The derivation of the kinematic relations for the martensitic transformations in steels is considered. Martensitic transformations are diffusion-less solid-state phase ones, occur at speeds close to the sonic speed and lead to changes in the type of the metal lattice. Therefore, when describing the kinematics of the martensitic transition, on the one hand, we are to take into account the basic physical phenomena such as restructuring lattice, accommodation of residual stresses caused by the restructuring; and on the other hand, - the existence of invariant (habitus) plane, making the transition possible at such high speeds. The derived kinematic relations are the part of a two-level mathematical model of solid-state phase transformations during thermomechanical processing of steels. The model is based on physical approaches of the theory of plasticity, allowing taking into account the physical mechanisms of deformation due to introduction of additional internal variables at the mesolevel. The derivation of the relations for the gradient of transformation deformation of mesolevel representative volume as a deformation with an invariant plane is presented. Analogues to the plastic deformation, the transformation deformation is given by a corresponding system of vectors, i.e. the vector normal to the invariant plane and the vector of the sliding direction (these vectors are not mutually perpendicular). These vectors are not known from crystallography, as their analogues in the theory of plastic shear on slip planes. They are calculated taking into account the magnitude of the changes in the lattice parameters at the phase transition and accommodative mechanisms. The results of calculation of transformation systems resulting due to accommodation of residual stresses by plastic shears and twinning on various possible systems in the martensite are given. After calculating transformation systems, gradients of deformation for the martensitic transition in steel and their geometric interpretation are made. The found eigenvalues of gradients give an insight into the volume change at the martensitic transformation. The results are compared with the available experimental and theoretical data.

martensitic transformations, the two-level model, the physical theory of plasticity, mathematical modeling.