Simulation of Solidification Parameters during Zr Based Bulk Metallic Glass Matrix Composite’s (BMGMCs) Additive Manufacturing — Oak Academic Publishing
Research ArticleOpen AccessGoogle Scholar indexed
Simulation of Solidification Parameters during Zr Based Bulk Metallic Glass Matrix Composite’s (BMGMCs) Additive Manufacturing
Eastern Engineering Solutions LLC, Detroit, MI, USA
1 Eastern Engineering Solutions LLC, Detroit, MI, USA
After a silence of three decades, bulk metallic glasses and their composites have re-emerged as a competent engineering material owing to their excellent mechanical properties not observed in any other engineering material known till date. However, they exhibit poor ductility and little or no toughness which make them brittle and they fail catastrophically under tensile loading. Exact explanation of this behaviour is difficult, and a lot of expensive experimentation is needed before conclusive results could be drawn. In present study, a theoretical approach has been presented aimed at solving this problem. A detailed mathematical model has been developed to describe solidification phenomena in zirconium based bulk metallic glass matrix composites during additive manufacturing. It precisely models and predicts solidification parameters related to microscale solute diffusion (mass transfer) and capillary action in these rapidly solidifying sluggish slurries. Programming and simulation of model is performed in MATLAB ® . Results show that the use of temperature dependent thermophysical properties yields a synergic effect for multitude improvement and refinement simulation results. Simulated values proved out to be in good agreement with prior simulated and experimental results.
Klement, W., Willens, R.H. and Duwez, P.O.L. (1960) Non-Crystalline Structure in Solidified Gold-Silicon Alloys. Nature, 187, 869-870. https://doi.org/10.1038/187869b0
Hays, C.C., Kim, C.P. and Johnson, W.L. (2000) Microstructure Controlled Shear Band Pattern Formation and Enhanced Plasticity of Bulk Metallic Glasses Containing in situ Formed Ductile Phase Dendrite Dispersions. Physical Review Letters, 84, 2901-2904. https://doi.org/10.1103/PhysRevLett.84.2901
Ashby, M.F. and Greer, A.L. (2006) Metallic Glasses as Structural Materials. Scripta Materialia, 54, 321-326. https://doi.org/10.1016/j.scriptamat.2005.09.051
Flores, K.M. and Dauskardt, R.H. (1999) Local Heating Associated with Crack Tip Plasticity in Zr-Ti-Ni-Cu-Be Bulk Amorphous Metals. Journal of Materials Research, 14, 638-643. https://doi.org/10.1557/JMR.1999.0642
Eckert, J., et al. (2007) Mechanical Properties of Bulk Metallic Glasses and Composites. Journal of Materials Research, 22, 285-301. https://doi.org/10.1557/jmr.2007.0050
Das, J., et al. (2009) Designing Bulk Metallic Glass and Glass Matrix Composites in Martensitic Alloys. Journal of Alloys and Compounds, 483, 97-101. https://doi.org/10.1016/j.jallcom.2008.08.139
Choi-Yim, H. and Johnson, W.L. (1997) Bulk Metallic Glass Matrix Composites. Applied Physics Letters, 71, 3808-3810. https://doi.org/10.1063/1.120512
