Geometrically necessary twins in bending of a magnesium alloy

Evidence for the formation of geometrically necessary twins (GNTs), or twins that accommodate a strain gradient in a multi-axial stress state, in quasi-static, room temperature three-point bending of a rolled magnesium alloy is presented. Electron backscatter diffraction analysis showed that {101¯2}<101¯1¯> extension twins (rather than {101¯1}<101¯2¯> contraction twins) form in arcs in the tension zone, and that twinned grains have very low Schmid factors. The main tensile stress component in the tension zone was nearly perpendicular to the c-axis of the parent grains. The mechanism for such unusual twinning behavior was analyzed from the perspective of strain components that are generated by {101¯2}<101¯1¯> twinning. After twinning, an extension strain component along the c-axis and a contraction strain component perpendicular to the c-axis of the parent lattice are generated simultaneously due to the misfit between the parent and the twin lattice. The contraction strain component by twinning provided an extra strain accommodation for the compressive strain in the tension zone produced by the bending, despite the fact that the local stress state strongly disfavored the {101¯2}<101¯1¯> twinning. Thus, the {101¯2}<101¯1¯> twins in the arcs in the tension zone of the bent specimen present the characteristic of being geometrically necessary, similar to geometrically necessary dislocations and boundaries.