0
Research Papers

A Mathematical Model-Based Optimization Method for Direct Metal Deposition of Multimaterials

[+] Author and Article Information
Jingyuan Yan

Mem. ASME
Mechanical Engineering,
Clemson University,
Clemson, SC 29630
e-mail: jingyuy@clemson.edu

Ilenia Battiato

Mechanical Engineering,
San Diego State University,
San Diego, CA 92182
e-mail: ibattiato@mail.sdsu.edu

Georges M. Fadel

Professor
Fellow ASME
Mechanical Engineering,
Clemson University,
Clemson, SC 29630
e-mail: fgeorge@clemson.edu

1Corresponding author.

Manuscript received September 8, 2016; final manuscript received April 3, 2017; published online May 10, 2017. Assoc. Editor: Zhijian J. Pei.

J. Manuf. Sci. Eng 139(8), 081011 (May 10, 2017) (10 pages) Paper No: MANU-16-1491; doi: 10.1115/1.4036424 History: Received September 08, 2016; Revised April 03, 2017

During the past few years, metal-based additive manufacturing technologies have evolved and may enable the direct fabrication of heterogeneous objects with full spatial material variations. A heterogeneous object has potentially many advantages, and in many cases can realize the appearance and/or functionality that homogeneous objects cannot achieve. In this work, we employ a preprocess computing combined with a multi-objective optimization algorithm based on the modeling of the direct metal deposition (DMD) of dissimilar materials to optimize the fabrication process. The optimization methodology is applied to the deposition of Inconel 718 and Ti–6Al–4V powders with prescribed powder feed rates. Eight design variables are accounted in the example, including the injection angles, injection velocities, and injection nozzle diameters for the two materials, as well as the laser power and scanning speed. The multi-objective optimization considers that the laser energy consumption and the powder waste during the fabrication process should be minimized. The optimization software modeFRONTIER® is used to drive the computation procedure with a matlab code. The results show the design and objective spaces of the Pareto optimal solutions and enable the users to select preferred setting configurations from the set of optimal solutions. A feasible design is selected which corresponds to a relatively low material cost, with laser power 370 W, scanning speed 55 mm/s, injection angles 15 deg, injection velocities 45 m/s for Inconel 718, 30 m/s for Ti–6Al–4V, and nozzle widths 0.5 mm under the given condition.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Hu, Y. , Fadel, G. M. , Blouin, V. Y. , and White, D. R. , 2006, “ Optimal Design for Additive Manufacturing of Heterogeneous Objects Using Ultrasonic Consolidation,” Virtual Phys. Prototyping, 1(1), pp. 53–62. [CrossRef]
Kou, X. Y. , and Tan, S. T. , 2007, “ Heterogeneous Object Modeling: A Review,” Comput. Aided Des., 39(4), pp. 284–301. [CrossRef]
Koizumi, M. , 1997, “ FGM Activities in Japan,” Compos. Part B, 28B(1–2), pp. 1–4. [CrossRef]
Punch, W. F. , Averill, R. C. , Goodman, E. D. , Lin, S. C. , and Ding, Y. , 1995, “ Using Genetic Algorithms to Design Laminated Composite Structures,” IEEE Expert, 10(1), pp. 42–49. [CrossRef]
Xing, A. , Zhao, J. , Huang, C. , and Zhang, J. , 1998, “ Development of an Advanced Ceramic Tool Material—Functionally Gradient Cutting Ceramics,” Mater. Sci. Eng., A248(1–2), pp. 125–131. [CrossRef]
