Indentation fracture mechanics toughness dependence on grain size and crack size: Application to alumina and WC–Co

Measurements, for alumina, of the indentation fracture mechanics stress intensity, K, at different grain sizes show a reversed trend in the material toughness property: at small crack sizes, although larger than the material grain size, K increases with decrease in grain size in accordance with a Hall–Petch (H–P) type dependence of being linearly dependent on the inverse square root of the grain diameter; whereas, at larger crack sizes, K reverses itself and increases with increase in grain size. The experimental results are interpreted here in terms of approximate equations obtained from the Bilby/Cottrell/Swinden (BCS) model for critical crack growth with an associated plastic zone size, s, at the crack tip. The particular variations in s associated with the two types of K dependencies, nevertheless, give a positive H–P grain size dependence, at sensibly constant crack size, for computed pre-crack fracture stresses, though of lesser H–P slope than the reference crack-free fracture stress. By comparison, K measurements for WC–Co cemented carbide systems show lower values both at smaller WC particle sizes and, especially, at smaller mean free path, λ, of the fracture-prone Co binder phase. Such result is predicted to occur if s is proportional to λ. The WC–Co system is of special interest, also, because H–P dependencies for the WC and Co constituent components in different alloy compositions make an important contribution, along with the contiguity of the WC particles, to determining the corresponding material hardness properties.