Quaternion correlation for tracking crystal motions

During in-situ mechanical tests performed on polycrystalline materials in a scanning electron microscope, crystal orientation maps may be recorded at different stages of deformation from electron backscattered diffraction (EBSD). The present study introduces a novel correlation technique that exploits the crystallographic orientation field as a surface pattern to measure crystal motions. Introducing a quaternion-based formalism reveals very convenient to handle crystal symmetry and orientation extraction. Spatial regularization is provided by a penalty to deviation of displacement fields from being the solution to a homogeneous linear elastic problem. This procedure allows the large scale features of the displacement field to be captured, mostly from grain boundaries, and a fair interpolation of the displacement to be obtained within the grains. From these data, crystal rotations can be estimated very accurately. Both synthetic and real experimental cases are considered to illustrate the method. Keyword: Digital Image Correlation, Displacement, EBSD, Regularization, Rotation