Additive manufacturing (AM) has enabled the creation of a near infinite set of functionally graded materials (FGMs). One limitation on the manufacturability and usefulness of these materials is the presence of undesirable phases along the gradient path. For example, such phases may increase brittleness, diminish corrosion resistance, or severely compromise the printability of the part altogether. In the current work, a design methodology is proposed to plan an FGM gradient path for any number of elements that avoids undesirable phases at a range of temperatures. Gradient paths can also be optimized for a cost function. A case study is shown to demonstrate the effectiveness of the methodology in the Fe–Ni–Cr system. Paths were successfully planned from 316 L Stainless Steel (316 L SS) to pure Cr that either minimize path length or maximize separation from undesirable phases. Examinations on the stochastic variability, parameter dependency, and computational efficiency of the method are also presented. Several avenues of future research are proposed that could improve the manufacturability, utility, and performance of FGMs through gradient path design.

References

1.
Carroll
,
B. E.
,
Otis
,
R. A.
,
Borgonia
,
J. P.
,
Suh
,
J.-O.
,
Dillon
,
R. P.
,
Shapiro
,
A. A.
,
Hofmann
,
D. C.
,
Liu
,
Z.-K.
, and
Beese
,
A. M.
,
2016
, “
Functionally Graded Material of 304l Stainless Steel and Inconel 625 Fabricated by Directed Energy Deposition: Characterization and Thermodynamic Modeling
,”
Acta Mater.
,
108
, pp.
46
54
.
2.
Hofmann
,
D. C.
,
Kolodziejska
,
J.
,
Roberts
,
S.
,
Otis
,
R.
,
Dillon
,
R. P.
,
Suh
,
J.-O.
,
Liu
,
Z.-K.
, and
Borgonia
,
J.-P.
,
2014
, “
Compositionally Graded Metals: A New Frontier of Additive Manufacturing
,”
J. Mater. Res.
,
29
(
17
), pp.
1899
1910
.
3.
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
.
4.
Garland
,
A.
, and
Fadel
,
G.
,
2015
, “
Design and Manufacturing Functionally Gradient Material Objects With an Off the Shelf Three-Dimensional Printer: Challenges and Solutions
,”
ASME J. Mech. Des.
,
137
(
11
), p.
111407
.
5.
Kou
,
X. Y.
, and
Tan
,
S. T.
,
2007
, “
A Systematic Approach for Integrated Computer-Aided Design and Finite Element Analysis of Functionally-Graded-Material Objects
,”
Mater. Des.
,
28
(
10
), pp.
2549
2565
.
6.
Hiller
,
J. D.
, and
Lipson
,
H.
,
2009
, “
Multi Material Topological Optimization of Structures and Mechanisms
,”
11th Annual Conference on Genetic and Evolutionary Computation (GECCO)
, pp.
1521
1528
.
7.
Kou
,
X. Y.
,
Parks
,
G. T.
, and
Tan
,
S. T.
,
2012
, “
Optimal Design of Functionally Graded Materials Using a Procedural Model and Particle Swarm Optimization
,”
Comput.-Aided Des.
,
44
(
4
), pp.
300
310
.
8.
Bobbio
,
L. D.
,
Otis
,
R. A.
,
Borgonia
,
J. P.
,
Dillon
,
R. P.
,
Shapiro
,
A. A.
,
Liu
,
Z.-K.
, and
Beese
,
A. M.
,
2017
, “
Additive Manufacturing of a Functionally Graded Material From Ti-6Al-4V to Invar: Experimental Characterization and Thermodynamic Calculations
,”
Acta Mater.
,
127
, pp.
133
142
.
9.
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
(
1
), p.
5357
.
10.
Reichardt
,
A.
,
Dillon
,
R. P.
,
Borgonia
,
J. P.
,
Shapiro
,
A. A.
,
McEnerney
,
B. W.
,
Momose
,
T.
, and
Hosemann
,
P.
,
2016
, “
Development and Characterization of Ti-6Al-4V to 304 L Stainless Steel Gradient Components Fabricated With Laser Deposition Additive Manufacturing
,”
Mater. Des.
,
104
, pp.
404
413
.
11.
Kaufman
,
L.
, and
Bernstein
,
H.
,
1970
,
Computer Calculation of Phase Diagrams. With Special Reference to Refractory Metals
, Academic Press, New York.
12.
Kaufman
,
L.
, and
Ågren
,
J.
,
2014
, “
Calphad, First and Second Generation–Birth of the Materials Genome
,”
Scr. Mater.
,
70
, pp.
3
6
.
13.
Andersson
,
J.-O.
,
Helander
,
T.
,
Höglund
,
L.
,
Shi
,
P.
, and
Sundman
,
B.
,
2002
, “
Thermo-Calc & DICTRA, Computational Tools for Materials Science
,”
Calphad
,
26
(
2
), pp.
273
312
.
14.
Galvan
,
E.
,
Malak
,
R. J.
,
Gibbons
,
S.
, and
Arroyave
,
R.
,
2017
, “
A Constraint Satisfaction Algorithm for the Generalized Inverse Phase Stability Problem
,”
ASME J. Mech. Des.
,
139
(
1
), p.
011401
.
15.
Adiyatov
,
O.
, and
Varol
,
H.
,
2013
, “
Rapidly-Exploring Random Tree Based Memory Efficient Motion Planning
,”
IEEE International Conference on Mechatronics and Automation (ICMA)
, pp.
