High resolution electron backscatter diffraction measurements of elastic strain variations in the presence of larger lattice rotations

Abstract

In this paper we explore methods of measuring elastic strain variations in the presence of larger lattice rotations (up to -11°) using high resolution electron backscatter diffraction. We have examined the fundamental equations which relate pattern shifts to the elastic strain tensor and modified them to a finite deformation framework from the original infinitesimal deformation one. We incorporate the traction free boundary condition into the minimisation problem for the finite deformation case (i.e. large rotations and small elastic strains). Numerical experiments show that this finite deformation kinematic analysis continues to work well, while the infinitesimal analysis fails, when the misorientation between test and reference pattern is made increasingly high. However, measurements on patterns simulated using dynamical diffraction theory indicated that this formulation is not sufficient to recover elastic strains accurately because the pattern shifts are not determined accurately when large rotations are present. To overcome this issue we remap the test pattern to an orientation that is close to that of reference pattern. This remapping was defined by a finite rotation matrix, which was estimated from the infinitesimal rotation matrix measured using cross-correlation. A second cross-correlation analysis between the reference pattern and the remapped test pattern allows the elastic strains to be recovered using the much simpler infinitesimal deformation theory. We have also demonstrated that accurate recovery of elastic strains requires accurate knowledge of the pattern centre if this remapping algorithm is used.