Contact mechanics of layered elastic materials: experiment and theory

Abstract

This paper reports an experimental and theoretical investigation of the indentation of a layered elastic solid, with special reference to the surface force apparatus (SFA). The contacting surfaces of the SFA comprise a 3-layer material: a thin mica surface layer on a thicker epoxy layer supported by a thick silica substrate. An existing finite element analysis of the deformation of ideal mica/epoxy/silica surfaces used in the SFA is adapted to compare with the experimental measurements of the variation of contact size with load, both with and without adhesion at the interface. This is in marked difference to the Johnson, Kendall and Roberts (JKR) theory for homogeneous solids. Experiments and finite element calculations were also carried out on the elastic indentation of a thin (5.5 µm) layer of mica on a very thick layer of epoxy (>100 µm). As input data for the calculations, the elastic moduli of the mica and epoxy were measured in separate indentation experiments. The stiffness of a layered solid can be expressed by an ‘effective modulus’ , which has been deduced from the experimental measurements and compared with the theoretical values with fair success. The work of adhesion is commonly measured in the SFA by observing the ‘pull-off force’ to separate the surfaces. The theory shows that, for a layered solid, the pull-force can vary significantly from the JKR value for a homogeneous solid. In particular, it was found that the mica surface energy, γsv, measured by SFA experiments using crossed cylinders of mean radius R, where the materials are layered and the mica/mica adhesion is high, can vary with the pull-off force Fp according to Fp/4πR < γsv < Fp/2πR, and for this particular experiment was given as γsv = Fp/3.5 πR as compared with γsv = Fp/3πR for homogeneous materials.