Abstract

Multi-scale, multi-physics, computational models are a promising tool to provide detailed insights to understand the process–structure–property–performance relationships in additive manufacturing (AM) processes. To take advantage of the strengths of both physics-based and data-driven models, we propose a novel, hybrid modeling framework for laser powder bed fusion (L-PBF) process. Our unbiased model-integration method combines physics-based, simulation data, and measurement data for approaching a more accurate prediction of melt-pool width. Both a high-fidelity computational fluid dynamics (CFD) model and experiments utilizing optical images are used to generate a combined dataset of melt-pool widths. From this aggregated data set, a hybrid model is developed using data-driven modeling techniques, including polynomial regression and Kriging methods. The performance of the hybrid model is evaluated by computing the average relative error and comparing it with the results of the simulations and surrogate models constructed from the original CFD model and experimental measurements. It is found that the proposed hybrid model performs better in terms of prediction accuracy and computational time. Future work includes a conceptual introduction to the use of an AM ontology to support improved model and data selection when constructing hybrid models. This study can be viewed as a significant step toward the use of hybrid models as predictive models with improved accuracy and without the sacrifice of speed.

References

1.
Bourell
,
D. L.
,
Beaman
,
J. J.
,
Marcus
,
H. L.
, and
Barlow
,
J. W.
,
1990
, “
Solid Freeform Fabrication: An Advanced Manufacturing Approach
,”
International Solid Freeform Fabrication Symposium
,
Austin, TX
, pp.
1
7
.
2.
Petrovic
,
V.
,
Vicente Haro Gonzalez
,
J.
,
Jordá Ferrando
,
O.
,
Delgado Gordillo
,
J.
,
Ramón Blasco Puchades
,
J.
, and
Portolés Griñan
,
L.
,
2011
, “
Additive Layered Manufacturing: Sectors of Industrial Application Shown Through Case Studies
,”
Int. J. Prod. Res.
,
49
(
4
), pp.
1061
1079
.
3.
Yan
,
C.
,
Hao
,
L.
,
Hussein
,
A.
, and
Raymont
,
D.
,
2012
, “
Evaluations of Cellular Lattice Structures Manufactured Using Selective Laser Melting
,”
Int. J. Mach. Tools Manuf.
,
62
, pp.
32
38
.
4.
Guo
,
N.
, and
Leu
,
M. C.
,
2013
, “
Additive Manufacturing: Technology, Applications and Research Needs
,”
Front. Mech. Eng.
,
8
(
3
), pp.
215
243
.
5.
Herderick
,
E.
,
2011
, “
Additive Manufacturing of Metals: A Review
,”
Materials Science and Technology Conference Exhibition. 2011, MS T’11
,
Columbus, OH
,
Oct. 16–20
.
6.
Hofmann
,
D. C.
,
Roberts
,
S.
,
Otis
,
R.
,
Kolodziejska
,
J.
,
Dillon
,
R. P.
,
Suh
,
J. O.
,
Shapiro
,
A. A.
,
Liu
,
Z. K.
, and
Borgonia
,
J. P.
,
2014
, “
Developing Gradient Metal Alloys Through Radial Deposition Additive Manufacturing
,”
Sci. Rep.
,
4
, pp.
1
8
.
7.
Gu
,
D.
,
2015
, “Laser Additive Manufacturing (AM): Classification, Processing Philosophy, and Metallurgical Mechanisms,”
Laser Additive Manufacturing of High-Performance Materials
,
Springer, Berlin, Heidelberg
.
8.
Bourell
,
D. L.
,
Leu
,
M. C.
, and
Rosen
,
D. W.
,
2009
, “
Roadmap for Additive Manufacturing: Identifying the Future of Freeform Processing
,”
Rapid Prototyp. J.
,
5
(
4
), pp.
169
178
.
9.
Read
,
N.
,
Wang
,
W.
,
Essa
,
K.
, and
Attallah
,
M. M.
,
2015
, “
Selective Laser Melting of AlSi10Mg Alloy: Process Optimisation and Mechanical Properties Development
,”
Mater. Des.
,
65
, pp.
417
424
.
10.
Criales
,
L. E.
,
Arısoy
,
Y. M.
, and
Özel
,
T.
