A discussion of the effect of inclusion volume fraction on the toughness of steel

When the fracture mode is ductile the toughness of steel depends on the fine-scale microstructure and the characteristics of the inclusions. The characteristics of the inclusions which influence toughness are volume fraction, spacing and resistance to void nucleation. The purpose of this paper is to discuss the effect of inclusion volume fraction on toughness. Results obtained from 9 nickel steel in which the inclusions are MnS suggest that for a constant fine-scale microstructure and fixed inclusion spacing the crack tip opening displacement at fracture scales as f−1/3 where f is the inclusion volume fraction. This dependence of the crack tip opening displacement on volume fraction has been evaluated for the low alloy steel investigated by Birkle et al. and the scaling seems to hold for this steel. When the inclusion volume fraction is changed at constant inclusion spacing the number of inclusion particles per unit volume remains the same and thus changing inclusion volume means that the sizes of the inclusion particles change. If the crack tip opening displacement scales as f−1/3 then this implies that the crack tip opening displacement would scale as the inverse of the particle size. That toughness would decrease with increasing inclusion size could be due to two factors. First, the Rice and Tracey equations for void growth predict that the rate of void growth increases with increasing particle size. Second, for a constant particle type, one would expect the void nucleation resistance of the particle to decrease with increasing particle size.