Loose abrasive lapping hardness of optical glasses and its interpretation

We present an interpretation of the lapping hardness of commercially available optical glasses in terms of a micromechanics model of material removal by subsurface lateral cracking. We analyze data on loose abrasive microgrinding, or lapping at fixed nominal pressure, for many commercially available optical glasses in terms of this model. The Schott and Hoya data on lapping hardness are correlated with the results of such a model. Lapping hardness is a function of the mechanical properties of the glass: The volume removal rate increases approximately linearly with Young's modulus, and it decreases with fracture toughness and (approximately) the square of the Knoop hardness. The microroughness induced by lapping depends on the plastic and elastic properties of the glass, depending on abrasive shape. This is in contrast to deterministic microgrinding (fixed infeed rate), where it is determined from the plastic and fracture properties of the glass. We also show that Preston's coefficient has a similar dependence as lapping hardness on glass mechanical properties, as well as a linear dependence on abrasive size for the case of brittle material removal. These observations lead to the definition of an augmented Preston coefficient during brittle material removal. The augmented Preston coefficient does not depend on glass material properties or abrasive size and thus describes the interaction of the glass surface with the coolant-immersed abrasive grain and the backing plate. Numerical simulations of indentation are used to locate the origin of subsurface cracks and the distribution of residual surface and subsurface stresses, known to cause surface (radial) and subsurface (median, lateral) cracks.