Abstract

We present a new sampling method for the multi-scale design of polycrystalline materials, which improves the computational time efficiency compared to the existing computational approaches. The solution strategy aims to find microstructure designs that optimize component-scale mechanical properties. The microstructure is represented with a probabilistic texture descriptor that quantifies the volume fractions of different crystallographic orientations. However, the original microstructure design space is high-dimensional and thus optimization in this domain is not favorable. Instead, we generate property closures, which are the reduced spaces of volume-averaged material properties that are computed in terms of the microstructural texture descriptors. We observe that the traditional design approaches which are based on sampling in the original microstructure space and sampling on the property closure are inefficient as they lead to highly concentrated design samples in the solution space. Therefore, we introduce a new sampling method in the property closure, which creates simplexes using the triangulation of the property hull and then generating samples for each simplex. Example problems include the optimization of Galfenol and α-titanium microstructures to improve non-linear material properties. The new sampling approach is shown to obtain better solutions while decreasing the required computational time compared to the previous microstructure design methods.

References

References
1.
Ashby
,
M. F.
,
1992
,
Materials Selection in Mechanical Design
,
Pergamon
,
Tarrytown, NY
, pp.
36
64
.
2.
Olson
,
G. B.
,
1997
, “
Computational Design of Hierarchically Structured Materials
,”
Science
,
277
(
5330
), pp.
1237
1242
. 10.1126/science.277.5330.1237
3.
Sigmund
,
O.
, and
Torquato
,
S.
,
1996
, “
Composites With Extremal Thermal Expansion Coefficients
,”
Appl. Phys. Lett.
,
69
(
21
), pp.
3203
3205
. 10.1063/1.117961
4.
Lakes
,
R.
,
2000
, “
Deformations in Extreme Matter
,”
Science
,
288
(
5473
), pp.
1976
1977
. 10.1126/science.288.5473.1976
5.
McDowell
,
D. L.
,
2018
, “Microstructure-Sensitive Computational Structure–Property Relations in Materials Design,”
Computational Materials System Design
,
Shin
,
D.
,
Saal
,
J.
, eds.,
Springer
,
Cham
, pp.
1
25
.
6.
Lemmon
,
T. S.
,
Homer
,
E. R.
,
Fromm
,
B. S.
,
Fullwood
,
D. T.
,
Jensen
,
B. D.
, and
Adams
,
B. L.
,
2007
, “
Heterogeneous Microstructure Sensitive Design for Performance Optimization of MEMS Switch
,”
J. Minerals Metals Mater. Soc.
,
59
(
9
), pp.
43
48
. 10.1007/s11837-007-0115-3
7.
Fullwood
,
D. T.
,
Niezgoda
,
S. R.
,
Adams
,
B. L.
, and
Kalidindi
,
S. R.
,
2010
, “
Microstructure Sensitive Design for Performance Optimization
,”
Prog. Mater. Sci.
,
55
(
6
), pp.
477
562
. 10.1016/j.pmatsci.2009.08.002
8.
Houskamp
,
J. R.
,
Proust
,
G.
, and
Kalidindi
,
S. R.
,
2007
, “
Integration of Microstructure-Sensitive Design With Finite Element Methods: Elastic-Plastic Case Studies in FCC Polycrystals
,”
Int. J. Multiscale Comput. Eng.
,
5
(
3–4
), pp.
261
272
. 10.1615/IntJMultCompEng.v5.i3-4.80
9.
Li
,
D.
,
Rollett
,
A. D.
,
Vialle
,
G.
, and
Garmestani
,
H.
,
2008
, “
Multiproperty Microstructure and Property Design of Magnetic Materials
,”
ASME J. Eng. Mater. Technol.
,
130
(
2
), p.
021023
. 10.1115/1.2870235
10.
Sundararaghavan
,
V.
, and
Zabaras
,
N.
,
2006
, “
Design of Microstructure-Sensitive Properties in Elasto-Viscoplastic Polycrystals Using Multi-Scale Homogenization
,”
Int. J. Plast.
,
22
(
10
), pp.
1799
1824
. 10.1016/j.ijplas.2006.01.001
11.
