effects of surface material properties and interfacial adhesion on the adhesive wear of rough surfaces in normal contact.     

原子尺度摩擦行为的分子动力学模拟

应用大规模分子动力学方法,模拟了具有原子级光滑和原子级粗糙形貌的刚性球形探头与弹性平面基体的干摩擦行为,研究了无/有粘附条件下的载荷与摩擦力、载荷与真实接触面积,以及摩擦力与真实接触面积之间的关系,对纳米尺度下的摩擦行为规律进行了分析。几种系统的真实接触面积－载荷关系都与相应的连续力学接触模型定性的一致,它们分别是Hertz光滑表面接触模型、Greenwood-Williamson粗糙表面接触模型和Maugis-Dugdale粘着接触模型。无论是由光滑表面还是粗糙表面构成的摩擦系统,在无粘附条件下摩擦力与载荷成正比,而摩擦力与真实接触面积之间没有一个简单的关系;在粘附条件下摩擦力与真实接触面积成正比,而摩擦力与载荷之间表现为Maugis-Dugdale模型预测的亚线性关系。我们的研究表明,当表面作用从无粘附到粘附时,控制摩擦力的决定因素从载荷转变为接触面积,摩擦行为从载荷控制摩擦转变为粘着控制摩擦。     

Unloading an elastic-plastic contact of rough surfaces

A statistical model for the unloading of elastic-plastic contact of rough surfaces is presented for a single load-unload cycle. The hystereses of load-separation and load real contact area behavior are analyzed for a wide range of surface roughness and loading conditions. The residual topography of the unloaded rough surfaces is also analyzed and the new distribution functions of asperity heights and summit radii of curvature along with a corresponding GW residual plasticity index are presented. A new modified plasticity index (MPI) is suggested which considers the energy dissipation due to unrecovered plastic deformations. This MPI varies from zero for purely elastic contacts to unity for purely plastic contacts and hence, can better define the level of plasticity of contacting rough surfaces compared to the original GW plasticity index.     

粗糙表面法向接触刚度的分形模型

提出了以往有关粗糙表面法向接触刚度理论研究工作的缺陷与不足,并在一定的前提假设下,基于球体与平面的接触理论和粗糙表面的分形接触理论,从理论上给出了具有尺度独立性的粗糙表面法向接触刚度分形模型,并进行了数字仿真研究。     

Surface Residual Stress Measurement Using Curvature Interferometry

Surface roughness plays an important role in the delamination wear caused by rough surface contact. A recent dislocation model analysis predicts that nano-scale contacts of surface steps induce nucleation of dislocations leading to pro-load and anti-load dislocation segregation near the contact surface. Such dislocation segregation generates a sub-layer of tensile residual stress in a much thicker layer of compressive residual stress near the surface. The tensile sub-layer thickness is expected to be about 50 to 100 times the step height. In order to verify the predictions of the model analysis, contact experiments are carried out on polycrystalline aluminum surface to determine the existence of the tensile sub-layer. The variation of the residual stress along the thickness direction is measured using a newly developed high sensitivity curvature-measurement interferometer. The residual stress distribution measured with sub-nanometer spatial resolution indicates that contact loading leads to formation of a highly stressed sub-layer of tensile residual stress within a much thicker layer of compressive residual stress. Implications of tensile residual stress for delamination wear are discussed.     

Thermo-mechanical modelling of the contact between rough surfaces using homogenisation technique

In this study, thermo-mechanical behaviour of contacting rough surfaces has been modelled. Firstly, a numerical microscopic contact model that considers the properties of engineering surfaces has been developed. Geometrical characteristics of rough surfaces are deduced using the standard procedure for roughness and waviness parameter determination according to the so-called “motif” procedure. Secondly, an equivalent macroscopic contact model using a homogenisation technique has been presented. The interfacial behaviour of this model has been governed by the curves deduced from the microscopic model. The transition from microscopic to macroscopic scale was also validated.     

