接触和摩擦与工业工程密切相关，广泛应用于机械、交通、通讯等领域。工程中的任何接触界面都不会是绝对光滑的，从微观来看，真实的接触界面由一系列微小接触对组成。粗糙表面接触摩擦行为研究的复杂性正在于此：整个表面的演化规律是接触过程中所涉及的所有微小接触对的结果。本文从组成粗糙表面的微小接触对出发，客观准确地表征粗糙表面，深入研究粗糙表面的接触演化规律，精确地预测界面的接触关系以及摩擦性能。本文的主要工作与研究成果如下：

1. 传统的粗糙表面分析多数使用半球假设、假设变形足够小、并假设接触对之间不会发生合并，本文针对这一问题开展了不同几何形貌的单接触对模型在大变形条件下的接触响应研究。

• 本文推导了适合高载荷接触条件的弹性理论解答来代替传统的赫兹解，对比了单接触对不同简化方式的异同；单接触对的弹塑性力学响应对其形状非常敏感，本文从不同角度分析了在粗糙表面中使用正弦形状表征界面粗糙度比半球形状的优势。
• 由于现有的工作无法定量反映基底变形效果，而基底变形在高载荷接触条件下不可忽略，本文提出了考虑基底变形的近似解析解，消除了传统模型中底部约束对接触关系预测的影响。
• 由于传统模型往往不考虑接触对之间的合并，本文提出了考虑合并的多接触对模型，研究了接触对合并的影响因素及相应的处理方法，结果表明：随着界面塑性的增强和接触对之间距离的减小，接触界面从相互作用主导接触关系逐渐转变为合并主导接触关系。

2. 以单接触对的接触响应研究为基础，本文建立了粗糙表面离散模型：消除了传统统计学模型对于单接触对半球形状、界面弹性、变形独立这三点假设的依赖，采用共轭梯度算法建立了考虑接触对之间相互作用的弹塑性接触模型，预测了更加精确的接触关系，为粗糙表面接触行为研究提供了一种新方法。通过分析接触过程中界面接触信息的演化过程，得出了相互作用导致接触面积增加并非由于发生接触的数量增加、而是由于接触饱和的结论。此外，通过与全细节有限元仿真结果对比，进一步明确了模型的精度，强调了粗糙表面表面形貌合理表征的重要性，并极大地提高了计算效率。
3. 关于界面滑动与摩擦问题，揭示了单接触对在法向载荷和切向载荷组合加载作用下发生滑动的机理，分析了摩擦系数的演化规律。

• 本文以二维平面应变摩擦模型为例，研究了滑动初期塑性屈服向完全滑移过渡的机理及两者之间的竞争机制。通过推导摩擦系数的半解析解以及大量的数值模拟，根据屈服准则和切向刚度准则，研究了材料塑性与界面强度对摩擦系数和界面滑动的影响：随着接触面塑性程度的增强，摩擦系数逐渐减小；界面强度越大，摩擦系数越趋于稳定，从而给出了摩擦系数的上限；而随着塑性的增强与界面强度的增大，接触面从滑移主导滑动逐渐过渡为塑性主导滑动。
• 本文以粗糙表面摩擦问题中常用的简化方式为例，推导和对比了不同摩擦模型在滑动过程中的理论解答，还开展了微动摩擦实验工作：以中熵合金-钢这对摩擦副为例，得到了典型的摩擦滞回曲线，分析了摩擦系数的影响因素。

Contact and friction are closely related and widely used in mechanical engineering, traffic and other fields. The real contact surface is not absolutely smooth, which is made up of a number of tiny contact pairs (asperities) as viewed in the micro-scale. This is just the complexity of the contact and friction behaviors of rough surfaces: the overall surface behavior is the result of all asperities which are involved during the contact. In this dissertation, the single asperity model is studied in depth, the rough surface is characterized objectively and accurately, so the contact and tribology behaviors of the surfaces will be predicted accurately. The main research work and results of the present dissertation are as shown below:

1. The rough surface analysis mostly uses hemi-spherical assumptions in traditional research, assuming that the deformation is small enough and asperity coalescing will not happen. In present research, the contact response of a single asperity with different profiles have been studied.

• The elastic theoretical solution for high load contact conditions has been deduced to replace the Hertz solution. The similarities and differences of the simplification methods of a single asperity have been discussed. The mechanical response of a single asperity is very sensitive to its profile when considering plasticity. Compared with the traditional hemi-spherical assumption, the advantages of using sinusoidal profile assumption in rough surface have been analyzed from different perspectives.
• In traditional work, the effects of substrate deformation cannot be predicted, which cannot be ignored under high load conditions. So in present study, an approximate analytical solution has been presented, and the influence of bottom constraint on contact relationship prediction in traditional model is eliminated.
• Asperity coalescing is often ignored in traditional research. In present study, a multi-asperities model is proposed and analyzed. The factors influencing the coalescing effect and the treatment methods are proposed. Results show that with the increase of the interface plasticity and the decrease of the initial distance between the contact pairs, the contact responses are dominated from interaction to coalescing.

2. Based on the contact response of a single asperity, the basic assumptions of the traditional statistical models are too ideal. A new parameter which can characterize rough surface has been proposed, and an elasto-plastic contact model considering interaction effect has been established, so the contact responses will be predicted more accurately. By analyzing the evolution of the contact interface during the contact process, it can be concluded that the increase of contact area is caused by asperity interaction instead of the increase of contact numbers. In addition, the accuracy of the model is further clarified by comparing the results with full-detailed finite element simulations. The importance of characterizing the rough surface is emphasized, and the computational efficiency is greatly improved.
3. The reason of sliding under the combined load of normal load and tangential load is revealed, and the evolution of friction coefficient is analyzed.

• A two-dimensional plane strain model is taken as an example to reveal the sliding mechanism of a single asperity under the combined normal and tangential loading. By deducing the semi-analytical solution of friction coefficient and lots of numerical simulations, the influence of plasticity and interfacial strength on friction coefficient has been analyzed according to yield criterion and tangential stiffness criterion. Results show that as the plasticity of the contact surface is increasing, the coefficient of friction is gradually decreasing. The higher the strength of the interface, the more friction coefficient tends to be stable, which gives the upper limit of the friction coefficient. With the enhancement of the interfacial plasticity and the increase of the interfacial strength, the contact surface gradually transforms from sliding-dominant to plastic-dominant.

Taking the simplification methods which are commonly used in rough surface friction problem as an example, the theoretical solutions of different friction models in sliding process are derived and compared, and fretting experiments are carried out in this dissertation. The friction pair of CrCoNi Medium Entropy Alloy/Steel is used in the fretting experiment. The frictional hysteresis loops are obtained and the factors affecting the friction coefficient are analyzed.