First principles based predictions of the toughness of a metal/oxide interface

We describe a first-principles-based strategy to predict the macroscopic toughness of a γ-Ni(Al)/α-Al 2 O 3 interface. Density functional theory calculations are used to ascertain energy changes upon displacing the two materials adjacent to the interface, with relaxation conducted over all atoms located within adjoining rows. Traction/displacement curves are obtained from derivatives of the energy. Calculations are performed in mode I (opening), mode II (shear) and at a phase angle of 45°. The shear calculations are conducted for displacements along <110> and <112> of the Ni lattice. A generalized interface potential function is used to characterize the results. Initial fitting to both the shear and normal stress results is required to calibrate the unknowns. Thereafter, consistency is established by using the potential to predict other traction quantities. The potential is incorporated as a traction/displacement function within a cohesive zone model and used to predict the steady-state toughness of the interface. For this purpose, the plasticity of the Ni alloy must be known, including the plasticity length scale. Measurements obtained for a γ-Ni superalloy are used and the toughness predicted over the full range of mode mixity. Additional results for a range of alloys are used to demonstrate the influences of yield strength and length scale.