Experimental and Finite Element Analysis on an Elastic–Plastic Hemispherical Asperity Contact Against a Rigid Flat in Plane Strain with Bilinear Hardening

Real surface contact occurs primarily at the asperities, whose morphologies vary based on different processing methods. To simplify this complexity, asperities are often idealized as regular geometric shapes such as spheres or hemispheres. This paper introduces a spherical asperity model under plane strain conditions, derived from finite element analysis. The model establishes relationships between interference and contact area, as well as interference and average contact pressure, which are dependent on the material properties of the asperities. Unlike many previous models that segmented asperity deformation into different stages based on the deformation state of the contact area, this model presents a unified expression that encompasses the elastic, elastic–plastic, and plastic deformation of spherical asperities. This unified approach eliminates potential discontinuities at critical points inherent in piecewise models. Additionally, due to the small contact area of asperities, accurately measuring the contact area during the deformation of a single asperity presents significant challenges. This study employs the digital image correlation (DIC) method to measure the contact area between the spherical asperity and the indenter, with model results validated against experimental data.