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

Abstract

e eutectoid decomposition of austenite is generally analysed as a steady-state transformation. Although such a time-invariant framework is appropriate for binary systems, in ternary Fe-C-Mn alloys, particularly in the three-phase regime, a characteristic non-stationary equilibrium condition results in the formation of a unique microstructure, called 'divergent pearlite' .In the present work, the isothermal growth of the divergent pearlite, under di erent transformation temperatures; 605°C, 625°C and 650°C, is investigated by adopting a phase-eld approach which establishes local-equilibrium (LE) condition across the interface. ough most theoretical approaches intend to setup such condition, the current numerical technique elegantly recovers the non-stationary partitioning equilibrium (P-LE). e thermodynamical framework, which dictates this unique equilibrium condition, is introduced by incorporating the CALPHAD-based data. In addition to rendering the microstructure which is consistent with the observed divergentpearlite, the factors governing the characteristic kinetics and phase distributions are analysed. In complete agreement with the existing studies, it is recognised that the non steady-state growth is induced by a proportional decrease in the matrix carbon-content, which reduces the transformation kinetics, by in uencing the Mn partitioning driving-force. e characteristic proportionality which exists between these governing factors is unraveled in the current investigation. Moreover, it is also identi ed that the transition from the non steady-state evolution in three-phase regime to predominantly steady state in two-phase regime, is continuous. In other words, at 1 higher undercooling, a resolvable segment of time-invariant growth is observed in the initial stages, which is subsequently followed by the divergent evolution.

Grand-potential based phase-field model for systems with interstitial sites

“…In order to explicate the ability of the present site-fraction based grand-potential approach to distinguish substitutional and interstitial diffusion accompanying a phase transformation, decomposition of austenite into ferrite is modelled in binary, Fe–C 42 , and ternary, Fe–C–Mn, systems 46 , 49 . A representative one- and two-dimensional domain with identical length of m is considered for this numerical treatment.…”

“…Previous analysis comparing the Table 3. Fitting coefficients describing energy contributions ternary Fe-C-Mn phases where A � FeCMn (T) and B � FeCMn (T) respectively denote the second-order terms associated with carbon and manganese, where the corresponding first-order coefficients are P � FeCMn (T) and Q � FeCMn (T) 20,46,49 . www.nature.com/scientificreports/ existing mole-fraction based model to the current site-fraction formalism seemingly suggests that, under equivalent supersaturation and appropriate fitting coefficients, both approaches might yield similar phase-fraction and evolution of concentrations.…”

The Interaction of Point Defects with Stress Fields Generated by Persistent Slip Bands in Face‐Centered Cubic Nickel

“…α<β γ αβ φ α φ β is used as the free energy potential. [27][28][29] The rest of the terms in Equation 1are discussed in the following paragraphs.…”

“…where hðφ α Þ is the typical interpolation function, and we choose hðφ α Þ ¼ φ α 2 ð3 À 2Þ2φ α . [30] The Gibbs energy of a given phase, G α m , at a given temperature, T, is written as a function of the number of vacant lattice sites, n Va , using the regular solution expression [26] (a) (b) Figure 1. Sketch of a) PSB with tensile internal stresses within the PSB.…”

“…[16–18] we assume a smooth interpolation of the bulk Gibbs energies, , as followswhere is the typical interpolation function, and we choose . [ 30 ] The Gibbs energy of a given phase, , at a given temperature, T , is written as a function of the number of vacant lattice sites, using the regular solution expression [ 26 ] where is the fraction of vacant lattice sites and is the number of atoms of Ni ...…”