Abstract
Additive manufacturing offers an unprecedented opportunity for the quick production of complex shaped parts directly from a powder precursor. But its application to functional materials in general and magnetic materials in particular is still at the very beginning. Here we present the first attempt to computationally study the microstructure evolution and magnetic properties of magnetic materials (e.g. Fe–Ni alloys) processed by selective laser melting (SLM). SLM process induced thermal history and thus the residual stress distribution in Fe–Ni alloys are calculated by finite element analysis (FEA). The evolution and distribution of the \(\gamma \)-Fe–Ni and \(\hbox {FeNi}_3\) phase fractions are predicted by using the temperature information from FEA and the output from CALculation of PHAse Diagrams (CALPHAD). Based on the relation between residual stress and magnetoelastic energy, magnetic properties of SLM processed Fe–Ni alloys (magnetic coercivity, remanent magnetization, and magnetic domain structure) are examined by micromagnetic simulations. The calculated coercivity is found to be in line with the experimentally measured values of SLM-processed Fe–Ni alloys. This computation study demonstrates a feasible approach for the simulation of additively manufactured magnetic materials by integrating FEA, CALPHAD, and micromagnetics.
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References
Arnold HD, Elmen GW (1923) Permalloy, an alloy of remarkable magnetic properties. J Frankl Inst 195(5):621–632. https://doi.org/10.1016/S0016-0032(23)90114-6
Kwiatkowski W, Tumanski S (1986) The permalloy magnetoresistive sensors-properties and applications. J Phys E Sci Instrum 19(7):502. https://doi.org/10.1088/0022-3735/19/7/002
Ganz AG (1946) Applications of thin Permalloy tape in wide-band telephone and pulse transformers. AIEE Trans 65(4):177–183. https://doi.org/10.1109/T-AIEE.1946.5059326
Ripka P (2008) Sensors based on bulk soft magnetic materials: advances and challenges. J Magn Magn Mater 320(20):2466–2473. https://doi.org/10.1016/j.jmmm.2008.04.079
Martin JH, Yahata BD, Hundley JM, Mayer JA, Schaedler TA, Pollock TM (2017) 3D printing of high-strength aluminium alloys. Nature 549(7672):365–369. https://doi.org/10.1038/nature23894
Kobryn PA, Semiatin SL (2001) The laser additive manufacture of Ti–6Al–4V. JOM 53(9):40–42. https://doi.org/10.1007/s11837-001-0068-x
Yan W, Ge W, Smith J, Lin S, Kafka OL, Lin F, Liu WK (2016) Multi-scale modeling of electron beam melting of functionally graded materials. Acta Mater 115:403–412. https://doi.org/10.1016/j.actamat.2016.06.022
Yan W, Qian Y, Ma W, Zhou B, Shen Y, Lin F (2017) Modeling and experimental validation of the electron beam selective melting process. Engineering 3(5):701–707. https://doi.org/10.1016/J.ENG.2017.05.021
Keller T, Lindwall G, Ghosh S, Ma L, Lane BM, Zhang F, Kattner UR, Lass EA, Heigel JC, Idell Y et al (2017) Application of finite element, phase-field, and CALPHAD-based methods to additive manufacturing of Ni-based superalloys. Acta Mater 139:244–253. https://doi.org/10.1016/j.actamat.2017.05.003
Wang YM, Voisin T, McKeown JT, Ye J, Calta NP, Li Z, Zeng Z, Zhang Y, Chen W, Roehling TT et al (2018) Additively manufactured hierarchical stainless steels with high strength and ductility. Nat Mater 17:63–71. https://doi.org/10.1038/NMAT5021
Johnson KL, Rodgers TM, Underwood OD, Madison JD, Ford KR, Whetten SR, Dagel DJ, Bishop JE (2018) Simulation and experimental comparison of the thermo-mechanical history and 3D microstructure evolution of 304L stainless steel tubes manufactured using LENS. Comput Mech 61(5):559–574. https://doi.org/10.1007/s00466-017-1516-y
