Squaring the circle – A curious phenomenon of fcc single crystals in spherical microindentation

Spherical microindentation into the (0 0 1) surface of a FCC single crystal made of the Ni-base superalloy CMSX-4 has shown a remaining indent shape, that looks rather like a square than like a circle. In order to investigate this curious phenomenon, a digital surface model of the indentation crater is generated applying a backscatter electron detector along with digital image processing. The experimental measurings indicate a direction dependent pile-up accompanied by locally extended contact zones, which explains the squared shape of the spherical indent. Finite element simulations are conducted by means of a phenomenological orthotropic elasto-plasticity model within the framework of a multiplicative decomposition of the deformation gradient. The constitutive equations are formulated with respect to the isoclinic intermediate configuration. The simulation is in qualitative agreement with the experiment. Various rates of strain hardening in the simulation reveal the overlap of pile-up/sink-in with the direction dependent pile-up due to the crystal’s anisotropy. The simulations predict that it is mainly the rate of strain hardening which shapes the anisotropy of the indentation topography.