Cheng, J.L. and Chen, G. (2013) \ Glass Formation of Zr-Cu-Ni-Al Bulk Metallic Glasses Correlated with L → Zr2Cu + ZrCu Pseudo Binary Eutectic Reaction. Journal of Alloys and Compounds, 577, 451-455. https://doi.org/10.1016/j.jallcom.2013.06.126
Chen, M. (2011) A Brief Overview of Bulk Metallic Glasses. NPG Asia Materials, 3, 82-90. https://doi.org/10.1038/asiamat.2011.30
Chen, M. (2008) Mechanical Behavior of Metallic Glasses: Microscopic Understanding of Strength and Ductility. Annual Review of Materials Research, 38, 445-469. https://doi.org/10.1146/annurev.matsci.38.060407.130226
Chen, H.S. (1974) Thermodynamic Considerations on the Formation and Stability of Metallic Glasses. Acta Metallurgica, 22, 1505-1511. https://doi.org/10.1016/0001-6160(74)90112-6
Akihisa, I., et al. (1988) Glass Transition Behavior of Al-Y-Ni and Al-Ce-Ni Amorphous Alloys. Japanese Journal of Applied Physics, 27, L1579. https://doi.org/10.1143/JJAP.27.L1579
Johnson, W.L., et al. (2011) Beating Crystallization in Glass-Forming Metals by Millisecond Heating and Processing. Science, 332, 828-833. https://doi.org/10.1126/science.1201362
Jiang, M.Q., et al. (2010) Fractal in Fracture of Bulk Metallic Glass. Intermetallics, 18, 2468-2471. https://doi.org/10.1016/j.intermet.2010.08.003
Qiao, J., Jia, H. and Liaw, P.K. (2016) Metallic Glass Matrix Composites. Materials Science and Engineering: R: Reports, 100, 1-69. https://doi.org/10.1016/j.mser.2015.12.001
Schroers, J. (2010) Processing of Bulk Metallic Glass. Advanced Materials, 22, 1566-1597. https://doi.org/10.1002/adma.200902776
Greer, A.L. (2010) Materials Science: A Cloak of Liquidity. Nature, 464, 1137-1138. https://doi.org/10.1038/4641137a
Yi, J., et al. (2016) Glass-Forming Ability and Crystallization Behavior of Al86Ni9La5 Metallic Glass with Si Addition. Advanced Engineering Materials, 18, 972-977. https://doi.org/10.1002/adem.201500354
Cheng, Y.Q., Sheng, H.W. and Ma, E. (2008) Relationship between Structure, Dynamics, and Mechanical Properties in Metallic Glass-Forming Alloys. Physical Review B, 78, 014207. https://doi.org/10.1103/PhysRevB.78.014207
Sarac, B. (2015) Microstructure-Property Optimization in Metallic Glasses. Springer, Berlin.
Greer, A.L. (2011) Metallic Glasses: Damage Tolerance at a Price. Nature Materials, 10, 88-89. https://doi.org/10.1038/nmat2949
Gu, X.W., et al. (2014) Mechanisms of Failure in Nanoscale Metallic Glass. Nano Letters, 14, 5858-5864. https://doi.org/10.1021/nl5027869
Schroers, J. and Johnson, W.L. (2004) Ductile Bulk Metallic Glass. Physical Review Letters, 93, 255506. https://doi.org/10.1103/PhysRevLett.93.255506
Schuh, C.A., Hufnagel, T.C. and Ramamurty, U. (2007) Mechanical Behavior of Amorphous Alloys. Acta Materialia, 55, 4067-4109. https://doi.org/10.1016/j.actamat.2007.01.052
Donovan, P.E. and Stobbs, W.M. (1981) The Structure of Shear Bands in Metallic Glasses. Acta Metallurgica, 29, 1419-1436. https://doi.org/10.1016/0001-6160(81)90177-2
Dodd, B. and Bai, Y. (2012) Adiabatic Shear Localization: Frontiers and Advances. Elsevier, Amsterdam.
