On the origins of ultra-high hardness and strain gradient plasticity in multi-phase nanocrystalline MoNbTaTiW based refractory high-entropy alloy

In this paper, we report a remarkably high hardness in fully-dense nanocrystalline multi-phase MoNbTaTiW based refractory high-entropy alloy which was prepared by ball milling and spark plasma sintering. A single phase BCC structure was realized after 30 h of milling whereas sintering led to the decomposition of the as-milled complex lattice into a BCC and two FCC phases. Vickers microindentation performed at various loads led to the observation of pronounced indentation size effect with hardness in the range 18.87-13.89 GPa. It appears that Ti and Fe (from processing media) are responsible for the multi-phase structure realized as well as extraordinarily high absolute hardness (13.89 GPa at 500 g load) and "density-normalized hardness". These values are the highest reported so far in the family of MoNbTaW alloys. Comprehensive analysis on strengthening mechanisms responsible for the extraordinarily high hardness observed in this alloy indicates that solid solution strengthening and grain boundary (Hall-Petch) strengthening are the dominant factors while lattice frictional stress and Taylor hardening also contribute to some extent. The strain gradient plasticity appears to follow the considerations based on the concept of geometrically necessary dislocations and the characteristic multi-phase structure of this alloy. The back stress that would develop in order to have compatible deformation during the indentation at low loads is also expected to contribute to higher hardness values observed at low indentation loads. The depth-independent hardness of 11.80 GPa and a characteristic length scale of 1.07 mu m were realized from the analysis. Achieving of ultra-high hardness in this alloy suggests that careful microstructural engineering as well as optimal addition of alloying elements would be beneficial towards development of novel structural materials based on multi-principal element approach.