A novel multiscale thermal analysis framework has been formulated to extract the physical interactions involved in localized spatiotemporal additive manufacturing processes such as the metal laser sintering. The method can be extrapolated to any other physical phenomenon involving localized spatiotemporal boundary conditions. The formulated framework, named feed forward dynamic adaptive mesh refinement and derefinement (FFD-AMRD), reduces the computational burden and temporal complexity needed to solve the many classes of problems. The current study is based on application of this framework to metals with temperature independent thermal properties processed using a moving laser heat source. The melt pool diameters computed in the present study were compared with melt pool dimensions measured using optical micrographs. The strategy developed in this study provides motivation for the extension of this simulation framework for future work on simulations of metals with temperature-dependent material properties during metal laser sintering.

Issue Section:
Research Papers
Topics:
Algorithms, Boundary-value problems, Errors, Finite element methods, Finite element model, Lasers, Metals, Sintering, Temperature, Finite element analysis, Simulation, Spatiotemporal phenomena, Materials properties, Stiffness, Manufacturing

References

1.
Berger
,
M. J.
, and
Oliger
,
J.
,
1984
, “
Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations
,”
J. Comput. Phys.
,
53
(
3
), pp.
484
–
512
.10.1016/0021-9991(84)90073-1
2.
Berger
,
M. J.
, and
Colella
,
P.
,
1989
, “
Local Adaptive Mesh Refinement for Shock Hydrodynamics
,”
J. Comput. Phys.
,
82
(
1
), pp.
64
–
84
.10.1016/0021-9991(89)90035-1
3.
Carey
,
G.
,
2006
, “
A Perspective on Adaptive Modeling and Meshing (AM&M)
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
4
), pp.
214
–
235
.10.1016/j.cma.2004.11.027
4.
Grätsch
,
T.
, and
Bathe
,
K. J.
,
2005
, “
A Posteriori Error Estimation Techniques in Practical Finite Element Analysis
,”
Comput. Struct.
,
83
(
4
), pp.
235
–
265
.10.1016/j.compstruc.2004.08.011
5.
Lax
,
P.
, and
Milgram
,
A.
,
1954
, “
Parabolic Equations
,”
Contributions to the Theory of Partial Differential Equations (Annals of Mathematics Studies)
, Vol.
33
,
Princeton University Press
,
Princeton, NJ
, pp.
167
–
190
.
6.
Akin
,
J. E.
,
2005
,
Finite Element Analysis With Error Estimators: An Introduction to the FEM and Adaptive Error Analysis for Engineering Students
,
Butterworth-Heinemann
, Elsevier Butterworth-Heinemann, Burlington, MA.
7.
Zienkiewicz
,
O. C.
, and
Zhu
,
J. Z.
,
1992
, “
The Superconvergent Patch Recovery and a Posteriori Error Estimates. Part 1: The Recovery Technique
,”
Int. J. Numer. Methods Eng.
,
33
(
7
), pp.
1331
–
1364
.10.1002/nme.1620330702
8.
Zhang
,
H.
,
Prasad
,
V.
, and
Moallemi
,
M. K.
,
1996
, “
Numerical Algorithm Using Multizone Adaptive Grid Generation for Multiphase Transport Processes With Moving and Free Boundaries
,”
Numer. Heat Transfer
,
29
(
4
), pp.
399
–
421
.10.1080/10407799608914989
9.
Huang
,
W.
,
Ren
,
Y.
, and
Russell
,
R. D.
,
1994
, “
Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
,”
SIAM J. Numer. Anal.
,
31
(
3
), pp.
709
–
730
.10.1137/0731038
10.
Smith
,
M.
,
Hodges
,
D.
, and
Cesnik
,
C.
,
1995
, “
An Evaluation of Computational Algorithms to Interface Between CFD and CSD Methodologies
,” Wright-Patterson Air Force Base Report No. WL-TR-96-3055, pp.
1
–
45
.
11.
Ahmed
,
F.
,
2006
,
Analysis of Data Transfer Methods Between Non-Matching Meshes in Multiphysics Simulations
,
Master's thesis, Universität Erlangen-Nürnberg
,
Erlangen, Germany
.
12.
Wendland
,
H.
,
2002
, “
Fast Evaluation of Radial Basis Functions: Methods Based on Partition of Unity
,”
Approximations Theory X: Wavelets, Splines, and Applications
,
Vanderbilt University Press
, Nashville, TN, pp.
473
–
483
.
13.
Beckert
,
A.
, and
Wendland
,
H.
,
2001
, “
Multivariate Interpolation for Fluid–Structure-Interaction Problems Using Radial Basis Functions
,”
Aerosp. Sci. Technol.
,
5
(
2
), pp.
