A parameter-free double-shear theory for lath martensite

A double-shear theory is introduced that predicts the commonly observed {5 5 7}_γ habit planes in low-carbon steels. The novelty of this theory is that 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}_γ 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}_γ habit planes depend sensitively on the lattice parameters of the face-centered cubic (f.c.c.) and body-centered cubic (b.c.c.) phases. Nonetheless, for various realistic lattice parameters in low-carbon steels, the predicted habit planes are near {5 5 7}_γ. 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 `Lath Martensite' is provided which allows the application of this model to any other material undergoing an f.c.c. to b.c.c. transformation.