A single nickel crystal was indented with a wedge indenter such that a two-dimensional deformation state with three effective plane strain slip systems was induced. The in-plane lattice rotation of the crystal lattice was measured with a three micrometer spatial resolution using orientation imaging microscopy. All non-zero components of the Nye dislocation density tensor were calculated from the lattice rotation field. A rigorous analytical expression was derived for the lower bound of the total geometrically necessary dislocation density. Existence and uniqueness of the lower bound were demonstrated, and the apportionment of the total geometrically necessary dislocation density onto the effective individual slip systems was determined. The lower bound solution reduces to the exact solution under circumstances in which only one or two of the effective slip systems were known to were activated. The results give insight into the active slip systems as well as the dislocation structures formed in the nickel crystal as a result of the wedge indentation.

Experimental Lower Bounds on Geometrically Necessary Dislocation Density. J.W.Kysar, Y.Saito, M.S.Oztop, D.Lee, W.T.Huh: International Journal of Plasticity, 2010, 26[8], 1097-123