Zhang B, Fenineche N-E, Zhu L, Liao H, Coddet C (2012) Studies of magnetic properties of permalloy (Fe–30%Ni) prepared by SLM technology. J Magn Magn Mater 324(4):495–500. https://doi.org/10.1016/j.jmmm.2011.08.030
Zhang B, Fenineche N-E, Liao H, Coddet C (2013) Microstructure and magnetic properties of Fe–Ni alloy fabricated by selective laser melting Fe/Ni mixed powders. J Mater Sci Technol 29(8):757–760. https://doi.org/10.1016/j.jmst.2013.05.001
Zhang B, Fenineche N-E, Liao H, Coddet C (2013) Magnetic properties of in-situ synthesized \(\text{ FeNi }_3\) by selective laser melting Fe–80%Ni powders. J Magn Magn Mater 336:49–54. https://doi.org/10.1016/j.jmmm.2013.02.014
Poirier E, Pinkerton FE, Kubic R, Mishra RK, Bordeaux N, Mubarok A, Lewis LH, Goldstein JI, Skomski R, Barmak K (2015) Intrinsic magnetic properties of L1\(_{0}\) FeNi obtained from meteorite NWA 6259. J Appl Phys 117(17):17E318. https://doi.org/10.1063/1.4916190
Bordeaux N, Montes-Arango AM, Liu J, Barmak K, Lewis LH (2016) Thermodynamic and kinetic parameters of the chemical order-disorder transformation in \(\text{ L1 }_0\) FeNi (tetrataenite). Acta Mater 103:608–615. https://doi.org/10.1016/j.actamat.2015.10.042
Moore JD, Klemm D, Lindackers D, Grasemann S, Träger R, Eckert J, Löber L, Scudino S, Katter M, Barcza A et al (2013) Selective laser melting of \(\text{ La(Fe Co, Si) }_{13}\) geometries for magnetic refrigeration. J Appl Phys 114(4):043907. https://doi.org/10.1063/1.4816465
Garibaldi M, Ashcroft I, Lemke JN, Simonelli M, Hague R (2018) Effect of annealing on the microstructure and magnetic properties of soft magnetic Fe–Si produced via laser additive manufacturing. Scr Mater 142:121–125. https://doi.org/10.1016/j.scriptamat.2017.08.042
Jhong KJ, Huang W-C, Lee WH (2016) Microstructure and magnetic properties of magnetic material fabricated by selective laser melting. Phys Procedia 83:818–824. https://doi.org/10.1016/j.phpro.2016.08.084
Shishkovsky I, Saphronov V (2016) Peculiarities of selective laser melting process for permalloy powder. Mater Lett 171:208–211. https://doi.org/10.1016/j.matlet.2016.02.099
Mikler CV, Chaudhary V, Soni V, Gwalani B, Ramanujan RV, Banerjee R (2017) Tuning the phase stability and magnetic properties of laser additively processed Fe–30at%Ni soft magnetic alloys. Mater Lett 199:88–92. https://doi.org/10.1016/j.matlet.2017.04.054
Mikler CV, Chaudhary V, Borkar T, Soni V, Choudhuri D, Ramanujan RV, Banerjee R (2017) Laser additive processing of Ni–Fe–V and Ni–Fe–Mo permalloys: microstructure and magnetic properties. Mater Lett 192:9–11. https://doi.org/10.1016/j.matlet.2017.01.059
Mikler CV, Chaudhary V, Borkar T, Soni V, Jaeger D, Chen X, Contieri R, Ramanujan RV, Banerjee R (2017) Laser additive manufacturing of magnetic materials. JOM 69(3):532–543. https://doi.org/10.1007/s11837-017-2257-2
Kustas AB, Susan DF, Johnson KL, Whetten SR, Rodriguez MA, Dagel DJ, Michael JR, Keicher DM, Argibay N (2018) Characterization of the Fe–Co–1.5V soft ferromagnetic alloy processed by Laser Engineered Net Shaping (LENS). Addit Manuf 21:41–52. https://doi.org/10.1016/j.addma.2018.02.006
Jaćimović J, Binda F, Herrmann LG, Greuter F, Genta J, Calvo M, Tomše T, Simon RA (2017) Net shape 3D printed NdFeB permanent magnet. Adv Eng Mater 19(8):1700098. https://doi.org/10.1002/adem.201700098
White EMH, Kassen AG, Simsek E, Tang W, Ott RT, Anderson IE (2017) Net shape processing of alnico magnets by additive manufacturing. IEEE Trans Magn 53(11):1–6. https://doi.org/10.1109/TMAG.2017.2711965
Popov V, Koptyug A, Radulov I, Maccari F, Muller G (2018) Prospects of additive manufacturing of rare-earth and non-rare-earth permanent magnets. Proc Manuf 21:100–108. https://doi.org/10.1016/j.promfg.2018.02.199
