Research Papers

Predicting Microstructure From Thermal History During Additive Manufacturing for Ti-6Al-4V

[+] Author and Article Information
Jeff Irwin

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
17 Reber Building,
University Park, PA 16801
e-mail: jei5028@psu.edu

Edward W. Reutzel, Jay Keist, Abdalla R. Nassar

Applied Research Laboratory,
The Pennsylvania State University,
University Park, PA 16801

Pan Michaleris

Associate Professor
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16801;
Pan Computing LLC,
State College, PA 16803

Manuscript received September 8, 2015; final manuscript received April 25, 2016; published online June 23, 2016. Assoc. Editor: Donggang Yao.

J. Manuf. Sci. Eng 138(11), 111007 (Jun 23, 2016) (11 pages) Paper No: MANU-15-1466; doi: 10.1115/1.4033525 History: Received September 08, 2015; Revised April 25, 2016

Due to the repeated thermal cycling that occurs with the processing of each subsequent layer, the microstructure of additively manufactured parts undergoes complex changes throughout the deposition process. Understanding and modeling this evolution poses a greater challenge than for single-cycle heat treatments. Following the work of Kelly and Charles, a Ti-6Al-4V microstructural model has been developed which calculates the phase fractions, morphology, and alpha lath width given a measured or modeled thermal history. Dissolution of the alpha phase is modeled as 1D plate growth of the beta phase, while alpha growth is modeled by the technique of Johnson–Mehl–Avrami (JMA). The alpha phase is divided into colony and basketweave morphologies based on an intragranular nucleation temperature. Evolution of alpha lath width is calculated using an Arrhenius equation. Key parameters of the combined Kelly–Charles model developed here are optimized using the Nelder–Mead simplex algorithm. For the deposition of two L-shaped geometries with different processing parameters, the optimized model gives a mean error over 24 different locations of 37% relative to experimentally measured lath widths, compared to 106% for the original Kelly–Charles model.

