A Modified Phase Field Model Based on Order Parameter Gradient and Simulation of Martensitic Transformation in Large Scale System

doi:10.11900/0412.1961.2017.00478

Acta Metall Sin

2018, Vol. 54

Issue (8): 1204-1214 DOI: 10.11900/0412.1961.2017.00478

Orginal Article

Current Issue | Archive | Adv Search

A Modified Phase Field Model Based on Order Parameter Gradient and Simulation of Martensitic Transformation in Large Scale System

Cheng WEI^1,², Changbo KE², Haitao MA^1,³, Xinping ZHANG²(

)

1 School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China
2 School of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China
3 Earthquake Engineering Research & Test Center, Guangzhou University, Guangzhou 510405, China;

Cite this article:

Cheng WEI, Changbo KE, Haitao MA, Xinping ZHANG. A Modified Phase Field Model Based on Order Parameter Gradient and Simulation of Martensitic Transformation in Large Scale System. Acta Metall Sin, 2018, 54(8): 1204-1214.

Download:

HTML

PDF(8188KB)
Export: BibTeX | EndNote (RIS)

Abstract

The materials design and fabrication based on predicting microstructure have been drawn increasing attention from scientists and engineers. Martensite microstructure, which is well observed in many materials, has significant influence on physical and mechanical properties of the materials. Some experimental studies have been launched to understand the featured microstructure and its evolution in martensitic transformations (MT). Meantime, numerical approaches are often employed to assist the experimental studies due to the complex and nonlinear nature of MT. The phase field method is one of the most powerful tools in predicting microstructure. Due to the diffuse-interface description, phase field method can be used to simulate arbitrary morphologies without tracking the interface. As a consequence, the interface must contain enough elements to obtain reasonable results by using finite element method. On the other hand, the width of the interface is several orders smaller than its real counterpart. More computational resources are required to resolve the phase field variables at the interface with the system size increased. Therefore, the simulation is restricted in smaller system even with state-of-the-art computer power. For arbitrary model formulations, the interfacial energy depends on the interfacial width and other specific properties of materials. However, the phase field models of martensitic transformation do not have enough degrees of freedom to increase the interfacial width without changing the interfacial energy. In the present study, a scalable phase field model by introducing a global modified function is constructed to study MT, the modified function takes into account the inhomogeneous nature of order parameter gradient across the interfacial region. Through adjusting the free energy density and gradient coefficient, meanwhile keeping the interfacial energy density unchanged, the interfacial width and system size are increased, yet the MT feature can be fully characterized. The simulation results show that the modified phase field model can well solve the drawbacks such as fast growth rate of martensite, artificial orientation relationship between the variants of martensite, and disordered martensite microstructure in large scale system.

Key words: martensitic transformation order parameter gradient interfacial width phase field method

Received: 15 November 2017

ZTFLH:

TF777.1

Fund: Supported by National Natural Science Foundation of China (No.51205135) and Key Project Program of Guangdong Provincial Natural Science Foundation (No.S2013020012805)

	Service

	E-mail this article
	Add to citation manager
	E-mail Alert
	RSS
	（）
	Articles by authors
	Cheng WEI
	Changbo KE
	Haitao MA
	Xinping ZHANG

URL:

https://www.ams.org.cn/EN/10.11900/0412.1961.2017.00478 OR https://www.ams.org.cn/EN/Y2018/V54/I8/1204

Fig.1 Global modification function (g_p) vs equivalent gradient (ν_p) at different width ratios (λ_m/λ), in which g_p does not adjust any coefficients in the non-interface region (ν_p=0, g_p=1), but modifies the coefficients in the interfacial region (see points A and B)

Fig.2 Morphological evolution of new phase (red color) simulated in systems with scales of 134 nm×134 nm (a1~a3), 1072 nm×1072 nm (b1~b3) and 4288 nm×4288 nm (c1~c3) at time of t=0.00 s (a1~c1), t=0.15 s (a2~c2) and t=0.45 s (a3~c3), and change of the equivalent radius with time (In which each simulation system owns the same initial square nucleus size of 10.72 nm×10.72 nm) (d)

