Size effects in spherical indentation of single crystal copper

A study of the size effects in the spherical indentation test of a copper single crystal is carried out. The main novelty of the approach is the analysis of a wide spectrum of parameters measured in the test that are predicted by the proposed model, and the prediction is verified experimentally for six different tip radii. Load-penetration depth curves, nominal hardness, pile-up and sink-in profiles, and the rotation and rotation gradient of the crystallographic lattice in the cross-section beneath the indenter have been measured and also calculated using 3D finite element simulations on the micro- and nanometer scale. Two gradient-effects are examined numerically within the Cosserat elastoplasticity framework with the gradient-enhanced hardening law. It is shown that a good prediction of the experimentally observed size effect on nominal hardness is achieved using the conventional power-hardening law, calibrated from the standard uniaxial compression test, enhanced with a term dependent on the lattice spin gradient term with no adjustable parameter. Furthermore, it has been found that the observed distribution of lattice rotation and decrease in the rotation magnitude with decreasing indenter radius can be qualitatively modelled by adjusting the coefficient of accumulated lattice curvature energy within the same framework.