Adhesive contact of an elastic semi-infinite solid with a rigid rough surface: Strength of adhesion and contact instabilities

The effect of adhesion on the contact behavior of elastic rough surfaces is examined within the framework of the multi-asperity contact model of Greenwood and Williamson (1966), known as the GW model. Adhesive surface interaction is modeled by nonlinear springs with a force–displacement relation governed by the Lennard–Jones (LJ) potential. Constitutive models are presented for contact systems characterized by low and high Tabor parameters, exhibiting continuous (stable) and discontinuous (unstable) surface approach, respectively. Constitutive contact relations are obtained by integrating the force–distance relation derived from the LJ potential with a finite element analysis of single-asperity adhesive contact. These constitutive relations are then incorporated into the GW model, and the interfacial force and contact area of rough surfaces are numerically determined. The development of attractive and repulsive forces at the contact interface and the occurrence of instantaneous surface contact (jump-in instability) yield a three-stage evolution of the contact area. It is shown that the adhesion parameter introduced by Fuller and Tabor (1975) governs the strength of adhesion of contact systems with a high Tabor parameter, whereas the strength of adhesion of contact systems with a low Tabor parameter is characterized by a new adhesion parameter, defined as the ratio of the surface roughness to the equilibrium interatomic distance. Applicable ranges of aforementioned adhesion parameters are interpreted in terms of the effective surface separation, obtained as the sum of the effective distance range of the adhesion force and the elastic deformation induced by adhesion. Adhesive strength of rough surfaces in the entire range of the Tabor parameter is discussed in terms of a generalized adhesion parameter, defined as the ratio of the surface roughness to the effective surface separation.     

Atomistic and continuum studies of stress and strain fields near a rapidly propagating crack in a harmonic lattice

Large-scale atomistic simulations of a mode I crack propagating in a harmonic lattice are presented. The objective of this work is to study the stress and strain fields near a rapidly propagating mode I crack. The asymptotic continuum mechanics solutions of the elastic fields are compared quantitatively with molecular-dynamics simulation results for different crack velocities. It is observed that both atomistic stress and atomistic strain can be successfully related to the corresponding continuum quantities. The study reveals that the atomistic simulation results agree well with the continuum theory predictions, which suggests that the continuum theory can be applied for nano-scale dynamic problems.     

An atomistic–continuum hybrid scheme for numerical simulation of droplet spreading on a solid surface

We present an atomistic–continuum hybrid method to investigate spreading dynamics of drops on solid surfaces. The Navier–Stokes equations are solved by the finite-volume method in a continuum domain comprised of the main body of the drop, and atomistic molecular dynamics simulations are used in a particle domain in the vicinity of the contact line. The spatial coupling between the continuum and particle domains is achieved through constrained dynamics of flux continuities in an overlap domain.     

基于共轭梯度法和快速傅立叶变换的粗糙表面微动接触数值研究

实际工程表面多为粗糙表面,研究粗糙表面的表面形貌对微动接触中压力和应力的影响具有重要意义。本文研究接触过程中法向载荷保持不变,切向载荷为周期性的交变载荷。首先,建立接触算法和模型,算法核心是利用共轭梯度法CGM(Conjugate gradient method)计算微动接触中的表面压力及切向应力并利用快速傅里叶变换FFT(Fast Fourier transform)加快计算速度。然后,对单峰表面、正弦表面和随机粗糙表面的接触进行数值研究。结果表明,表面幅值对切向载荷-位移曲线以及接触过程中的能量耗散有影响,表面幅值越大,相同切向载荷作用下产生的切向位移越大,能量耗散也越大。     

粗糙表面统计接触模型的提出与发展

工程表面在微观尺度上是粗糙的，粗糙表面之间的接触状态对于多种物理现象都有重要影响，因此，粗糙表面间的接触建模方法一直是摩擦学领域研究的热点. 由Greenwood和Williamson提出的GW统计接触模型是最受认可的粗糙面接触模型，回顾了基于统计分析的粗糙面接触模型的发展，根据对GW模型主要缺点的改进，介绍了统计接触模型的研究现状，总结了统计接触模型未来可能的研究热点.      