,
2016
, “
Sensitivity Analysis of Material and Process Parameters in Finite Element Modeling of Selective Laser Melting of Inconel 625
,”
Int. J. Adv. Manuf. Technol.
,
86
(
9–12
), pp.
2653
2666
.
11.
Criales
,
L. E.
,
Arısoy
,
Y. M.
,
Lane
,
B.
,
Moylan
,
S.
,
Donmez
,
A.
, and
Özel
,
T.
,
2017
, “
Laser Powder Bed Fusion of Nickel Alloy 625: Experimental Investigations of Effects of Process Parameters on Melt Pool Size and Shape With Spatter Analysis
,”
Int. J. Mach. Tools Manuf.
,
121
, pp.
22
36
.
12.
Schoinochoritis
,
B.
,
Chantzis
,
D.
, and
Salonitis
,
K.
,
2014
, “
Simulation of Metallic Powder Bed Additive Manufacturing Processes With the Finite Element Method: A Critical Review
,”
Proc. Inst. Mech. Eng. Part B: J. Eng. Manuf.
,
231
(
1
), pp.
96
117
.
13.
King
,
W. E.
,
Anderson
,
A. T.
,
Ferencz
,
R. M.
,
Hodge
,
N. E.
,
Kamath
,
C.
,
Khairallah
,
S. A.
, and
Rubenchik
,
A. M.
,
2015
, “
Laser Powder Bed Fusion Additive Manufacturing of Metals; Physics, Computational, and Materials Challenges
,”
Appl. Phys. Rev.
,
2
(
4
), p.
041304
.
14.
Moges
,
T.
,
Ameta
,
G.
, and
Witherell
,
P.
,
2019
, “
A Review of Model Inaccuracy and Parameter Uncertainty in Laser Powder Bed Fusion Models and Simulations
,” ASME
J. Manuf. Sci. Eng.
,
141
(
4
), p.
040801
.
15.
Moges
,
T.
,
Yan
,
W.
,
Lin
,
S.
,
Ameta
,
G.
,
Fox
,
J.
, and
Witherell
,
P.
,
2018
, “
Quantifying Uncertainty in Laser Powder Bed Fusion Additive Manufacturing Models and Simulations
,”
Solid Freeform Fabrication Symposium
,
Austin, TX
, pp.
1913
1928
.
16.
DebRoy
,
T.
,
Wei
,
H. L.
,
Zuback
,
J. S.
,
Mukherjee
,
T.
,
Elmer
,
J. W.
,
Milewski
,
J. O.
,
Beese
,
A. M.
,
Wilson-Heid
,
A.
,
De
,
A.
, and
Zhang
,
W.
,
2018
, “
Additive Manufacturing of Metallic Components—Process, Structure and Properties
,”
Prog. Mater. Sci.
,
92
, pp.
112
224
.
17.
Hu
,
Z.
, and
Mahadevan
,
S.
,
2017
, “
Uncertainty Quantification in Prediction of Material Properties During Additive Manufacturing
,”
Scr. Mater.
,
135
, pp.
135
140
.
18.
Wu
,
Q.
,
Lu
,
J.
,
Liu
,
C.
,
Fan
,
H.
,
Shi
,
X.
,
Fu
,
J.
, and
Ma
,
S.
,
2017
, “
Effect of Molten Pool Size on Microstructure and Tensile Properties of Wire Arc Additive Manufacturing of Ti-6Al-4V Alloy
,”
Materials (Basel)
,
10
(
7
), pp.
1
11
.
19.
Moges
,
T.
,
Yang
,
Z.
,
Jones
,
K.
,
Feng
,
S.
,
Witherell
,
P.
, and
Lu
,
Y.
,
2020
, “
Hybrid Modeling Approach for Melt Pool Prediction in Laser Powder Bed Fusion Additive Manufacturing
,”
Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE 2020
,
St. Louis, MO
,
Aug. 17–19
, pp.
1
14
.
20.
Shao
,
T.
, and
Krishnamurty
,
S.
,
2008
, “
A Clustering-Based Surrogate Model Updating Approach to Simulation-Based Engineering Design
,”
ASME J. Mech. Des.
,
130
(
4
), p.
041101
.
21.
Malekipour
,
E.
, and
El-Mounayri
,
H.
