A 3D Hough transform for indexing EBSD and Kossel patterns

Abstract

SummaryA three-dimensional Hough transform is designed for the detection of conic curves (hyperbolae and ellipses) formed by the gnomonic projection of diffraction Kossel cones. This new procedure is applied to a high-angular-accuracy analysis of electron backscatter diffraction (EBSD) patterns and to a fully automatic indexing of X-ray Kossel patterns in the SEM. The high-accuracy analysis of EBSD patterns allows for the determination of local elastic strains, without any reference pattern, and with a spatial resolution of a few tens of nanometres. An accuracy of 2 × 10 −4 is achieved on geometrically calculated diagrams. This paper presents also the first fully automatic indexing of Kossel patterns. This automatic indexing procedure can be applied to local texture analysis, as well as to local elastic strain measurements. Although the spatial resolution of Kossel is about 1 μm, the accuracy of strain measurement is in this case much higher than that presently obtained on EBSD.

Coupling Diffraction Contrast Tomography with the Finite Element Method

“…Let us take a cubic grain of size d ¼ 50 mm. For voxel-based meshing, the number of elements can readily be calculated as (d/a) 3 , with a the element size at the grain boundary. For free meshing with tetrahedron, a geometric progression of the element size can be used with coarser elements at the center of the grain, for this value of q.…”

“…[1] Large scale simulations on polycrystalline volume elements can now be performed with sufficient local discretization to predict the transgranular plastic strain fields. They are necessary for comparison with results of sophisticated 2D and 3D full field measurements providing strain fields based on grid methods and/or image correlation techniques, [2] lattice rotation fields by means of Electron Back Scattered Diffraction (EBSD), [3,4,5] elastic strain fields using for instance micro-diffraction techniques. [6] Even though continuum crystal plasticity constitutive equations do not account for the intricate dislocation mechanisms at work during plastic deformation, the continuum mechanical model gives relevant information about the strain heterogeneities induced in a polycrystal by the strong incompatibilities that develop at grain boundaries.…”

Micromechanical modelling of twinning-induced plasticity steels

“…[6,9]. Development of micromechanical techniques to measure stress fields using Kossel [21], Kikuchi [22] or Laue microdiffraction diagrams [23], in addition to measurement techniques for kinematic fields, will clearly be of great interest for a direct determination of the local constitutive relation at the local (micron) scale, a necessary step for giving micromechanical models the status of quantitative predictive tools.…”

Cementite Residual Stress Analysis in Gas-nitrided Low Alloy Steels

“…Maurice and al. developed a method using 3D Hough transform [12] while Wilkinson and al. compared Kikuchi patterns with a reference taken from an identical crystal orientation [13].…”