Gao, Y.F., et al. (2011) On the Shear-Band Direction in Metallic Glasses. Acta Materialia, 59, 4159-4167. https://doi.org/10.1016/j.actamat.2011.03.039
Greer, A.L., Cheng, Y.Q. and Ma, E. (2013) Shear Bands in Metallic Glasses. Materials Science and Engineering: R: Reports, 74, 71-132. https://doi.org/10.1016/j.mser.2013.04.001
Jiang, M.Q., Wang, W.H. and Dai, L.H. (2009) Prediction of Shear-Band Thickness in Metallic Glasses. Scripta Materialia, 60, 1004-1007. https://doi.org/10.1016/j.scriptamat.2009.02.039
Leng, Y. and Courtney, T.H. (1991) Multiple Shear Band Formation in Metallic Glasses in Composites. Journal of Materials Science, 26, 588-592. https://doi.org/10.1007/BF00588291
Hajlaoui, K., et al. (2007) Unusual Room Temperature Ductility of Glassy Copper-Zirconium Caused by Nanoparticle Dispersions That Grow during Shear. Materials Science and Engineering: A, 449-451, 105-110. https://doi.org/10.1016/j.msea.2006.01.168
Zhang, Y. and Greer, A.L. (2007) Correlations for Predicting Plasticity or Brittleness of Metallic Glasses. Journal of Alloys and Compounds, 434-435, 2-5. https://doi.org/10.1016/j.jallcom.2006.08.094
Lewandowski, J., Wang, W.-H. and Greer, A. (2005) Intrinsic Plasticity or Brittleness of Metallic Glasses. Philosophical Magazine Letters, 85, 77-87. https://doi.org/10.1080/09500830500080474
Kruzic, J.J. (2016) Bulk Metallic Glasses as Structural Materials: A Review. Advanced Engineering Materials, 18, 1308-1331. https://doi.org/10.1002/adem.201600066
Nishiyama, N., et al. (2012) The World’s Biggest Glassy Alloy Ever Made. Intermetallics, 30, 19-24. https://doi.org/10.1016/j.intermet.2012.03.020
Schroers, J. (2005) The Superplastic Forming of Bulk Metallic Glasses. JOM, 57, 35-39. https://doi.org/10.1007/s11837-005-0093-2
Guo, G.-Q., et al. (2015) Detecting Structural Features in Metallic Glass via Synchrotron Radiation Experiments Combined with Simulations. Metals, 5, 2093-2108. https://doi.org/10.3390/met5042093
Guo, G.-Q., et al. (2015) How Can Synchrotron Radiation Techniques Be Applied for Detecting Microstructures in Amorphous Alloys? Metals, 5, 2048-2057. https://doi.org/10.3390/met5042048
Zimmermann, G., et al. (2011) Investigation of Columnar-to-Equiaxed Transition in Solidification Processing of AlSi Alloys in Microgravity—The CETSOL Project. Journal of Physics: Conference Series, 327, 012003. https://doi.org/10.1088/1742-6596/327/1/012003
Zu, F.-Q. (2015) Temperature-Induced Liquid-Liquid Transition in Metallic Melts: A Brief Review on the New Physical Phenomenon. Metals, 5, 395-417. https://doi.org/10.3390/met5010395
Kim, D.H., et al. (2013) Phase Separation in Metallic Glasses. Progress in Materials Science, 58, 1103-1172. https://doi.org/10.1016/j.pmatsci.2013.04.002
Ott, R.T., et al. (2005) Micromechanics of Deformation of Metallic-Glass-Matrix Composites from in situ Synchrotron Strain Measurements and Finite Element Modeling. Acta Materialia, 53, 1883-1893. https://doi.org/10.1016/j.actamat.2004.12.037
Rappaz, M. and Gandin, C.A. (1993) Probabilistic Modelling of Microstructure Formation in Solidification Processes. Acta Metallurgica et Materialia, 41, 345-360. https://doi.org/10.1016/0956-7151(93)90065-Z
Kurz, W., Giovanola, B. and Trivedi, R. (1986) Theory of Microstructural Development during Rapid Solidification. Acta Metallurgica, 34, 823-830. https://doi.org/10.1016/0001-6160(86)90056-8
Wei, Y.H., et al. (2007) Numerical Simulation of Columnar Dendritic Grain Growth during Weld Solidification Process. Science and Technology of Welding and Joining, 12, 138-146. https://doi.org/10.1179/174329307X164427
Rappaz, M. and Blank, E. (1986) Simulation of Oriented Dendritic Microstructures Using the Concept of Dendritic Lattice. Journal of Crystal Growth, 74, 67-76. https://doi.org/10.1016/0022-0248(86)90249-6
Rappaz, M., et al. (1989) Development of Microstructures in Fe-15Ni-15Cr Single Crystal Electron Beam Welds. Metallurgical Transactions A, 20, 1125-1138. https://doi.org/10.1007/BF02650147
Rappaz, M., et al. (1990) Analysis of Solidification Microstructures in Fe-Ni-Cr Single-Crystal Welds. Metallurgical Transactions A, 21, 1767-1782. https://doi.org/10.1007/BF02672593
Gandin, C.-A., Rappaz, M. and Tintillier, R. (1993) Three-Dimensional Probabilistic Simulation of Solidification Grain Structures: Application to Superalloy Precision Castings. Metallurgical Transactions A, 24, 467-479. https://doi.org/10.1007/BF02657334
Zhang, J., et al. (2013) Probabilistic Simulation of Solidification Microstructure Evolution during Laser-Based Metal Deposition. 24th Annual International Solid Freeform Fabrication Symposium—An Additive Manufacturing Conference, Austin, 2013, TX, 739-748.
