Adhesive contact analysis between power-law surface and axisymmetric wavy surface considering the van der Waals force

Abstract

In the present paper, an adhesive contact between a half-region with axisymmetric wavy surface and a rigid indenter with a profile described by a power-law is analyzed. At first, solutions with and without the adhesive force are derived using the Guduru's theory. A numerical analysis of the adhesive contact is conducted simultaneously using a conjugate gradient method and a convolution integral. In the numerical analysis, the van der Waals force described by the Lennard Jones potential is employed as the adhesive force. The obtained result in the theory is well agreed with that in the numerical analysis. Next, an axisymmetric adhesive contact problem between an elastic wavy surface and a rigid indenter is solved using the JKR theory and the developed numerical method. The result of derived solution based on the JKR theory is compared with that considering the van der Waals force. When the amplitude of wavy surface, A, is less than the atomic equilibrium distance, ε, the maximum adhesion forces for the theory and the numerical analysis are well agreed with each other. On the other hand, in case of A > ε, the adhesion force for the numerical analysis is less than that for the theoretical analysis. In the theoretical analysis, it is assumed that the valley part adheres to the indenter regardless of the wave amplitude. In case of the numerical analysis considering the van der Waals force, the valley part does not adhere to the indenter in A > ε. The maximum adhesion force considering the van der Waals force in the approaching process of the indenter is compared with that in the separating process. In case of A = ε, the maximum adhesion force in the separating process is about 2.4 times that in the approaching process.

Keywords

• adhesive contact
• wavy surface
• power-law surface
• axisymmetirc problem
• van der waals force