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

Abstract

Fracture toughness (𝐾Ic) and fracture strength (𝜎f) 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 TMB₂ (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 (KIc ≈ 1.7–2.9 MPa ⋅ √m, 𝜎f ≈ 1.6–2.4GPa) are extrapolated using scaling laws previously established for monocrystal ceramics. Considering TiB₂ as a representative system, additional simulations explore loading conditions ranging from pure Mode-I (opening) to Mode-II (sliding). TiB₂ 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 TiB₂ (0001) thin films. This study establishes K-controlled, MLIP-based simulations as predictive tools for orientation- and mode-ependent fracture in ceramics.