Abstract:

Cylindrical indentation has become a common method for determining Young’s modulus and the adhesion energy of materials. In this study, an analytical method is developed for incompressible elastic thin layers based on Kerr’s model. The contact pressure is solved by Betti’s reciprocal theorem, with assistance from a reference solution without adhesion. Explicit relations among the indentation force F, the depth δ, and the contact half-width a are derived up to the second order. Furthermore, the pull-off force is determined, and a simple method for extracting Young’s modulus using two characteristic points (the pull-off point and the zero-force point) is provided. Comparisons with numerical results demonstrate that the second-order solutions are considerably more accurate than the first-order solutions for the F-a and δ-a relations. Finally, the indentation experiments are conducted, demonstrating that the proposed formulae are capable of determining Young’s modulus and the adhesion energy based on the experimental data.

Key words: cylindrical contact, thin layer, incompressible, asymptotic solution