Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction

The deformation around a 500-nm deep Berkovich indent in a large grained Fe sample has been studied using high resolution electron back scatter diffraction (EBSD). EBSD patterns were obtained in a two-dimensional map around the indent on the free surface. A cross-correlation-based analysis of small shifts in many sub-regions of the EBSD patterns was used to determine the variation of elastic strain and lattice rotations across the map at a sensitivity of ∼±10^-4. Elastic strains were smaller than lattice rotations, with radial strains found to be compressive and hoop strains tensile as expected. Several analyses based on Nye's dislocation tensor were used to estimate the distribution of geometrically necessary dislocations (GNDs) around the indent. The results obtained using different assumed dislocation geometries, optimisation routines and different contributions from the measured lattice rotation and strain fields are compared. Our favoured approach is to seek a combination of GND types which support the six measurable (of a possible nine) gradients of the lattice rotations after correction for the 10 measurable elastic strain gradients, and minimise the total GND line energy using an L¹ optimisation method. A lower bound estimate for the noise on the GND density determination is ∼±10¹² m^-2 for a 200-nm step size, and near the indent densities as high as 10¹⁵ m^-2 were measured. For comparison, a Hough-based analysis of the EBSD patterns has a much higher noise level of ∼±10¹⁴m^-2 for the GND density.