125
–
134
.10.1016/S1270-9638(00)01087-7
14.
Wendland
,
H.
,
2006
, “
Computational Aspects of Radial Basis Function Approximation
,”
Stud. Comput. Math.
,
12
, pp.
231
–
256
.10.1016/S1570-579X(06)80010-8
15.
Chandrupatla
,
T. R.
,
Belegundu
,
A. D.
,
Ramesh
,
T.
, and
Ray
,
C.
,
1997
,
Introduction to Finite Elements in Engineering
,
Prentice Hall
,
Upper Saddle River, NJ
, pp.
279
–
300
.
16.
Murti
,
V.
, and
Valliappan
,
S.
,
1986
, “
Numerical Inverse Isoparametric Mapping in Remeshing and Nodal Quantity Contouring
,”
Comput. Struct.
,
22
(
6
), pp.
1011
–
1021
.10.1016/0045-7949(86)90161-6
17.
Ceniceros
,
H. D.
, and
Hou
,
T. Y.
,
2001
, “
An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions
,”
J. Comput. Phys.
,
172
(
2
), pp.
609
–
639
.10.1006/jcph.2001.6844
18.
Adjerid
,
S.
, and
Flaherty
,
J. E.
,
1986
, “
A Moving Finite Element Method With Error Estimation and Refinement for One-Dimensional Time Dependent Partial Differential Equations
,”
SIAM J. Numer. Anal.
,
23
(
4
), pp.
778
–
796
.10.1137/0723050
19.
Liao
,
G.
,
Liu
,
F.
,
Gary
,
C.
,
Peng
,
D.
, and
Osher
,
S.
,
2000
, “
Level-Set-Based Deformation Methods for Adaptive Grids
,”
J. Comput. Phys.
,
159
(
1
), pp.
103
–
122
.10.1006/jcph.2000.6432
20.
Hyman
,
J. M.
, and
Li
,
S.
,
1998
, “
Interactive and Dynamic Control of Adaptive Mesh Refinement With Nested Hierarchical Grids
,” Report No. 5462.
21.
Wang
,
L.
, and
Moriwaki
,
T.
,
2003
, “
A Novel Meshing Algorithm for Dynamic Finite Element Analysis
,”
Precision Eng.
,
27
(
3
), pp.
245
–
257
.10.1016/S0141-6359(03)00005-9
22.
Boussetta
,
R.
,
Coupez
,
T.
, and
Fourment
,
L.
,
2006
, “
Adaptive Remeshing Based on a Posteriori Error Estimation for Forging Simulation
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
48
), pp.
6626
–
6645
.10.1016/j.cma.2005.06.029
23.
Matsumoto
,
M.
,
Shiomi
,
M.
,
Osakada
,
K.
, and
Abe
,
F.
,
2002
, “
Finite Element Analysis of Single Layer Forming on Metallic Powder Bed in Rapid Prototyping by Selective Laser Processing
,”
Int. J. Mach. Tools Manuf.
,
42
(
1
), pp.
61
–
67
.10.1016/S0890-6955(01)00093-1
24.
Shiomi
,
M.
,
Yoshidome
,
A.
,
Abe
,
F.
, and
Osakada
,
K.
,
1999
, “
Finite Element Analysis of Melting and Solidifying Processes in Laser Rapid Prototyping of Metallic Powders
,”
Int. J. Mach. Tools Manuf.
,
39
(
2
), pp.
237
–
252
.10.1016/S0890-6955(98)00036-4
25.
Verhaeghe
,
F.
,
Craeghs
,
T.
,
Heulens
,
J.
, and
Pandelaers
,
L.
,
2009
, “
A Pragmatic Model for Selective Laser Melting With Evaporation
,”
Acta Mater.
,
57
(
20
), pp.
6006
–
6012
.10.1016/j.actamat.2009.08.027
26.
Zaeh
,
M. F.
, and
Branner
,
G.
,
2010
, “
Investigations on Residual Stresses and Deformations in Selective Laser Melting
,”
Prod. Eng.
,
4
(
1
), pp.
35
–
45
.10.1007/s11740-009-0192-y
27.
Dai
,
K.
, and
Shaw
,
L.
,
2004
, “
Thermal and Mechanical Finite Element Modeling of Laser Forming From Metal and Ceramic Powders
,”
Acta Mater.
,
52
(
1
), pp.
69
–
80
.10.1016/j.actamat.2003.08.028
28.
Kolossov
,
S.
,
Boillat
,
E.
,
Glardon
,
R.
,
Fischer
,
P.
, and
Locher
,
M.
,
2004
, “
3D FE Simulation for Temperature Evolution in the Selective Laser Sintering Process
,”
Int. J. Mach. Tools Manuf.
