Abstract

Compositionally graded alloys, a subclass of functionally graded materials (FGMs), utilize localized variations in composition with a single metal part to achieve higher performance than traditional single material parts. In previous work [Kirk, T., Galvan, E., Malak, R., and Arroyave, R., 2018, “Computational Design of Gradient Paths in Additively Manufactured Functionally Graded Materials,” J. Mech. Des., 140, p. 111410. 10.1115/1.4040816], the authors presented a computational design methodology that avoids common issues which limit a gradient alloy’s feasibility, such as deleterious phases, and optimizes for performance objectives. However, the previous methodology only samples the interior of a composition space, meaning designed gradients must include all elements in the space throughout the gradient. Because even small amounts of additional alloying elements can introduce new deleterious phases, this characteristic often neglects potentially simpler solutions to otherwise unsolvable problems and, consequently, discourages the addition of new elements to the state space. The present work improves upon the previous methodology by introducing a sampling method that includes subspaces with fewer elements in the design search. The new method samples within an artificially expanded form of the state space and projects samples outside the true region to the nearest true subspace. This method is evaluated first by observing the sample distribution in each subspace of a 3D, 4D, and 5D state space. Next, a parametric study in a synthetic 3D problem compares the performance of the new sampling scheme to the previous methodology. Lastly, the updated methodology is applied to design a gradient from stainless steel to equiatomic NiTi that has practical uses such as embedded shape memory actuation and for which the previous methodology fails to find a feasible path.

