基于真应力应变关系的粗糙表面法向接触模型

摘要

A modeling method for normal elastic-plastic contact of rough surfaces was presented. Based on elastic-plastic finite element contact model of asperity,normal contact characteristics be-tween asperities of 40Cr,45,Q235 and rigid plane were studied respectively.In finite element model, the true stress-strain relationships of the three materials were used and the influences of the different hardening behaviors on contact characteristics of asperity were investigated.As a result,unified func-tion expressions of contact variables of asperity were built in three stages:elastic,elastic-plastic, plastic deformation.Based on the contact analysis of asperity,a normal elastic-plastic contact model of rough surfaces was built by probabilistic statistics method.By the presented method,the changes of contact variables of asperity in the contact model depended entirely on results of elastic-plastic finite element and it was unnecessary to divide the deformation process of asperity into different deformation stages,which avoided non-continuity and non-smoothness of contact variables between different sta-ges and arbitrariness of choice of interpolation function in elastic-plastic deformation stage.Compared with other contact models,the calculated results of the model are confirmed.%提出一种粗糙表面的法向弹塑性接触分析的建模方法。基于微凸体的弹塑性有限元接触模型，分别研究了40Cr、45和 Q235三种钢材料的微凸体与刚性平面的法向接触特性。有限元模型中采用三种材料的真应力应变关系，考察了不同强化特性对微凸体接触性质的影响。建立了微凸体在弹性、弹塑性、塑性变形阶段统一的接触变量变化规律的表达式。在此基础上应用概率统计理论建立粗糙表面法向弹塑性接触模型。所建立的接触模型中微凸体接触变量的变化规律完全基于弹塑性有限元模型的计算结果，无需将微凸体的变形过程区分为不同的变形阶段，避免了接触变量在各阶段采用不同函数表达式带来的连续性和光滑性问题，以及在弹塑性阶段采用插值函数的随意性问题。通过与其他接触模型的计算结果相比较，证明了所提出接触模型的合理性。