,
44
(
2
), pp.
117
–
123
.10.1016/j.ijmachtools.2003.10.019
29.
Roberts
,
I. A.
,
Wang
,
C. J.
,
Esterlein
,
R.
,
Stanford
,
M.
, and
Mynors
,
D. J.
,
2009
, “
A Three-Dimensional Finite Element Analysis of the Temperature Field During Laser Melting of Metal Powders in Additive Layer Manufacturing
,”
Int. J. Mach. Tools Manuf.
,
49
(
12
), pp.
916
–
923
.10.1016/j.ijmachtools.2009.07.004
30.
Hussein
,
A.
,
Hao
,
L.
,
Yan
,
C.
, and
Everson
,
R.
,
2013
, “
Finite Element Simulation of the Temperature and Stress Fields in Single Layers Built Without-Support in Selective Laser Melting
,”
Mater. Des.
,
52
, pp.
638
–
647
.10.1016/j.matdes.2013.05.070
31.
Childs
,
T. H. C.
,
Hauser
,
C.
, and
Badrossamay
,
M.
,
2005
, “
Selective Laser Sintering (Melting) of Stainless and Tool Steel Powders: Experiments and Modelling
,”
Proc. Inst. Mech. Eng., Part B
,
219
(
4
), pp.
339
–
357
.10.1243/095440505X8109
32.
Boillat
,
E.
, 2003, “
Finite Element Methods on Non-Conforming Grids by Penalizing the Matching Constraint
,”
ESAIM: Math. Mod. Num. Anal.
,
37
(
2
), pp.
357
–
372
.10.1051/m2an:2003031
33.
Pal
,
D.
,
Patil
,
N.
,
Rafi
,
K.
,
Zeng
,
K.
,
Moreland
,
A.
,
Hicks
,
A.
,
Beeler
,
D.
, and
Stucker
,
B.
,
2014
, “
A Feed Forward Dynamic Adaptive Mesh Refinement and De-Refinement (FFD-AMRD) Strategy for Problems With Non-Linear Spatiotemporally Periodic Localized Boundary Conditions
,”
ASME J. Manuf. Sci. Eng.
(in press).
34.
Brandal
,
G.
,
Satoh
,
G.
,
Yao
,
Y. L.
, and
Naveed
,
S.
,
2013
, “
Beneficial Interface Geometry for Laser Joining of NiTi to Stainless Steel Wires
,”
ASME J. Manuf. Sci. Eng.
,
135
(
6
), p.
061006
.10.1115/1.4025495
35.
Tan
,
H.
, and
Yao
,
Y. L.
,
2013
, “
Laser Joining of Continuous Glass Fiber Composite Preforms
,”
ASME J. Manuf. Sci. Eng.
,
135
(
1
), p.
011010
.10.1115/1.4023270
36.
Yilbas
,
B. S.
,
Akhtar
,
S.
, and
Karatas
,
C.
,
2013
, “
Laser Treatment of Rene-41: Thermal and Microstructural Analysis
,”
ASME J. Manuf. Sci. Eng.
,
135
(
3
), p.
034502
.10.1115/1.4024289
37.
Amano
,
R. S.
,
Marek
,
S.
,
Schultz
,
B. F.
, and
Rohatgi
,
P. K.
,
2014
, “
Laser Engineered Net Shaping Process for 316L/15% Nickel Coated Titanium Carbide Metal Matrix Composite
,”
ASME J. Manuf. Sci. Eng.
,
136
(
5
), p.
051007
.10.1115/1.4027758
38.
Caslaru
,
R.
,
Sealy
,
M. P.
,
Guo
,
Y. B.
, and
Wei
,
X. T.
,
2014
, “
Fabrication and Tribological Functions of Microdent Arrays on Ti–6Al–4V Surface by Laser Shock Peening
,”
ASME J. Manuf. Sci. Eng.
,
136
(
5
), p.
051020
.10.1115/1.4027918
39.
Hsu
,
S. T.
, and
Yao
,
Y. L.
,
2014
, “
Effect of Film Formation Method and Annealing on Morphology and Crystal Structure of Poly(l-Lactic Acid) Films
,”
ASME J. Manuf. Sci. Eng.
,
136
(
2
), p.
021006
.10.1115/1.4025909
40.
Hsu
,
S. T.
,
Tan
,
H.
, and
Yao
,
Y. L.
,
2014
, “
Effect of Laser-Induced Crystallinity Modification on Biodegradation Profile of Poly(l-Lactic Acid)
,”
ASME J. Manuf. Sci. Eng.
,
136
(
1
), p.
011005
.10.1115/1.4025394
41.
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
.10.1115/1.4028509
42.
