Rigorous version of ınfinitesimal deformation approach to the crystallography of fcc bcc martensitic phase transformation observed in Fe-31 wt Ni and zirconia alloys

Following the mathematical approach of Kelly (2003), rigorous version of infinitesimal deformation approach (ID) was applied to analyze fcc  bcc martensitic phase transformation observed in Fe-31wt Ni alloys considering the twinning shear system as the lattice invariant system (LIS). The expressions for crystallographical parameters associated with the martensitic phase transformation such as habit plane orientation, rotation matrix, total shape deformation matrix, orientation relationships between austenite and martensite phases, etc., have been obtained by using the rigorous version of infinitesimal deformation approach, taking into account only the information about the lattice parameters of the austenite and martensite phases. The habit plane orientation obtained from the infinitesimal deformation approach (ID), for example, for the value of volume fraction 0.39876 in Fe-31wt Ni alloy, is found as (0, 0.58033, 0.81438) while the habit plane obtained from rigorous version of (ID) approach associated with the martensite transformation is (0.185064, 0.594242, 0.782705) which is an agreement with that calculated from the Wechsler-Lieberman-Read (W-L-R) theory. The difference between the two habit plane orientations is 10.8 0 . Moreover, the calculations carried out for zirconia, in which there are small values of the principal distortions, in the present study certainly indicate that infinitesimal deformation approach (ID) gives almost the same results as (W-L-R) theory. For the other crystallographical parameters, such as magnitude of total shape deformation, volume fraction, orientation relationship, the rigorous version of (ID) approach gives essentially the same crystallographical solutions as those calculated (W-L-R) theory. So, it is concluded that the rigorous version of (ID) approach in the habit plane orientation is better than the infinitesimal deformation approach (ID) for the alloys in question.