Extended Rice–Thomson analysis and atomistic simulations revealing grain boundary effects on fracture in refractory high-entropy alloys

Understanding how grain boundaries mediate fracture remains a critical challenge in designing ductile, high-performance refractory alloys. Here, we extend the Rice-Thomson criterion to account for the angle between cracks and the impinging grain boundaries (GBs), capturing the competition between intergranular fracture and dislocation-mediated plasticity. Using machine learning interatomic potentials, we performed molecular statics simulations to probe fracture mechanisms in nanocrystalline NbMoTaW and Nb₄₅Ta₂₅Ti₁₅Hf₁₅, each with two different grain sizes, revealing trends consistent with experimental observations and the extended Rice model. Comparison with averaged R-curves for bulk samples demonstrates that GBs enhance ductility in Nb₄₅Ta₂₅Ti₁₅Hf₁₅ in both grain sizes investigated. In contrast, GBs only locally improve fracture resistance in NbMoTaW when cracks are temporarily pinned at GBs inclined at high angles from the crack, but generally promote brittle intergranular fracture. These contrasting behaviors are attributed to differences in GB cohesion, reflecting clear alloying trends that align with ab-initio calculations and trends observed experimentally. Our results bridge classical fracture theory, atomistic simulations, and experimental observations, providing a comprehensive understanding of the fracture mechanisms in nanocrystalline refractory complex concentrated alloys.