Jeong
,
N.
, and
Rosen
,
D. W.
,
2014
, “
Microstructure Feature Recognition for Materials Using Surfacelet-Based Methods for Computer-Aided Design-Material Integration
,”
ASME J. Manuf. Sci. Eng.
,
136
(
6
), p.
061021
.10.1115/1.4028621
43.
Shen
,
N.
, and
Ding
,
H.
,
2014
, “
Physics-Based Microstructure Simulation for Drilled Hole Surface in Hardened Steel
,”
ASME J. Manuf. Sci. Eng.
,
136
(
4
), p.
044504
.10.1115/1.4027732
44.
Joshi
,
S.
,
Tewari
,
A.
, and
Joshi
,
S.
,
2013
, “
Influence of Preheating on Chip Segmentation and Microstructure in Orthogonal Machining of Ti6Al4V
,”
ASME J. Manuf. Sci. Eng.
,
135
(
6
), p.
061017
.10.1115/1.4025741
45.
Wang
,
H.
,
Hsu
,
S. T.
,
Tan
,
H.
,
Yao
,
Y. L.
,
Chen
,
H.
, and
Azer
,
M. N.
,
2013
, “
Predictive Modeling for Glass-Side Laser Scribing of Thin Film Photovoltaic Cells
,”
ASME J. Manuf. Sci. Eng.
,
135
(
5
), p.
051004
.10.1115/1.4024818
46.
King
,
W.
,
Anderson
,
A. T.
,
Ferencz
,
R. M.
,
Hodge
,
N. E.
,
Kamath
,
C.
, and
Khairallah
,
S. A.
,
2014
, “
Overview of Modeling and Simulation of Metal Powder-Bed Fusion Process at Lawrence Livermore National Laboratory
,”
Mater. Sci. Technol.
(to be published).
47.
Li
,
Z. L.
, and
Zhu
,
L. M.
,
2014
, “
Envelope Surface Modeling and Tool Path Optimization for Five-Axis Flank Milling Considering Cutter Runout
,”
ASME J. Manuf. Sci. Eng.
,
136
(
4
), p.
041021
.10.1115/1.4027415
48.
Lutey
,
A. H.
,
2013
, “
Modeling of Thin-Film Single and Multilayer Nanosecond Pulsed Laser Processing
,”
ASME J. Manuf. Sci. Eng.
,
135
(
6
), p.
061003
.10.1115/1.4025494
49.
Jamshidinia
,
M.
,
Kong
,
F.
, and
Kovacevic
,
R.
,
2013
, “
Numerical Modeling of Heat Distribution in the Electron Beam Melting® of Ti–6Al–4V
,”
ASME J. Manuf. Sci. Eng.
,
135
(
6
), p.
061010
.10.1115/1.4025746
50.
Patel
,
B. C.
, and
Jain
,
A.
,
2013
, “
Thermal Modeling of Ultraviolet Nanoimprint Lithography
,”
ASME J. Manuf. Sci. Eng.
,
135
(
6
), p.
064501
.10.1115/1.4025564
51.
Li
,
M.
,
Tang
,
L.
,
Landers
,
R. G.
, and
Leu
,
M. C.
,
2013
, “
Extrusion Process Modeling for Aqueous-Based Ceramic Pastes—Part 1: Constitutive Model
,”
ASME J. Manuf. Sci. Eng.
,
135
(
5
), p.
051008
.10.1115/1.4025014
52.
Nikishkov
,
G. P.
,
2010
,
Programming Finite Elements in Java™
,
Springer Science and Business Media
,
Springer-Verlag London Limited, London
.
53.
Dhondt
,
G.
,
2014
, “
Eight-Node Brick Element (C3D8 and F3D8)
,”
CalculiX CrunchiX USER'S MANUAL version 2.7
[Accessed on Mar. 9, 2015], http://web.mit.edu/calculix_v2.7/CalculiX/ccx_2.7/doc/ccx/node26.html
54.
Beeler
,
D.
,
Stucker
,
B.
,
Pal
,
D.
,
Patil
,
N.
, and
Zeng
,
K.
,
2012
, “
Computational Modeling of Ti6Al4V Alloy Processed Using Direct Metal Laser Sintering Process
,” Air Force Research Laboratory Report No. AFRL-rX-WP-TR-2012-0510.
55.
Trefethen
,
L. N.
, and
Bau
,
D.
, III,
1997
,
Numerical Linear Algebra
, Vol.
50
,
SIAM
,
Industrial and Applied Mathematics, Philadelphia, PA
.10.1137/1.9780898719574
56.
McCormac
,
J. C.
, and
Elling
,
R. E.
,
1984
,
Structural Analysis
,
Harper and Row
,
New York
.
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