Energy, Adhesion, and the Elastic Foundation

Abstract

A theory for elastic contact adhesion between a rigid sphere and an elastic foundation is developed. The theory derives relationships between the contact deformation and the externally applied force. The derivation is based on elastic contact between a sphere and a thin linearelastic foundation in which the strain energies are balanced by the work of indentation and the change in surface energy. Contacting regimes where there is either compressive strain energy or only tensile strain energy (pull-off regime) are both treated. The model is non-dimensionalized and an order of magnitude analysis is performed in order to develop simplified closed form solutions; the simplified model is then evaluated and compared to the full solution. This theory finds that the adhesion force is significantly larger for an elastic foundation in which the surface elements act independently as compared to more traditional solutions for elastic solids. The theory gives an adhesion force of F adh ffi 7pRDc:

Lateral Contact Stiffness and the Elastic Foundation

“…The relationship among the composite elastic modulus E 0 , indentation depth d, indenter radius R, film thickness t, and applied normal force F n has previously been derived for elastic foundations with and without adhesion [11,13]. These derivations typically have a spherical body contacting a planar surface.…”

“…The approximate solution that comes from order-of-magnitude analysis under the conditions of no adhesion [11,13] is given in Eq. 5, and this expression can be directly solved to give an expression for the contact area as a function of the applied normal load, as shown below…”

“…In macroscopic tribology the transfer films or tribofilms of polymeric materials [6,7] and solid lubricants [8,9] thin films ultimately provide lubrication and protection. Models and approximate solutions for the contact using the mechanics of elastic foundations under the condition of plane strain have been developed for a variety of geometric conditions and some include the effects of adhesion [10][11][12][13]. There have also been a number of finite-element solutions to the contact of compliant elastic layers that were performed in an effort to derive approximate solutions [14][15][16][17].…”

An Approximate JKR Model of Elliptical Contact Between Thin Incompressible Elastic Coatings Covering Rigid Cylinders

“…The leading-order asymptotic solution of the axisymmetric JKR-type adhesive contact problem for a thin elastic compressible layer was obtained in [13]. Approximate theories of adhesive contact for a Winkler-type elastic foundation were recently developed in a number of works [14][15][16].…”

“…2, the solution error for ρ ≥ 0.8 will be less than 0.5% for any loading scenario. In the case when ρ < 0.8, it is recommended to perform the a posteriori error analysis using (14) and to apply the constructed analytical solution up to an admissible level of accuracy.…”