Dimiduk
,
D. M.
,
2011
, “Microstructure–Property–Design Relationships in the Simulation Era: An Introduction,”
Computational Methods for Microstructure–Property Relationships
,
Ghosh
,
S.
,
Dimiduk
,
D.
, eds.,
Springer
,
Boston, MA
, pp.
1
29
.
12.
McDowell
,
D. L.
,
Choi
,
H. J.
,
Panchal
,
J.
,
Austin
,
R.
,
Allen
,
J.
, and
Mistree
,
F.
,
2007
, “
Plasticity-Related Microstructure–Property Relations for Materials Design
,”
Key Eng. Mater.
,
340–341
, pp.
21
30
. 10.4028/www.scientific.net/KEM.340-341.21
13.
Lyon
,
M.
, and
Adams
,
B. L.
,
2004
, “
Gradient-Based Non-Linear Microstructure Design
,”
J. Mech. Phys. Solids
,
52
(
11
), pp.
2569
2586
. 10.1016/j.jmps.2004.04.009
14.
Ganapathysubramanian
,
S.
, and
Zabaras
,
N.
,
2004
, “
Design Across Length Scales: A Reduced-Order Model of Polycrystal Plasticity for the Control of Microstructure-Sensitive Material Properties
,”
Comput. Methods Appl. Mech. Eng.
,
193
(
45–47
), pp.
5017
5034
. 10.1016/j.cma.2004.04.004
15.
Xu
,
H.
,
Li
,
Y.
,
Brinson
,
C.
, and
Chen
,
W.
,
2014
, “
A Descriptor-Based Design Methodology for Developing Heterogeneous Microstructural Materials System
,”
ASME J. Mech. Des.
,
136
(
5
), p.
051007
. 10.1115/1.4026649
16.
Liu
,
Y.
,
Greene
,
M. S.
,
Chen
,
W.
,
Dikin
,
D. A.
, and
Liu
,
W. K.
,
2013
, “
Computational Microstructure Characterization and Reconstruction for Stochastic Multiscale Material Design
,”
Comput. Aided Des.
,
45
(
1
), pp.
65
76
. 10.1016/j.cad.2012.03.007
17.
Xu
,
H.
,
Liu
,
R.
,
Choudhary
,
A.
, and
Chen
,
W.
,
2015
, “
A Machine Learning-Based Design Representation Method for Designing Heterogeneous Microstructures
,”
ASME J. Mech. Des.
,
137
(
5
), p.
051403
. 10.1115/1.4029768
18.
Cang
,
R.
,
Xu
,
Y.
,
Chen
,
S.
,
Liu
,
Y.
,
Jiao
,
Y.
, and
Ren
,
M. Y.
,
2017
, “
Microstructure Representation and Reconstruction of Heterogeneous Materials Via Deep Belief Network for Computational Material Design
,”
ASME J. Mech. Des.
,
139
(
7
), p.
071404
. 10.1115/1.4036649
19.
Yang
,
Z.
,
Li
,
X.
,
Brinson
,
L. C.
,
Choudhary
,
A. N.
,
Chen
,
W.
, and
Agrawal
,
A.
,
2018
, “
Microstructural Materials Design Via Deep Adversarial Learning Methodology
,”
ASME J. Mech. Des.
,
140
(
11
), p.
111416
. 10.1115/1.4041371
20.
Sundararaghavan
,
V.
, and
Zabaras
,
N.
,
2009
, “
A Statistical Learning Approach for the Design of Polycrystalline Materials
,”
Stat. Anal. Data Mining
,
1
(
5
), pp.
306
321
. 10.1002/sam.10017
21.
Liu
,
R.
,
Kumar
,
A.
,
Chen
,
Z.
,
Agrawal
,
A.
,
Sundararaghavan
,
V.
, and
Choudhary
,
A.
,
2015
, “
A Predictive Machine Learning Approach for Microstructure Optimization and Materials Design
,”
Nat. Sci. Rep.
,
5
(
11551
), pp.
1
12
. 10.1038/srep11551
22.
Paul
,
A.
,
Acar
,
P.
,
Liao
,
W.
,
Choudhary
,
A.
,
Sundararaghavan
,
V.
, and
Agrawal
,
A.