Li L, Tirado A, Nlebedim IC, Rios O, Post B, Kunc V, Lowden RR, Lara-Curzio E, Fredette R, Ormerod J et al (2016) Big area additive manufacturing of high performance bonded NdFeB magnets. Sci Rep 6:36212. https://doi.org/10.1038/srep36212
Paranthaman MP, Shafer CS, Elliott AM, Siddel DH, McGuire MA, Springfield RM, Martin J, Fredette R, Ormerod J (2016) Binder jetting: a novel NdFeB bonded magnet fabrication process. JOM 68(7):1978–1982. https://doi.org/10.1007/s11837-016-1883-4
Li L, Post B, Kunc V, Elliott AM, Paranthaman MP (2017) Additive manufacturing of near-net-shape bonded magnets: prospects and challenges. Scr Mater 135:100–104. https://doi.org/10.1016/j.scriptamat.2016.12.035
Huber C, Abert C, Bruckner F, Groenefeld M, Schuschnigg S, Teliban I, Vogler C, Wautischer G, Windl R, Suess D (2017) 3D printing of polymer-bonded rare-earth magnets with a variable magnetic compound fraction for a predefined stray field. Sci Rep 7(1):9419. https://doi.org/10.1038/s41598-017-09864-0
Huber C, Abert C, Bruckner F, Pfaff C, Kriwet J, Groenefeld M, Teliban I, Vogler C, Suess D (2017) Topology optimized and 3D printed polymer-bonded permanent magnets for a predefined external field. J Appl Phys 122(5):053904. https://doi.org/10.1063/1.4997441
Smith J, Xiong W, Yan W, Lin S, Cheng P, Kafka OL, Wagner GJ, Cao J, Liu WK (2016) Linking process, structure, property, and performance for metal-based additive manufacturing: computational approaches with experimental support. Comput Mech 57(4):583–610. https://doi.org/10.1007/s00466-015-1240-4
Markl M, Körner C (2016) Multiscale modeling of powder bed-based additive manufacturing. Annu Rev Mater Res 46:93–123. https://doi.org/10.1146/annurev-matsci-070115-032158
Yan W, Lin S, Kafka OL, Lian Y, Yu C, Liu Z, Yan J, Wolff S, Wu H, Ndip-Agbor E et al (2018) Data-driven multi-scale multi-physics models to derive process-structure-property relationships for additive manufacturing. Comput Mech 61(5):521–541. https://doi.org/10.1007/s00466-018-1539-z
Yang YP, Jamshidinia M, Boulware P, Kelly SM (2018) Prediction of microstructure, residual stress, and deformation in laser powder bed fusion process. Comput Mech 1–17. https://doi.org/10.1007/s00466-017-1528-7
ABAQUS (2017) Dassault Systemes Simulia Corporation
Cacciamani G, De Keyzer J, Ferro R, Klotz UE, Lacaze J, Wollants P (2006) Critical evaluation of the Fe–Ni, Fe–Ti and Fe–Ni–Ti alloy systems. Intermetallics 14(10–11):1312–1325. https://doi.org/10.1016/j.intermet.2005.11.028
Smith J, Xiong W, Cao J, Liu WK (2016) Thermodynamically consistent microstructure prediction of additively manufactured materials. Comput Mech 57(3):359–370. https://doi.org/10.1007/s00466-015-1243-1
Costa L, Vilar R, Reti T, Deus AM (2005) Rapid tooling by laser powder deposition: process simulation using finite element analysis. Acta Mater 53(14):3987–3999. https://doi.org/10.1016/j.actamat.2005.05.003
Li Y, Gu D (2014) Parametric analysis of thermal behavior during selective laser melting additive manufacturing of aluminum alloy powder. Mater Des 63:856–867. https://doi.org/10.1016/j.matdes.2014.07.006
Mercelis P, Kruth J-P (2006) Residual stresses in selective laser sintering and selective laser melting. Rapid Prototyp J 12(5):254–265. https://doi.org/10.1108/13552540610707013
Shu YC, Lin MP, Wu KC (2004) Micromagnetic modeling of magnetostrictive materials under intrinsic stress. Mech Mater 36(10):975–997. https://doi.org/10.1016/j.mechmat.2003.04.004
Lukas HL, Fries SG, Sundman B (2007) Computational thermodynamics: the Calphad method. Cambridge University Press, Cambridge
Perron A, Roehling JD, Turchi PEA, Fattebert J-L, McKeown JT (2018) Matching time and spatial scales of rapid solidification: dynamic TEM experiments coupled to CALPHAD-informed phase-field simulations. Modell Simul Mater Sci Eng 26(1):014002. https://doi.org/10.1088/1361-651X/aa9a5b