,
2018
, “
Common Defects and Contributing Parameters in Powder Bed Fusion AM Process and Their Classification for Online Monitoring and Control: A Review
,”
Int. J. Adv. Manuf. Technol.
,
95
(
1–4
), pp.
527
550
.
22.
Marrey
,
M.
,
Malekipour
,
E.
,
El-Mounayri
,
H.
, and
Faierson
,
E. J.
,
2019
, “
A Framework for Optimizing Process Parameters in Powder Bed Fusion (PBF) Process Using Artificial Neural Network (ANN)
,”
Procedia Manuf.
,
34
, pp.
505
515
.
23.
Hu
,
Z.
, and
Mahadevan
,
S.
,
2017
, “
Uncertainty Quantification and Management in Additive Manufacturing: Current Status, Needs, and Opportunities
,”
Int. J. Adv. Manuf. Technol.
,
93
(
5–8
), pp.
2855
2874
.
24.
Smith
,
J.
,
Xiong
,
W.
,
Yan
,
W.
,
Lin
,
S.
,
Cheng
,
P.
,
Kafka
,
O. L.
,
Wagner
,
G. J.
,
Cao
,
J.
, and
Liu
,
W. K.
,
2016
, “
Linking Process, Structure, Property, and Performance for Metal-Based Additive Manufacturing: Computational Approaches With Experimental Support
,”
Comput. Mech.
,
57
(
4
), pp.
583
610
.
25.
Devesse
,
W.
,
De Baere
,
D.
, and
Guillaume
,
P.
,
2014
, “
The Isotherm Migration Method in Spherical Coordinates With a Moving Heat Source
,”
Int. J. Heat Mass Transfer
,
75
, pp.
726
735
.
26.
Lopez
,
F.
,
Witherell
,
P.
, and
Lane
,
B.
,
2016
, “
Identifying Uncertainty in Laser Powder Bed Fusion Additive Manufacturing Models
,”
ASME J. Mech. Des
,
138
(
11
), p.
114502
.
27.
Lin
,
S.
,
Smith
,
J.
,
Liu
,
W. K.
, and
Wagner
,
G. J.
,
2017
, “
An Energetically Consistent Concurrent Multiscale Method for Heterogeneous Heat Transfer and Phase Transition Applications
,”
Comput. Meth. Appl. Mech. Eng.
,
315
, pp.
100
120
.
28.
Wolff
,
S. J.
,
Lin
,
S.
,
Faierson
,
E. J.
,
Liu
,
W. K.
,
Wagner
,
G. J.
, and
Cao
,
J.
,
2017
, “
A Framework to Link Localized Cooling and Properties of Directed Energy Deposition (DED)-Processed Ti-6Al-4 V
,”
Acta Mater.
,
132
, pp.
106
117
.
29.
Romano
,
J.
,
Ladani
,
L.
, and
Sadowski
,
M.
,
2015
, “
Thermal Modeling of Laser Based Additive Manufacturing Processes Within Common Materials
,”
Procedia Manuf.
,
1
, pp.
238
250
.
30.
Li
,
Y.
, and
Gu
,
D.
,
2014
, “
Parametric Analysis of Thermal Behavior During Selective Laser Melting Additive Manufacturing of Aluminum Alloy Powder
,”
Mater. Des.
,
63
, pp.
856
867
.
31.
Manvatkar
,
V.
,
De
,
A.
, and
Debroy
,
T.
,
2014
, “
Heat Transfer and Material Flow During Laser Assisted Multi-Layer Additive Manufacturing
,”
J. Appl. Phys.
,
116
(
12
), pp.
1
8
.
32.
Gan
,
Z.
,
Lian
,
Y.
,
Lin
,
S. E.
,
Jones
,
K. K.
,
Liu
,
W. K.
, and
Wagner
,
G. J.
,
2019
, “
Benchmark Study of Thermal Behavior, Surface Topography, and Dendritic Microstructure in Selective Laser Melting of Inconel 625
,”
Integr. Mater. Manuf. Innov.
,
8
(
2
), pp.
178
193
.
33.
Gan
,
Z.
,
Liu
,
H.
,
Li
,
S.
,
He
,
X.
, and
Yu
,
G.
,
2017
, “
Modeling of Thermal Behavior and Mass Transport in Multi-Layer Laser Additive Manufacturing of Ni-Based Alloy on Cast Iron
,”
Int. J. Heat Mass Transfer
,
111
, pp.