,
2019
, “
Microstructure Optimization With Constrained Design Objectives Using Machine Learning-Based Feedback-Aware Data-Generation
,”
Comput. Mater. Sci.
,
160
, pp.
334
351
. 10.1016/j.commatsci.2019.01.015
23.
Acar
,
P.
, and
Sundararaghavan
,
V.
,
2019
, “
Stochastic Design Optimization of Microstructural Features Using Linear Programming for Robust Material Design
,”
AIAA J.
,
57
(
1
), pp.
448
455
. 10.2514/1.J057377
24.
Acar
,
P.
, and
Sundararaghavan
,
V.
,
2016
, “
Linear Solution Scheme for Microstructure Design With Process Constraints
,”
AIAA J.
,
54
(
12
), pp.
4022
4031
. 10.2514/1.J055247
25.
Acar
,
P.
, and
Sundararaghavan
,
V.
,
2016
, “
Utilization of a Linear Solver for Multiscale Design and Optimization of Microstructures
,”
AIAA J.
,
54
(
5
), pp.
1751
1759
. 10.2514/1.J054822
26.
Johnson
,
O. K.
, and
Kurniawana
,
C.
,
2018
, “
An Efficient Algorithm for Generating Diverse Microstructure Sets and Delineating Properties Closures
,”
Acta Mater.
,
147
, pp.
313
321
. 10.1016/j.actamat.2018.01.004
27.
Lemmon
,
T. S.
,
Homer
,
E. R.
,
Fromm
,
B. S.
,
Fullwood
,
D. T.
,
Jensen
,
B. D.
, and
Adams
,
B. L.
,
2007
, “
Heterogeneous Microstructure Sensitive Design for Performance Optimization of MEMS Switch
,”
J. Minerals Metals Mater. Soc.
,
59
(
9
), pp.
43
48
. 10.1007/s11837-007-0115-3
28.
Adams
,
B. L.
,
Henrie
,
A.
,
Henrie
,
B.
,
Lyon
,
M.
,
Kalidindi
,
S. R.
, and
Garmestani
,
H.
,
2001
, “
Microstructure-Sensitive Design of a Compliant Beam
,”
J. Mech. Phys. Solids
,
49
(
8
), pp.
1639
1663
. 10.1016/S0022-5096(01)00016-3
29.
Kalidindi
,
S. R.
,
Houskamp
,
J. R.
,
Lyons
,
M.
, and
Adams
,
B. L.
,
2004
, “
Microstructure Sensitive Design of an Orthotropic Plate Subjected to Tensile Load
,”
Int. J. Plast.
,
20
(
8–9
), pp.
1561
1575
. 10.1016/j.ijplas.2003.11.007
30.
Fast
,
T.
,
Knezevic
,
M.
, and
Kalidindi
,
S. R.
,
2008
, “
Application of Microstructure Sensitive Design to Structural Components Produced From Hexagonal Polycrystalline Metals
,”
Comput. Mater. Sci.
,
43
(
2
), pp.
374
383
. 10.1016/j.commatsci.2007.12.002
31.
Sintay
,
D. S.
, and
Adams
,
B. L.
,
2005
, “
Microstructure Design for a Rotating Disk: With Application to Turbine Engines
,”
Proceedings of the IDETC/CIE, 31st Design Automation Conference
,
Long Beach, CA
,
24–28 Sept
, pp.
823
834
.
32.
Sundararaghavan
,
V.
, and
Zabaras
,
N.
,
2007
, “
Linear Analysis of Texture–Property Relationships Using Process-Based Representations of Rodrigues Space
,”
Acta Mater.
,
55
(
5
), pp.
1573
1587
. 10.1016/j.actamat.2006.10.019
33.
Heinz
,
A.
, and
Neumann
,
P.
,
1991
, “
Representation of Orientation and Disorientation Data for Cubic, Hexagonal, Tetragonal and Orthorhombic Crystals
,”
Acta Crystallogr.
,
47
(
6
), pp.
780
789
. 10.1107/S0108767391006864
34.
Adams
,
B. L.
,
Henrie
,
A.
,
Henrie
,
B.
,
Lyon
,
M.
,
Kalidindi
,
S. R.
, and
Garmestani
,
H.
