A General Load–Displacement Relationship Between Random Rough Surfaces in Elastic, Non-adhesive Contact, with Application in Metal Additive Manufacturing

The load–displacement relationship between two rough surfaces in contact determines physical properties such as thermal and electrical conductivity, contact stiffness, and leakage rate. Thus, many researchers have studied the relationship between the mean pressure and the mean gap of isotropic, Gaussian, random rough surfaces in contact, using theoretical and numerical multi-asperity models, and using fractal models that account for multi-scale roughness. However, fractal models are sometimes difficult to use in practice because they require numerical solution. Hence, in this paper, we provide best-fit regression equations that approach the numerical solutions of fractal models to enable straightforward use in engineering applications. We show that the load–displacement relationship between random rough surfaces is best approximated by an exponential function and by a complementary error function depending on the magnitude of the gap between the surfaces. We illustrate the application of the best-fit regression equations for contact of an as-built Inconel 718 surface manufactured with laser powder bed fusion. This work enables applying complex contact models to engineering problems in a straightforward fashion.