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A Mechanics-Based Phase-Field Model and Finite Element Simulations for Microstructure Evolution during Solidification of Ti-6Al-4V

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Abstract

In this paper, a mechanics-based phase-field model at the microscale is introduced for microstructure evolution during solidification. The couple phase-field model consists of Allen–Cahn equation for phase order parameter, Cahn–Hilliard equation for composition, heat conduction and elasticity equations. The introduced elastic energy allows for volumetric inelastic strains due to melting/solidification as well as a thermodynamically consistent solid-melt interface stress and consequently, residual stresses during solidification at the microscale and deformation can be captured. The computational microcell is considered at the melt-solid interface and the temperature as a time dependent function is used for its boundary conditions to solve the coupled phase-field model. Using COMSOL FE code, examples of columnar growth are studied. As result, the suppressive effect of elastic driving forces and the reduction in solidification rate, due to the volumetric inelastic strains, on solidification are revealed. The inelastic surface stress, concentrated inside the interface, can change the morphology of solidified structure but does not show a remarkable effect on the solidification rate. The thermal strain was included which reduced the effect of volumetric transformation strain and consequently, the internal stresses near constrained regions were decreased. The effect of undercooling was studied which showed that increasing the undercooling increased the temperature gradient in the vertical direction and near the interface and solidification rate and significantly changed the morphology of solidified structure, as a homogeneous growth was resolved for larger undercooling while a columnar growth was obtained for smaller undercooling. Solidification was studied under mechanical loading which showed external loading changes the stress distribution and magnitude and the morphology of solidified structure. Effect of an inclusion on solidification was also investigated. The inclusion represented a more homogeneous distribution of stress and temperature with different magnitudes compared to the rest of the sample, creating a directional solidification toward the inclusion.

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References

  1. W.E. Frazier, Metal Additive Manufacturing: A Review, J. Mater. Eng. Perform., 2014, 23, p 1917–1928.

    Article  CAS  Google Scholar 

  2. D. Herzog, V. Seyda, E. Wycisk and C. Emmelmann, Additive Manufacturing of Metals, Acta Mater. Mater., 2016, 117, p 371–392.

    Article  CAS  Google Scholar 

  3. W.J. Sames, F.A. List, S. Pannala, R.R. Dehoff and S.S. Babu, The Metallurgy and Processing Science of Metal Additive Manufacturing, Int. Mater. Rev., 2016, 61, p 315–360.

    Article  CAS  Google Scholar 

  4. L. Wu and J. Zhang, Phase Field Simulation of Dendritic Solidification of Ti-6Al-4V During Additive Manufacturing Process, JOM, 2018, 70, p 2392–2399.

    Article  CAS  Google Scholar 

  5. R.S. Mishra and S. Thapliyal, Design Approaches for Printability-Performance Synergy in Al Alloys for Laser-Powder Bed Additive Manufacturing, Mater. Des., 2021, 204, p 109640.

    Article  CAS  Google Scholar 

  6. N.S. Bailey, K.-M. Hong and Y.C. Shin, Comparative Assessment of Dendrite Growth and Microstructure Predictions During Laser Welding of Al 6061 via 2D and 3D Phase Field Models, Comput. Mater. Sci.. Mater. Sci., 2020, 172, p 109291.

    Article  CAS  Google Scholar 

  7. S. Sahoo and K. Chou, Phase-Field Simulation of Microstructure Evolution of Ti-6Al-4V in Electron Beam Additive Manufacturing Process, Addit. Manuf.. Manuf., 2016, 9, p 14–24.

    CAS  Google Scholar 

  8. C. Tang and H. Du, Phase Field Modelling of Dendritic Solidification Under Additive Manufacturing Conditions, JOM, 2022, 74, p 2996–3009.

    Article  CAS  Google Scholar 

  9. J.H.K. Tan, S.L. Sing and W.Y. Yeong, Microstructure Modelling for Metallic Additive Manufacturing: A Review, Virtual Phys. Prototyping, 2020, 15, p 87–105.

    Article  Google Scholar 

  10. T.M. Rodgers, J.D. Madison and V. Tikare, Simulation of Metal Additive Manufacturing Microstructures Using Kinetic Monte Carlo, Comput. Mater. Sci.. Mater. Sci., 2017, 135, p 78–89.

    Article  Google Scholar 

  11. H.L. Wei, J.W. Elmer and T. DebRoy, Three-Dimensional Modeling of Grain Structure Evolution During Welding of an Aluminum Alloy, Acta Mater. Mater., 2017, 126, p 413–425.

    Article  CAS  Google Scholar 

  12. T. Carozzani, C.-A. Gandin, H. Digonnet, M. Bellet, K. Zaidat and Y. Fautrelle, Direct Simulation of a Solidification Benchmark Experiment, Metall. Mater. Trans. A, 2013, 44, p 873–887.

    Article  CAS  Google Scholar 

  13. X. Li and W. Tan, Numerical Investigation of Effects of Nucleation Mechanisms on Grain Structure in Metal Additive Manufacturing, Comput. Mater. Sci.. Mater. Sci., 2018, 153, p 159–169.

