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Research Papers

An Analytical Computation of Temperature Field Evolved in Directed Energy Deposition

[+] Author and Article Information
Jianyi Li

Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: jxl1080@psu.edu

Qian Wang

Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: quw6@psu.edu

Panagiotis (Pan) Michaleris

Autodesk, Inc.,
200 Innovation Boulevard,
State College, PA 16803
e-mail: pan.michaleris@autodesk.com

1Corresponding author.

Manuscript received November 16, 2017; final manuscript received June 14, 2018; published online July 9, 2018. Assoc. Editor: Zhijian J. Pei.

J. Manuf. Sci. Eng 140(10), 101004 (Jul 09, 2018) (13 pages) Paper No: MANU-17-1714; doi: 10.1115/1.4040621 History: Received November 16, 2017; Revised June 14, 2018

This paper presents an analytical computation of temperature field evolved in a directed energy deposition process, using single-bead walls as illustrating examples. Essentially, the temperature field evolution during the deposition of a wall is computed by super-position of the temperature field generated by the laser source depositing the current bead and that induced from each of the past beads (layers). First, the transient solution to a point heat source in a semi-infinite body is applied to describe each individual temperature field. Then, to better describe temperature contribution from a past bead, a pair of virtual heat sources with positive and negative powers is assigned for each past bead to compute the temperature field under cooling. In addition, mirrored heat sources through a reflexion technique are introduced to define adiabatic boundaries of the part and to account for substrate thickness. In the end, three depositions of Ti-6AL-4V walls with different geometries and interlayer dwell times on an Optomec® laser engineering net shaping (LENS) system are used to validate the proposed analytical computation, where predicted temperatures at several locations of the substrate show reasonable agreement with the in situ temperature measurements with prediction error rate ranging from 12% to 27%. Furthermore, temperature distributions predicted by the proposed model are compared to finite element simulations. The proposed analytical computation for temperature field could be potentially used in model-based feedback control for thermal history in the deposition, which could affect microstructure evolution and other properties of the final part.

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References

Kelly, S. , and Kampe, S. , 2004, “ Microstructural Evolution in Laser-Deposited Multilayer Ti-6AL-4V Builds—Part I: Microstructural Characterization,” Met. 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,” Met. Mater. Trans. A, 35(6), pp. 1869–1879. [CrossRef]
Irwin, J. , Reutzel, E. W. , Michaleris, P. , Keist, J. , and Nassar, A. R. , 2016, “ Predicting Microstructure From Thermal History During Additive Manufacturing for Ti-6AL-4V,” ASME J. Manuf. Sci. Eng., 138(11), p. 111007. [CrossRef]
Hodge, N. E. , Ferencz, R. M. , and Solberg, J. M. , 2014, “ Implementation of a Thermomechanical Model for the Simulation of Selective Laser Melting,” Comput. Mech., 54(1), pp. 33–51. [CrossRef]
Yang, Y.-P. , and Babu, S. S. , 2010, “ An Integrated Model to Simulate Laser Cladding Manufacturing Process for Engine Repair Applications,” Weld. World, 54(9–10), pp. R298–R307. [CrossRef]
Marimuthu, S. , Clark, D. , Allen, J. , Kamara, A. M. , Mativenga, P. , Li, L. , and Scudamore, R. , 2013, “ Finite Element Modeling of Substrate Thermal Distortion in Direct Laser Additive Manufacture of an Aero-Engine Component,” Proc. Inst. Mech. Eng., Part C, 227(9), pp. 1987–1999. [CrossRef]
Michaleris, P. , 2014, “ Modeling Metal Deposition in Heat Transfer Analysis of Additive Manufacturing Processes,” Finite Elem. Anal. Des., 86(1), pp. 51–60. [CrossRef]
Heigel, J. C. , Michaleris, P. , and Reutzel, E. W. , 2015, “ Thermo-Mechanical Model Development and Validation of Directed Energy Deposition Additive Manufacturing of Ti–6Al–4V,” Addit. Manuf., 5, pp. 9–19. [CrossRef]
Gouge, M. , and Michaleris, P. , 2017, Thermal-Mechanical Modeling of Additive Manufacturing, Science & Technology, Elsevier, Amsterdam, The Netherlands.
Peng, H. , Go, D. B. , Gong, S. , Shankar, M. R. , Gatrell, B. A. , Budzinski, J. , Ostiguy, P. , Attardo, R. , Tomonto, C. , Neidig, J. , and Hoelzle, D. , 2016, “ Part-Scale Model for Fast Prediction of Thermal Distortion in DMLS Additive Manufacturing—Part 1: A Thermal Circuit Network Model,” Solid Freeform Fabrication Symposium, Austin, Texas, Aug. 8–10, pp. 297–382.
Li, J. , Wang, Q. , Michaleris, P. (Pan) , Reutzel, E. W. , and Nassar, A. R. , 2017, “ An Extended Lumped-Parameter Model of Melt–Pool Geometry to Predict Part Height for Directed Energy Deposition,” ASME J. Manuf. Sci. Eng., 139(9), p. 091016. [CrossRef]
Rykalin, N. N. , 1960, Calculation of Heat Processes in Welding, Moscow, Russia.
Perret, W. , Schwenk, C. , and Rethmeier, M. , 2010, “ Comparison of Analytical and Numerical Welding Temperature Field Calculation,” Comput. Mater. Sci., 47(4), pp. 1005–1015. [CrossRef]
Rosenthal, D. , 1946, “ The Theory of Moving Sources of Heat and Its Application to Metal Treatments,” Trans. ASME, 68(8), pp. 849–866.
Li, J. , Wang, Q. , and Michaleris, P. , 2018, “ Towards Computational Modeling of Temperature Field Evolution in Directed Energy Deposition Processes,” ASME Paper No. DSCC2018-8973.
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Figures