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Cai, J. , Li, F. , Liu, T. , Chen, B. , and He, M. , 2011, “ Constitutive Equations for Elevated Temperature Flow Stress of Ti–6Al–4V Alloy Considering the Effect of Strain,” Mater. Des., 32(3), pp. 1144–1151. [CrossRef]
Majorell, A. , Srivatsa, S. , and Picu, R. , 2002, “ Mechanical Behavior of Ti–6Al–4V at High and Moderate Temperatures—Part I: Experimental Results,” Mater. Sci. Eng.: A, 326(2), pp. 297–305. [CrossRef]
Tiley, J. , Searles, T. , Lee, E. , Kar, S. , Banerjee, R. , Russ, J. , and Fraser, H. L. , 2004, “ Quantification of Microstructural Features in α/β Titanium Alloys,” Mater. Sci. Eng.: A, 372(1), pp. 191–198. [CrossRef]
Searles, T. , Tiley, J. , Tanner, A. , Williams, R. , Rollins, B. , Lee, E. , Kar, S. , Banerjee, R. , and Fraser, H. L. , 2005, “ Rapid Characterization of Titanium Microstructural Features for Specific Modelling of Mechanical Properties,” Meas. Sci. Technol., 16(1), p. 60. [CrossRef]
Costa, L. , Vilar, R. , Reti, T. , and Deus, A. , 2005, “ Rapid Tooling by Laser Powder Deposition: Process Simulation Using Finite Element Analysis,” Acta Mater., 53(14), pp. 3987–3999. [CrossRef]
Kar, S. , Searles, T. , Lee, E. , Viswanathan, G. , Fraser, H. , Tiley, J. , and Banerjee, R. , 2006, “ Modeling the Tensile Properties in β-Processed α/β Ti Alloys,” Metall. Mater. Trans. A, 37(3), pp. 559–566. [CrossRef]
Avrami, M. , 1939, “ Kinetics of Phase Change. I General Theory,” J. Chem. Phys., 7(12), pp. 1103–1112. [CrossRef]
Avrami, M. , 1940, “ Kinetics of Phase Change. II Transformation-Time Relations for Random Distribution of Nuclei,” J. Chem. Phys., 8(2), pp. 212–224. [CrossRef]
Avrami, M. , 1941, “ Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III,” J. Chem. Phys., 9(2), pp. 177–184. [CrossRef]
Johnson, W. A. , and Mehl, R. F. , 1939, “ Reaction Kinetics in Processes of Nucleation and Growth,” Trans. AIME, 135(8), pp. 396–415.
Kolmogorov, A. N. , 1937, “ On the Statistical Theory of the Crystallization of Metals,” Bull. Acad. Sci. USSR, Math. Ser., 1, pp. 355–359.
Malinov, S. , Markovsky, P. , Sha, W. , and Guo, Z. , 2001, “ Resistivity Study and Computer Modelling of the Isothermal Transformation Kinetics of Ti–6Al–4V and Ti–6Al–2Sn–4Zr–2Mo–0.08 Si Alloys,” J. Alloys Compd., 314(1), pp. 181–192. [CrossRef]
Mudge, R. P. , and Wald, N. R. , 2007, “ Laser Engineered Net Shaping Advances Additive Manufacturing and Repair,” Weld. J., 86(1), pp. 44–48.
Melchels, F. P. , Feijen, J. , and Grijpma, D. W. , 2010, “ A Review on Stereolithography and Its Applications in Biomedical Engineering,” Biomaterials, 31(24), pp. 6121–6130. [CrossRef] [PubMed]
Kobryn, P. , and Semiatin, S. , 2001, “ The Laser Additive Manufacture of Ti-6Al-4V,” JOM, 53(9) pp. 40–42. [CrossRef]
Mahesh, M. , Wong, Y. , Fuh, J. , and Loh, H. , 2004, “ Benchmarking for Comparative Evaluation of RP Systems and Processes,” Rapid Prototyping J., 10(2), pp. 123–135. [CrossRef]
Sheng, W. , Xi, N. , Chen, H. , Chen, Y. , and Song, M. , 2003, “ Surface Partitioning in Automated CAD-Guided Tool Planning for Additive Manufacturing,” 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2003, Oct. 27–31, IEEE, Piscataway, NJ, Vol. 2, pp. 2072–2077.
Galantucci, L. , Lavecchia, F. , and Percoco, G. , 2009, “ Experimental Study Aiming to Enhance the Surface Finish of Fused Deposition Modeled Parts,” CIRP Ann.-Manuf. Technol., 58(1), pp. 189–192. [CrossRef]
Huang, Y. , Leu, M. C. , Mazumder, J. , and Donmez, A. , 2015, “ Additive Manufacturing: Current State, Future Potential, Gaps and Needs, and Recommendations,” ASME J. Manuf. Sci. Eng., 137(1), p. 014001. [CrossRef]
Panhalkar, N. , Paul, R. , and Anand, S. , 2014, “ Increasing Part Accuracy in Additive Manufacturing Processes Using a KD Tree Based Clustered Adaptive Layering,” ASME J. Manuf. Sci. Eng., 136(6), p. 061017. [CrossRef]
Kelly, S. M. , 2004, “ Thermal and Microstructure Modeling of Metal Deposition Processes With Application to Ti-6Al-4V,” Ph.D. dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA.
Paul, S. , Gupta, I. , and Sing, R. K. , 2015, “ Characterization and Modeling of Microscale Preplaced Powder Cladding Via Fiber Laser,” ASME J. Manuf. Sci. Eng., 137(3), p. 031019. [CrossRef]
Huang, Q. , Nouri, H. , Xu, K. , Chen, Y. , Sosina, S. , and Dasgupta, T. , 2014, “ Statistical Predictive Modeling and Compensation of Geometric Deviations of Three-Dimensional Printed Products,” ASME J. Manuf. Sci. Eng., 136(6), p. 061008. [CrossRef]
Cheng, B. , Price, S. , Lydon, J. , Cooper, K. , and Chou, K. , 2014, “ On Process Temperature in Powder-Bed Electron Beam Additive Manufacturing: Model Development and Validation,” ASME J. Manuf. Sci. Eng., 136(6), p. 061018. [CrossRef]
Kelly, S. , and Kampe, S. , 2004, “ Microstructural Evolution in Laser-Deposited Multilayer Ti-6Al-4V Builds: Part I. Microstructural Characterization,” Metall. Mater. Trans. A, 35(6), pp. 1861–1867. [CrossRef]