Huang, J. , and Fadel, G. , 2000, “ Heterogeneous Flywheel Modeling and Optimization,” Mater. Des., 21(2), pp. 111–125. [CrossRef]
Huang, J. , and Fadel, G. M. , 2001, “ Bi-Objective Optimization Design of Heterogeneous Injection Mold Cooling Systems,” ASME J. Mech. Des., 123(2), pp. 226–239. [CrossRef]
Müller, E. , Drašar, Č. , Schilz, J. , and Kaysser, W. A. , 2003, “ Functionally Graded Materials for Sensor and Energy Applications,” Mater. Sci. Eng., A362(1–2), pp. 17–39. [CrossRef]
Watari, F. , Yokoyama, A. , Omori, M. , Hirai, T. , Kondo, H. , Uo, M. , and Kawasaki, T. , 2004, “ Biocompatibility of Materials and Development to Functionally Graded Implant for Bio-Medical Application,” Compos. Sci. Technol., 64(6), pp. 893–908. [CrossRef]
Charudilaka, S. , 2007, “ A Study of Two Commercial Systems for Polishing Aluminum Oxide, Zirconia and Feldspathic Dental Porcelain,” Master’s thesis, University of Connecticut, Storrs, CT.
Balla, V. K. , Bandyopadhyay, P. P. , Bose, S. , and Bandyopadhyay, A. , 2007, “ Compositionally Graded Yttria-Stabilized Zirconia Coating on Stainless Steel Using Laser Engineered Net Shaping (LENS),” Scr. Mater., 57(9), pp. 861–864. [CrossRef]
Krishna, B. V. , Bose, S. , and Bandyopadhyay, A. , 2008, “ Fabrication of Porous NiTi Shape Memory Alloy Structures Using Laser Engineered Net Shaping,” J. Biomed. Mater. Res. Part B: Appl. Biomater., 89B(2), pp. 481–490. [CrossRef]
Hofmann, D. C. , Roberts, S. , Otis, R. , Kolodziejska, J. , Dillon, R. P. , Suh, J. , Shapiro, A. A. , Liu, Z. , and Borgonia, J. , 2014, “ Developing Gradient Metal Alloys Through Radial Deposition Additive Manufacturing,” Nat. Sci. Rep., 4, p. 5357. [CrossRef]
Schwendner, K. I. , Banerjee, R. , Collins, P. C. , Brice, C. A. , and Fraser, H. L. , 2001, “ Direct Laser Deposition of Alloys From Elemental Powder Blends,” Scr. Mater., 45(10), pp. 1123–1129. [CrossRef]
Collins, P. C. , Banerjee, R. , and Fraser, H. L. , 2003, “ The Influence of the Enthalpy of Mixing During the Laser Deposition of Complex Titanium Alloys Using Elemental Blends,” Scr. Mater., 48(10), pp. 1445–1450. [CrossRef]
Domack, M. S. , and Baughman, J. M. , 2005, “ Development of Nickel-Titanium Graded Composition Components,” Rapid Prototyping J., 11(1), pp. 41–51. [CrossRef]
Zhong, M. , Liu, W. , Zhang, Y. , and Zhu, X. , 2006, “ Formation of WC/Ni Hard Alloy Coating by Laser Cladding of W/C/Ni Pure Element Powder Blend,” Int. J. Refract. Met. Hard Mater., 24(6), pp. 453–460. [CrossRef]
Yue, T. M. , and Li, T. , 2008, “ Laser Cladding of Ni/Cu/Al Functionally Graded Coating on Magnesium Substrate,” Surf. Coat. Technol., 202(23), pp. 3043–3049. [CrossRef]
Lewis, G. K. , and Schlienger, E. , 2000, “ Practical Considerations and Capabilities for Laser Assisted Direct Metal Deposition,” Mater. Des., 21(4), pp. 417–423. [CrossRef]
Liu, W. , and DuPont, J. N. , 2003, “ Fabrication of Functionally Graded TiC/Ti Composites by Laser Engineered Net Shaping,” Scr. Mater., 48(9), pp. 1337–1342. [CrossRef]
Pintsuk, G. , Brünings, S. E. , Döring, J.-E. , Linke, J. , Smid, I. , and Xue, L. , 2003, “ Development of W/Cu—Functionally Graded Materials,” Fusion Eng. Des., 66–68, pp. 237–240. [CrossRef]
Yakovlev, A. , Trunova, E. , Grevey, D. , Pilloz, M. , and Smurov, I. , 2005, “ Laser-Assisted Direct Manufacturing of Functionally Graded 3D Objects,” Surf. Coat. Technol., 190(1), pp. 15–24. [CrossRef]
