Analysis of Shuffling in Hexagonal Close-Packed Materials

Hexagonal close-packed (hcp) metals rely on twinning to accommodate plastic deformation at room temperature. These twins often impede dislocation mobility and can lead to brittle failure. Significant research has been done to identify methods to mitigate this brittle failure; however, a gap exists in the work on the mechanisms behind the brittle failure. All hcp twin modes require atomic shuffling to place sheared atoms in the correct lattice sites. While shuffling for the 10-12 twin is well defined, most of the shuffle processes for twinning in hcp are not defined, and the displacement field due to the introduction of a twin has not been detailed. This work serves to present new mechanical equations to compute atomic shuffles and introduce an algorithm to calculate the displacement map and insert an arbitrarily shaped twin into a defect-free lattice using those shuffle vectors. We substantiate the algorithm by placing 10-12, 10-11, and 2-1-12 twins in Mg and Ti and show that the twins undergo glissile transformation using molecular dynamics.