Equivalence of Eshelby inclusion theory and Wechsler–Lieberman–Read, Bowles–Mackenzie martensite-crystallography theories

We consider the relationship of the Eshelby inclusion theory to the Wechsler–Lieberman–Read, Bowles–Mackenzie (WLR–BM) theories of martensite crystallography. The WLR–BM theories proceed by solving for an invariant plane strain and by assuming a lattice invariant deformation, often (110) twinning or its equivalent. Eshelby’s theory estimates the strain, stress, and minimum strain energy of an ellipsoidal inclusion (or inhomogeneity) transforming in a constraining matrix. We use a Lagrangean finite-strain definition for the eigenstrain. We pay special attention to the crystallographic twinning plane and to twin coherency, specifically how they affect the eigenstrain. Focusing on many crystallographic features, including the habit plane and shape change, we find identical (within numerical accuracy) predictions of the crystallographic and energy-minimization theories for the Fe–31Ni f.c.c.–b.c.c. steel transformation, which shows enormous principal strains (0.13, 0.13, 0.20). The identity surprises us because we substitute finite strains into the infinitesimal strain inclusion theory. The inclusion-model contains all crystallographic features and, thus, is complete. This approach to martensite crystallography offers enormous new research possibilities. We enumerate twelve.