The grain size is a key characteristic to strongly affect the mechanical properties and performance, and the presence of additional phases plays an important role in affecting the microstructure evolution. In this work, a phase field model was adopted for immobile second-phase particles distributed at grain boundaries and analysed its pinning effect on polycrystalline grain growth. According to the size and distribution characteristics of second-phase particles in extruded AZ80 magnesium alloy, the effects of the particle morphology, particle size and volume fraction on the grain growth were investigated. The results showed that small-sized rod high-dispersion particles exhibit a stronger pinning effect on grain boundary migration. In addition, the generalised Zener relation of Rlim = 2.49rsp/fsp−0.322 was obtained for the particles located at grain boundaries.
TourretDLiuHLlorcaJ.Phase-field modeling of microstructure evolution: recent applications, perspectives and challenges. Prog Mater Sci. 2021;123:100810.
2.
WuYLuoQQinE-w.Influencing factors of abnormal grain growth in Mg alloy by phase field method. Mater Today Commun. 2020;22:100790.
3.
ZhangYMLiuLL.Phase field simulation of abnormal grain growth mediated by initial particle size distribution. Adv Powder Techno. 2021;32(9):3395–3404.
4.
KundinJAlmeidaRSMSalamaHPhase-field simulation of abnormal anisotropic grain growth in polycrystalline ceramic fibers. Comput Mater Sci. 2020;185:109926.
5.
ChangKChenLQKrillCEEffect of strong nonuniformity in grain boundary energy on 3-D grain growth behavior: A phase-field simulation study. Comput Mater Sci. 2017;127:67–77.
6.
ChangKKwonJRheeC-K.Role of second-phase particle morphology on 3D grain growth: A phase-field approach. Comput Mater Sci. 2016;124:438–443.
7.
WuYZongYPJinJF.Grain growth in a nanostructured AZ31 Mg alloy containing second phase particles studied by phase field simulations. Sci China Mater. 2016;59(5):355–362.
8.
MohseniMEivaniARVafaeenezhadHAn experimental and theoretical investigation of the effect of second-phase particles on grain growth during the annealing of hot-rolled AZ61 magnesium alloy. J Mater Res Technol. 2021;15:3585–3597.
9.
JinXLiangYBiJEnhanced strength and ductility of Al0.9CoCrNi2.1 eutectic high entropy alloy by thermomechanical processing. Materialia. 2020;10.
10.
SathiyamoorthiPParkJMMoonJAchieving high strength and high ductility in Al0.3CoCrNi medium-entropy alloy through multi-phase hierarchical microstructure. Materialia. 2019;8.
11.
JuanCCTsaiMHTsaiCWSimultaneously increasing the strength and ductility of a refractory high-entropy alloy via grain refining. Mater Lett. 2016;184:200–203.
12.
LeeDAgustianingrumMPParkNSynergistic effect by Al addition in improving mechanical performance of CoCrNi medium-entropy alloy. J Alloys Compd. 2019;800:372–378.
13.
JodiDEParkJParkN.Precipitate behavior in nitrogen-containing CoCrNi medium-entropy alloys. Mater Charact. 2019;157.
14.
Darvishi KamachaliRAbbondandoloASiburgKFGeometrical grounds of mean field solutions for normal grain growth. Acta Mater. 2015;90:252–258.
15.
MiyoshiETakakiTOhnoMUltra-large-scale phase-field simulation study of ideal grain growth. npj Comput Mater. 2017;3(1).
16.
MiyoshiETakakiTOhnoMCorrelation between three-dimensional and cross-sectional characteristics of ideal grain growth: large-scale phase-field simulation study. J Mater Sci. 2018;53(21):15165–15180.
17.
IvasishinOMShevchenkoSVVasilievNL3D Monte-Carlo simulation of texture-controlled grain growth. Acta Mater. 2003;51(4):1019–1034.
18.
YuQEscheSK.Three-dimensional grain growth modeling with a Monte Carlo algorithm. Mater Lett. 2003;57(30):4622–4626.
19.
AndersonMPGrestGSSrolovitzDJ.Computer simulation of normal grain growth in three dimensions. Philos Mag B. 2006;59(3):293–329.
20.
ZöllnerDStreitenbergerP.Three-dimensional normal grain growth: Monte Carlo Potts model simulation and analytical mean field theory. Scripta Mater. 2006;54(9):1697–1702.
21.
HanFBTangBKouHCCellular automata modeling of static recrystallization based on the curvature driven subgrain growth mechanism. J Mater Sci. 2013;48(20):7142–7152.
22.
LiZQWangJSHuangHB.Grain boundary curvature based 2D cellular automata simulation of grain coarsening. J Alloys Compd. 2019;791:411–422.
23.
OgawaJNatsumeY.Cellular automaton modelling to predict multi-phase solidification microstructures for Fe-C peritectic alloys. IOP Conf Ser: Mater Sci Eng. 2020;861(1).
24.
JamshidianMZiGRabczukT.Phase field modeling of ideal grain growth in a distorted microstructure. Comput Mater Sci. 2014;95:663–671.
25.
OgawaJNatsumeY.Three-dimensional large-scale grain growth simulation using a cellular automaton model. Comput Mater Sci. 2021;199.
26.
MoelansNBlanpainBWollantsP.Phase field simulations of grain growth in two-dimensional systems containing finely dispersed second-phase particles. Acta Mater. 2006;54(4):1175–1184.
27.
VanherpeLMoelansNBlanpainBPinning effect of spheroid second-phase particles on grain growth studied by three-dimensional phase-field simulations. Comput Mater Sci. 2010;49(2):340–350.
28.
SuwaYSaitoYOnoderaH.Phase field simulation of grain growth in three dimensional system containing finely dispersed second-phase particles. Scripta Mater. 2006;55(4):407–410.
29.
ZhaoZGXinWYZhengC.Phase-field method simulation of the effect of hard particles with different shapes on two-phase grain growth. Acta Metall Sin. 2013;48(2):227–234.
30.
ManoharPAFerryMChandraT.Five decades of the Zener equation. ISIJ Int. 1998;38(9):913–924.
31.
ChangKKwonJRheeC-K.Effect of particle-matrix coherency on Zener pinning: A phase-field approach. Comput Mater Sci. 2018;142:297–302.
32.
HuGWZengLCDuHCombined effects of solute drag and Zener pinning on grain growth of a NiCoCr medium-entropy alloy. Intermetallics. 2021;136:107271.
33.
SchwarzeCDarvishi KamachaliRSteinbachI.Phase-field study of zener drag and pinning of cylindrical particles in polycrystalline materials. Acta Mater. 2016;106:59–65.
34.
ChakrabartiTMannaS.Zener pinning through coherent precipitate: A phase-field study. Comput Mater Sci. 2018;154:84–90.
35.
FanDChenLQ.Computer simulation of grain growth using a continuum field model. Acta Mater. 1997;45(2):611–622.
36.
MullinsWW.Two-dimensional motion of idealized grain boundaries. J Appl Phys. 1956;27(8):900–904.
37.
PalmerMRajanKGlicksmanMTwo-dimensional grain growth in rapidly solidified succinonitrile films. Metall Mater Trans A. 1995;26(5):1061–1066.
38.
LeeK. Analysis and control of microstructure in binary alloys. University of Maryland, College Park; 2004.
39.
RingerSPLiWBEasterlingKE.On the interaction and pinning of grain boundaries by cubic shaped precipitate particles. Acta Metall Mater. 1989;37(3):831–841.
40.
DohertyRDSrolovitzDJRollettADOn the volume fraction dependence of particle limited grain growth. Scr Metall. 1987;21(5):675–679.
