Habit planes, inclusion theory, and twins

This study follows a previous one by the authors, who calculated martensite habit planes by two methods: (1) invariant-plane strain based on a theory proposed by Wechsler–Lieberman–Read (WLR) and Bowles–Mackenzie (BM) and (2) elastic-strain energy minimization of a thin-disc inclusion based on a theory similar to those described by Eshelby, Mura, Khachaturyan, and others. Our previous study considered three example materials (In–Tl, Au–Cd, Fe–Ni) but neglected twins. The present study introduces twins. Our model contains specifically the twinning plane, often (011)A, and the WLR angle φ, the relative rigid-body rotation to ensure twin-interface coherency. We focused on the much-studied f.c.c.–b.c.c. transition in Fe–31Ni. Using inclusion theory, we found that the two-Bain strain (twinned) theory gives much better agreement with invariant-plane-strain theory calculations and with observation than did the twin-free theory.