354
359
.
16.
Karaman
,
S.
, and
Frazzoli
,
E.
,
2011
, “
Sampling-Based Algorithms for Optimal Motion Planning
,”
Int. J. Rob. Res.
,
30
(
7
), pp.
846
894
.
17.
Lozano-Pérez
,
T.
, and
Wesley
,
M. A.
,
1979
, “
An Algorithm for Planning Collision-Free Paths Among Polyhedral Obstacles
,”
Commun. ACM
,
22
(
10
), pp.
560
570
.
18.
Denny
,
J.
,
Greco
,
E.
,
Thomas
,
S.
, and
Amato
,
N. M.
,
2014
, “
MARRT: Medial Axis Biased Rapidly-Exploring Random Trees
,”
IEEE International Conference on Robotics and Automation (ICRA),
pp.
90
97
.
19.
Hwang
,
Y. K.
, and
Ahuja
,
N.
,
1992
, “
Gross Motion Planning-a Survey
,”
ACM Comput. Surv. (CSUR)
,
24
(
3
), pp.
219
291
.
20.
Raja
,
P.
, and
Pugazhenthi
,
S.
,
2012
, “
Optimal Path Planning of Mobile Robots: A Review
,”
Int. J. Phys. Sci.
,
7
(
9
), pp.
1314
1320
.
21.
Masehian
,
E.
, and
Sedighizadeh
,
D.
,
2007
, “
Classic and Heuristic Approaches in Robot Motion Planning-A Chronological Review
,”
World Acad. Sci., Eng. Technol.
,
1
(5), pp.
228
233
.https://waset.org/Publication/classic-and-heuristic-approaches-in-robot-motion-planning-a-chronological-review-/10300
22.
Mac
,
T. T.
,
Copot
,
C.
,
Tran
,
D. T.
, and
De Keyser
,
R.
,
2016
, “
Heuristic Approaches in Robot Path Planning: A Survey
,”
Rob. Auton. Syst.
,
86
, pp.
13
28
.
23.
Abu-Odeh
,
A.
,
Galvan
,
E.
,
Kirk
,
T.
,
Mao
,
H.
,
Chen
,
Q.
,
Mason
,
P.
,
Malak
,
R.
, and
Arroyave
,
R.
,
2017
, “
Exploration of the High Entropy Alloy Space as a Constraint Satisfaction Problem
,” eprint arXiv:1712.02442.
24.
Tax
,
D. M.
, and
Duin
,
R. P.
,
1999
, “
Support Vector Domain Description
,”
Pattern Recognit. Lett.
,
20
(
11–13
), pp.
1191
1199
.
25.
Vapnik
,
V.
,
1995
,
The Nature of Statistical Learning Theory
,
Springer
,
New York
.
26.
Schölkopf
,
B.
, and
Smola
,
A. J.
,
2002
,
Learning With Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
,
MIT Press
,
Cambridge, MA
.
27.
Basudhar
,
A.
, and
Missoum
,
S.
,
2008
, “
Adaptive Explicit Decision Functions for Probabilistic Design and Optimization Using Support Vector Machines
,”
Comput. Struct.
,
86
(
19–20
), pp.
1904
1917
.
28.
Shahan
,
D. W.
, and
Seepersad
,
C. C.
,
2012
, “
Bayesian Network Classifiers for Set-Based Collaborative Design
,”
ASME J. Mech. Des.
,
134
(
7
), p.
071001
.
29.
Matthews
,
J.
,
Klatt
,
T.
,
Morris
,
C.
,
Seepersad
,
C. C.
,
Haberman
,
M.
, and
Shahan
,
D.
,
2016
, “
Hierarchical Design of Negative Stiffness Metamaterials Using a Bayesian Network Classifier
,”
ASME J. Mech. Des.
,
138
(
4
), p.
041404
.
30.
Elbanhawi
,
M.
, and
Simic
,
M.
,
2014
, “
Sampling-Based Robot Motion Planning: A Review
,”
IEEE Access
,
2
, pp.
56
77
.
31.
Hou
,
J.
,
Guo
,
J.
,
Zhou
,
L.
, and
Ye
,
H.
,
2006
, “
Sigma Phase Formation and Its Effect on Mechanical Properties in the Corrosion-Resistant Superalloy k44
,”
Z. Für Metallkunde
,
97
(
2
), pp.
174
181
.
32.
Hsieh
,
C.-C.
, and
Wu
,
W.
,
2012
, “
Overview of Intermetallic Sigma (σ) Phase Precipitation in Stainless Steels
,”
ISRN Metall.
,
2012
, pp. 1–16.
33.
Mao
,
H.
,
Chen
,
H.-L.
, and
Chen
,
Q.
,
2017
, “
TCHEA1: A Thermodynamic Database Not Limited for “High Entropy” Alloys
,”
J. Phase Equilib. Diffus.
,
38
(
4
), pp.
353
368
.
34.
Montgomery
,
D. C.
,
2017
,
Design and Analysis of Experiments
,
Wiley
, New York.
35.
Powers
,
D. M.
,
2011
, “
Evaluation: From Precision, Recall and f-Measure to Roc, Informedness, Markedness and Correlation
,”
J. Mach. Learn. Technol.
,
2
(
1
), pp.
37
63
.http://hdl.handle.net/2328/27165
You do not currently have access to this content.