  Mechanical properties of steels are significantly enhanced by retained
austenite. Particularly, it has been shown that a recently developed
heat-treatment technique called Quenching and Partitioning (Q\&P) stabilises
austenite effectively. In the present work, the phase-field approach is adopted
to simulate the phase transformation and carbon diffusion, which respectively
accompanies the quenching and partitioning process of the polycrystalline Fe-C
system. By incorporating the chemical driving-force from the CALPHAD database,
the elastic phase-field model, which recovers the sharp-interface solutions,
simulates the martensite (alpha') transformation at three different quenching
temperatures. The resulting martensite volume-fractions are in complete
agreement with the analytical predictions. For the first time, in this study,
the constrained carbon equilibrium (CCE) condition is introduced in the
polycrystalline set-up to yield the predicted partitioning endpoints. Under the
CCE condition, the carbon partitioning in two alloys of varying composition is
analysed through the phase-field model which employs chemical potential as the
dynamic variable. The volume fraction and distribution of retained austenite is
determined from the carbon distribution and its temporal evolution during the
partitioning is investigated. It is identified that in the initial stages of
partitioning carbon gets accumulated in the austenite ($\gamma$) along the
$\gamma\alpha'$-interface, owing to the substantial difference in the
diffusivities and CCE endpoints. This accumulation stabilises the austenite
adjacent to the interface. However, depending on the martensite volume-fraction
and the alloy composition, the evolution of the stabilised austenite varies.
Furthermore, the influence of the phase distribution on the kinetics of the
temporal evolution of retained austenite is elucidated.
