Critical radius for interface separation of a compressively stressed film from a rough surface

Surfaces are often roughened so that coatings under residual compression will remain intact and adherent. By representing surface roughness as a sinusoidal surface and comparing the elastic strain and surface energies of a compressively stressed film, it is shown that there exists a critical radius of curvature below which interface separation is energetically favored. As with many other residual stress problems in thin films, separation depends on a dimensionless group, in this case ((RET)-E-2/h(3)sigma(b)(2)) where R is the local radius of curvature, Gamma the fracture resistance of the interface and E, h and sigma(b) are the film modulus, film thickness and residual stress, respectively. (C) 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.