Fracture of coherent interfaces between an fcc metal matrix and the Cr23C6 carbide precipitate from first principles

Abstract

It is known that microcrack initiation in metallic alloys containing second-phase particles may be caused by either an interfacial or an intraprecipitate fracture. So far, the dependence of these features on properties of the precipitate and the interface is not clearly known. The present study aims to determine the key properties of carbide-metal interfaces controlling the energy and critical stress of fracture, based on density functional theory (DFT) calculations. We address coherent interfaces between a fcc iron or nickel matrix and a frequently observed carbide, the ${M}_{23}{\mathrm{C}}_{6}$, for which a simplified chemical composition ${\mathrm{Cr}}_{23}{\mathrm{C}}_{6}$ is assumed. The interfacial properties such as the formation and Griffith energies, and the effective Young's modulus are analyzed as functions of the magnetic state of the metal lattice, including the paramagnetic phase of iron. Interestingly, a simpler antiferromagnetic phase is found to exhibit similar interfacial mechanical behavior to the paramagnetic phase. A linear dependence is determined between the surface (and interface) energy and the variation of the number of chemical bonds weighted by the respective bond strength, which can be used to predict the relative formation energy for the surface and interface with various chemical terminations. Finally, the critical stresses of both intraprecipitate and interfacial fractures due to a tensile loading are estimated via the universal binding energy relation (UBER) model, parametrized on the DFT data. The validity of this model is verified in the case of intraprecipitate fracture, against results from DFT tensile test simulations. In agreement with experimental evidences, we predict a much stronger tendency for an interfacial fracture for this carbide. In addition, the calculated interfacial critical stresses are fully compatible with available experimental data in steels, where the interfacial carbide-matrix fracture is only observed at incoherent interfaces.