Constitutive modeling of the slip-twinning transition in martensitic transformations

Martensite is the result of a diffusionless displacive phase transition. In Fe-based alloys it transforms the FCC to the BCC, BCT, or HCP structures and occurs at high strain rates. It has two typical morphologies, known as lath and plate. A quantitative constitutive description of the slip-twinning transition in the martensitic transformation is presented. It is based on the temperature and strain-rate sensitivities of slip, which are much higher than those for twinning. Thus, twinning becomes a favored deformation mechanism at low temperatures and high strain rates. The Hall-Petch coefficient, for the inclusion of grain size effects, is two times larger for twinning than slip. Constitutive relationships for slip and twinning are presented and applied to the martensitic transformation in steels; the lath-to-plate morphology change observed with increasing carbon content is successfully predicted as a function of grain size by calculations incorporating the two modes of deformation. A simple calculation of the strain rates during martensitic transformation is also provided. This methodology is applied to the Fe–C system and can be extended to the Fe–Ni–C system and to thermoelastic martensites, where twinning is favored over slip to enhance reversibility.