Quantifying texture evolution during hot rolling of magnesium Twin Roll Cast strip

The influence of manufacturing processes on the microstructure and corrosion of the AZ91D magnesium alloy evaluated using a computational image analysis

“…In comparison with conventional hot-rolling, which usually results in a strong grain orientation and therefore significantly affects the corrosion properties of magnesium alloys [11][12][13], the TRC process is less associated in producing distinct textures. Investigations of Gorelova et al [14] revealed only a weak texture within a twin-roll casted AZ31 magnesium sheet, with the {0 0 0 1}-pole figures showing two different maximums indicating a weak casting texture and a weak basal texture as a result of deformation during the TRC process. However, there is not sufficient information available in the literature about the influence of the TRC process, including casting speed, pouring temperature and roll properties, on the corrosion properties of magnesium alloys.…”

Statistics of ambiguous rotations

“…An alternative randomization test rejects independence for large values of the correlation coefficient r defined in (11). For K 1 = K 2 = C 1 and t 1 = t 2 = t C 1 of Table 2, this is one of the tests considered by Rivest & Chang (2006).…”

“…]. An alternative randomization test rejects independence for large values of the correlation coefficient r defined in (11). For…”

Symmetrized Bingham distribution for representing texture: parameter estimation with respect to crystal and sample symmetries

“…Points on S 3 are represented by the set of unit quaternions U , which is isomorphic to special unitary group of degree 2, SU (2), and is a double covering group of the rotation group SO(3). The Bingham distribution on S 3 , or the quaternion Bingham, is a convenient probability distribution to model texture and can represent common texture components including fibers, sheets, uniform, or anisotropic spreads around individual orientations [15][16][17][18][19]. While the Bingham distribution is very flexible, there are ODFs for which a Bingham model is not suitable, such as the cone fiber textures explored in [20,21].…”

“…2.8 states that the symmetrized Bingham distribution is a finite mixture of the standard quaternion Bingham distributions, with each component a) having equal weight b) having principal directions rotated by Q c i VQ s j = V ij and c) having the same concentration parameters Λ. A similar weighted mixture mixture was defined in [18] and termed the Pseudo-Bingham distribution.…”