Phase-field analysis of quenching and partitioning in a polycrystalline Fe-C system under constrained-carbon equilibrium condition

Abstract

Mechanical properties of steels are signi cantly enhanced by retained austenite. Particularly, it has been shown that a recently developed heat-treatment technique called enching and Partitioning (Q&P) stabilises austenite e ectively. In the present work, the phase-eld approach is adopted to simulate the phase transformation and carbon di usion, 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-eld model, which recovers the sharp-interface solutions, simulates the martensite (α ) transformation at three di erent quenching temperatures. e resulting martensite volume-fractions are in complete agreement with the analytical predictions. For the rst 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-eld model which employs chemical potential as the dynamic variable. e volume fraction and distribution of retained austenite is determined from the carbon distribution and its temporal evolution during the partitioning is investigated. It is identi ed that in the initial stages of partitioning carbon gets accumulated in the austenite (γ) along the γα -interface, owing to the substantial di erence in the di usivities and CCE endpoints. is accumulation stabilises the austenite adjacent to the interface. However, depending on the martensite volume-fraction and the alloy composition, the evolution of the arXiv:1812.04306v1 [cond-mat.mtrl-sci] 11 Dec 2018 stabilised austenite varies. Furthermore, the in uence of the phase distribution on the kinetics of the temporal evolution of retained austenite is elucidated.

The non-steady-state growth of divergent pearlite in Fe–C–Mn steels: a phase-field investigation

“…Furthermore, a empts are being made to distinguish the la ice-occupancy of the alloying elements in the current phaseeld approach. In subsequent works, quantitative conditions will additionally be incorporated by relaxing the simpli cations pertaining to the equal interfacial energy-densities and anisotropic conditions [43,44,45].…”

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

“…The phase-field approach, based on the grand-potential formalism, has been employed extensively to model solidification [81][82][83][84] and solid-state transformation [85,86], including multicomponent systems [87,88]. Furthermore, this technique is also combined with an elastic model, in order to analyze chemoelastic transformations [89,90]. Much different from these conventional studies, this approach has recently been adopted to investigate energy-minimizing, curvaturedriven transformations, where the phase field behaves in a conserved fashion [91][92][93][94][95].…”

“…However, the efficiency of scalar and tensorial mobilities, in the context of coupled second-order conservative and nonconservative systems of equations, remains to be evaluated and is reserved for a future investigation. As the underlying grand-potential model was successfully extended to multiphysics (e.g., mechanics [89,90]), the current surface-diffusion model suits an easy amplification in future applications as well.…”

Limitations of preserving volume in Allen-Cahn framework for microstructural analysis

“…where functionals F intf (φ( x, t), ∇φ( x, t)) and F bulk (η( x, t), φ( x, t)) represent the contribution of the di use interface and bulk region, respectively. e driving-force for the phase transformation is introduced in the bulk contribution through an appropriate variable, η( x, t) [13,14]. Depending on the system considered, the nature and the description of the variable changes [15,16,17].…”