The effect of roughness of self-similar fractal surfaces on the real contact area, effective interfacial energy and adhesion

Effective interfacial energy and the real contact area for contact between a hard substrate and a rough elastic solid in the case that both rough surfaces are self-similar fractal are investigated using the Persson's theory of contact mechanics and its extension for two rough surfaces. In addition, the effect of different Hurst exponents on elastic solids and the presence of non-zero compressive stress about 11 GPa has been investigated in this paper. Our purpose in this study is to compare the difference and variations between adhesion and the effective contact area of the self-similar fractal surfaces with the self-affine fractal surfaces. By solving the equations and numerical calculations, it is determined that the observed effects on the self-affine fractal surfaces are also observed in this case, and effective interfacial energy, contact area and adhesion in a larger roughness amplitude than the self-affine fractal surfaces disappears and by applying non-zero compressive stress, the surfaces remain in contact, and increasing the roughness will not eliminate the contact surface.