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Erschienen in: Computational Mechanics 4/2013

01.10.2013 | Original Paper

Finite element simulation of phase field model for nanoscale martensitic transformation

verfasst von: Hui She, Yulan Liu, Biao Wang, Decai Ma

Erschienen in: Computational Mechanics | Ausgabe 4/2013

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Abstract

A finite element framework of a phase field model for nanoscale martensitic transformation is proposed on the basis of time-dependent Ginzburg–Landau kinetic equations. The bulk total free energy consists of the chemical driving energy, the interfacial energy, the elastic energy, the inertial energy (for a dynamic case), the energy due to applied field and the effects of surface energy which need to be considered at the nanoscale. Single-variant and multi-variant martensitic phase transformations in a nano-sized NiAl plate are considered. The numerical results show the effects of each energy item on the phase transformation and the self-accommodating twinned morphologies as the result of strain energy minimization.

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Literatur
1.
Zurück zum Zitat Chen L-Q, Wang Y (1996) The continuum field approach to modeling microstructural evolution. JOM 48:13–18CrossRef Chen L-Q, Wang Y (1996) The continuum field approach to modeling microstructural evolution. JOM 48:13–18CrossRef
2.
Zurück zum Zitat Barrales-Mora LA, Mohles V, Konijnenberg PJ, Molodov DA (2007) A novel implementation for the simulation of 2-D grain growth with consideration to external energetic fields. Comput Mater Sci 39(1):160–165CrossRef Barrales-Mora LA, Mohles V, Konijnenberg PJ, Molodov DA (2007) A novel implementation for the simulation of 2-D grain growth with consideration to external energetic fields. Comput Mater Sci 39(1):160–165CrossRef
3.
Zurück zum Zitat Boettinger WJ, Warren JA, Beckermann C, Karma A (2002) Phase-field simulation of solidification. Annu Rev Mater Res 32:163–194CrossRef Boettinger WJ, Warren JA, Beckermann C, Karma A (2002) Phase-field simulation of solidification. Annu Rev Mater Res 32:163–194CrossRef
4.
Zurück zum Zitat Wang YU, Jin YM, Cuitino AM, Khachaturyan AG (2001) Phase field microelasticity theory and modeling of multiple dislocation dynamics. Appl Phys Lett 78(16):2324–2326CrossRef Wang YU, Jin YM, Cuitino AM, Khachaturyan AG (2001) Phase field microelasticity theory and modeling of multiple dislocation dynamics. Appl Phys Lett 78(16):2324–2326CrossRef
5.
Zurück zum Zitat Patoor E, Lagoudas DC, Entchev PB, Brinson LC, Gao X (2006) Shape memory alloys, Part I: general properties and modeling of single crystals. Mech Mater 38:391–429CrossRef Patoor E, Lagoudas DC, Entchev PB, Brinson LC, Gao X (2006) Shape memory alloys, Part I: general properties and modeling of single crystals. Mech Mater 38:391–429CrossRef
6.
Zurück zum Zitat Olson GB, Hartman H (1982) Martensite and life : displacive transformations as biological processes. J Phys Colloques 43(C4):855–865 Olson GB, Hartman H (1982) Martensite and life : displacive transformations as biological processes. J Phys Colloques 43(C4):855–865
7.
Zurück zum Zitat Bhattacharya K (2003) Why it forms and how it gives rise to the shape-memory effect. Oxford University Press, New York Bhattacharya K (2003) Why it forms and how it gives rise to the shape-memory effect. Oxford University Press, New York
8.
Zurück zum Zitat James RD, Hane KF (2000) Martensitic transformations and shape-memory materials. Acta Mater 48(1):197–222CrossRef James RD, Hane KF (2000) Martensitic transformations and shape-memory materials. Acta Mater 48(1):197–222CrossRef
9.
Zurück zum Zitat Artemev A, Jin Y, Khachaturyan AG (2001) Three-dimensional phase field model of proper martensitic transformation. Acta Mater 49(7):1165–1177CrossRef Artemev A, Jin Y, Khachaturyan AG (2001) Three-dimensional phase field model of proper martensitic transformation. Acta Mater 49(7):1165–1177CrossRef
10.
Zurück zum Zitat Khachaturyan AG (1983) Theory of structural transformation in solids. Wiley, New York Khachaturyan AG (1983) Theory of structural transformation in solids. Wiley, New York
11.
