Multilevel Model for Describing Martensitic Transformation: Formation of the Polyhedral Martensite Structure

Multilevel models of inelastic deformation that take into account microstructure evolution are promising for technology development for creating functional material structures with optimal performance characteristics. The paper discusses the mathematical formulation of a direct multilevel model to describe the inelastic deformation of a polycrystal representative volume (analogous to a macrosample), taking into account the formation and the martensitic structure evolution during the transformation process. The model considers three structural-scale levels. At the macro level, the boundary value problem is solved, the fields of stresses, strains and other model variables are determined. At mesolevel-I, a homogeneous original austenite grain is considered, in which a martensitic transition occurs due to external influences. For a detailed description of the material response at the grain level, an auxiliary scale level is introduced into consideration, i.e. mesolevel-II. At this level, the geometric features of the martensite packet formation are explicitly studied. An original method has been developed to describe martensite polyhedral structure, the construction of which is carried out when the new phase volume fraction in the austenite grain reaches a critical value. A packet description as union of polyhedra consisting of thin plates allows one to introduce the geometric characteristics of the structural elements into the model, in particular, plates and packet boundaries, linear dimensions, volumes etc., and supplement them with crystallographic orientations. The resulting geometric characteristics of martensite package with subsequent processing is transferred to an individual grain level. This makes it possible to take into account the mechanisms of deformation and hardening that occur during the interaction of phases. The results are presented of polyhedral martensite packet structure formations in AISI 304 steel in numerical experiments on uniaxial deformation at room temperature and strain rate 10–5s–1.