On direct estimation of hardening exponent in crystal plasticity from the spherical indentation test

Abstract A novel methodology is proposed for estimating the strain hardening exponent of a metal single crystal directly from the spherical indentation test, without the need of solving the relevant inverse problem. The attention is focused on anisotropic piling-up and sinking-in that occur simultaneously in different directions, in contrast to the standard case of axial symmetry for isotropic materials. To correlate surface topography parameters with the value of material hardening exponent, a finite-element study of spherical indentation has been performed within a selected penetration depth range using a finite-strain crystal plasticity model. It is shown how the power-law hardening exponent can be estimated from the measured pile-up/sink-in pattern around the residual impression after indentation in a (001)-oriented fcc single crystal of a small initial yield stress. For this purpose, a new parameter of surface topography is defined as the normalized material volume displaced around the nominal contact zone, calculated by integration of the local residual height (positive or negative) over a centered circular ring. That indicator can be easily determined from an experimental topography map available in a digital form. Comparison is made with the estimates based on measurements of the contact area and the slope of the load–penetration depth curve in logarithmic coordinates. The proposed methodology is extended to estimation of the hardening exponent simultaneously with the initial yield stress when the latter is not negligible. Experimental verification for a Cu single crystal leads to promising conclusions.