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Various models describing the multiscale phenomena of contact mechanics and friction have been developed recently. The power spectral density (PSD) of three-dimensional (3D) surface topography is one of key elements used to formulate these mechanics models. However, the statistical variation of the PSDs of isotropic and self-affine fractal surfaces is not well understood. This paper presents a method to correct the PSD of 3D surface topography to perform statistical and spatial characterizations in a wavenumber space. To validate this data-processing methodology, we applied the areal-corrected PSD to numerical surface models and two real surface specimens made of abrasive grindstone and worn tire rubber and assessed the variation of surface roughness across scales through visual and statistical approaches.

By studying the physical properties of natural rubber compounds cured by compression in a test mold which has a unidirectional outer flow of excess rubber from the mold when vulcanization starts, we found that the tear strength of the test pieces where the direction of the stretching was parallel to the outer flow was lower than that of the test pieces with the direction perpendicular to it. Similar anisotropies were also observed in tensile strength, modulus, tanδ, Payne's effect, etc. Some anisotropies similar to the experiments were observed in the OCTA calculation with a non-crosslinked natural rubber model. The causes of anisotropies were considered.