Finite-size corrections to the JKR technique for measuring adhesion: Soft spherical caps adhering to flat, rigid surfaces

Adhesion measurements based on the fracture mechanics analysis of Johnson, Kendall, and Roberts (JKR) provide a very convenient method for measuring the energy of adhesion, G, for elastomeric materials against a variety of substrates. The JKR approach utilizes linear elastic fracture mechanics, and is based on the assumptions that the contact geometry is characterized by a single radius of curvature, and that the relevant dimensions of the adhering bodies are large compared to the dimensions of the contact area. The assumption of large sample size is not necessarily valid for the commonly employed geometry consisting of a soft, spherical cap pressed against a flat, rigid surface. The implications of the resultant finite-size corrections are studied here using two different model systems: a cross-linked poly(n-butyl acrylate) homopolymer and a gel made from an acrylic triblock copolymer diluted with 2-ethylhexanol. The compliance of the spherical caps is found to deviate significantly from the value assumed in a standard JKR analysis. This discrepancy is independent of the contact area, however. Determinations of the fracture energy which are based on the relationship between the load and contact area are, therefore, not affected by this correction to the compliance. The modified compliance does need to be accounted for when the fracture energy is determined from the relationship between the contact area and the relative displacements of the adhering bodies. Use of this relationship is shown to provide a particularly powerful method for determining the modulus and/or adhesion energy for low-modulus solids.