Kieback, B. , Neubrand, A. , and Riedel, H. , 2003, “ Processing Techniques for Functionally Graded Materials,” Mater. Sci. Eng. A, 362(1–2), pp. 81–105. [CrossRef]
Han, L. , Liou, F. W. , and Phatak, K. M. , 2004, “ Modeling of Laser Cladding With Powder Injection,” Metall. Mater. Trans. B, 35(6), pp. 1139–1150. [CrossRef]
Wang, L. , Felicelli, S. D. , and Craig, J. E. , 2009, “ Experimental and Numerical Study of the LENS Rapid Fabrication Process,” ASME J. Manuf. Sci. Eng., 131(4), p. 041019 [CrossRef]
Kamara, A. M. , Wang, W. , Marimuthu, S. , and Li, L. , 2011, “ Modeling of the Melt Pool Geometry in the Laser Deposition of Nickel Alloys Using the Anisotropic Enhanced Thermal Conductivity Approach,” Proc. Inst. Mech. Eng., Part B, 225(1), pp. 87–99. [CrossRef]
Wen, S. Y. , Shin, Y. C. , Murthy, J. Y. , and Sojka, P. E. , 2009, “ Modeling of Coaxial Powder Flow for the Laser Direct Deposition Process,” Int. J. Heat Mass Transfer, 52(25–26), pp. 5867–5877. [CrossRef]
Wen, S. , and Shin, Y. , 2011, “ Modeling of the Off-Axis High Power Diode Laser Cladding Process,” ASME J. Heat Transfer, 133(3), p. 031007. [CrossRef]
Balu, P. , Leggett, P. , and Kovacevic, R. , 2012, “ Parametric Study on a Coaxial Multi-Material Powder Flow in Laser-Based Powder Deposition Process,” J. Mater. Process. Technol., 212(7), pp. 1598–1610. [CrossRef]
Grujicic, M. , Hu, Y. , Fadel, G. M. , and Keicher, D. M. , 2001, “ Optimization of the LENS Rapid Fabrication Process for In-Flight Melting of Feed Powder,” J. Mater. Synth. Process., 9(5), pp. 223–233. [CrossRef]
Liu, C. , and Liu, J. , 2003, “ Thermal Process of a Powder Particle in Coaxial Laser Cladding,” Opt. Laser Technol., 35(2), pp. 81–86. [CrossRef]
Yan, J. , Masoudi, N. , Battiato, I. , and Fadel, G. , 2015, “ Optimization of Process Parameters in Laser Engineered Net Shaping (LENS) Deposition of Multi-Materials,” ASME Paper No. DETC2015-47856.
Toyserkani, E. , Khajepour, A. , and Corbin, S. , 2004, “ 3-D Finite Element Modeling of Laser Cladding by Powder Injection: Effects of Laser Pulse Shaping on the Process,” Opt. Lasers Eng., 41(6), pp. 849–867. [CrossRef]
Saedodin, S. , Akbari, M. , Raisi, A. , and Torabi, M. , 2010, “ Calculation and Investigation of Temperature Distribution and Melt Pool Size Due to a Moving Laser Heat Source Using the Solution of Hyperbolic Heat Transfer Equation,” World Appl. Sci. J., 11(10), pp. 1273–1281.
Urbanic, R. J. , Saqib, S. M. , and Aggarwal, K. , 2016, “ Using Predictive Modeling and Classification Methods for Single and Overlapping Bead Laser Cladding to Understand Bead Geometry to Process Parameter Relationships,” ASME J. Manuf. Sci. Eng., 138(5), p. 051012. [CrossRef]
Mazumder, J. , Dutta, D. , Kikuchi, N. , and Ghosh, A. , 2000, “ Closed Loop Direct Metal Deposition: Art to Part,” Opt. Lasers Eng., 34(4–6), pp. 397–414. [CrossRef]
Toyserkani, E. , 2003, “ Modeling and Control of Laser Cladding by Powder Injection,” Ph.D. thesis, University of Waterloo, Waterloo, ON, Canada.
Salehi, D. , and Brandt, M. , 2006, “ Melt Pool Temperature Control Using LabVIEW in Nd:YAG Laser Blown Powder,” Int. J. Adv. Manuf. Technol., 29(3–4), pp. 273–278. [CrossRef]
Peyre, P. , Aubry, P. , Fabbro, R. , Neveu, R. , and Longuet, A. , 2008, “ Analytical and Numerical Modeling of the Direct Metal Deposition Laser Process,” J. Phys. D: Appl. Phys., 41(2), p. 025403. [CrossRef]
