Numerical simulations of spherical indentation of superelastic-plastic thin films

Depth sensing indentation is a useful tool to characterize the mechanical behavior of shape memory alloys (SMAs), which are often used in small volumes, such as thin films. However, it is difficult to interpret these test results since SMAs exhibit various phenomena such as superelasticity (SE), shape memory effect and plasticity. Hence, in this work, a finite element investigation of spherical indentation of a SMA thin film bonded to a stiff elastic substrate as well as a bulk SMA specimen is performed pertaining to two fixed temperatures, which are below and above the austenite finish temperature ( Af ). A SMA constitutive model which can represent the combined effects of SE and plasticity is employed. The simulations are aimed at revealing the roles of above two phenomena as well as influence of the substrate on the indentation response. While the load-depth ( P−h ) curve for the thin film rises well above that of the bulk SE sample as h increases, the inclusion of plasticity reduces this deviation. The Oliver–Pharr modulus is close to the Young’s modulus pertaining to the parent austenite phase at small h and tends to that of martensite at large h for bulk samples, whereas it reaches a minimum and thereafter increases corresponding to the thin film specimens. The mean contact pressure versus indentation strain curves for both specimens agree quite well which enables interpretation based on expanding cavity models. The results are rationalized from the evolution of transformed martensite and plastic zone underneath the indenter.