Analysis of the Grain Size Evolution for Ferrite Formation in Fe-C-Mn Steels Using a 3D Model Under a Mixed-Mode Interface Condition

Abstract

A 3D model has been developed to predict the average ferrite grain size and grain size distribution for an austenite-to-ferrite phase transformation during continuous cooling of an Fe-C-Mn steel. Using a Voronoi construction to represent the austenite grains, the ferrite is assumed to nucleate at the grain corners and to grow as spheres. Classical nucleation theory is used to estimate the density of ferrite nuclei. By assuming a negligible partition of manganese, the moving ferrite-austenite interface is treated with a mixed-mode model in which the soft impingement of the carbon diffusion fields is considered. The ferrite volume fraction, the average ferrite grain size, and the ferrite grain size distribution are derived as a function of temperature. The results of the present model are compared with those of a published phase-field model simulating the ferritic microstructure evolution during linear cooling of an Fe-0.10C-0.49Mn (wt pct) steel. It turns out that the present model can adequately reproduce the phase-field modeling results as well as the experimental dilatometry data. The model presented here provides a versatile tool to analyze the evolution of the ferrite grain size distribution at low computational costs.

Fundamentals and application of solid-state phase transformations for advanced high strength steels containing metastable retained austenite

“…This effect of the geometrical conditions on the overall transformation kinetics is generally overlooked but can be very large [61]. There are now several two/three-dimensional models for the kinetics of the austenite decomposition which consider grain size variations, nucleation site distributions, soft/ hard impingement conditions and cooling rate [62][63][64]. Of particular interest is a recent work by Toloui and Militzer [64] showing that the austenite decomposition kinetics as well as the fractions and morphologies of the products in a TRIP steel production can be well simulated by an integrated phase field model with fitting effective interface mobilities.…”

Modelling study on the three-dimensional neutron depolarisation response of the evolving ferrite particle size distribution during the austenite–ferrite phase transformation in steels

“…The magnetic particles are assumed to be spherical and centred at the grain corners of the nonmagnetic phase, as discussed in [14]. For the austenite-ferrite microstructure in low-alloyed steels, the parent austenite grain corners, edges and surface are the preferred nucleation sites for the ferrite particles [15].…”

“…To study the influence of grain size distribution, computations are carried out for a series of given microstructures, composed of (paramagnetic) austenite and (ferromagnetic) ferrite, that evolved as a function of temperature [14]. The saturation magnetisation of ferrite M s is calculated with the formula proposed by Arrott and Heinrich [27].…”

“…For an identical particle system (mono-disperse), the average particle size can be calculated with Equation (9). For a poly-disperse system, ξ(σ > 0) can be expressed as a function of ∕⟨R⟩ with Equation (14), as shown in Figure 6. The effective size δ can then be calculated with Equation (9).…”

“…In the above simulations, the value of σ/R is set as a constant. During the austenite-to-ferrite phase transformations in steels, σ/R is found to vary between 0 and 0.7 [14,28], but once nucleation is completed σ/R tends to fluctuate around a constant value. This behaviour simplifies the above 3DND analysis to obtain a reliable experimental estimate of the magnetic particle size (ferrite grain size) and size distribution during phase transformations in steels.…”