Fig.3 Morphological evolution of new phase (red color) simulated with employing the global modification function in systems with scales of 1072 nm×1072 nm (a1~a3) and 4288 nm×4288 nm (b1~b3) at time of t=0.00 s (a1, b1), t=0.15 s (a2, b2) and t=0.45 s (a3, b3), and change of the equivalent radius with time (In which each simulation system owns the same initial square nucleus size of 10.72 nm×10.72 nm) (c)

Fig.4 Morphological evolution of two R-phase variants in their initial states (variant 1 in blue and variant 2 in red) (a) simulated in systems with different scales of 101 nm×67 nm (b), 2010 nm×1340 nm (c) and 20100 nm×13400 nm (d), and change of strain energy density with time (e)

Fig.5 Morphologicl evolution of two R-phase variants (variant 1 in blue and variant 2 in red) simulated with employing the global modification function in systems with scales of 2010 nm×1340 nm (a) and 20100 nm×13400 nm (b), and change of strain energy density with time (c)

Fig.6 Schematic configuration of four R-phase variants in the (001) plane with variants 1 and 4 (a), and variants 1 and 2 (b)

Fig.7 Morphological evolution of B2-R phase transformation simulated in systems with scales of 101 nm×101 nm (a1~a3), 2010 nm×2010 nm (b1~b3) and 20100 nm×20100 nm (c1~c3) at time of t=0.05 s (a1~c1), t=0.50 s (a2~c2), t=40.10 s (a3), t=16.52 s (b3) and t=16.13 s (c3), and change of strain energy density with time (d) (In which the blue region stands for B2-phase, the light blue region stands for variant 1, the green region stands for variant 2, the yellow region stands for variant 3, and the red region stands for variant 4)

Fig.8 Morphological evolution of B2-R phase transformation simulated with employing the global modification function in systems with scales of 2010 nm×2010 nm (a1~a3) and 20100 nm×20100 nm (b1~b3) at time of t=0.05 s (a1, b1), t=0.50 s (a2, b2), t=67.71 s (a3), t=83.76 s (b3), and change of strain energy density with time (c) (In which the blue region stands for B2-phase, the light blue region stands for variant 1, the green region stands for variant 2, the yellow region stands for variant 3, and the red region stands for variant 4)

