Phase-field modeling of diffusion controlled phase ... - KTH Mechanics

Acta Materialia 51 (2003) 1327–1339www.actamat-journals.comThe phase-field approach and solute drag modeling of thetransition to massive g → a transformation in binary Fe-CalloysI. Loginova a , J. Odqvist b,∗ , G. Amberg a ,J.Ågren baDepartment of Mechanics, KTH, 100 44 Stockholm, SwedenbDepartment of Materials Science and Engineering, KTH, 100 44 Stockholm, SwedenReceived 18 April 2002; accepted 25 October 2002AbstractThe transition between diffusion controlled and massive transformation g →α in Fe–C alloys is investigated bymeans of phase-field simulations and thermodynamic functions assessed by the Calphad technique as well as diffusionalmobilities available in the literature. A gradual variation in properties over an incoherent interface, having a thicknessaround 1 nm, is assumed. The phase-field simulations are compared with a newly developed technique to model solutedrag during phase transformations. Both approaches show qualitatively the same behavior and predict a transition toa massive transformation at a critical temperature below the T 0 line and close to the a/a + g phase boundary. It isconcluded that the quantitative difference between the two predictions stems from different assumptions on how theproperties vary across the phase interface yielding a lower dissipation of Gibbs energy by diffusion in the phase-fieldsimulations. The need for more detailed information about the actual variation in interfacial properties is emphasized.© 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.Keywords: Diffusion; Thermodynamics; Gibbs energy; Dissipation; Interfacial properties1. IntroductionIf austenite (g) in low-carbon iron alloys isquenched to sufficiently low temperatures, but stillabove the martensite start temperature M s , it willbe decomposed by a massive transformation thatyields a characteristic blocky or massive microstructure.The massive transformation is partitionlesslike the martensitic transformation, i.e. it∗Corresponding author. Fax: +46-8-100411.E-mail address: joakim@met.kth.se (J. Odqvist).does not involve any composition change, and thuslong-range diffusion is unnecessary. The growth ofmassive ferrite (a) occurs with a constant growthrate that is more or less independent of crystallographicorientation relationships in contrast to themartensitic transformation. Thermodynamically apartitionless transformation g →a is possiblebelow the T 0 temperature, at which a and g of thesame composition have same Gibbs energy. However,at what temperature the massive transformationreally becomes kinetically possible has beena matter of considerable controversy over theyears. It may be argued that if the interfacial reac-1359-6454/03/$30.00 © 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.doi:10.1016/S1359-6454(02)00527-X