The influence of phase boundaries on multiphase superhard materials demonstrating positive deviation from the rule of mixtures

A model for hardness in multiphase materials is derived that assumes crack propagation is impeded by phase boundaries. The phase boundary surface area density is determined statistically and the crack impedance scales linearly with this quantity. For the ( 1 − x ) AlMgB 14 − x TiB 2 material system experimentally determined hardness values and micrographs at x=0.6 are used to accurately calculate the hardness of the microstructure for ( 0 < x < 1 ) . The model predicts that refining the microstructure of this system such that the particle size is less than 0.25 μ m will increase the hardness, making it superhard.