A dislocation theory-based model for brittle-to-ductile transition in multi-principal element alloys

Multi-principal element alloys (MPEAs) have drawn great interest due to their superior mechanical properties compared to the conventional alloys. However, it is unclear in these two aspects: i) how to predict the brittle-to-ductile transition temperature (BDTT) and fracture toughness of MPEAs using theory and model; ii) how to quantify the influences of the complicated alloy composition variation and microstructural parameter on the BDTT and fracture toughness of MPEAs. These issues are critical to both the underlying mechanisms and practical engineering applications. Here, we develop a dislocation theory-based model accounting for the modified lattice friction stress model, the composition-dependent strength model, and the critical energy model to determine the BDTT and corresponding fracture toughness in body-centered cubic MPEAs. The calculated yield stress and BDTT of the as-cast MPEA agree well with the experiments. Subsequently, the BDTT and fracture toughness of TiVNbTa-based MPEAs are obtained as a function of the element concentration fluctuation. The effects of microstructure parameters, such as component randomness and short-range ordering described by the standard deviation of the interplaner potential perturbation and short-range correlation length, on the BDTT and fracture toughness are further elucidated. Importantly, a microstructure-based BDT criterion is proposed to evaluate whether MPEA is ductile or brittle at a given temperature. These results are conducive to the development and application of MPEAs in extreme environments.