This paper discusses the relation between fractal dimension and roughness index for fractal surfaces of solids. The applicability of the relation to fracture of $\mathrm{Mode}\mathrm{}\mathrm{I}\mathrm{I}\mathrm{I}+\mathrm{M}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{}\mathrm{I}$ complex loading is shown. The applicability to other rough surfaces is discussed.

• Received 13 January 1999

DOI:https://doi.org/10.1103/PhysRevE.60.5121