Current studies on tailoring the coefficient of thermal expansion (CTE) of materials focused on either exploring the composition of the bulk material or the design of composites which strongly depend on a few negative CTE materials or fibers. In this work, an approach to achieve a wide range of tailorable CTEs through a dual-constituent triangular lattice material is studied. Theoretical analyses explicitly reveal that through rational arrangement of commonly available positive CTE constituents, tailorable CTEs, including negative, zero, and large positive CTEs can be easily achieved. We experimentally demonstrate this approach through CTE measurements of the specimens, which were exclusively fabricated from common alloys. The triangular lattice material fabricated from positive CTE alloys is shown to yield large positive (41.6 ppm/°C), near-zero (1.9 ppm/°C), and negative (−32.9 ppm/°C) CTEs. An analysis of the collapse strength and stiffness ensures the robust mechanical properties. Moreover, hierarchal triangular lattice material is proposed, and with certain constituents, wide range of tailorable CTEs can be easily obtained through the rationally hierarchal structure design. The triangular lattice material presented here integrates tailorable CTEs, lightweight characteristic, and robust mechanical properties, and is very promising for engineering applications where precise control of thermally induced expansion is in urgently needed.

References

References
1.
Weiss
,
D. J.
,
2007
, “
Magnetic Force and Thermal Expansion as Failure Mechanisms of Electrothermal MEMS Actuators Under Electrostatic Discharge Testing
,”
ASME J. Appl. Mech.
,
74
(
5
), pp.
996
1005
.
2.
Yeh
,
H.-L.
, and
Yeh
,
H.-Y.
,
2001
, “
Effect of Transverse Moduli on Through-Thickness Hygrothermal Expansion Coefficients of Composite Laminates
,”
ASME J. Appl. Mech.
,
68
(
6
), pp.
878
879
.
3.
Dvorak
,
G. J.
, and
Chen
,
T. Y.
,
1989
, “
Thermal Expansion of Three-Phase Composite Materials
,”
ASME J. Appl. Mech.
,
56
(
2
), pp.
418
422
.
4.
Karunaratne
,
M. S. A.
,
Kyaw
,
S.
,
Jones
,
A.
,
Morrell
,
R.
, and
Thomson
,
R. C.
,
2016
, “
Modelling the Coefficient of Thermal Expansion in Ni-Based Superalloys and Bond Coatings
,”
J. Mater. Sci.
,
51
(
9
), pp.
4213
4226
.
5.
Lauren
,
A. N.
,
Vladimir
,
K.
,
Erich
,
M. S.
, and
Hans
,
D. R.
,
2014
, “
Negative Thermal Expansion in a Zirconium Tungstate/Epoxy Composite at Low Temperatures
,”
J. Mater. Sci.
,
49
(
1
), pp.
392
396
.https://doi.org/10.1007/s10853-013-7716-8
6.
Evans
,
J. S. O.
,
Mary
,
T. A.
, and
Sleight
,
A. W.
,
1998
, “
Negative Thermal Expansion in Sc2 (WO4)3
,”
J. Solid State Chem.
,
137
(
1
), pp.
148
160
.
7.
Liu
,
Y.
,
Withers
,
R. L.
, and
Norén
,
L.
,
2003
, “
An Electron Diffraction, XRD and Lattice Dynamical Investigation of the Average Structure and Rigid Unit Mode (RUM) Modes of Distortion of Microporous AlPO4-5
,”
Solid State Sci.
,
5
(
3
), pp.
427
434
.
8.
Sleight
,
A. W.
,
1998
, “
Compounds That Contract on Heating
,”
Inorg. Chem.
,
37
(
12
), pp.
2854
2860
.
9.
Ito
,
T.
,
Suganuma
,
T.
, and
Wakashima
,
K.
,
1999
, “
Glass Fiber/Polypropylene Composite Laminates With Negative Coefficients of Thermal Expansion
,”
J. Mater. Sci. Lett.
,
18
(
17
), pp.
1363
1365
.
10.
Kelly
,
A.
,
Stearn
,
R.
, and
McCartney
,
L.
,
2006
, “
Composite Materials of Controlled Thermal Expansion
,”
Compos. Sci. Technol.
,
66
(
2
), pp.
154
159
.
11.
Sigmund
,
O.
, and
Torquato
,
S.
,
1996
, “
Composites With Extremal Thermal Expansion Coefficients
,”
Appl. Phys. Lett.
,
69
(
21
), p.
3203
.
12.
Liu
,
C.
,
Du
,
Z. L.
,
Zhang
,
W. S.
,
Zhu
,
Y. C.
, and
Guo
,
X.
,
2017
, “
Additive Manufacturing-Oriented Design of Graded Lattice Structures Through Explicit Topology Optimization
,”
ASME J. Appl. Mech.