    Article  CAS  Google Scholar 

  14. M. Javanbakht and V.I. Levitas, Athermal Resistance to Phase Interface Motion Due to Precipitates: A Phase Field Study, Acta Mater. Mater., 2023, 242, p 118489.

    Article  CAS  Google Scholar 

  15. V.I. Levitas, M. Javanbakht, Phase-field approach to martensitic phase transformations: effect of martensite–martensite interface energy, 2011, 102, pp. 652–665

  16. A.V. Idesman, V.I. Levitas and E. Stein, Elastoplastic materials with martensitic phase transition and twinning at finite strains: numerical solution with the finite element method, Comput. Methods Appl. Mech. Eng., 1999, 173, p 71–98.

    Article  Google Scholar 

  17. H. Jafarzadeh, G.H. Farrahi, V.I. Levitas and M. Javanbakht, Phase field theory for fracture at large strains including surface stresses, Int. J. Eng. Sci., 2022, 178, p 103732.

    Article  Google Scholar 

  18. N. Moelans, B. Blanpain and P. Wollants, Quantitative analysis of grain boundary properties in a generalized phase field model for grain growth in anisotropic systems, Phys. Rev. B, 2008, 78, p 024113.

    Article  Google Scholar 

  19. E. Bakhtiyari, M. Javanbakht and M. Asle Zaeem, Evolution of edge dislocations under elastic and inelastic strains: a nanoscale phase-field study, Math. Mech. Solids, 2023, 1081, p 2865.

    Google Scholar 

  20. V.I. Levitas and M. Javanbakht, Phase field approach to interaction of phase transformation and dislocation evolution, Appl. Phys. Lett., 2013, 102, p 251904.

    Article  Google Scholar 

  21. M. Javanbakht and M.S. Ghaedi, Phase field approach for void dynamics with interface stresses at the nanoscale, Int. J. Eng. Sci., 2020, 154, p 103279.

    Article  Google Scholar 

  22. J.C. Ramirez, C. Beckermann, A. Karma and H.J. Diepers, Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion, Phys. Rev. E, 2004, 69, p 051607.

    Article  CAS  Google Scholar 

  23. B. Echebarria, R. Folch, A. Karma and M. Plapp, Quantitative Phase-Field Model of Alloy Solidification, Phys. Rev. E, 2004, 70, p 061604.

    Article  Google Scholar 

  24. R. Acharya, J.A. Sharon and A. Staroselsky, Prediction of Microstructure in Laser Powder Bed Fusion Process, Acta Mater. Mater., 2017, 124, p 360–371.

    Article  CAS  Google Scholar 

  25. J. Berry, A. Perron, J.-L. Fattebert, J.D. Roehling, B. Vrancken, T.T. Roehling et al., Toward Multiscale Simulations of Tailored Microstructure Formation in Metal Additive Manufacturing, Mater. Today, 2021, 51, p 65–86.

    Article  CAS  Google Scholar 

  26. K. Karayagiz, L. Johnson, R. Seede, V. Attari, B. Zhang, X. Huang et al., Finite Interface Dissipation Phase Field Modeling of Ni–Nb Under Additive Manufacturing Conditions, Acta Mater. Mater., 2020, 185, p 320–339.

    Article  CAS  Google Scholar 

  27. L.-X. Lu, N. Sridhar and Y.-W. Zhang, Phase Field Simulation of Powder Bed-Based Additive Manufacturing, Acta Mater. Mater., 2018, 144, p 801–809.

    Article  CAS  Google Scholar 

  28. D. Tourret and A. Karma, Growth Competition of Columnar Dendritic Grains: A Phase-Field Study, Acta Mater. Mater., 2015, 82, p 64–83.

    Article  CAS  Google Scholar 

  29. J. Park, J.-H. Kang and C.-S. Oh, Phase-Field Simulations and Microstructural Analysis of Epitaxial Growth During Rapid Solidification of Additively Manufactured AlSi10Mg Alloy, Mater. Des., 2020, 195, p 108985.

    Article  CAS  Google Scholar 

  30. M. Yang, L. Wang and W. Yan, Phase-Field Modeling of Grain Evolutions in Additive Manufacturing from Nucleation, Growth, to Coarsening, npj Comput. Mater., 2021, 7, p 56.

    Article  Google Scholar 

  31. Z. Zhang, X.X. Yao and P. Ge, Phase-Field-Model-Based Analysis of the Effects of Powder Particle on Porosities and Densities in Selective Laser Sintering Additive Manufacturing, Int. J. Mech. Sci., 2020, 166, p 105230.

    Article  Google Scholar 

  32. P.W. Liu, Z. Wang, Y.H. Xiao, R.A. Lebensohn, Y.C. Liu, M.F. Horstemeyer et al., Integration of Phase-Field Model and Crystal Plasticity for the Prediction of Process-Structure-Property Relation of Additively Manufactured Metallic Materials, Int. J. Plast., 2020, 128, p 102670.

