Extension of R–K constitutive relation to phase transformation phenomena

In this paper an extension of the Rusinek–Klepaczko (RK) constitutive relation is presented. The new formulation proposed, allows defining the phase transformation effect observed on macroscopic scale using a phenomenological approach. The key point is to introduce in the original formulation of RK model a new stress component based on evolution of martensite, which takes into account strain, strain rate and temperature effects. Analytical predictions of the extended constitutive relation are compared with experimental results for 301Ln2B steel. This material is chosen since the phase transformation is well observed during quasi-static loading inducing a strong increase of strain hardening rate during plastic deformation. Satisfactory agreement between analytical and experimental observations has been obtained. The phenomenological extension of RK model allows to reduce substantially the computational time in comparison with models based on physical background, for example [Papatriantafillou I, Agoras M, Aravas N, Haidemenopoulos G. Constitutive modeling and finite element methods for TRIP steels. Comput Methods Appl Mech Eng 2006;195:5094–114]. At the same time, the number of material constants defining the extended RK model is reduced. Seven constants are needed to identify the RK model in its original formulation and five are added for the description of phase transformation process.