Roughness of glass surfaces formed by sub-critical crack growth

This paper presents a study on the roughness of glass fracture surfaces formed as a consequence of sub-critical crack growth. Double-cantilever-beam specimens were used in these studies to form fracture surfaces with areas under well-defined crack velocities and stress intensity factors. Roughness depends on crack velocity: the slower the velocity, the rougher the surface. Ranging from approximately 1 × 10^?10 m/s to approximately 10 m/s, the velocities were typical of those responsible for the formation of fracture mirrors in glass. Roughness measurements were made using atomic force microscopy on two glass compositions: silica glass and soda lime silica glass. For silica glass, the RMS roughness, R_q, decreased from about 0.5 nm at a velocity of 1 × 10^?10 m/s to about 0.35 nm at a velocity of 10 m/s. For soda lime silica glass, the roughness decreased from about 2 nm to about 0.7 nm in a highly non-linear fashion over the same velocity range. We attributed the roughness and the change in roughness to microscopic stresses associated with nanometer scale compositional and structural variations within the glass microstructure. A theory developed to explain these results is in agreement with the data collected in the current paper. The RMS roughness of glass also depends on the area used to measure the roughness. As noted in other studies, fracture surfaces in glass exhibit a self-affine behavior. Over the velocities studied, the roughness exponent, ζ, was approximately 0.3 for silica glass and varied from 0.18 to 0.28 for soda lime silica glass. The area used for these measurements ranged from (0.5 μm)² to (5.0 μm)². These values of the roughness exponent are consistent with values obtained when the scale of the measurement tool exceeds a critical size, as reported earlier in the literature.