Zurück zum Zitat Wang Y, Khachaturyan AG (1997) Three-dimensional field model and computer modeling of martensitic transformations. Acta Mater 45(2):759–773CrossRef Wang Y, Khachaturyan AG (1997) Three-dimensional field model and computer modeling of martensitic transformations. Acta Mater 45(2):759–773CrossRef
12.
Zurück zum Zitat Chen L-Q (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32(1):113–140CrossRef Chen L-Q (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32(1):113–140CrossRef
13.
Zurück zum Zitat Moelans N, Blanpain B, Wollants P (2008) An introduction to phase-field modeling of microstructure evolution. CALPHAD 32(2):268–294CrossRef Moelans N, Blanpain B, Wollants P (2008) An introduction to phase-field modeling of microstructure evolution. CALPHAD 32(2):268–294CrossRef
14.
Zurück zum Zitat Lei CH, Li LJ, Shu YC, Li JY (2010) Austenite–martensite interface in shape memory alloys. Appl Phys Lett 96(14):141910CrossRef Lei CH, Li LJ, Shu YC, Li JY (2010) Austenite–martensite interface in shape memory alloys. Appl Phys Lett 96(14):141910CrossRef
15.
Zurück zum Zitat Li LJ, Yang Y, Shu YC, Li JY (2010) Continuum theory and phase-field simulation of magnetoelectric effects in multiferroic bismuth ferrite. J Mech Phys Solids 58(10):1613–1627MathSciNetCrossRefMATH Li LJ, Yang Y, Shu YC, Li JY (2010) Continuum theory and phase-field simulation of magnetoelectric effects in multiferroic bismuth ferrite. J Mech Phys Solids 58(10):1613–1627MathSciNetCrossRefMATH
16.
Zurück zum Zitat Shu YC, Yen JH (2008) Multivariant model of martensitic microstructure in thin films. Acta Mater 56(15):3969–3981MathSciNetCrossRef Shu YC, Yen JH (2008) Multivariant model of martensitic microstructure in thin films. Acta Mater 56(15):3969–3981MathSciNetCrossRef
17.
Zurück zum Zitat Levitas VI, Preston DL (2002) Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite to martensite. Phys Rev B 66(13):134206CrossRef Levitas VI, Preston DL (2002) Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. I. Austenite to martensite. Phys Rev B 66(13):134206CrossRef
18.
Zurück zum Zitat Levitas VI, Preston DL (2002) Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. II. Multivariant phase transformations and stress space analysis. Phys Rev B 66(13):134207CrossRef Levitas VI, Preston DL (2002) Three-dimensional Landau theory for multivariant stress-induced martensitic phase transformations. II. Multivariant phase transformations and stress space analysis. Phys Rev B 66(13):134207CrossRef
19.
Zurück zum Zitat Chen LQ, Shen J (1998) Applications of semi-implicit Fourier-spectral method to phase field equations. Comput Phys Commun 108:147–158CrossRefMATH Chen LQ, Shen J (1998) Applications of semi-implicit Fourier-spectral method to phase field equations. Comput Phys Commun 108:147–158CrossRefMATH
20.
Zurück zum Zitat Yamanaka A, Takaki T, Tomita Y (2008) Elastoplastic phase-field simulation of self- and plastic accommodations in martensitic transformation. Mater Sci Eng A 491:378–384CrossRef Yamanaka A, Takaki T, Tomita Y (2008) Elastoplastic phase-field simulation of self- and plastic accommodations in martensitic transformation. Mater Sci Eng A 491:378–384CrossRef
21.
Zurück zum Zitat Mahapatra DR, Melnik RVN (2006) Finite element analysis of phase transformation dynamics in shape memory alloys with a consistent Landau–Ginzburg free energy model. Mech Adv Mater Struct 13(6):443–455CrossRef Mahapatra DR, Melnik RVN (2006) Finite element analysis of phase transformation dynamics in shape memory alloys with a consistent Landau–Ginzburg free energy model. Mech Adv Mater Struct 13(6):443–455CrossRef
22.
Zurück zum Zitat Alexander VI, Joon-Yeoun C, Valery IL (2008) Finite element modeling of dynamics of martensitic phase transitions. Appl Phys Lett 93(4):043102CrossRef Alexander VI, Joon-Yeoun C, Valery IL (2008) Finite element modeling of dynamics of martensitic phase transitions. Appl Phys Lett 93(4):043102CrossRef
23.
Zurück zum Zitat Cho JY (2009) Finite element model of martensitic phase transformation. Ph.D. thesis, Texas Tech. University Cho JY (2009) Finite element model of martensitic phase transformation. Ph.D. thesis, Texas Tech. University