709
722
.
34.
Mukherjee
,
T.
,
Wei
,
H. L.
,
De
,
A.
, and
DebRoy
,
T.
,
2018
, “
Heat and Fluid Flow in Additive Manufacturing—Part I: Modeling of Powder Bed Fusion
,”
Comput. Mater. Sci.
,
150
, pp.
304
313
.
35.
Mukherjee
,
T.
, and
DebRoy
,
T.
,
2018
, “
Mitigation of Lack of Fusion Defects in Powder Bed Fusion Additive Manufacturing
,”
J. Manuf. Processes
,
36
, pp.
442
449
.
36.
Khairallah
,
S. A.
,
Anderson
,
A. T.
,
Rubenchik
,
A.
, and
King
,
W. E.
,
2016
, “
Laser Powder-Bed Fusion Additive Manufacturing: Physics of Complex Melt Flow and Formation Mechanisms of Pores, Spatter, and Denudation Zones
,”
Acta Mater.
,
108
, pp.
36
45
.
37.
Lee
,
Y.
, and
Farson
,
D. F.
,
2016
, “
Simulation of Transport Phenomena and Melt Pool Shape for Multiple Layer Additive Manufacturing
,”
J. Laser Appl.
,
28
(
1
), p.
012006
.
38.
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
.
39.
Ghosh
,
S.
,
Ma
,
L.
,
Levine
,
L. E.
,
Ricker
,
R. E.
,
Stoudt
,
M. R.
,
Heigel
,
J. C.
, and
Guyer
,
J. E.
,
2018
, “
Single-Track Melt-Pool Measurements and Microstructures in Inconel 625
,”
JOM
,
70
(
6
), pp.
1011
1016
.
40.
Tapia
,
G.
,
Khairallah
,
S.
,
Matthews
,
M.
,
King
,
W. E.
, and
Elwany
,
A.
,
2018
, “
Gaussian Process-Based Surrogate Modeling Framework for Process Planning in Laser Powder-Bed Fusion Additive Manufacturing of 316L Stainless Steel
,”
Int. J. Adv. Manuf. Technol.
,
94
(
9–12
), pp.
3591
3603
.
41.
Yang
,
Z.
,
Yan
,
L.
,
Yeung
,
H.
, and
Krishnamurty
,
S.
,
2019
, “
From Scan Strategy to Melt Pool Prediction: A Neighboring-Effect Modeling Method
,”
Proceedings of the ASME Design Engineering Technical Conference
,
Anaheim, CA
,
Aug. 18–21
, pp.
1
11
.
42.
Wang
,
Z.
,
Liu
,
P.
,
Ji
,
Y.
,
Mahadevan
,
S.
,
Horstemeyer
,
M. F.
,
Hu
,
Z.
,
Chen
,
L.
, and
Chen
,
L.-Q.
,
2019
, “
Uncertainty Quantification in Metallic Additive Manufacturing Through Physics-Informed Data-Driven Modeling
,”
JOM
,
71
(
8
), pp.
2625
2634
.
43.
Razvi
,
S. S.
,
Feng
,
S.
,
Narayanan
,
A.
,
Lee
,
Y.-T. T.
, and
Witherell
,
P.
,
2019
, “
A Review of Machine Learning Applications in Additive Manufacturing
,”
Proceedings of 39th Computers and Information in Engineering Conference
,
Anaheim, CA
,
Aug. 18–21
, American Society of Mechanical Engineers, New York.
44.
Fathi
,
A.
, and
Mozaffari
,
A.
,
2014
, “
Vector Optimization of Laser Solid Freeform Fabrication System Using a Hierarchical Mutable Smart Bee-Fuzzy Inference System and Hybrid NSGA-II/Self-Organizing Map
,”
J. Intell. Manuf.
,
25
(
4
), pp.
775
795
.
45.
Lu
,
Z. L.
,
Li
,
D. C.
,
Lu
,
B. H.
,
Zhang
,
A. F.
,
Zhu
,
G. X.
, and
Pi
,
G.
,
2010
, “
The Prediction of the Building Precision in the Laser Engineered Net Shaping Process Using Advanced Networks
,”
Opt. Lasers Eng.