Swartzendruber LJ, Itkin VP, Alcock CB (1991) The Fe–Ni (iron–nickel) system. J Phase Equilib 12(3):288–312. https://doi.org/10.1007/BF02649918
Andersson J-O, Helander T, Höglund L, Shi P, Sundman B (2002) Thermo-Calc & DICTRA, computational tools for materials science. Calphad 26(2):273–312. https://doi.org/10.1016/S0364-5916(02)00037-8
Gulliver GH (1913) The quantitative effect of rapid cooling upon the constitution of binary alloys. J Inst Met 9(1):120–157
Scheil E (1942) Remarks on the crystal layer formation. Z Metallkd 34:70
Chen L-Q (2002) Phase-field models for microstructure evolution. Annu Rev Mater Res 32(1):113–140. https://doi.org/10.1146/annurev.matsci.32.112001.132041
Fidler J, Schrefl T (2000) Micromagnetic modelling-the current state of the art. J Phys D Appl Phys 33(15):R135. https://doi.org/10.1088/0022-3727/33/15/201
Kronmüller H, Fähnle M (2003) Micromagnetism and the microstructure of ferromagnetic solids. Cambridge University Press, Cambridge
Yi M, Gutfleisch O, Xu B-X (2016) Micromagnetic simulations on the grain shape effect in Nd–Fe–B magnets. J Appl Phys 120(3):033903. https://doi.org/10.1063/1.4958697
Agramunt-Puig S, Del-Valle N, Navau C, Sanchez A (2014) Controlling vortex chirality and polarity by geometry in magnetic nanodots. Appl Phys Lett 104(1):012407. https://doi.org/10.1063/1.4861423
Fletcher R, Reeves CM (1964) Function minimization by conjugate gradients. Comput J 7(2):149–154. https://doi.org/10.1093/comjnl/7.2.149
Polak E, Ribiere G (1969) Note sur la convergence de méthodes de directions conjuguées. Rev Française D’informatique et de Recherche Opérationnelle. Série Rouge 3(16):35–43. https://doi.org/10.1051/m2an/196903R100351
Donahue MJ, Porter DG (2017) OOMMF software package. https://doi.org/10.4231/D3XS5JJ23
Gilbert TL (2004) A phenomenological theory of damping in ferromagnetic materials. IEEE Trans Magn 40(6):3443–3449. https://doi.org/10.1109/TMAG.2004.836740
Yi M, Xu B-X (2014) A constraint-free phase field model for ferromagnetic domain evolution. Proc R Soc A 470(2171):20140517. https://doi.org/10.1098/rspa.2014.0517
Yi M, Zhang H, Gutfleisch O, Xu B-X (2017) Multiscale examination of strain effects in Nd–Fe–B permanent magnets. Phys Rev Appl 8(1):014011. https://doi.org/10.1103/PhysRevApplied.8.014011
Bonin R, Schneider ML, Silva TJ, Nibarger JP (2005) Dependence of magnetization dynamics on magnetostriction in NiFe alloys. J Appl Phys 98(12):123904. https://doi.org/10.1063/1.2143121
Amidror I (2002) Scattered data interpolation methods for electronic imaging systems: a survey. J Electron Imaging 11(2):157–176. https://doi.org/10.1117/1.1455013
Xiong W, Zhang H, Vitos L, Selleby M (2011) Magnetic phase diagram of the Fe–Ni system. Acta Mater 59(2):521–530. https://doi.org/10.1016/j.actamat.2010.09.055
Acknowledgements
The support from the German Science Foundation (DFG YI 165/1-1 and DFG XU 121/7-1), the Profile Area From Material to Product Innovation—PMP (TU Darmstadt), the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant agreement No 743116), and the LOEWE research cluster RESPONSE (Hessen, Germany) is acknowledged. The authors also greatly appreciate their access to the Lichtenberg High Performance Computer of Technische Universität Darmstadt.
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Yi, M., Xu, BX. & Gutfleisch, O. Computational study on microstructure evolution and magnetic property of laser additively manufactured magnetic materials. Comput Mech 64, 917–935 (2019). https://doi.org/10.1007/s00466-019-01687-2
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DOI: https://doi.org/10.1007/s00466-019-01687-2