基于分子动力学-格林函数法的微凸体接触数值分析

表面接触是摩擦的先决条件,其真实接触面积、压应力大小、空间分布等一直是接触力学关注的核心问题.采用分子动力学-格林函数法(GFMD)模拟粗糙面的接触过程,验证了其在大规模接触分析中的高效及准确性,同时探讨了由微球体组成的粗糙面的接触力学特性,并分析了分子尺度下的结果和传统力学模型计算结果的差异.结果表明,单个微凸体接触结果和分子动力学-格林函数法模拟所得非常接近,误差在5%以内.数值模拟发现,在微凸体高度符合高斯分布的情况下,接触面积和接触力成线性关系;在相同接触面积下,微凸体模型得出的接触力偏高,是上限值.微凸体模型没有考虑微凸体间的相互影响,实际是高估了弹性体的刚度;实际接触过程中微凸体相互影响,微凸体对临域形变影响尤其大,使接触区域更加离散.GFMD模型可以准确计算数十亿量级别分子、原子接触过程中真实接触面积及分布,为后续摩擦、滑移等分析提供可靠的参考.     

粗糙颗粒的随机离散元模拟——随机法向接触定律

真实颗粒的力学性质会受到其随机粗糙表面的影响,然而在传统离散元模拟中通常假设颗粒具有光滑表面,因此有必要在定量考虑颗粒表面粗糙度的基础上改进离散元的接触模型。本文基于经典 Greenwood-Williamson(GW)模型通过理论分析和数值模拟提出了一种可以考虑颗粒表面粗糙度的法向接触定律;开发了基于 Newton-Raphson迭代的数值计算方法,通过输入颗粒重叠量和一系列表面粗糙系数计算总接触力;讨论了改进计算方法效率和准确性的相关问题。相对于 GW模型中接触关系的复杂积分表示,拟合得到新随机接触定律的表达式具有类似 Hertz定律的简单结构,只包含一个表征颗粒表面粗糙度标准偏差的新增参数,σ,可以方便的引入当前离散元模拟程序中进行计算。     

Estimation of anisotropic elastic properties of nanocomposites using atomistic-continuum interphase model

We have revised classical micromechanics by accounting for the effect of interface to predict the effective anisotropic elastic properties of heterogeneous materials containing nano-inhomogeneities. In contrast to sharp interface between the matrix and inhomogeneity, we introduce the concept of interphase to account for the interfacial-stress effect at the nano-scale. The interphase’s constitutive properties are derived from atomistic simulations and then incorporated in a micromechanics-based interphase model to compute effective properties of nanocomposites. This scale transition approach bridges the gap between discrete atomic level interactions and continuum mechanics. An advantage of this approach is that it combines atomistic with continuum models that consider inhomogeneity and interphase morphology. It thereby enables us to account simultaneously for both the shape and the anisotropy of a nano-inhomogeneity and interphase at the continuum level when we compute material’s overall properties. In so doing, it frees us from making any assumptions about the interface characteristics between matrix and the nano-inhomogeneity.     

Surface effects in non-uniform nanobeams: Continuum vs. atomistic modeling

Nanobeams are expected to be one of the key structural elements in nanotechnology. Contrary to macroscopic structures, surface effects can strongly influence the stress and deformation properties of nano-devices. In addition, at such small scales, material non-uniformity becomes significant and must be considered.In this work, a continuum model for nanobeams, including both surface effects and material heterogeneity is developed. The model treats the surfaces as separate material layers with finite thickness. The continuum solution is compared with atomistic simulations, from which the effective bulk and surface properties are computed independently. A special case of self-deflection due to surface non-uniformities, which is important for design of nanosensors, is studied. A comparison between continuum and atomistic solutions reveals differences, which originate from local transition effects in the neighborhood of strong non-uniformities. This discrepancy is addressed by defining an effective length, found by correlating the beam deflections from both methods.