,
84
(
8
), p.
081008
.
13.
Mai
,
S. P.
,
Wen
,
S. C.
, and
Lu
,
J.
,
2015
, “
Lattice Structures Made From Surface-Modified Steel Sheets
,”
ASME J. Appl. Mech.
,
82
(
1
), p.
011007
.
14.
Hammetter
,
C. I.
, and
Zok
,
F. W.
,
2013
, “
Compressive Response of Pyramidal Lattices Embedded in Foams
,”
ASME J. Appl. Mech.
,
81
(
1
), p.
011006
.
15.
Lakes
,
R.
,
1996
, “
Cellular Solid Structures With Unbounded Thermal Expansion
,”
J. Mater. Sci. Lett.
,
15
(
6
), pp.
475
477
.http://silver.neep.wisc.edu/~lakes/HiAlpha.pdf
16.
Lakes
,
R.
,
2007
, “
Cellular Solids With Tunable Positive or Negative Thermal Expansion of Unbounded Magnitude
,”
Appl. Phys. Lett.
,
90
(
22
), p.
221905
.
17.
Jefferson
,
G.
,
Parthasarathy
,
T. A.
, and
Kerans
,
R. J.
,
2009
, “
Tailorable Thermal Expansion Hybrid Structures
,”
Int. J. Solids Struct.
,
46
(
11–12
), pp.
2372
2387
.
18.
Lim
,
T. C.
,
2005
, “
Anisotropic and Negative Thermal Expansion Behavior in a Cellular Microstructure
,”
J. Mater. Sci.
,
40
(
12
), pp.
3275
3277
.
19.
Lim
,
T.-C.
,
2012
, “
Negative Thermal Expansion Structures Constructed From Positive Thermal Expansion Trusses
,”
J. Mater. Sci.
,
47
(
1
), pp.
368
373
.
20.
Wang
,
P.
,
Fan
,
H. L.
, and
Xu
,
B. B.
,
2015
, “
Collapse Criteria for High Temperature Ceramic Lattice Truss Materials
,”
Appl. Therm. Eng.
,
89
, pp.
505
513
.
21.
Steeves
,
C. A.
,
Lucato
,
S. L.
, and
He
,
M.
,
2007
, “
Concepts for Structurally Robust Materials That Combine Low Thermal Expansion With High Stiffness
,”
J. Mech. Phys. Solids
,
55
(
9
), pp.
1803
1822
.
22.
Wei
,
K.
,
Chen
,
H. S.
,
Pei
,
Y. M.
, and
Fang
,
D. N.
,
2016
, “
Planar Lattices With Tailorable Coefficient of Thermal Expansion and High Stiffness Based on Dual-Material Triangle Unit
,”
J. Mech. Phys. Solids
,
86
, pp.
173
191
.
23.
Miller
,
W.
,
Mackenzie
,
D.
, and
Smith
,
C.
,
2008
, “
A Generalised Scale-Independent Mechanism for Tailoring of Thermal Expansivity: Positive and Negative
,”
Mech. Mater.
,
40
(
4–5
), pp.
351
361
.
24.
Yan
,
M. G.
,
2001
,
China Aeronautical Materials Handbook
,
China Standard Press
,
Beijing, China
.
25.
Sigmund
,
O.
, and
Torquato
,
S.
,
1997
, “
Design of Materials With Extreme Thermal Expansion Using a Three-Phase Topology Optimization Method
,”
J. Mech. Phys. Solids
,
45
(
6
), pp.
1037
1067
.
26.
Wang
,
B.
,
Yan
,
J.
, and
Cheng
,
G.
,
2011
, “
Optimal Structure Design With Low Thermal Directional Expansion and High Stiffness
,”
Eng. Optim.
,
43
(
6
), pp.
581
595
.
27.
Yamamoto
,
N.
,
Gdoutos
,
E.
, and
Toda
,
R.
,
2014
, “
Thin Films With Ultra-Low Thermal Expansion
,”
Adv. Mater.
,
26
(
19
), pp.
3076
3080
.
28.
Yuan
,
Y.
,
Huang
,
J. Y.
, and
Peng
,
X. L.
,
2014
, “
Accurate Displacement Measurement Via a Self-Adaptive Digital Image Correlation Method Based on a Weighted ZNSSD Criterion
,”
Opt. Lasers Eng.
,
52
, pp.
75
85
.
29.
Miller
,
W.
,
Smith
,
C. W.
,
Mackenzie
,
D. S.
, and
Evans
,
K. E.
,
2009
, “
Negative Thermal Expansion: A Review
,”
J. Mater. Sci.
,
44
(
20
), pp.
5441
5451
.
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