Estimating geometric dislocation densities in polycrystalline materials from orientation imaging microscopy

Herein we consider polycrystalline materials which can be taken as statistically homogeneous and whose grains carry no or negligible elastic strains. Our objective is to obtain, from orientation imaging microscopy (OIM), estimates of ensemble averages of geometrically necessary dislocation (GND) densities for specific texture components of the polycrystal in question. Let image be the GND tensor in the current configuration and image be its Euclidean norm. Let image denote the density of geometrically necessary dislocations of type α, and image the lower-bound estimate of image as obtained from image minimization. We present algorithms by which the ensemble averages image, image, and two upper bounds of image over specific texture components can be evaluated from OIM scans of three mutually-orthogonal planar cross-sections of the polycrystalline material. Within the present context, the algorithms for recovery of the aforementioned quantities from OIM scans are general: they are formulated for arbitrary lattice orientations in grains of any crystal symmetry; there is no a priori restriction that the gradient of lattice orientation in the direction perpendicular to an OIM scan plane be zero or be otherwise ascertained by another method. The algorithms including their mathematical basis, which accounts for the non-Euclidean nature of the space of crystal orientations, are described in detail. OIM measurements were conducted on samples of a continuous-cast AA5754 aluminum hot band to generate data for trying out the algorithms. The results of the computations are presented.