Kelly, S. , and Kampe, S. , 2004, “ Microstructural Evolution in Laser-Deposited Multilayer Ti-6Al-4V Builds: Part II. Thermal Modeling,” Metall. Mater. Trans. A, 35(6), pp. 1869–1879. [CrossRef]
Christian, J. W. , 2002, The Theory of Transformations in Metals and Alloys (Part I + II), Newnes, Burlington, MA.
Kriczky, D. A. , Irwin, J. , Reutzel, E. W. , Michaleris, P. , Nassar, A. R. , and Craig, J. , 2015, “ 3D Spatial Reconstruction of Thermal Characteristics in Directed Energy Deposition Through Optical Thermal Imaging,” J. Mater. Process. Technol., 221(1), pp. 172–186. [CrossRef]
Fan, Y. , Cheng, P. , Yao, Y. , Yang, Z. , and Egland, K. , 2005, “ Effect of Phase Transformations on Laser Forming of Ti–6Al–4V Alloy,” J. Appl. Phys., 98(1), p. 013518. [CrossRef]
Crespo, A. , 2011, Modelling of Heat Transfer and Phase Transformations in the Rapid Manufacturing of Titanium Components, INTECH Open Access Publisher, Rijeka, Croatia.
Charles, C. , 2008, “ Modelling Microstructure Evolution of Weld Deposited Ti-6Al-4V,” Licentiate thesis, Luleå University of Technology, Luleå, Sweden.
Charles, C. , and Järvstråt, N. , 2009, “ Modelling Ti-6Al-4V Microstructure by Evolution Laws Implemented as Finite Element Subroutines: Application to TIG Metal Deposition,” 8th International Conference Trends in Welding Research, Pine Mountain, GA, June 1–6, pp. 477–485.
Murgau, C. C. , Pederson, R. , and Lindgren, L. , 2012, “ A Model for Ti–6Al–4V Microstructure Evolution for Arbitrary Temperature Changes,” Modell. Simul. Mater. Sci. Eng., 20(5), p. 055006. [CrossRef]
Carroll, B. E. , Palmer, T. A. , and Beese, A. M. , 2015, “ Anisotropic Tensile Behavior of Ti–6Al–4V Components Fabricated With Directed Energy Deposition Additive Manufacturing,” Acta Mater., 87(1), pp. 309–320. [CrossRef]
Husain, A. , Sehgal, D. , and Pandey, R. , 2004, “ An Inverse Finite Element Procedure for the Determination of Constitutive Tensile Behavior of Materials Using Miniature Specimen,” Comput. Mater. Sci., 31(1), pp. 84–92. [CrossRef]
Hess, R. , Wang, S. , and Gao, C. , 1991, “ Generalized Technique for Inverse Simulation Applied to Aircraft Maneuvers,” J. Guid., Control, Dyn., 14(5), pp. 920–926. [CrossRef]
Calvello, M. , and Finno, R. J. , 2004, “ Selecting Parameters to Optimize in Model Calibration by Inverse Analysis,” Comput. Geotech., 31(5), pp. 410–424. [CrossRef]
Goldak, J. , Chakravarti, A. , and Bibby, M. , 1984, “ A New Finite Element Model for Welding Heat Sources,” Metall. Trans. B, 15(2) pp. 299–305. [CrossRef]
Reddy, J. N. , 1993, An Introduction to the Finite Element Method, Vol. 2, McGraw-Hill, New York.
Michaleris, P. , 2014, “ Modeling Metal Deposition in Heat Transfer Analyses of Additive Manufacturing Processes,” Finite Elem. Anal. Des., 86(1), pp. 51–60. [CrossRef]
Irwin, J. , and Michaleris, P. , 2015, “ A Line Heat Input Model for Additive Manufacturing,” ASME Paper No. MANU-15-1327.
Gouge, M. F. , Heigel, J. C. , Michaleris, P. , and Palmer, T. A. , 2015, “ Modeling Forced Convection in the Thermal Simulation of Laser Cladding Processes,” Int. J. Adv. Manuf. Technol., pp. 1–14.
Heigel, J. , Michaleris, P. , and Reutzel, E. , 2014, “ Thermo-Mechanical Model Development and Validation of Directed Energy Deposition Additive Manufacturing of Ti–6Al–4V,” Addit. Manuf., 5, pp. 9–19.
Denlinger, E. R. , Heigel, J. C. , and Michaleris, P. , 2014, “ Residual Stress and Distortion Modeling of Electron Beam Direct Manufacturing Ti-6Al-4V,” Proc. Inst. Mech. Eng., Part B, 229(10), pp. 1803–1813.
Ahmed, T. , and Rack, H. , 1998, “ Phase Transformations During Cooling in α+ β Titanium Alloys,” Mater. Sci. Eng.: A, 243(1), pp. 206–211. [CrossRef]
Gil, F. , Ginebra, M. , Manero, J. , and Planell, J. , 2001, “ Formation of α-Widmanstätten Structure: Effects of Grain Size and Cooling Rate on the Widmanstätten Morphologies and on the Mechanical Properties in Ti6Al4V Alloy,” J. Alloys Compd., 329(1), pp. 142–152. [CrossRef]
Elmer, J. , Palmer, T. , Babu, S. , Zhang, W. , and DebRoy, T. , 2004, “ Phase Transformation Dynamics During Welding of Ti–6Al–4V,” J. Appl. Phys., 95(12), pp. 8327–8339. [CrossRef]
Nelder, J. A. , and Mead, R. , 1965, “ A Simplex Method for Function Minimization,” Comput. J., 7(4), pp. 308–313. [CrossRef]
Gao, F. , and Han, L. , 2012, “ Implementing the Nelder–Mead Simplex Algorithm With Adaptive Parameters,” Comput. Optim. Appl., 51(1), pp. 259–277. [CrossRef]
Chlebus, E. , Kuźnicka, B. , Kurzynowski, T. , and Dybała, B. , 2011, “ Microstructure and Mechanical Behaviour of Ti–6Al–7Nb Alloy Produced by Selective Laser Melting,” Mater. Charact., 62(5), pp. 488–495. [CrossRef]
Tayon, W. A. , Shenoy, R. N. , Redding, M. R. , Bird, R. K. , and Hafley, R. A. , 2014, “ Correlation Between Microstructure and Mechanical Properties in an Inconel 718 Deposit Produced Via Electron Beam Freeform Fabrication,” ASME J. Manuf. Sci. Eng., 136(6), p. 061005. [CrossRef]