Tang, L. , and Landers, R. G. , 2011, “ Layer-to-Layer Height Control for Laser Metal Deposition Process,” ASME J. Manuf. Sci. Eng., 133(2), p. 021009. [CrossRef]
Cao, X. , and Ayalew, B. , 2015, “ Partial Differential Equation-Based Multivariable Control Input Optimization for Laser-Aided Powder Deposition Processes,” ASME J. Manuf. Sci. Eng., 138(3), p. 031001. [CrossRef]
Morville, S. , Carin, M. , Peyre, P. , Gharbi, M. , Carron, D. , Masson, P. L. , and Fabbro, R. , 2012, “ 2D Longitudinal Modeling of Heat Transfer and Fluid Flow During Multilayered Direct Laser Metal Deposition Process,” J. Laser Appl., 24(3), p. 032008. [CrossRef]
Chande, T. , and Mazumder, J. , 1985, “ Two-Dimensional, Transient Model for Mass Transport in Laser Surface Alloying,” J. Appl. Phys., 57(6), pp. 2226–2232. [CrossRef]
Qi, H. , and Mazumder, J. , 2006, “ Numerical Simulation of Heat Transfer and Fluid Flow in Coaxial Laser Cladding Process for Direct Metal Deposition,” J. Appl. Phys., 100(2), p. 024903. [CrossRef]
Vetter, P. A. , Fontaine, J. , Engel, T. , Lagrange, L. , and Marchione, T. , 1993, “ Characterization of Laser-Material Interaction During Laser Cladding Process,” Trans. Eng. Sci., 2, pp. 185–194.
Antipas, G. S. E. , 2015, “ Experimental and First Principles Assessment of Plasma Attenuation During Laser Treatment of an Al Alloy,” Trans. IMF, 93(1), pp. 53–56. [CrossRef]
Luo, Y. , Tang, X. , Lu, F. , Chen, Q. , and Cui, H. , 2015, “ Spatial Distribution Characteristics of Plasma Plume on Attenuation of Laser Radiation Under Subatmospheric Pressure,” Appl. Opt., 54(5), pp. 1090–1096. [CrossRef] [PubMed]
Ranz, W. E. , and Marshall, W. R. , 1952, “ Evaporation From Drops—Part I,” Chem. Eng. Prog., 48(3), pp. 141–146.
Ranz, W. E. , and Marshall, W. R. , 1952, “ Evaporation From Drops—Part II,” Chem. Eng. Prog., 48(4), pp. 173–180.
Gu, S. , McCartney, D. G. , Eastwick, C. N. , and Simmons, K. , 2004, “ Numerical Modeling of In-Flight Characteristic of Inconel 625 Particles During High-Velocity Oxy-Fuel Thermal Spraying,” J. Therm. Spray Technol., 13(2), pp. 200–213. [CrossRef]
Yan, J. , Battiato, I. , and Fadel, G. M. , 2014, “ Optimization of Multi-Materials In-Flight Melting in Laser Engineered Net Shaping (LENS) Process,” Symposium on Solid Freeform Fabrication (SFF), University of Texas at Austin, Austin, TX, Aug. 4–6, pp. 1158–1178.
Jouvard, J. M. , Grevey, D. F. , Lemoine, F. , and Vannes, A. B. , 1997, “ Continuous Wave Nd:YAG Laser Cladding Modeling: A Physical Study of Track Creation During Low Power Processing,” J. Laser Appl., 9(1), pp. 43–50. [CrossRef]
Lin, J. , 2000, “ Laser Attenuation of the Focused Powder Streams in Coaxial Laser Cladding,” J. Laser Appl., 12(1), pp. 28–33. [CrossRef]
Pinkerton, A. J. , 2007, “ An Analytical Model of Beam Attenuation and Powder Heating During Coaxial Laser Direct Metal Deposition,” J. Phys. D: Appl. Phys., 40(23), pp. 7323–7334. [CrossRef]
Zhou, J. , and Liu, H. , 2009, Laser Rapid Manufacturing Technology and Application, Chemical Industry Press, Beijing, China, Chap. 6.
Tabernero, I. , Lamikiz, A. , Martínez, S. , Ukar, E. , and Lacalle, L. N. , 2012, “ Modeling of Energy Attenuation Due to Powder Flow—Laser Beam Interaction During Laser Cladding Process,” J. Mater. Process. Technol., 212(2), pp. 516–522. [CrossRef]
