Phase Transformation of Ni-Ti Shape Memory Alloy Investigated by Multi-Phase-Field Method and Microscopic Data
Multi-phase-field (MPF) method which is capable of using several phase-field variables is applied to simulate martensitic transition in micro-scale Ni-Ti shape-memory alloy (SMA). By modeling Ni-Ti SMA specimen in MPF simulation assuming only three major variants of martensite crystal in monoclinic...
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| Published in | TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A Vol. 77; no. 780; pp. 1320 - 1330 |
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| Language | Japanese |
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The Japan Society of Mechanical Engineers
2011
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| Abstract | Multi-phase-field (MPF) method which is capable of using several phase-field variables is applied to simulate martensitic transition in micro-scale Ni-Ti shape-memory alloy (SMA). By modeling Ni-Ti SMA specimen in MPF simulation assuming only three major variants of martensite crystal in monoclinic structure, the detailed manner of forming martensite variants and interaction between them are observed. We adjust several free energy (densities) usually used for the phase-field functional to Ni-Ti SMA properties, e.g. chemical free energy, elastic strain energy, gradient energy, and double-well potential energy. Especially in the formulation of elastic strain energy, to express austenite (cubic)-to-martensite (monoclinic) transition of Ni-Ti alloy, microscopic parameter available from experimental result for lattice mismatch between austenite and martensite is brought into free energy functional. We discuss the different growth of martensite variants depending on initial condition for martensite nucleus, in which some arbitrary area in the computation domain is provided with random number. It is confirmed that a martensite variant with a positive lattice mismatch (i.e. the direction of larger edge in monoclinic unit) grows preferentially in the case of tensile loading in that direction. In compression, a variant with the most negative mismatch in the compressive direction grows strongly. The starting time of loading is sometimes a factor for the resulted variant structures. We found that, once a lamellae structure is formed, the relation between direction of further loading and that of lamellae interface plane dominates the resulted structural combination of variants. |
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| AbstractList | Multi-phase-field (MPF) method which is capable of using several phase-field variables is applied to simulate martensitic transition in micro-scale Ni-Ti shape-memory alloy (SMA). By modeling Ni-Ti SMA specimen in MPF simulation assuming only three major variants of martensite crystal in monoclinic structure, the detailed manner of forming martensite variants and interaction between them are observed. We adjust several free energy (densities) usually used for the phase-field functional to Ni-Ti SMA properties, e.g. chemical free energy, elastic strain energy, gradient energy, and double-well potential energy. Especially in the formulation of elastic strain energy, to express austenite (cubic)-to-martensite (monoclinic) transition of Ni-Ti alloy, microscopic parameter