Phase Field Study on the Austenite/Ferrite Transition in Low Carbon Steel

Analysis of Transformation Plasticity in Steel Using a Finite Element Method Coupled with a Phase Field Model

“…If we consider polycrystalline system where ferrite phase coexists with austenite phase, the governing equation of phase field model for austenite-to-ferrite transformation is [16] : where α and γ represent ferrite ( α -iron) and austenite ( γ -iron), respectively. The order parameter φ q (q = 1, 2, 3, …, n) gives the orientation state of a point in a polycrystalline system containing n grains, and the sum of all phase-field values in a point (i, j, k) is conserved as: If q>n/2, we define φ q as the orientation state of a point in the polycrystalline ferrite phase.…”

“…u q and f q ( u q ) are carbon concentration and the free energy density of q grain. is the chemical potential of carbon, and we used the following constitutive equation [14] , [16] : The total free energy functional F includes the grain boundary (GB) or interphase boundary (IB) energy density F GB [16] : The parameters ω rq , ε rq , and M qr in Eqs. (8) and (11) have the definite relationship with the GB or IB energy σ qr with its width 2 ξ qr as follows: and the mobility M qr is determined by the GB or IB mobility.…”

“…Recently Cha et al . [16] proposed the PFM for the ferrite growth in the austenite poly-crystal including the effect of transformation stress.…”

“…In this study, we adopted the PFM proposed by Cha et al . [16] to describe the ferrite growth in the polycrystalline austenite microstructure. The effect of transformation stress, which requires expensive cost in the calculation, was not considered because our focus is not to develop rigorous PFM, rather than to investigate transformation plasticity associated with realistic evolution of microstructure.…”

Heat treatment analysis of multiphase steels through the use of a coupled phase field and finite element model methodology

“…The initial studies for the austenite to ferrite phase transition that employs the PFM were performed by Parisier et al [10] and Yeon et al [11]. Other PFM and MPFM simulations for austenite decomposition were also proposed [12][13][14][15] and some authors (e.g. [16][17][18][19][20]) performed continuous cooling in low carbon steels and dual-phase steels to study the overall transformation kinetics.…”