[1]	Krauss G. Martensite in steel: Strength and structure [J]. Mater. Sci. Eng., 1999, A273-275: 40
[2]	Waitz T, Kazykhanov V, Karnthaler H P.Martensitic phase transformations in nanocrystalline NiTi studied by TEM[J]. Acta Mater., 2004, 52: 137
[3]	Zhang Z Q, Dong L M, Yang Y, et al.Influences of quenching temperature on the microstructure and deformation behaviors of TC16 titanium alloy[J]. Acta Metall. Sin., 2011, 47: 1257(张志强, 董利民, 杨洋等. 淬火温度对TC16钛合金显微组织及变形行为的影响[J]. 金属学报, 2011, 47: 1257)
[4]	Kinney C C, Pytlewski K R, Khachaturyan A G, et al.The microstructure of lath martensite in quenched 9Ni steel[J]. Acta Mater., 2014, 69: 372
[5]	Zhang S H, Wang P, Li D Z, et al.Investigation of trip effect in ZG06Cr13Ni4Mo martensitic stainless steel by in situ synchrotron high energy X-ray diffraction[J]. Acta Metall. Sin., 2015, 51: 1306(张盛华, 王培, 李殿中等. ZG06Cr13Ni4Mo马氏体不锈钢中TRIP效应的同步辐射高能X射线原位研究[J]. 金属学报, 2015, 51: 1306)
[6]	Chen L Q.Phase-field models for microstructure evolution[J]. Annu. Rev. Mater. Res., 2002, 32: 113
[7]	Wang Y, Khachaturyan A G.Three-dimensional field model and computer modeling of martensitic transformations[J]. Acta Mater., 1997, 45: 759
[8]	Khachaturyan A G.Theory of Structural Transformations in Solids[M]. New York: Wiley, 1983: 198
[9]	Levitas V I, Preston D L.Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite?martensite[J]. Phys. Rev., 2002, 66B: 134206
[10]	Levitas V I, Preston D L.Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. II. Multivariant phase transformations and stress space analysis[J]. Phys. Rev., 2002, 66B: 134207
[11]	Yamanaka A, Takaki T, Tomita Y.Elastoplastic phase-field simulation of self-and plastic accommodations in cubic→tetragonal martensitic transformation[J]. Mater. Sci. Eng., 2008, A491: 378
[12]	Yamanaka A, Takaki T, Tomita Y.Elastoplastic phase-field simulation of martensitic transformation with plastic deformation in polycrystal[J]. Int. J. Mech. Sci., 2010, 52: 245
[13]	Idesman A V, Cho J Y, Levitas V I.Finite element modeling of dynamics of martensitic phase transitions[J]. Appl. Phys. Lett., 2008, 93: 043102.
[14]	Man J, Zhang J H, Rong Y H.Three-dimensional phase field study on strain self-accommodation in martenstic transformation[J]. Acta Metall. Sin., 2010, 46: 775(满蛟, 张骥华, 戎咏华. 马氏体相变中应变自协调效应的三维相场研究[J]. 金属学报, 2010, 46: 775)
[15]	Ke C B, Ma X, Zhang X P.Phase field simulation of effects of pores on B2-R phase transformation in NiTi shape memory alloy[J]. Acta Metall. Sin., 2011, 47: 129(柯常波, 马骁, 张新平. 孔隙对NiTi形状记忆合金中B2-R相变影响的相场模拟[J]. 金属学报, 2011, 47: 129)
[16]	She H, Liu Y, Wang B.Phase field simulation of heterogeneous cubic→tetragonal martensite nucleation[J]. Int. J. Solids Struct., 2013, 50: 1187
[17]	Shen C, Chen Q, Wen Y H, et al.Increasing length scale of quantitative phase field modeling of growth-dominant or coarsening-dominant process[J]. Scr. Mater., 2004, 50: 1023
[18]	Artemev A, Jin Y, Khachaturyan A G.Three-dimensional phase field model of proper martensitic transformation[J]. Acta Mater., 2001, 49: 1165
[19]	Zhong Y, Zhu T.Phase-field modeling of martensitic microstructure in NiTi shape memory alloys[J]. Acta Mater., 2014, 75: 337
[20]	Cahn J W, Hilliard J E.Free energy of a nonuniform system. I. Interfacial free energy[J]. J. Chem. Phys., 1958, 28: 258
[21]	Gunton J D, Miguel M, Sahni P S.Phase Transitions and Critical Phenomena[M]. New York: Academic, 1983: 267
[22]	Moelans N, Blanpain B, Wollants P.An introduction to phase-field modeling of microstructure evolution[J]. Calphad, 2008, 32: 268
[23]	Bhattacharya K, Kohn R V.Symmetry, texture and the recoverable strain of shape-memory polycrystals[J]. Acta Mater., 1996, 44: 529
[24]	Wagner M F X, Windl W. Lattice stability, elastic constants and macroscopic moduli of NiTi martensites from first principles[J]. Acta Mater., 2008, 56: 6232
[25]	Jin Y M, Artemev A, Khachaturyan A G.Three-dimensional phase field model of low-symmetry martensitic transformation in polycrystal: Simulation of ζ′ martensite in AuCd alloys[J]. Acta Mater., 2001, 49: 2309
[26]	Bhattacharya K.Microstructure of Martensite: Why it Forms and How it Gives Rise to the Shape-Memory Effect [M]. Oxford: Oxford University Press, 2003: 46
[27]	Fukuda T, Saburi T, Doi K, et al. Nucleation and self-accommodation of the R-phase in Ti-Ni alloys [J]. Mater. Trans., 1992, 33: 271

