Determination of fracture toughness of bulk materials and thin films by nanoindentation: comparison of different models

Fracture toughness is an important technical material parameter, which, for bulk materials, can be determined by macroscopic crack extension experiments. For thin coatings, this classical method is not applicable. However, during the last 25 years, techniques have been developed which allow fracture toughness determination from indentation experiments by measuring crack lengths generated during controlled indentation. For its evaluation, a number of different models have been proposed which partly yield significant different results. In the present work, cube corner nanoindentation was performed using a Hysitron Triboscope on a number of different bulk (single crystal silicon, fused silica, single crystal sapphire) and thin film materials (Si-DLC, aC, SnO(2), ZnO:Al, ITO). Crack lengths were measured by AFM-based methods and six different models, including a crack-energy-based and a thin film model, were used for evaluation. The models are validated by comparing mean deviations of experimental and literature values. Best agreement over all was found for the two models of Niihara and co-workers for halfpenny [J. Mater. Sci. Lett. 1 (1982) p. 13] and Palmquist cracks [J. Mater. Sci. Lett. 2 (1983) p. 221]. The energy-based approach of Li et al. [Acta Mater. 45 (1997) p. 4453] also yields good results, which is remarkable since it does not contain any empirical constants. The crack-energy-based model, however, could not be applied to all materials since it is based on pop-ins in the indentation curve, which were not observed for all materials. A discussion of possible sources of error is given.