Machine-learning potentials predict orientation- and mode-dependent fracture in refractory diborides

Fracture toughness ($K_{\mathrm{Ic}}$) and fracture strength (${\sigma }_f$) are key criteria in the selection and design of reliable ceramics. However, their experimental characterization remains challenging—especially for ceramic thin films, where size and interfacial effects hinder accurate and reproducible measurements. Here, machine-learning interatomic potentials (MLIPs) trained on ab initio datasets of single crystal models deformed up to fracture are used to characterize transgranular cleavage in pre-cracked ceramic diboride TMB${}_2$ (TM = Ti, Zr, Hf) lattices through stress intensity factor ($K$)-controlled loading. Mode-I simulations performed across distinct crack geometries show that fracture is primarily driven by straight crack extension along the original plane. The corresponding macroscale fracture-initiation properties ($K_{\mathrm{Ic}}\approx 1.7$–$2.9\mathrm{MPa}\cdot \sqrt{\text{m}}$, ${\sigma }_f\approx 1.6$–$2.4\mathrm{GPa}$) are extrapolated using scaling laws previously established for monocrystal ceramics. Considering TiB${}_2$ as a representative system, additional simulations explore loading conditions ranging from pure Mode-I (opening) to Mode-II (sliding). TiB${}_2$ models containing prismatic cracks exhibit their lowest fracture resistance under mixed-mode conditions, where the crack deflects onto pyramidal planes—as confirmed by nanoindentation tests on TiB${}_2$(0001) thin films. This study establishes $K$-controlled, MLIP-based simulations as predictive tools for orientation- and mode-dependent fracture in ceramics.