24.
Zurück zum Zitat Cho JY, Idesman AV, Levitas VI, Park T (2012) Finite element simulations of dynamics of multivariant martensitic phase transitions based on Ginzburg–Landau theory. Int J Solids Struct 49(14):1973–1992CrossRef Cho JY, Idesman AV, Levitas VI, Park T (2012) Finite element simulations of dynamics of multivariant martensitic phase transitions based on Ginzburg–Landau theory. Int J Solids Struct 49(14):1973–1992CrossRef
25.
Zurück zum Zitat She H, Liu Y, Wang B (2013) Phase field simulation of heterogeneous cubic to tetragonal martensite nucleation. Int J Solids Struct 50:1187–1191CrossRef She H, Liu Y, Wang B (2013) Phase field simulation of heterogeneous cubic to tetragonal martensite nucleation. Int J Solids Struct 50:1187–1191CrossRef
26.
Zurück zum Zitat Finel A, Le Bouar Y, Gaubert A, Salman U (2010) Phase field methods: microstructures, mechanical properties and complexity. Comptes Rendus Physique 11:245–256CrossRef Finel A, Le Bouar Y, Gaubert A, Salman U (2010) Phase field methods: microstructures, mechanical properties and complexity. Comptes Rendus Physique 11:245–256CrossRef
27.
Zurück zum Zitat She H, Wang B (2009) A geometrically nonlinear finite element model of nanomaterials with consideration of surface effects. Finite Elem Anal Des 45:463–467MathSciNetCrossRef She H, Wang B (2009) A geometrically nonlinear finite element model of nanomaterials with consideration of surface effects. Finite Elem Anal Des 45:463–467MathSciNetCrossRef
28.
Zurück zum Zitat Gao W, Yu S, Huang G (2006) Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnology 17(4):1118–1122CrossRef Gao W, Yu S, Huang G (2006) Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnology 17(4):1118–1122CrossRef
29.
Zurück zum Zitat Park HS, Klein PA, Wagner GJ (2006) A surface Cauchy–Born model for nanoscale materials. Int J Numer Methods Eng 68(10):1072–1095MathSciNetCrossRefMATH Park HS, Klein PA, Wagner GJ (2006) A surface Cauchy–Born model for nanoscale materials. Int J Numer Methods Eng 68(10):1072–1095MathSciNetCrossRefMATH
30.
Zurück zum Zitat Dingreville R, Qu J, Mohammed C (2005) Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J Mech Phys Solids 53(8):1827–1854MathSciNetCrossRefMATH Dingreville R, Qu J, Mohammed C (2005) Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J Mech Phys Solids 53(8):1827–1854MathSciNetCrossRefMATH
31.
Zurück zum Zitat Miller RE, Shenoy VB (2000) Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3):139–147 Miller RE, Shenoy VB (2000) Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3):139–147
32.
Zurück zum Zitat Shenoy VB (2005) Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Phys Rev B 71(9):094104 Shenoy VB (2005) Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Phys Rev B 71(9):094104
33.
Zurück zum Zitat Levitas VI, Levin VA, Zingerman KM, Freiman EI (2009) Displacive phase transitions at large strains: phase-field theory and simulations. Phys Rev Lett 103(2):025702CrossRef Levitas VI, Levin VA, Zingerman KM, Freiman EI (2009) Displacive phase transitions at large strains: phase-field theory and simulations. Phys Rev Lett 103(2):025702CrossRef
34.
Zurück zum Zitat Levitas VI, Lee D-W, Preston DL (2010) Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations. Int J Plast 26(3):395–422CrossRefMATH Levitas VI, Lee D-W, Preston DL (2010) Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations. Int J Plast 26(3):395–422CrossRefMATH
35.
Zurück zum Zitat Bando Y (1964) Characteristics of phase transformation in metallic fine particles (martensitic transformation of FeNi alloys and ordering of CuAu and Cu3Au alloys). T Jpn I Met 5:135–141 Bando Y (1964) Characteristics of phase transformation in metallic fine particles (martensitic transformation of FeNi alloys and ordering of CuAu and Cu3Au alloys). T Jpn I Met 5:135–141
Metadaten
Titel
Finite element simulation of phase field model for nanoscale martensitic transformation
verfasst von
Hui She
Yulan Liu
Biao Wang
Decai Ma
Publikationsdatum
01.10.2013
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 4/2013
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-013-0856-5

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