[1]	JIANG Jiang, HAO Shijie, JIANG Daqiang, GUO Fangmin, REN Yang, CUI Lishan. Quasi-Linear Superelasticity Deformation in an In Situ NiTi-Nb Composite[J]. 金属学报, 2023, 59(11): 1419-1427.
[2]	LI Wei, JIA Xingqi, JIN Xuejun. Research Progress of Microstructure Control and Strengthening Mechanism of QPT Process Advanced Steel with High Strength and Toughness[J]. 金属学报, 2022, 58(4): 444-456.
[3]	CHEN Wei, CHEN Hongcan, WANG Chenchong, XU Wei, LUO Qun, LI Qian, CHOU Kuochih. Effect of Dilatational Strain Energy of Fe-C-Ni System on Martensitic Transformation[J]. 金属学报, 2022, 58(2): 175-183.
[4]	YUAN Jiahua, ZHANG Qiuhong, WANG Jinliang, WANG Lingyu, WANG Chenchong, XU Wei. Synergistic Effect of Magnetic Field and Grain Size on Martensite Nucleation and Variant Selection[J]. 金属学报, 2022, 58(12): 1570-1580.
[5]	ZHAO Yuhong, JING Jianhui, CHEN Liwen, XU Fanghong, HOU Hua. Current Research Status of Interface of Ceramic-Metal Laminated Composite Material for Armor Protection[J]. 金属学报, 2021, 57(9): 1107-1125.
[6]	WANG Jinliang, WANG Chenchong, HUANG Minghao, HU Jun, XU Wei. The Effects and Mechanisms of Pre-Deformation with Low Strain on Temperature-Induced Martensitic Transformation[J]. 金属学报, 2021, 57(5): 575-585.
[7]	ZUO Liang, LI Zongbin, YAN Haile, YANG Bo, ZHAO Xiang. Texturation and Functional Behaviors of Polycrystalline Ni-Mn-X Phase Transformation Alloys[J]. 金属学报, 2021, 57(11): 1396-1415.
[8]	XIAO Fei, CHEN Hong, JIN Xuejun. Research Progress in Elastocaloric Cooling Effect Basing on Shape Memory Alloy[J]. 金属学报, 2021, 57(1): 29-41.
[9]	CHEN Lei , HAO Shuo , MEI Ruixue , JIA Wei , LI Wenquan , GUO Baofeng . Intrinsic Increment of Plasticity Induced by TRIP and Its Dependence on the Annealing Temperature in a Lean Duplex Stainless Steel[J]. 金属学报, 2019, 55(11): 1359-1366.
[10]	Lishan CUI, Daqiang JIANG. Progress in High Performance Nanocomposites Based ona Strategy of Strain Matching[J]. 金属学报, 2019, 55(1): 45-58.
[11]	Jincheng WANG, Chunwen GUO, Junjie LI, Zhijun WANG. Recent Progresses in Competitive Grain Growth During Directional Solidification[J]. 金属学报, 2018, 54(5): 657-668.
[12]	Zhaozhao WEI, Xiao MA, Xinping ZHANG. Topological Modelling of the B2-B19' Martensite Transformation Crystallography in NiTi Alloy[J]. 金属学报, 2018, 54(10): 1461-1470.
[13]	Jilan YANG, Yuankai JIANG, Jianfeng GU, Zhenghong GUO, Haiyan CHEN. Effect of Austenitization Temperature on the Dry Sliding Wear Properties of a Medium Carbon Quenching and Partitioning Steel[J]. 金属学报, 2018, 54(1): 21-30.
[14]	Kejian LI,Zhipeng CAI,Yao WU,Jiluan PAN. Research on Austenite Transformation of FB2 Heat-Resistant Steel During Welding Heating Process[J]. 金属学报, 2017, 53(7): 778-788.
[15]	Xue WANG,Lei HU,Dongxu CHEN,Songtao SUN,Liquan LI. Effect of Martensitic Transformation on Stress Evolution in Multi-Pass Butt-Welded 9%Cr Heat-Resistant Steel Pipes[J]. 金属学报, 2017, 53(7): 888-896.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Shared

Discussed