Abstract
Few models are devoted to investigate the effect of 3D fractal dimension Ds on contact area and asperity interactions. These models used statistical approaches or two-dimensional deterministic simulations without considering the asperity interactions and elastic–plastic transition regime. In this study, a complete 3D deterministic model is adopted to simulate the contact between fractal surfaces which are generated using a modified two-variable Weierstrass–Mandelbrot function. This model incorporates the asperity interactions and considers the different deformation modes of surface asperities which range from entirely elastic through elastic-plastic to entirely plastic contact. The simulations reveal that the elastoplastic model is more appropriate to calculate the contact area ratio and pressure field. It is also shown that the influence of the asperity interactions cannot be neglected, especially at lower fractal dimension Ds and higher load.
Highlights
The topographies of interacting surfaces play a central role in studies of physical phenomena, which are relevant to many engineering applications
A complete 3D deterministic model is adopted to simulate the contact between fractal surfaces which are generated using a modified two-variable Weierstrass–Mandelbrot function
For all Ds values, the real contact area is linearly dependent on the contact load
Summary
The topographies of interacting surfaces play a central role in studies of physical phenomena, which are relevant to many engineering applications. The properties of fractal geometry make it relevant for describing surface topographies over a wide range of length scales.[16,17,18] Numerous statistical models considering the multiscale fractal nature of rough surfaces have been established. The statistical models described above are important to the understanding of multiscale properties of rough contact, but they do not take into account the asperity interactions and do not give the local contact parameters, the scale effect of roughness in contact problems are investigated in our previous study.[13] The Hölder exponent was used to characterize the scale of roughness and study the scale effect of high spatial frequencies on elastic contact between solids. A complete 3D deterministic model is adopted to study the contact between fractal surfaces.[24] This model incorporates the asperity interactions and considers the different deformation modes of surface roughness which range from entirely elastic through elastic-plastic to entirely plastic contact interface. Some concluding remarks and prospects are proposed in the last section of the paper
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