,
2001
, “
Microstructure-Sensitive Design of a Compliant Beam
,”
J. Mech. Phys. Solids
,
49
(
8
), pp.
1639
1663
. 10.1016/S0022-5096(01)00016-3
35.
Kalidindi
,
S. R.
,
Houskamp
,
J.
,
Lyons
,
M.
, and
Adams
,
B. L.
,
2004
, “
Microstructure Sensitive Design of an Orthotropic Plate Subjected ToTensile Load
,”
Int. J. Plast.
,
20
(
8–9
), pp.
1561
1575
. 10.1016/j.ijplas.2003.11.007
36.
Kumar
,
A.
, and
Dawson
,
P. R.
,
2000
, “
Computational Modeling of F.C.C. Deformation Textures Over Rodrigues Space
,”
Acta Mater.
,
48
(
10
), pp.
2719
2736
. 10.1016/S1359-6454(00)00044-6
37.
Kumar
,
A.
, and
Dawson
,
P. R.
,
2000
, “
Modeling Crystallographic Texture Evolution With Finite Elements Over Neo-Eulerian Orientation Spaces
,”
Comput. Methods Appl. Mech. Eng.
,
153
(
3–4
), pp.
259
302
. 10.1016/S0045-7825(97)00072-8
38.
Acar
,
P.
,
2019
, “
Uncertainty Quantification for Ti-7Al Alloy Microstructure With an Inverse Analytical Model (AUQLin)
,”
Materials
,
12
(
11
), p.
1773
. 10.3390/ma12111773
39.
Acar
,
P.
, and
Sundararaghavan
,
V.
,
2017
, “
Uncertainty Quantification of Microstructural Properties Due to Variability in Measured Pole Figures
,”
Acta Mater.
,
124
, pp.
100
108
. 10.1016/j.actamat.2016.10.070
40.
Acar
,
P.
, and
Sundararaghavan
,
V.
,
2017
, “
Uncertainty Quantification of Microstructural Properties Due to Experimental Variations
,”
AIAA J.
,
55
(
8
), pp.
2824
2832
. 10.2514/1.J055689
41.
Acar
,
P.
,
2018
, “
Reliability Based Design Optimization of Microstructures With Analytical Formulation
,”
ASME J. Mech. Des.
,
140
(
11
), p.
111402
. 10.1115/1.4040881
42.
Acar
,
P.
,
Srivastava
,
S.
, and
Sundararaghavan
,
V.
,
2017
, “
Stochastic Design Optimization of Microstructures With Utilization of a Linear Solver
,”
AIAA J.
,
55
(
9
), pp.
3161
3168
. 10.2514/1.J056000
43.
Acar
,
P.
,
2019
, “
Machine Learning Approach for Identification of Microstructure-Process Linkages
,”
AIAA J.
,
57
(
8
), pp.
3608
3614
http://dx.doi.org/10.2514/1.J058244.
44.
Acar
,
P.
,
2019
, “
Multi-Scale Computational Modeling of Lightweight Aluminum–Lithium Alloys
,”
Heliyon
,
5
(
3
), p.
e01225
. 10.1016/j.heliyon.2019.e01225
45.
Acar
,
P.
,
2019
, “
Eliminating Mesh Sensitivities in Microstructure Design With an Adjoint Algorithm
,”
Finite Elements Anal. Des.
,
154
, pp.
22
29
. 10.1016/j.finel.2018.10.001
46.
Acar
,
P.
,
2018
, “
Crystal Plasticity Model Calibration for Ti–7Al Alloy With a Multi-Fidelity Computational Scheme
,”
Integr. Mater. Manuf. Innov.
,
7
(
4
), pp.
186
194
. 10.1007/s40192-018-0120-0
47.
Acar
,
P.
,
Sundararaghavan
,
V.
, and
De Graef
,
M.
,
2018
, “
Computational Modeling of Crystallographic Texture Evolution Over Cubochoric Space
,”
Modell. Simul. Mater. Sci. Eng.
,
26
(
6
), p.
065012
. 10.1088/1361-651X/aad20b
48.
Lekhnitskii
,
S. G.
,
1968
,
Anisotropic Plates
,
Gordon and Breach
,
New York
, p.
534
.
You do not currently have access to this content.