CORRIGENDUM: Nature of hardness evolution in nanocrystalline NiTi shape memory alloys during solid-state phase transition

Due to a distinct nature of thermomechanical smart materials' reaction to applied loads, a revolutionary approach is needed to measure the hardness and to understand its size effect for pseudoelastic NiTi shape memory alloys (SMAs) during the solid-state phase transition. Spherical hardness is increased with depths during the phase transition in NiTi SMAs. This behaviour is contrary to the decrease in the hardness of NiTi SMAs with depths using sharp tips and the depth-insensitive hardness of traditional metallic alloys using spherical tips. In contrast with the common dislocation theory for the hardness measurement, the nature of NiTi SMAs' hardness is explained by the balance between the interface and the bulk energy of phase transformed SMAs. Contrary to the energy balance in the indentation zone using sharp tips, the interface energy was numerically shown to be less dominant than the bulk energy of the phase transition zone using spherical tips.