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Effect of microstructure on the elasto-viscoplastic deformation of dual phase titanium structures

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Abstract

The present study is devoted to the creation of a process–structure–property database for dual phase titanium alloys, through a synthetic microstructure generation method and a mesh-free fast Fourier transform based micromechanical model that operates on a discretized image of the microstructure. A sensitivity analysis is performed as a precursor to determine the statistically representative volume element size for creating 3D synthetic microstructures based on additively manufactured Ti–6Al–4V characteristics, which are further modified to expand the database for features of interest, e.g., lath thickness. Sets of titanium hardening parameters are extracted from literature, and The relative effect of the chosen microstructural features is quantified through comparisons of average and local field distributions.

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References

  1. Frazier WE (2014) Metal additive manufacturing: a review. J Mater Eng Perform 23(6):1917–28

    Article  Google Scholar 

  2. Lutjering G, Williams JC (2003) Titanium. Springer, New York

    Book  Google Scholar 

  3. Lutjering G (1998) Influence of processing on microstructure and mechanical properties of \(\alpha + \beta \) titanium alloys. Mater Sci Eng A 243(1–2):32–45

    Article  Google Scholar 

  4. Semiatin SL, Seetharaman V, Weiss I (1996) The thermomechanical processing of alpha/beta titanium alloys. J Mater 49(6):33–39

    Google Scholar 

  5. Kobryn PA, Semiatin SL (2003) Microstructure and texture evolution during solidification processing of Ti–6Al–4V. J Mater Process Technol 135:330–339

    Article  Google Scholar 

  6. RMI Titanium Company (2000) Titanium alloy guide. RMI Titanium Company an RTI International Metals, Inc. Company, pp 1–45

  7. Zhai Y, Galarraga H, Lados DA (2015) Microstructure evolution, tensile properties, and fatigue damage mechanisms in Ti–6Al–4V alloys fabricated by two additive manufacturing techniques. Procedia Eng 114:658–666

    Article  Google Scholar 

  8. Murr LE, Esquivel EV et al (2009) Microstructures and mechanical properties of electron beam-rapid manufactured Ti–6Al–4V biomedical prototypes compared to wrought Ti–6Al–4V. Mater Charact 60:96–105

    Article  Google Scholar 

  9. Swarnakar AK, Van der Biest O, Baufeld B (2010) Thermal expansion and lattice parameters of shaped metal deposited Ti–6Al–4V. J Alloys Compd 509(6):2723–28

    Article  Google Scholar 

  10. Gockel J, Beuth J (2013) Understanding Ti–6Al–4V microstructure control in additive manufacturing via process maps. In: Solid freeform fabrication proceedings, pp 666–674

  11. Bontha S, Klingbeil NW, Kobryn PA, Fraser HL (2009) Effects of process variables and size-scale on solidification microstructure in beam-based fabrication of bulky 3D structures. Mater Sci Eng A 513–514:311–318

    Article  Google Scholar 

  12. Beese AM et al (2015) Anisotropic tensile behavior of Ti–6Al–4V components fabricated with directed energy deposition additive manufacturing. Acta Mater 87:309–320

    Article  Google Scholar 

  13. Kanit T, Forest S, Galliet I, Mounoury D, Jeulin D (2003) Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Solids Struct 40(13–14):3647–3679

    Article  MATH  Google Scholar 

  14. Fan ZG, Wu Y, Zhao X, Lu Y (2004) Simulation of polycrystalline structure with Voronoi diagram in Laguerre geometry based on random closed packing of spheres. Comput Mater Sci 29(3):301–308

    Article  Google Scholar 

  15. Groeber MA, Ghosh S, Uchic MD, Dimiduk DM (2007) Developing a robust 3-D characterization–representation framework for modeling polycrystalline materials. J Mater 59(9):32–36

    Google Scholar 

  16. Groeber MA, Ghosh S, Uchic MD, Dimiduk DM (2008) A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 2: Synthetic structure generation. Acta Mater 56(6):1274–1287

    Article  Google Scholar 

  17. Saylor DM, Fridy J, El-Dasher BS, Jung KY, Rollett AD (2004) Statistically representative three-dimensional microstructures based on orthogonal observation sections. Metall Mater Trans A 35A(7):1969–1979

    Article  Google Scholar 

  18. Venkataramani G, Kirane K, Ghosh S (2008) Microstructural parameters affecting creep induced load shedding in Ti-6242 by a size dependent crystal plasticity FE model. Int J Plast 24:428–454

    Article  MATH  Google Scholar 

  19. Thomas J, Groeber M, Ghosh S (2012) Image-based crystal plasticity FE framework for microstructure dependent properties of Ti–6Al–4V alloys. Mater Sci Eng A 553:164–175

    Article  Google Scholar 

  20. Zhang M, Zhang J, McDowell DL (2007) Microstructure-based crystal plasticity modeling of cyclic deformation of Ti–6Al–4V. Int J Plast 23:1328–1348

    Article  MATH  Google Scholar 

  21. Przybyla CP, McDowell DL (2010) Simulation-based extreme value marked correlations in fatigue of advanced engineering alloys. Procedia Eng 2:1045–1056

    Article  Google Scholar 

  22. Simonelli M, Tse YY, Tuck C (2012) Further understanding of Ti–6Al–4V selective laser melting using texture analysis. In: Solid freeform fabrication proceedings, pp 480–491

  23. Gong X, Lydon J, Cooper K, Chou K (2014) Beam speed effects on Ti–6Al–4V microstructures in electron beam additive manufacturing. J Mater Res 29(17):1951–1959

    Article  Google Scholar 

  24. Gong H, Gu H, Zeng K, Dilip JJS et al (2014) Melt pool characterization for selective laser melting of Ti–6Al–4V pre-alloyed powder. In: Solid freeform fabrication proceedings, pp 256–267

