A phenomenological dislocation theory for martensitic transformation in ductile materials: From micro- to macroscopic description

An extension of the classical phenomenological dislocation theory U.F. Kocks and H. Mecking, Prog. Mater. Sci. 48 (2003) p. 171, Y. Estrin, J. Mater. Processing Technol. 80–81 (1998) p. 33 is proposed to develop a viscoplastic constitutive equation for steels undergoing (α′) martensitic phase transformation. Such a class of metallic material exhibits an additional inelastic strain resulting from the phase transformation itself and from the plastic accommodation in parent (austenite) and product (martensite) phases due to different sources of internal stresses. This inelastic strain, known as the transformation-induced plasticity (TRIP) strain, enhances ductility at an appropriate strength level due to the typical properties of martensite. The principal features of martensitic transformation at different scales are discussed and a macroscopic model derived from microscopic considerations. The material is considered as a combination of two viscoplastic phases, where the martensitic one is considered as a strengthening phase with evolving volume fraction. The methodology consists of two parts: a combination of two kinetics laws, which describe the material response at a given microstructure with the corresponding evolution equations of the appropriate internal variables and provide the constitutive equation of the two phases; a viscoplastic self-consistent homogenization technique that provides the constitutive equation of the two-phase composite material. The model could be regarded as a semi-phenomenological approach with sufficient link between microstructure and overall properties, and therefore with good predictive capabilities. Its simplicity allows a modular structure for its implementation in metal forming codes.