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Fig. 1

Coordinate systems used in Rosenthal's solution

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Fig. 2

Illustration of computation of temperature field for a single-bead wall

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Fig. 3

Illustration of using a pair of heat sources with positive and negative power values to simulate the cooling effect after the real heat source is off or moved to another location

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Fig. 4

Illustration of achieving adiabatic boundary condition on a plane using the reflexion technique, which assumes a mirrored heat source (represented by a dashed circle) running in parallel with the original heat source (represented by a solid circle)

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Fig. 5

Illustration of defining mirrored heat sources (“bt,” “fr,” and “bk”) to render the substrate's bottom surface (the part under the wall) and the front- and back-sides of the wall to be adiabatic. Side view of the wall is shown in the figure.

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Fig. 6

Single-bead walls (figure from Ref. [8]): (a) wall 1: 62 layers with no interlayer dwell time, (b) wall 2: another 62 layers built on top of wall 1 with no interlayer dwell time, (c) wall 3: 62 layers with 20 s interlayer dwell time

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Fig. 12

Initial temperatures along the wall distance predicted by model 1, model 4, and FEA. For FEA, temperature of the point with s=6r=9 mm is picked as the initial temperature at the deposition point. (a) Example even layers and (b) example odd layers.

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Fig. 11

Initial temperatures along the wall distance predicted by model 1, model 4, and FEA. For FEA, temperature of the point with s=2r=3 mm is picked as the initial temperature at the deposition point. (a) Example even layers and (b) example odd layers.

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Fig. 10

Schematic plot of the build part to show the locations of measurements by the thermocouples [8]: (a) bottom of the substrate and (b) isometric view of the part

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Fig. 9

Initial temperatures along the wall distance: comparison among model 1, model 4, and FEA. For FEA, temperature at the point with distance s=4r=6 mm ahead of the laser is picked to represent the initial temperature at the deposition point. (a) Example even layers and (b) example odd layers. Laser scans from left to right on odd layers and right to left on even layers.

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Fig. 8

A snapshot of the FEA simulation to illustrate how the temperature value is picked to be compared to the proposed models. (a) Temperature contour and (b) temperature along line A. The temperature value of the circle point with a distance of s=4r=6 mm ahead of the laser along line A is picked to represent the initial temperature at the deposition point due to past beads.

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Fig. 7

Predicted temperature histories by model 1–4 versus in situ temperature measurements: (a) TC1 of wall 1, (b) TC1 and TC3 of wall 2, and (c) TC2 of wall 3

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