A Parameter Free Double Shear Theory for Lath Martensite

Abstract

A double shear theory is introduced that predicts the commonly observed {5 5 7} habit planes in low-carbon steels. The novelty of this theory is that no parameter fitting is necessary. Instead, the shearing systems are chosen in analogy to the original (single shear) phenomenological theory of martensite crystallography as those that are macroscopically equivalent to twinning. Out of all the resulting double shear theories, the ones leading to certain {h h k} habit planes naturally arise as those having small shape strain magnitude and satisfying a condition of maximal compatibility, thus making any parameter fitting unnecessary. An interesting finding is that the precise coordinates of the predicted {h h k} habit planes depend sensitively on the lattice parameters of the fcc (face-centered cubic) and bcc (body-centered cubic) phases. Nonetheless, for various realistic lattice parameters in low carbon steels, the predicted habit planes are near {5 5 7}. The examples of Fe-0.252C and Fe-0.6C are analyzed in detail along with the resulting orientation relationships which are consistently close to the Kurdjumov-Sachs model. Furthermore, a MATLAB app (available at github.com/AntonMu/LathApp) is provided which allows the application of this model to any other material undergoing an fcc to bcc transformation.