References

1.
Aremu
,
A. O.
,
Brennan-Craddock
,
J. P. J.
,
Panesar
,
A.
,
Ashcroft
,
I. A.
,
Hague
,
R. J. M.
,
Wildman
,
R. D.
, and
Tuck
,
C.
,
2017
, “
A Voxel-Based Method of Constructing and Skinning Conformal and Functionally Graded Lattice Structures Suitable for Additive Manufacturing
,”
Addit. Manuf.
,
13
(
1
), pp.
1
13
.
2.
Attarilar
,
S.
,
Salehi
,
M. T.
,
Al-Fadhalah
,
K. J.
,
Djavanroodi
,
F.
, and
Mozafari
,
M.
,
2019
, “
Functionally Graded Titanium Implants: Characteristic Enhancement Induced by Combined Severe Plastic Deformation
,”
PLoS One
,
14
(
8
), p.
e0221491
.
3.
Cross
,
S. R.
,
Woollam
,
R.
,
Shademan
,
S.
, and
Schuh
,
C. A.
,
2013
, “
Computational Design and Optimization of Multilayered and Functionally Graded Corrosion Coatings
,”
Corros. Sci.
,
77
(
12
), pp.
297
307
.
4.
Simonenko
,
E. P.
,
Simonenko
,
N. P.
,
Nikolaev
,
V. A.
,
Papynov
,
E. K.
,
Shichalin
,
O. O.
,
Gridasova
,
E. A.
,
Maiorov
,
V. Y.
,
Grishin
,
A. V.
,
Sevastyanov
,
V. G.
, and
Kuznetsov
,
N. T.
,
2019
, “
Sol–Gel Synthesis of Functionally Graded SiC–TiC Ceramic Material
,”
Russ. J. Inorg. Chem.
,
64
(
11
), pp.
1456
1463
.
5.
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
(
6
), p.
5357
.
6.
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
(
4
), pp.
133
142
.
7.
Loh
,
G. H.
,
Pei
,
E.
,
Harrison
,
D.
, and
Monzón
,
M. D.
,
2018
, “
An Overview of Functionally Graded Additive Manufacturing
,”
Addit. Manuf.
,
23
(
10
), pp.
34
44
.
8.
Vaezi
,
M.
,
Chianrabutra
,
S.
,
Mellor
,
B.
, and
Yang
,
S.
,
2013
, “
Multiple Material Additive Manufacturing—Part 1: A Review
,”
Virtual Phys. Protot.
,
8
(
1
), pp.
19
50
.
9.
Oxman
,
N.
,
2011
, “
Variable Property Rapid Prototyping
,”
Virtual Phys. Protot.
,
6
(
1
), pp.
3
31
.
10.
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
.
11.
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
.
12.
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 304L Stainless Steel Gradient Components Fabricated With Laser Deposition Additive Manufacturing
,”
Mater. Des.
,
104
(
8
), pp.
404
413
.
13.
Meng
,
W.
,
Xiaohui
,
Y.
,
Zhang
,
W.
,
Junfei
,
F.
,
Lijie
,
G.
,
Qunshuang
,
M.
, and
Bing
,
C.
,
2020
, “
Additive Manufacturing of a Functionally Graded Material From Inconel625 to Ti6Al4V by Laser Synchronous Preheating
,”
J. Mater. Process. Technol.
,
275
(
1
), p.
116368
.
14.
Chen
,
B.
,
Su
,
Y.
,
Xie
,
Z.
,
Tan
,
C.
, and
Feng
,
J.
,
2020
, “
Development and Characterization of 316L/Inconel625 Functionally Graded Material Fabricated by Laser Direct Metal Deposition
,”
Optics Laser Technol.
,
123
(
3
), p.
105916
.
15.
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
(
4
), pp.
46
54
.
16.
Ansari
,
M.
,
Jabari
,
E.
, and
Toyserkani
,
E.
,
2021
, “
Opportunities and Challenges in Additive Manufacturing of Functionally Graded Metallic Materials Via Powder-Fed Laser Directed Energy Deposition: A Review
,”
J. Mater. Process. Technol.
,
294
(
8
), p.
117117
.
17.
Moustafa
,
A. R.
,
Durga
,
A.
,
Lindwall
,
G.
, and
Cordero
,
Z. C.
,
2020
, “
Scheil Ternary Projection (STeP) Diagrams for Designing Additively Manufactured Functionally Graded Metals
,”
Addit. Manuf.
,
32
(
3
), p.
101008
.
18.
Kirk
,
T.
,
Galvan
,
E.
,
Malak
,
R.
, and
Arroyave
,
R.
,
2018
, “
Computational Design of Gradient Paths in Additively Manufactured Functionally Graded Materials
,”
ASME J. Mech. Des.
,
140
(
11
), p.
111410
.
19.
Adiyatov
,
O.
, and
Varol
,
H. A.
,
2013
, “
Rapidly-Exploring Random Tree Based Memory Efficient Motion Planning
,”
International Conference on Mechatronics and Automation
,
Takamatsu, Japan
,
Aug. 4–7
, IEEE, pp.
354
359
.
20.
Karaman
,
S.
, and
Frazzoli
,
E.
,
2011
, “
Sampling-Based Algorithms for Optimal Motion Planning
,”
Int. J. Rob. Res.
,
30
(
7
), pp.
846
894
.
21.
Kirk
,
T.
,
Malak
,
R.
, and
Arroyave
,
R.
,
2020
, “
Computational Design of Compositionally Graded Alloys for Property Monotonicity
,”
ASME J. Mech. Des.
,
143
(
11
), p.
031704
.
22.
Eliseeva
,
O. V.
,
Kirk
,
T.
,
Samimi
,
P.
,
Malak
,
R.
,
Arróyave
,
R.
,
Elwany
,
A.
, and
Karaman
,
I.
,
2019
, “
Functionally Graded Materials Through Robotics-Inspired Path Planning
,”
Mater. Des.
,
182
(
11
), p.
107975
.
23.
Grimme
,
Christian
,
2015
, “
Picking a Uniformly Random Point from an Arbitrary Simplex
,”
ResearchGate
.
24.
Chen
,
Y.
, and
Ye
,
X.
,
2011
, “
Projection Onto a Simplex
,”
arXiv
. https://arxiv.org/abs/1101.6081
25.
Kirk
,
T. Q.
,
2020
, “
Computational Design of Compositionally Graded Alloys
,” Doctoral dissertation,
Texas A&M University, Department of Mechanical Engineering
,
College Station, TX
.
26.
Woronow
,
A.
,
1993
, “
Generating Random Numbers on a Simplex
,”
Comput. Geosci.
,
19
(
1
), pp.
81
88
.
27.
Otis
,
R. A.
,
2016
, “
Software Architecture for CALPHAD Modeling of Phase Stability and Transformations in Alloy Additive Manufacturing Processes
,”
Doctoral dissertation, Pennsylvania State University, Department of Materials Science and Engineering, University Park, PA
.
28.
Turk
,
G.
,
1990
, “Generating Random Points in Triangles,”
Graphics Gems
,
A. S.
Glassner
, ed.,
Academic Press
,
San Diego, CA
, pp.
24
28
.
29.
NASA
,
2021
, “
Space Technology Research Grants Program, Early Career Faculty Appendix to NASA Research Announcement (NRA): Space Technology—Research, Development, Demonstration, and Infusion 2021 (SpaceTech–REDDI–2021)
,” 80HQTR21NOA01.
30.
Thermo-Calc Software High Entropy Alloys Database Version 4, Accessed February 2021.
31.
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
.
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