  25. Nassar AR, Reutzel EW (2015) Additive manufacturing of Ti–6Al–4V using a pulsed laser beam. Metall Mater Trans A 46(6):2781–2789

    Article  Google Scholar 

  26. Al-Bermani SS, Blackmore ML, Zhang W, Todd I (2010) The origin of microstructural diversity, texture, and mechanical properties in electron beam melted Ti–6Al–4V. Metall Mater Trans A 41(13):3422–3434

    Article  Google Scholar 

  27. Antonysamy AA, Meyer J, Prangnell PB (2013) Effect of build geometry on the \(\beta \)-grain structure and texture in additive manufacture of Ti–6Al–4V by selective electron beam melting. Mater Charact 84:153–168

    Article  Google Scholar 

  28. Elmer JW, Palmer TA, Babu SS, Zhang W, DebRoy T (2004) Phase transformation dynamics during welding of Ti–6Al–4V. J Appl Phys 95(12):8327–8339

    Article  Google Scholar 

  29. Groeber MA, Jackson M (2014) DREAM.3D: a digital representation environment for the analysis of microstructure in 3D. Integr Mater Manuf Innov 3:5

    Article  Google Scholar 

  30. Sachs G (1928) Plasticity problems in metals. Trans Faraday Soc 24:84–92

    Article  Google Scholar 

  31. Taylor GI (1938) Plastic strain in metals. J Inst Met 62:307–324

    Google Scholar 

  32. Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc R Soc Lond Ser A Math Phys Eng Sci A241:376–396

    Article  MathSciNet  MATH  Google Scholar 

  33. Molinari A, Canova GR, Ahzi S (1987) A self consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall 35:2983–94

    Article  Google Scholar 

  34. Lebensohn RA, Turner PA, Signorelli JW, Canova GR, Tomé SN (1998) Calculation of intergranular stresses based on a large-strain viscoplastic self-consistent polycrystal model. Model Simul Mater Sci Eng 6(4):447–65

    Article  Google Scholar 

  35. Moulinec H, Suquet P (1998) A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput Methods Appl Mech Eng 157(1–2):69–94

    Article  MathSciNet  MATH  Google Scholar 

  36. Prakash A, Lebensohn RA (2009) Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms. Modell Simul Mater Sci Eng 17:064010

    Article  Google Scholar 

  37. Lebensohn RA, Liu Y, Castañeda PP (2004) On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations. Acta Mater 52:5347–61

    Article  Google Scholar 

  38. Lebensohn RA (2001) N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform. Acta Mater 49:2723–37

  39. Lebensohn RA, Kanjarla AK, Eisenlohr P (2012) An elasto-viscoplastic formulation based on fast fourier transforms for the prediction of micromechanical fields in polycrystalline materials. Int J Plast 32:59–69

    Article  Google Scholar 

  40. Mura T (1988) Micromechanics of defects in solids. Martinus-Nijhoff, Dodrecht

    Google Scholar 

  41. Lebensohn RA, Tome CN, Ponte CastaNeda P (2007) Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations. Philos Mag 87(28):4287–4322

  42. Voce E (1955) A practical strain hardening function. Metallurgia 51:219–226

    Google Scholar 

  43. Gockel BT (2016) Constitutive response of a near-alpha titanium alloy as a function of temperature and strain rate. The Ohio State University. Electronic Thesis or Dissertation, Carnegie Mellon University

  44. Mandal S, Gockel BT, Balachandran S, Banerjee D, Rollett AD (2017) Simulation of plastic deformation in Ti-5553 alloy using a self-consistent viscoplastic model. Int J Plast 94:57–73

  45. Bieler TR, Semiatin SL (2002) The origins of heterogeneous deformation during primary hot working of Ti–6Al–4V. Int J Plast 18(9):1165–1189

    Article  MATH  Google Scholar 

  46. Facchini L, Magalini M, Robotti P, Molinari A (2009) Microstructure and mechanical properties of Ti–6Al–4V produced by electron beam melting of pre-alloyed powders. Rapid Prototyp J 15(3):171–178

    Article  Google Scholar 

  47. Stapleton AM et al (2008) Evolution of lattice strain in Ti–6Al–4V during tensile loading at room temperature. Acta Mater 56:6186–6196

    Article  Google Scholar 

  48. Ozturk T et al (2016) Simulation domain size requirements for elastic response of 3D polycrystalline materials. Model Simul Mater Sci Eng 24:015006

    Article  Google Scholar 

  49. Werner E, Wesenjak R, Fillafer A, Meier F, Krempaszky C (2016) Microstructure-based modelling of multiphase materials and complex structures. Contin Mech Thermodyn 28:1325–1346

    Article  MathSciNet  MATH  Google Scholar 

  50. Boyle KP, Curtin WA (2005) Grain interactions in crystal plasticity. NUMISHEET2005 778:433–438

    Google Scholar 

  51. Barton NR, Dawson PR (2001) On the spatial arrangement of lattice orientations in hot-rolled multiphase titanium. Model Simul Mater Sci Eng 9:433–463

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Science Foundation, under the Award No. DMREF-1435544. For computing resources, this research extensively used local computer clusters and resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Dr. Ricardo Lebensohn is acknowledged for his FFT based models and his valuable support on the code/algorithm development.

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  1. Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

    Tugce Ozturk & Anthony D. Rollett

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  1. Tugce Ozturk
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Correspondence to Tugce Ozturk.

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Ozturk, T., Rollett, A.D. Effect of microstructure on the elasto-viscoplastic deformation of dual phase titanium structures. Comput Mech 61, 55–70 (2018). https://doi.org/10.1007/s00466-017-1467-3

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