available from experimental result for lattice mismatch between austenite and martensite is brought into free energy functional. We discuss the different growth of martensite variants depending on initial condition for martensite nucleus, in which some arbitrary area in the computation domain is provided with random number. It is confirmed that a martensite variant with a positive lattice mismatch (i.e. the direction of larger edge in monoclinic unit) grows preferentially in the case of tensile loading in that direction. In compression, a variant with the most negative mismatch in the compressive direction grows strongly. The starting time of loading is sometimes a factor for the resulted variant structures. We found that, once a lamellae structure is formed, the relation between direction of further loading and that of lamellae interface plane dominates the resulted structural combination of variants. |
| Author | MATSUKI, Takanobu SAITOH, Ken-ichi |
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| Cites_doi | 10.1016/S1359-6454(00)00071-9 10.2472/jsms.54.193 10.1016/j.msea.2007.08.066 10.2320/matertrans.47.742 10.1016/j.pmatsci.2004.10.001 10.1103/PhysRevB.58.13590 10.2320/materia.42.397 10.1016/S0167-2789(97)00226-1 10.1088/0953-8984/22/39/395403 10.1016/S0167-2789(99)00129-3 10.1016/j.scriptamat.2010.02.001 10.2320/matertrans.44.2503 10.1002/mawe.200800368 10.2320/materia.48.555 10.2472/jsms.57.1217 |
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| References_xml | – reference: (24) 船久保熙康，形状記憶合金 (1984), pp. 53-55, 産業図書． – reference: (30) Koyama, T. and Onodera, H., “Phase-field simulation of microstructure changes in Ni2MnGa ferromagnetic alloy under external stress and magnetic fields”, Mater.Trans., Vol.44, No.12 (2003), pp.2503-2508. – reference: (29) 小山敏幸，“Phase-field法に関する最近の進展と今後の展望”，まてりあ，vol. 42, No. 5 (2003), pp. 397-405. – reference: (2) 戸伏壽昭，田中喜久昭，堀川宏，松本實，形状記憶材料とその応用 (1995), pp. 112-127, コロナ社． – reference: (8) Gloanec, A.-L., Cerracchio, P., Reynier, B., Van, Herpen A. and Riberty, P., “Fatigue crack initiation and propagation of a TiNi shape memory alloy” , Scr. Mater., Vol. 62, No. 10 (2010), pp. 786-789. – reference: (7) 木村英彦，秋庭義明，田中啓介，田中充，“TiNiの疲労き裂伝ぱにおよぼすマルテンサイトの影響”，日本機械学会年次大会講演論文集，vol. 1 (2005), pp. 455-456. – reference: (20) 山中晃徳，高木知弘，冨田佳宏，“マルテンサイト変態による組織形成過程のPhase-Fieldシミュレーション”，日本機械学会計算力学講演会講演論文集，vol. 20 (2007), pp. 515-516. – reference: (23) Saitoh, K., Sato, T., Shinke, N., “Atomic dynamics and energetics of martensitic transformation in nickel-titanium shape memory alloy”, Mater. Trans., Vol.47, No.3 (2006), pp.742-749. – reference: (13) 佐藤知広，齋藤賢一，新家昇，“分子動力学法を用いたNi-Ti合金に対する相変態の観察と構造解析”，材料，vol. 54, No. 2 (2005), pp. 193-200. – reference: (22) Artemev, A., Wang, Y., Khachaturyan, A. G., Acta Materialia, Vol. 48 (2000), pp. 2503-2518. – reference: (4) 新谷研一ほか，“粉末冶金法と塑性加工により作製した傾斜機能TiNi形状記憶合金ワイヤの熱・力学的特性”，日本機械学会年次大会講演論文集，vol. 1 (2009), pp. 189-190. – reference: (28) Janssens, K. G. G., Raabe, D., Kozeschnik, E. and Miodownik, M. A., Computational Materials Engineering (2007), Elsevier. – reference: (9) Otsuka, K., Ren, X., “Physical metallurgy of Ti-Ni-based shape memory alloys”, Progress in Materials Science, Vol. 50, No. 5 (2005), pp. 511-678. – reference: (19) 山中晃徳，高木知弘，冨田佳宏，“Fe-C合金のγ→α変態による組織形成Phase-fieldシミュレーション”，日本機械学会計算力学講演会講演論文集，vol. 19 (2006), pp. 359-360. – reference: (3) 西田稔，山内清，大方一三，“形状記憶合金の基礎と応用”，資源と素材，vol. 11, No. 10 (2005), pp. 713-718. – reference: (21) Yamanaka, A., Takaki, T., Tomita, Y., “Coupled simulation of microstructural formation and deformation behavior of ferrite-pearlite steel by phase-field method and homogenization method”, Mater.Sci.Eng.,A, Vol.480 (2008), pp.244-252. – reference: (33) 山中晃徳，高木知弘，冨田佳宏，“Phase-Field法によるマルテンサイト変態の3次元シミュレーション”，日本機械学会第22回計算力学講演会CD-ROM論文集 (2009), 1107. – reference: (34) 小山敏幸，“弾性ひずみエネルギー評価法(1)”，http://tkoyama.web.nitech.ac.jp/docs/Lecture_H20/H20_Chapter_7.pdf (参照日 2011年3月16日)． – reference: (31) 小山敏幸，“Javaによる実践的化学技術プログラミング(III)－マルテンサイト変態のPhase-fieldシミュレーション－”，まてりあ，vol. 48, No. 11 (2009), pp. 555-560. – reference: (16) Tiaden, J., Nestler, B., Diepers, H.J. and Steinbach, I., “The multiphase-field model with an integrated concept for modelling solute diffusion”, Physica D, Vol. 115 (1998), pp. 73-86. – reference: (6) 岡部洋二，“形状記憶合金を用いたスマート複合材料構造 －損傷抑制と形状制御－”，生産研究，vol. 61, No. 6 (2009), pp. 977-983. – reference: (15) 上原拓也，浅井千尋，大野信忠，“多結晶モデルによる形状記憶合金の変形挙動に関する分子動力学シミュレーション”，材料，vol. 57, No. 12 (2008), pp. 1217-1223. – reference: (17) Steinbach, I. and Pezzolla, F., “A generalized field method for multiphase transformations using interface fields”, Physica D, Vol. 134 (1999), pp. 385-393. – reference: (27) Emmeerich, H., The Diffuse Interface Approach in Materials Science —Thermodynamic Concepts and Applications of Phase-Field Models—, (2002), Springer. – reference: (11) Wang, X.M., Lu, Z.Z., Yue, Z.F., Deng, C.H., “FEM analysis of localized deformation behavior in pseudoelastic NiTi shape memory alloys ”, Mat.-wiss. u. Werkstofftech., Vol. 39 , No. 11 (2008), pp. 816-821. – reference: (32) 小山敏幸，“Phase-field法3(結晶変態，ドメイン形成)”， http://tkoyama.web.nitech.ac.jp/docs/Lecture_H20/H20_Chapter_13.pdf (参照日 2011年3月16日)． – reference: (12) 都井裕，李 宗，田谷稔，“形状記憶合金はりの超弾性挙動の有限要素解析 その1 引張挙動と圧縮挙動が対称の場合”，生産研究，vol. 53, No. 5/6 (2001), pp. 306-309. – reference: (25) Sanati, M., Albers, R.C. and Pinski, F.J., “Electronic and Crystal Structure of NiTi Martensite”, Phys.Rev.B, Vol. 58, No. 20 (1998), pp. 13590-13593. – reference: (5) 戸伏壽昭，杉本義樹，伊達功祐，林俊一，“SMAとSMPによる形状記憶複合材料の作製と2方向変形特性”，日本機械学会東海支部総会講演会講演論文集，vol. 58 (2009), pp. 97-98. – reference: (26) 高木知弘，“フェーズフィールド法の基礎と応用(1)－フェーズフィールド法とは？その1－”，機械の研究，vol. 61, No. 3 (2009), pp. 353-359. – reference: (1) 仲庭正義，“材料の素顔に迫る(身近な形状記憶合金)”，つうしん (2000), pp. 2-3, 住友金属テクノロジー． – reference: (10) 都井裕，何劼，“形状記憶合金素子の動的繰返し応答シミュレーション”，生産研究，vol. 62, No. 1 (2010), pp. 107-110. – reference: (18) 高木知弘，“フェーズフィールド法の基礎と応用(14)－マルチフェーズフィールドモデルその1－”，機械の研究，vol. 62, No. 4 (2010), pp. 449-453. – reference: (14) Purja Pun G.P., Mishin, Y., “Molecular dynamics simulation of the martensitic phase transformation in NiAl alloys”, J. 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| Snippet | Multi-phase-field (MPF) method which is capable of using several phase-field variables is applied to simulate martensitic transition in micro-scale Ni-Ti... |
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| SubjectTerms | Computational Mechanics Elasticity Free Energy Nickel and Titanium Numerical Simulation Phase Transformation Phase-Field Method Shape Memory Alloy |
| Title | Phase Transformation of Ni-Ti Shape Memory Alloy Investigated by Multi-Phase-Field Method and Microscopic Data |
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