Zhou, X., et al. (2016) Simulation of Microstructure Evolution during Hybrid Deposition and Micro-Rolling Process. Journal of Materials Science, 51, 6735-6749. https://doi.org/10.1007/s10853-016-9961-0
Gu, C., et al. (2017) A Three-Dimensional Cellular Automaton Model of Dendrite Growth with Stochastic Orientation during the Solidification in the Molten Pool of Binary Alloy. Science and Technology of Welding and Joining, 22, 47-58. https://doi.org/10.1080/13621718.2016.1183962
Nastac, L. (1999) Numerical Modeling of Solidification Morphologies and Segregation Patterns in Cast Dendritic Alloys. Acta Materialia, 47, 4253-4262. https://doi.org/10.1016/S1359-6454(99)00325-0
Laurentiu, N. and Doru, M.S. (1997) Stochastic Modelling of Microstructure Formation in Solidification Processes. Modelling and Simulation in Materials Science and Engineering, 5, 391. https://doi.org/10.1088/0965-0393/5/4/008
Von Neumann, J. and Burks, A.W. (1996) Theory of Self-Reproducing Automata. University of Illinois Press, Urbana, IL.
Reuther, K. and Rettenmayr, M. (2014) Perspectives for Cellular Automata for the Simulation of Dendritic Solidification—A Review. Computational Materials Science, 95, 213-220. https://doi.org/10.1016/j.commatsci.2014.07.037
Mullins, W.W. and Sekerka, R.F. (1964) Stability of a Planar Interface during Solidification of a Dilute Binary Alloy. Journal of Applied Physics, 35, 444-451. https://doi.org/10.1063/1.1713333
Langer, J.S. and Müller-Krumbhaar, J. (1977) Stability Effects in Dendritic Crystal Growth. Journal of Crystal Growth, 42, 11-14. https://doi.org/10.1016/0022-0248(77)90171-3
Bobadilla, M., Lacaze, J. and Lesoult, G. (1988) Influence des conditions de solidification sur le déroulement de la solidification des aciers inoxydables austénitiques. Journal of Crystal Growth, 89, 531-544. https://doi.org/10.1016/0022-0248(88)90216-3
Rafique, M.M.A., Qiu, D. and Easton, M. (2017) Modeling and Simulation of Microstructural Evolution in Zr Based Bulk Metallic Glass Matrix Composites during Solidification. MRS Advances, 2, 3591-3606.
Wu, K., Li, R. and Zhang, T. (2013) Crystallization and Thermophysical Properties of Cu46Zr47Al6Co1 Bulk Metallic Glass. AIP Advances, 3, 112115. https://doi.org/10.1063/1.4832235
Yamasaki, M., Kagao, S. and Kawamura, Y. (2005) Thermal Diffusivity and Conductivity of Zr55Al10Ni5Cu30 Bulk Metallic Glass. Scripta Materialia, 53, 63-67. https://doi.org/10.1016/j.scriptamat.2005.03.021
Flemings, M.C. (1974) Solidification Processing. McGraw-Hill, New York.
Yang, L., et al. (2009) Nanoscale Solute Partitioning in Bulk Metallic Glasses. Advanced Materials, 21, 305-308. https://doi.org/10.1002/adma.200801183
Mills, K.C. (2002) Front Matter A2—Recommended Values of Thermophysical Properties for Selected Commercial Alloys. Woodhead Publishing, Cambridge, iii.
Grimvall, G. (1999) Front Matter A2—Thermophysical Properties of Materials. Elsevier Science B.V., Amsterdam, iii.
Valencia, J.J. and Quested, P. (2001) Thermophysical Properties. Modeling for Casting and Solidification Processing, 189.
Choy, C.L., et al. (1991) Thermal Conductivity of Amorphous Alloys above Room Temperature. Journal of Applied Physics, 70, 4919-4925. https://doi.org/10.1063/1.349037