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Fig. 1

Equilibrium α and β phase fractions from Ref. [21]

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Fig. 2

An illustration of the concept of equivalent time

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Fig. 3

Kinetic parameter for α growth from Ref. [21]

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Fig. 4

A flowchart for the thermomicrostructural model

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Fig. 5

The order of the eight deposition hatches for odd layers (left) and even layers (right)

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Fig. 6

Locations of the cross sections (dashed lines) for α lath width measurement, superimposed on the 4 s dwell build

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Fig. 7

Two representative micrographs used for measuring lath width. The top two are original grayscale images, while the lower two are black and white binary images after the thresholding process (a) 0 s dwell, z = 5 mm, w¯  = 0.62 μm, grayscale, (b) 4 s dwell, z = 30 mm, w¯  = 1.58 μm, grayscale, (c) 0 s dwell, z = 5 mm, w¯  = 0.62 μm, binary, and (d) 4 s dwell, z = 30 mm, w¯  = 1.58 μm, binary.

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Fig. 8

Temperature profile ( °C) at the end of the final laser pass for 0 s dwell

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Fig. 9

α lath width (μm) after the part has cooled (a) 0 s dwell and (b) 4 s dwell

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Fig. 10

Experimental lath width measurements compared to the results of two different microstructure models. In Fig. 10(b), the results of the original model are off the scale, with lath widths as large as 3.2 μm (a) validation, 0 s dwell, one-bead leg, (b) calibration, 0 s dwell, three-bead leg, (c) validation, 4 s dwell, one-bead leg, and (d) calibration, 4 s dwell, three-bead leg.

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Fig. 11

Phase fractions, lath width, and temperature versus time for both models at a single point in the middle of the three-bead leg (a) Kelly–Charles model and (b) optimized model

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Fig. 12

Colony-α phase fraction after the part has cooled (a) 0 s dwell and (b) 4 s dwell

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Fig. 13

The reheating bands, as observed in a cross-section macrograph (left) and in the simulation results (right), for the one-bead leg of the 0 s dwell part

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Fig. 14

Cross sections of both legs of both parts. From top to bottom: one-bead leg 0 s dwell, three-bead leg 0 s dwell, one-bead leg 4 s dwell, and three-bead leg 4 s dwell.




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