Abstract

The advent of additive manufacturing (AM) has enabled the prototyping of periodic and non-periodic metamaterials (a.k.a. lattice or cellular structures) that could be deployed in a variety of engineering applications where certain combinations of performance features are desirable. For example, these structures could be used in a variety of naval engineering applications where lightweight, large surface area, energy absorption, heat dissipation, and acoustic bandgap control are desirable. Furthermore, combining the multifunctional design optimization of these structures with progressive degradation due to cyclic loading could lead to fatigue-activated attritable systems with potentially tailorable performances not yet in reach by current conventional systems. Nevertheless, in order to deploy these complex geometry structures their multiphysics response has to be well understood and characterized. The objective of the current effort is to describe an initial approach for designing a uniaxial metamaterial specimen for fatigue testing as the first step toward the design of multi-axial fatigue test coupons. In order to compare bending- and stretching-dominated structures, two strut-based lattices made of Ti-6Al-4V alloy consisting of the octet and tetrakaidecahedron (or Kelvin) cells are examined. The specimens are designed to fail in the central area of the specimen where edge effects are minimized. Finite element results of the relevant structural mechanics are implemented and exercised to compare the performance of the eight relevant geometries and to evaluate the effect of relative density on fatigue life.

Graphical Abstract Figure
Graphical Abstract Figure
Close modal

References

1.
Michopoulos
,
J.
,
Iliopoulos
,
A.
,
Steuben
,
J.
,
Birnbaum
,
A.
, and
Lambrakos
,
S.
,
2018
, “
On the Multiphysics Modeling Challenges for Metal Additive Manufacturing Processes
,”
Addit. Manuf.
,
22
, pp.
784
799
.
2.
Martukanitz
,
R.
,
Michaleris
,
P.
,
Palmer
,
T.
,
DebRoy
,
T.
,
Liu
,
Z.
,
Otis
,
R.
,
Heo
,
T.
, and
Chen
,
L.
,
2014
, “
Toward an Integrated Computational System for Describing the Additive Manufacturing Process for Metallic Materials
,”
Addit. Manuf.
,
1–4
(
9
), pp.
52
63
.
3.
Steuben
,
J.
,
Iliopoulos
,
A.
, and
Michopoulos
,
J.
,
2016
, “
Implicit Slicing for Functionally Tailored Additive Manufacturing
,”
Comput.-Aided Design
,
77
, pp.
107
119
.
4.
Gibson
,
I.
,
Rosen
,
D.
, and
Stucker
,
B.
,
2015
, “
Design for Additive Manufacturing
,”
Additive Manufacturing Technologies
, New York, pp.
399
435
.
5.
Wang
,
Y.
,
Xu
,
H.
, and
Pasini
,
D.
,
2017
, “
Multiscale Isogeometric Topology Optimization for Lattice Materials
,”
Comput. Methods Appl. Mech. Eng.
,
316
(
4
), pp.
568
585
.
6.
Wang
,
X.
,
Xu
,
S.
,
Zhou
,
S.
,
Xu
,
W.
,
Leary
,
M.
,
Choong
,
P.
,
Qian
,
M.
,
Brandt
,
M.
, and
Xie
,
Y. M.
,
2016
, “
Topological Design and Additive Manufacturing of Porous Metals for Bone Scaffolds and Orthopaedic Implants: A Review
,”
Biomaterials
,
83
(
3
), pp.
127
141
.
7.
Huang
,
X.
,
Zhou
,
S.
,
Xie
,
Y.
, and
Li
,
Q.
,
2013
, “
Topology Optimization of Microstructures of Cellular Materials and Composites for Macrostructures
,”
Comput. Mater. Sci.
,
67
(
2
), pp.
397
407
.
8.
Liu
,
K.
, and
Tovar
,
A.
,
May 19 - 24, 2013
, “
Multiscale Topology Optimization of Structures and Non-Periodic Lattice Materials
,”
10th World Congress on Structural and Multidisciplinary Optimization
,
Orlando, FL
.
9.
Coelho
,
P.
,
Fernandes
,
P.
,
Guedes
,
J.
, and
Rodrigues
,
H.
,
2008
, “
A Hierarchical Model for Concurrent Material and Topology Optimisation of Three-Dimensional Structures
,”
Struct. Multidiscipl. Optim.
,
35
(
2
), pp.
107
115
.
10.
Sivapuram
,
R.
,
Dunning
,
P.
, and
Kim
,
A.
,
2016
, “
Simultaneous Material and Structural Optimization by Multiscale Topology Optimization
,”
Struct. Multidiscipl. Optim.
,
54
(
5
), pp.
1267
1281
.
11.
Iliopoulos
,
A.
,
Jones
,
R.
,
Michopoulos
,
J.
,
Phan
,
N.
, and
Raman
,
R. S.
,
2018
, “
Crack Growth in a Range of Additively Manufactured Aerospace Structural Materials
