Load-induced local phase transformation and modulus of shape memory alloys under spherical indentation by finite element method

Shape memory alloys are a unique class of materials that are capable of large reversible deformations under external stimuli such as stress or temperature. The present study examines the phase transformations and mechanical responses of NiTi and NiTiHf shape memory alloys under the loading of a spherical indenter by using a finite element model. It is found that the indentation unloading curves exhibit distinct changes in slopes due to the reversible phase transformations in the SMAs. The normalized contact stiffness (F/S2) of the SMAs varies with the indentation load (depth) as opposed to being constant for conventional single-phase materials. The load-induced phase transformation that occurred under the spherical indenter was simulated numerically. It is observed that the phase transformation phenomenon in the SMA induced by an indentation load is distinctly different from that induced by a uniaxial load. A pointed indenter produces a localized deformation, resulting in a stress (load) gradient in the specimen. As a result, the transformation of phases in SMAs induced by an indenter can only be partially completed. The overall modulus of the SMAs varies continuously with the indentation load (depth) as the average volumetric fraction of the martensite phase varies. For NiTi (Ea > Em), the modulus decreases with the depth, while for NiTiHf (Ea < Em), the modulus increases with the depth. The predicted young modules during indentation modeling agree well with experimental results. Finally, the phase transformation of the SMAs under the indenter is not affected by the post-yield behavior of the materials.