Fu, Y. , Loredo, A. , Martin, B. , and Vannes, A. B. , 2002, “ A Theoretical Model for Laser and Powder Particles Interaction During Laser Cladding,” J. Mater. Process. Technol., 128(1–3), pp. 106–112. [CrossRef]
Huang, Y. , Liang, G. , Su, J. , and Li, J. , 2005, “ Interaction Between Laser Beam and Powder Stream in the Process of Laser Cladding With Powder Feeding,” Model. Simul. Mater. Sci. Eng., 13(1), pp. 47–56. [CrossRef]
Liu, J. , Li, L. , Zhang, Y. , and Xie, X. , 2005, “ Attenuation of Laser Power of a Focused Gaussian Beam During Interaction Between a Laser and Powder in Coaxial Laser Cladding,” J. Phys. D: Appl. Phys., 38(10), pp. 1546–1550. [CrossRef]
He, X. , and Mazumder, J. , 2007, “ Transport Phenomena During Direct Metal Deposition,” J. Appl. Phys., 101(5), p. 053113. [CrossRef]
Osman, T. , and Boucheffa, A. , 2009, “ Analytical Solution for the 3D Steady State Condition in a Solid Subjected to a Moving Rectangular Heat Source and Surface Cooling,” C. R. Méc., 337(2), pp. 107–111. [CrossRef]
Goldak, J. , Chakravarti, A. , and Bibby, M. , 1984, “ A New Finite Element Model for Welding Heat Sources,” Metall. Trans. B, 15B(2), pp. 299–305. [CrossRef]
Wang, H. , Zhang, Y. , and Chen, K. , 2016, “ Modeling of Temperature Distribution in Laser Welding of Lapped Martensitic Steel M1500 and Softening Estimation,” ASME J. Manuf. Sci. Eng., 138(11), p. 111006. [CrossRef]
Valsecchi, B. , Previtali, B. , and Gariboldi, E. , 2012, “ Fibre Laser Cladding of Turbine Blade Leading Edges: The Effect of Specific Energy on Clad Dilution,” Int. J. Struct. Integr., 3(4), pp. 377–395. [CrossRef]
Heigel, J. C. , Michaleris, P. , and Palmer, T. A. , 2015, “ In Situ Monitoring and Characterization of Distortion During Laser Cladding of Inconel 625,” J. Mater. Process. Technol., 220, pp. 135–145. [CrossRef]
Chen, H. , Pinkerton, A. J. , and Li, L. , 2011, “ Fibre Laser Welding of Dissimilar Alloys of Ti-6Al-4V and Inconel 718 for Aerospace Applications,” Int. J. Adv. Manuf. Technol., 52(9), pp. 977–987. [CrossRef]
Lahoz, R. , and Puértolas, J. A. , 2004, “ Training and Two-Way Shape Memory in NiTi Alloys: Influence on Thermal Parameters,” J. Alloys Compd., 381(1–2), pp. 130–136. [CrossRef]
Ross, R. B. , 1992, Metallic Materials Specification Handbook, Springer Science + Business Media, B. V., Dordrecht, The Netherland.
Boivineau, M. , Cagran, C. , Doytier, D. , Eyraud, V. , Nadal, M. H. , Wilthan, B. , and Pottlacher, G. , 2006, “ Thermophysical Properties of Solid and Liquid Ti–6Al–4V (TA6V) Alloy,” Int. J. Thermophys., 27(2), pp. 507–529. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The schematic of the modifiable coaxial DMD process

Grahic Jump Location
Fig. 2

The cross-sectional view of the working space

Grahic Jump Location
Fig. 3

Illustration of the intersection line between the laser beam and the powder jet

Grahic Jump Location
Fig. 4

Schematic for the substrate heating model

Grahic Jump Location
Fig. 5

Illustration of a particle’s longest traveling distance in laser beam

Grahic Jump Location
Fig. 6

Graphical optimization flow chart in modeFRONTIER®

Grahic Jump Location
Fig. 7

Scatter of the designed two objective functions

Grahic Jump Location
Fig. 8

Design histories of the eight design variables (pictures share the same legend as (a))

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In