A crack extension force correlation for hard materials

Increasingly, the essential, robust character of many nanoscale devices requires knowledge of their fracture toughness. For most brittle materials the technique of choice has been indentation mechanics but little insight into the fracture mechanism(s) has resulted since these have generally been treated as brittle fracture dominated by the true surface energy. Linear elastic fracture mechanics approaches have been invoked to describe indentation fracture but do not address why the surface energy from fracture toughness is most often slightly or even substantially greater than the true surface energy. In the present study we invoke a crack extension force correlation that demonstrates why this is the case at least in fracture measurements based on indentation mechanics. The proposed correlation is different from previous ones in that it focuses on observations of indentation-induced dislocation activity prior to fracture. Allowing the resistance side of the crack extension force analysis to incorporate small amounts of plasticity gives a relationship that is consistent with 22 relatively brittle intermetallics, semiconductors and ceramics. This explains why measured strain energy release rates can be 2 to 5 times as large as surface energies measured in vacuum or calculated by pseudopotentials using the local density approximation.