The role of strain accommodation during the variant selection of primary twins in magnesium

Samples of magnesium alloys AM30 and AZ31 were deformed in tension at room temperature and a strain rate of 0.1 s−1 to strains of 0.08 and 0.15. Of the numerous contraction twins that formed, the orientations of 977 were determined by electron backscatter diffraction techniques. The orientations of their host grains were also measured, so that the Schmid factors (SFs) applicable to each of the six contraction twins that could potentially form in each grain could also be calculated. About half of the observed twins were of the “high SF” (0.3–0.5) type, while nearly half had “low” SFs (0.15–0.30). Furthermore, 5% of the observed twins had associated Schmid factors of only 0.03–0.15, i.e. these were of the “very low SF” type. Of particular interest is the observation that many potential “high Schmid factor” twins did not form. The presence of the low and very low SF twins and the absence of many potential high SF twins are explained in terms of the accommodation strains that are or would be required to permit their formation. These were calculated by rotating the twinning shear displacement gradient tensor into the crystallographic reference frame of the neighboring grain. It is shown that the very high plastic anisotropy of Mg grains permits the “easy” accommodations to take place but conversely prevents accommodation of the potential twinning shears when these are “difficult” (when these involve high critical resolved shear stresses). The twins that appear require little or no “difficult” accommodation.