,
48
(
5
), pp.
519
525
.
46.
Yang
,
Z.
,
Eddy
,
D.
,
Krishnamurty
,
S.
,
Grosse
,
I.
,
Denno
,
P.
,
Witherell
,
P. W.
, and
Lopez
,
F.
,
2018
, “
Dynamic Metamodeling for Predictive Analytics in Advanced Manufacturing
,”
Smart Sustainable Manuf. Syst.
,
2
(
1
), p.
20170013
.
47.
Kamath
,
C.
,
2016
, “
Data Mining and Statistical Inference in Selective Laser Melting
,”
Int. J. Adv. Manuf. Technol.
,
86
(
5–8
), pp.
1659
1677
.
48.
Tran
,
H. C.
, and
Lo
,
Y.
,
2019
, “
Systematic Approach for Optimal Determining Optimal Processing Parameters to Produce Part With High Density in Selective Laser Melting Process
,”
Int. J. Adv. Manuf. Technol.
,
105
, pp.
4443
4460
.
49.
Yang
,
Z.
,
Lu
,
Y.
,
Yeung
,
H.
, and
Krishnamurty
,
S.
,
2020
, “
From Scan Strategy to Melt Pool Prediction: A Neighboring-Effect Modeling Method
,”
J. Comput. Inf. Sci. Eng.
,
20
(
5
).
50.
Akhil
,
V.
,
Raghav
,
G.
,
Arunachalam
,
N.
, and
Srinivas
,
D. S.
,
2020
, “
Image Data-Based Surface Texture Characterization and Prediction Using Machine Learning Approaches for Additive Manufacturing
,”
J. Comput. Inf. Sci. Eng.
,
20
(
2
), pp.
1
16
.
51.
Abrahart
,
R. J.
,
See
,
L. M.
, and
Solomatine
,
D.
,
2008
,
Practical Hydroinformatics
,
Water Science and Technology Library 68 Springer-Verlag Berlin/Heidelberg
.
52.
Reinhart
,
R. F.
,
Shareef
,
Z.
, and
Steil
,
J. J.
,
2017
, “
Hybrid Analytical and Data-Driven Modeling for Feed-Forward Robot Control
,”
Sensors (Switzerland)
,
17
(
2
), pp.
1
19
.
53.
Moges
,
T.
,
Witherell
,
P.
, and
Ameta
,
G.
,
2019
, “
On Characterizing Uncertainty Sources in Laser Powder Bed Fusion Additive Manufacturing Models
,”
Proceedings of the ASME 2019 International Mechanical Engineering Congress and Exposition IMECE2019
,
Salt Lake City, UT
,
Nov. 11–14
, pp.
1
15
.
54.
Witherell
,
P.
,
Feng
,
S. C.
,
Martukanitz
,
R.
,
Simpson
,
T. W.
,
John
,
D. B. S.
,
Michaleris
,
P.
,
Liu
,
Z. K.
, and
Chen
,
L. Q.
,
2014
, “
Toward Metamodels for Composable and Reusable Additive Manufacturing Process Models
,”
Proceedings of the ASME Design Engineering Technical Conference
,
Buffalo, NY
,
Aug. 17–20
, pp.
1
10
.
55.
Assouroko
,
I.
,
Lopez
,
F.
, and
Witherell
,
P.
,
2016
, “
A Method for Characterizing Model Fidelity in Laser Powder Bed Fusion Additive Manufacturing
,”
Proceedings of the ASME 2016 International Mechanical Engineering Congress & Exposition ASME IMECE 2016
,
Phoenix, AZ
,
Nov. 11–17
, pp.
1
13
.
56.
Capriccioli
,
A.
, and
Frosi
,
P.
,
2009
, “
Multipurpose ANSYS FE Procedure for Welding Processes Simulation
,”
Fusion Eng. Des.
,
84
(
2–6
), pp.
546
553
.
57.
Pawel
,
R. E.
, and
Williams
,
R. K.
,
1985
, “
Survey of Physical Property Data for Several Alloys
,”
Oak Ridge National Laboratory
,
(ORNL/TM-9616)
,
Oak Ridge, TN
.
58.
Corporation, S. M.
,
2013
, “
Inconel Alloy 625
,” www.specialmetals.com,
625
(
2
), pp.
