考虑粗糙结合面弹塑性接触的黏滑摩擦建模

提出一种同时考虑粗糙面上微凸体弹性变形和塑性接触的切向黏滑摩擦建模方法。采用Hertz弹性理论和Mindlin解描述弹性接触微凸体的切向载荷和相对变形的关系；采用AF(Abbott-Firstone)塑性理论和Fujimoto模型描述塑性接触微凸体切向载荷和相对变形的关系。再利用GW(Greenwood-Williamson)模型统计分析方法建立粗糙表面切向载荷和相对变形之间的关系。将模型与仅考虑微凸体弹性接触情况的模型进行对比，并研究了不同塑性指数对切向载荷和相对变形关系的影响。结果表明：与完全弹性接触模型相比，本文模型引入了塑性接触理论，能够更好地描述粗糙表面切向载荷和相对变形关系，并且考虑不同接触条件下弹性变形微凸体和塑性变形微凸体对切向接触载荷的贡献，在微滑移阶段，主要由弹性接触变形影响，而在进入宏观滑移阶段之后，切向行为主要由塑性变形影响。界面切向载荷由黏着和滑移接触作用共同决定，随着切向变形的增加，滑移接触力逐渐增加，而黏着接触力先增加后减少，反映了界面由微滑移逐渐向宏滑移演化的过程。随着塑性指数的增加，粗糙面上发生塑性接触的微凸体数目逐渐增加，切向黏滑行为主要受到塑性接触特征的控制。

Stick-slip Friction Model for Elastic-plastic Contact of Rough Surfaces

A tangential stick-slip friction model for the contact of rough surfaces is proposed in this paper. The elastically- and plastically-deformed asperities are considered simultaneously to model the rough surfaces. For the elastically-deformed asperities, the classic solutions of the Hertz elastic contact model and the Mindlin micro-slip model are used to model the relation between load and deformation. For the plastically-deformed asperities, the fully-plastic contact theory of Abbott and Firestone, and the Fujimoto tangential contact model are implemented. The relation between tangential load and deformation of rough surfaces is formulated using the GW (Greenwood, J.A. and Williamson, J.B.P) probability statistics approach. The proposed model is compared with the model where only elastically-deformed asperities are considered. The effect of plastic index on the tangential behavior of rough surfaces is also investigated. A comparison of the results with the fully-elastic contact model shows that the proposed model can better describe the nonlinear relationship between the tangential load of contact and the deformation of rough surfaces. The model is more physically-based as a supplement to the plastic contact theory, with the consideration of the contribution of elastically-deformed and plastically-deformed asperities to the total tangential load of contact resulted from different contact forces. In the micro-slip regime, the tangential load is mainly affected by the elastic deformation; while within the macro-slip regime, the tangential behavior is mainly dominated by the plastic deformation. The total tangential load of rough surfaces is the resultant of the stick and slip contacts. With the increase of tangential deformation, the slip contact force increases to the critical macro-slip force, while the stick contact force increases first and then decreases to zero, which shows the evolutional process from the micro-slip regime to the macro-slip regime. With the increase of the plastic index, the relationship between tangential load and deformation is mainly controlled by the plastically-deformed asperities evolved from the elastically-deformed asperities. A tangential stick-slip friction model for the contact of rough surfaces is proposed in this paper. The elastically- and plastically-deformed asperities are considered simultaneously to model the rough surfaces. For the elastically-deformed asperities, the classic solutions of the Hertz elastic contact model and the