考虑硬度变化的结合面法向接触刚度分形模型*

基于分形几何理论,考虑微凸体因应变硬化而造成弹塑性变形阶段硬度随变形量变化而变化,建立结合面第一、第二弹塑性变形阶段单次加载刚度分形模型。推导出在计入硬度变化的情况下,单个微凸体在弹塑性变形阶段法向接触刚度与接触面积之间的关系式,进而得出结合面在弹塑性变形阶段法向接触刚度与接触面积、接触载荷之间量纲为一的关系式,并通过仿真分析得出相关参数对结合面法向接触刚度的影响。仿真结果显示:考虑硬度变化时,结合面量纲一法向接触刚度的值与法向实际接触载荷、实际接触面积之间存在关系;结合面法向接触刚度随着分形维数D的增大而增大;分形维数一定时,结合面法向接触刚度随表面长度尺度参数G值增大而增大。

Fractal Model of Normal Contact Stiffness of the Joint Interfaces with Considering Hardness Changes

Based on the fractal geometry theory,considering the hardness of the asperity changes with the amount of deformation in elastoplastic deformation stage due to strain hardening,the fractal models of the single load stiffness in the first and second elastic plastic deformation stages of the joint interface are established.The relation between the normal contact stiffness and contact area of a single asperity in the elastic plastic deformation stage is derived when hardness variation is taken into account.Then,the dimensionality of the relationship between the normal contact stiffness,contact area and contact load of the joint interface in the elastic plastic deformation stage is obtained.Through simulation analysis,the influence of relevant parameters on the normal contact stiffness of the joint interface was obtained.Simulation results show that when hardness variation is considered,there is a relationship between the dimensionless normal contact stiffness and the actual contact load and the actual contact area.The normal contact stiffness is increased with the increase of fractal dimension D,when the fractal dimension is fixed,the normal contact stiffness of the joint interface is increased with the increase of the profile scale parameter G.