    Article  CAS  Google Scholar 

  33. J.-Q. Li and T.-H. Fan, Phase-Field Modeling of Metallic Powder-Substrate Interaction in Laser Melting Process, Int. J. Heat Mass Transf., 2019, 133, p 872–884.

    Article  CAS  Google Scholar 

  34. V.I. Levitas and K. Samani, Coherent Solid/Liquid Interface with Stress Relaxation in a Phase-Field Approach to the Melting/Solidification Transition, Phys. Rev. B, 2011, 84, p 140103.

    Article  Google Scholar 

  35. M. Javanbakht, S.S. Eskandari and M. Silani, Surface Induced Melting of Long Al Nanowires: Phase Field Model and Simulations for Pressure Loading and Without It, Nanotechnology, 2022, 33, p 425705.

    Article  Google Scholar 

  36. V.I. Levitas and M. Javanbakht, Surface Tension and Energy in Multivariant Martensitic Transformations: Phase-Field Theory, Simulations, and Model of Coherent Interface, Phys. Rev. Lett., 2010, 105, p 165701.

    Article  PubMed  Google Scholar 

  37. A. Safdar, L.Y. Wei, A. Snis and Z. Lai, Evaluation of Microstructural Development in Electron Beam Melted Ti-6Al-4V, Mater CharactCharact, 2012, 65, p 8–15.

    Article  CAS  Google Scholar 

  38. S. Ghosh, K. McReynolds, J.E. Guyer and D. Banerjee, Simulation of Temperature, Stress and Microstructure Fields During Laser Deposition of Ti-6Al-4V, Modell. Simul. Mater. Sci. Eng., 2018, 26, p 075005.

    Article  Google Scholar 

  39. B. Radhakrishnan, S. Gorti and S.S. Babu, Phase Field Simulations of Autocatalytic Formation of Alpha Lamellar Colonies in Ti-6Al-4V, Metall. Mater. Trans. A, 2016, 47, p 6577–6592.

    Article  CAS  Google Scholar 

  40. K.C. Mills, Ti: Ti-6 Al-4 V (IMI 318), in Recommended Values of Thermophysical Properties for Selected Commercial Alloys, ed: Woodhead Publishing, 2002.

  41. L. Nastac, Solute Redistribution, Liquid/Solid Interface Instability, and Initial Transient Regions During the Unidirectional Solidification of Ti-6-4 and Ti-17 Alloys, TMS Annu. Meet., 2012, 15, p 123–130.

    Google Scholar 

  42. J. Ba, X.H. Zheng, R. Ning, J.H. Lin, J. Qi, J. Cao, et al. C/SiC Composite-Ti6Al4V Joints Brazed with Negative Thermal Expansion ZrP2WO12 Nanoparticle Reinforced AgCu Alloy. J. Eur. Ceram. Soc. 2018, 39.

  43. A. Fallahnejad, E. Barchiesi, M. Javanbakht, A.A.S. Nami, Investigating the Effect of Nanovoid Inelastic Surface Stress and the Austenite–Martensite Interface Inelastic Stress on the Martensitic Growth at the Nanovoid Surface. Contin. Mech. Thermodyn. 2023.

  44. Q. Huang, N. Hu, X. Yang, R. Zhang and Q. Feng, Microstructure and Inclusion of Ti-6Al-4V Fabricated By Selective Laser Melting, Front. Mater. Sci., 2016, 10, p 428–431.

    Article  Google Scholar 

  45. C. Piconi, 1.105—Alumina, in Comprehensive Biomaterials, P. Ducheyne, Ed., ed Oxford: Elsevier, 2011, pp. 73–94.

  46. D. Dixit, R. Pal, G. Kapoor, M. Stabenau, 6-Lightweight composite materials processing, in Lightweight Ballistic Composites (Second Edition), A. Bhatnagar, Ed., ed: Woodhead Publishing, 2016, pp. 157–216.

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Acknowledgments

The help of Isfahan University of Technology and Iran national Science Foundation is gratefully acknowledged.

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  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Farhad Boorani Koopaei, Mahdi Javanbakht & Mohammad Silani

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  1. Farhad Boorani Koopaei
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Correspondence to Mahdi Javanbakht.

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This invited article is part of a special topical issue of the Journal of Materials Engineering and Performance on Residual Stress Analysis: Measurement, Effects, and Control. The issue was organized by Rajan Bhambroo, Tenneco, Inc.; Lesley Frame, University of Connecticut; Andrew Payzant, Oak Ridge National Laboratory; and James Pineault, Proto Manufacturing on behalf of the ASM Residual Stress Technical Committee.

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Boorani Koopaei, F., Javanbakht, M. & Silani, M. A Mechanics-Based Phase-Field Model and Finite Element Simulations for Microstructure Evolution during Solidification of Ti-6Al-4V. J. of Materi Eng and Perform (2024). https://doi.org/10.1007/s11665-024-09356-z

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