1
28
.
59.
Simpson
,
T. W.
,
Mauery
,
T. M.
,
Korte
,
J. J.
, and
Mistree
,
F.
,
1998
, “
Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization
,”
Proceedings of 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
,
St. Louis, MO
,
Sept. 2–4
, p.
4755
.
60.
Cressie
,
N.
,
2015
,
Statistics for Spatial Data
,
John Wiley & Sons, Inc.
,
New York
.
61.
Simpson
,
T. W.
,
Booker
,
A. J.
,
Ghosh
,
D.
,
Giunta
,
A. A.
,
Koch
,
P. N.
, and
Yang
,
R.
,
2004
, “
Approximation Methods in Multidisciplinary Analysis and Optimization: A Panel Discussion
,”
Struct. Multidiscipl. Optim.
,
27
(
5
), pp.
302
313
.
62.
Sacks
,
J.
,
Welch
,
W.
,
Mitchell
,
T.
, and
Wynn
,
H.
,
1989
, “
Design and Analysis of Computer Experiments
,”
Stat. Sci.
,
4
(
4
), pp.
409
423
.
63.
Yang
,
Z.
,
Eddy
,
D.
,
Krishnamurty
,
S.
,
Grosse
,
I.
,
Denno
,
P.
, and
Lopez
,
F.
,
2016
, “
Investigating Predictive Metamodeling for Additive Manufacturing
,”
Proceedings of the ASME 2016 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
,
Charlotte, NC
,
Aug. 21–24
, Vol.
1A-2016
, pp.
1
10
.
64.
Fox
,
J. C.
,
Lane
,
B. M.
, and
Yeung
,
H.
,
2017
, “
Measurement of Process Dynamics Through Coaxially Aligned High Speed Near-Infrared Imaging in Laser Powder Bed Fusion Additive Manufacturing
,”
Proceedings of the SPIE 10214, Thermosense Thermal Infrared Applications XXXIX
, 1(301), p.
1021407
.
65.
Yang
,
Z.
,
Eddy
,
D.
,
Krishnamurty
,
S.
,
Grosse
,
I.
,
Denno
,
P.
,
Lu
,
Y.
, and
Witherell
,
P.
,
2017
, “
Investigating Grey-Box Modeling for Predictive Analytics in Smart Manufacturing
,”
Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Cleveland, OH
,
Aug. 6–9
, Vol.
2B
, pp.
1
10
.
66.
Yeung
,
H.
,
Yang
,
Z.
, and
Yan
,
L.
,
2020
, “
A Meltpool Prediction Based Scan Strategy for Powder Bed Fusion Additive Manufacturing
,”
Addit. Manuf.
,
35
, p.
101383
.
67.
Kim
,
S.
,
Rosen
,
D. W.
,
Witherell
,
P.
, and
Ko
,
H.
,
2019
, “
A Design for Additive Manufacturing Ontology to Support Manufacturability Analysis
,”
J. Comput. Inf. Sci. Eng.
,
19
, p.
041014
.
68.
Roh
,
B.
,
Kumara
,
S. R. T.
,
Simpson
,
T. W.
, and
Witherell
,
P.
,
2016
, “
Ontology-Based Laser and Thermal Metamodels for Metal-Based Additive Manufacturing
,”
Proceedings of the ASME 2016 International Design Engineering Technical Conference and Computers and Information in Engineering Conference IDETC/CIE 2016
,
Charlotte, NC
,
Aug. 21–24
, pp.
1
8
.
69.
Witherell
,
P.
,
Feng
,
S.
,
Simpson
,
T. W.
,
Saint John
,
D. B.
,
Michaleris
,
P.
,
Liu
,
Z.-K.
,
Chen
,
L.-Q.
, and
Martukanitz
,
R.
,
2014
, “
Toward Metamodels for Composable and Reusable Additive Manufacturing Process Models
,”
ASME J. Manuf. Sci. Eng.
,
136
(
6
), p.
061025
.
70.
Zhang
,
Y.
,
Shapiro
,
V.
, and
Witherell
,
P.
,
2019
, “
Towards Thermal Simulation of Powder Bed Fusion on Path Level
,”
Proceedings of the ASME 2019 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2019
,
Anaheim, CA
,
Aug. 18–21
.
You do not currently have access to this content.