Normal Contact Mechanics Model of Fixed Joint Interface Adopting Anisotropic Fractal Geometrical Theory

With anisotropic fractal geometrical theory, the fixed joint interface normal contact mechanics model, considering the feature of the asperity's deformation, the continuous and smooth principle of normal load exerting surface asperity as well as distinguishing an asperity real micro contact area when the asperity is in elastic or plastic deformation, is established. The anisotropic three-dimensional fractal profile surface is simulated using Weierstrass-Mandelbrot function with two unknown variables. The mathematical expressions of critical elastic deformation micro contact truncated area demarcating the elastic and plastic regimes, joint interface dimensionless normal load, and joint interface dimensionless normal contact stiffness are deduced. The digital simulation results make clear that real contact area increases with the increases of the joint interface normal load when fractal dimension and fractal roughness about surface topography are constant. Joint interface normal contact stiffness adds with increasing real contact area, joint interface normal load, relating factor or material property parameter. Joint interface normal contact stiffness enhances as the increase of fractal dimension from 1. However, joint interface normal contact stiffness sometimes diminishes as the augment of fractal dimension close to 2. Establishing normal contact mechanics model helps to analyze the real contact conditions between fixed contact surfaces.