On anomalous depth-dependency of the hardness of NiTi shape memory alloys in spherical nanoindentation

An experimental study on the indentation hardness of NiTi shape memory alloys (SMAs) by using a spherical indenter tip and a finite element investigation to understand the experimental results are presented in this paper. It is shown that the spherical indentation hardness of NiTi SMAs increases with the indentation depth. The finding is contrary to the recent study on the hardness of NiTi SMAs using a sharp Berkovich indenter tip, where the interfacial energy plays a dominant role at small indentation depths. Our numerical investigation indicates that the influence of the interfacial energy is not significant on the spherical indentation hardness of SMAs. Furthermore, the depth dependency of SMA hardness under a spherical indenter is explained by the elastic spherical contact theory incorporating the deformation effect of phase transformation of SMAs. Hertz theory for purely elastic contact shows that the spherical hardness increases with the square root of the indentation depth. The phase transformation beneath the spherical tip weakens the depth effect of a purely elastic spherical hardness. This study enriches our knowledge on the basic concept of hardness for SMAs under spherical indentation at micro- and nanoscales.