,”
Aerospace
,
5
(
4
), p.
118
.
12.
Benedetti
,
M.
,
Du Plessis
,
A.
,
Ritchie
,
R.
,
Dallago
,
M.
,
Razavi
,
S.
, and
Berto
,
F.
,
2021
, “
Architected Cellular Materials: A Review on Their Mechanical Properties Towards Fatigue-Tolerant Design and Fabrication
,”
Mater. Sci. Eng.: R: Rep.
,
144
, p.
100606
.
13.
Huynh
,
L.
,
Rotella
,
J.
, and
Sangid
,
M.
,
2016
, “
Fatigue Behavior of IN718 Microtrusses Produced Via Additive Manufacturing
,”
Mater. Des.
,
105
(
9
), pp.
278
289
.
14.
Kelly
,
C.
,
Francovich
,
J.
,
Julmi
,
S.
,
Safranski
,
D.
,
Guldberg
,
R.
,
Maier
,
H.
, and
Gall
,
K.
,
2019
, “
Fatigue Behavior of As-Built Selective Laser Melted Titanium Scaffolds With Sheet-Based Gyroid Microarchitecture for Bone Tissue Engineering
,”
Acta Biomater.
,
94
, pp.
610
626
.
15.
Brenne
,
F.
,
Niendorf
,
T.
, and
Maier
,
H.
,
2013
, “
Additively Manufactured Cellular Structures: Impact of Microstructure and Local Strains on the Monotonic and Cyclic Behavior Under Uniaxial and Bending Load
,”
J. Mater. Process. Technol.
,
213
(
9
), pp.
1558
1564
.
16.
Burr
,
A.
,
Persenot
,
T.
,
Doutre
,
P.
,
Buffiere
,
J.
,
Lhuissier
,
P.
,
Martin
,
G.
, and
Dendievel
,
R.
,
2020
, “
A Numerical Framework to Predict the Fatigue Life of Lattice Structures Built by Additive Manufacturing
,”
Int. J. Fatigue
,
139
, p.
105769
.
17.
Lietaert
,
K.
,
Cutolo
,
A.
,
Boey
,
D.
, and
Van Hooreweder
,
B.
,
2018
, “
Fatigue Life of Additively Manufactured Ti6Al4V Scaffolds Under Tension-Tension, Tension-Compression and Compression-Compression Fatigue Load
,”
Sci. Rep.
,
8
(
1
), p.
4957
.
18.
Tomažinčič
,
D.
,
Nečemer
,
B.
,
Vesenjak
,
M.
, and
Klemenc
,
J.
,
2019
, “
Low-Cycle Fatigue Life of Thin-Plate Auxetic Cellular Structures Made From Aluminium Alloy 7075-t651
,”
Fatigue Fract. Eng. Mater. Struct.
,
42
(
5
), pp.
1022
1036
.
19.
Raghavendra
,
S.
,
Dallago
,
M.
,
Zanini
,
F.
,
Carmignato
,
S.
,
Berto
,
F.
, and
Benedetti
,
M.
,
2023
, “
A Probabilistic Average Strain Energy Density Approach to Assess the Fatigue Strength of Additively Manufactured Cellular Lattice Materials
,”
Int. J. Fatigue
,
172
, p.
107601
.
20.
Apetre
,
N.
,
Arcari
,
A.
,
Michopoulos
,
J.
,
Rodriguez
,
S.
,
Iliopoulos
,
A.
,
Steuben
,
J.
, and
Graber
,
B.
,
2023
, “
Towards Fatigue-Tolerant Design of Additively Manufactured Metamaterials
,” Proceedings of the ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference,
ASME
, Paper No. DETC2023-117512.
21.
Ashby
,
M.
,
2013
, “
Designing Architectured Materials
,”
Scr. Mater.
,
68
(
1
), pp.
4
7
.
22.
Al-Ketan
,
O.
,
Rowshan
,
R.
, and
Al-Rub
,
R.
,
2018
, “
Topology-Mechanical Property Relationship of 3D Printed Strut, Skeletal, and Sheet Based Periodic Metallic Cellular Materials
,”
Addit. Manuf.
,
19
, pp.
167
183
.
23.
Ashby
,
M.
,
2006
, “
The Properties of Foams and Lattices
,”
Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci.
,
364
(
1838
), pp.
15
30
.
24.
Deshpande
,
V.
,
Ashby
,
M.
, and
Fleck
,
N.
,
2001
, “
Foam Topology: Bending Versus Stretching Dominated Architectures
,”
Acta Mater.
,
49
(
6
), pp.
1035
1040
.
25.
Evans
,
A.
,
Hutchinson
,
J.
,
Fleck
,
N.
,
Ashby
,
M.
, and
Wadley
,
H.
,
2001
, “
The Topological Design of Multifunctional Cellular Metals
,”
Prog. Mater. Sci.
,
46
(
3–4
), pp.
309
327
.
26.
Gibson
,
L.
, and
Ashby
,
M.
,
1997
,
Cellular Solids
,
Cambridge University Press, Cambridge
.
27.
COMSOL AB
,
2023
, Comsol Multiphysics ® v. 6.1. Stockholm, Sweden.
28.
Ma
,
Q.
,
Zhang
,
L.
,
Ding
,
J.
,
Qu
,
S.
,
Fu
,
J.
,
Zhou
,
M.
,
Fu
,
M.
,
Song
,
X.
, and
Wang
,
M.
,
2021
, “
Elastically-Isotropic Open-Cell Minimal Surface Shell Lattices With Superior Stiffness Via Variable Thickness Design
,”
Addit. Manuf.
,
47
, p.
102293
.
29.
Soyarslan
,
C.
,
Blümer
,
V.
, and
Bargmann
,
S.
,
2019
, “
Tunable Auxeticity and Elastomechanical Symmetry in a Class of Very Low Density Core-Shell Cubic Crystals
,”
Acta Mater.
,
177
, pp.
280
292
.
30.
Zener
,
C.
,
1948
,
Elasticity and An elasticity of Metals
,
University of Chicago Press
,
Chicago, IL
.
31.
Clayton
,
J.
,
2010
,
Nonlinear Mechanics of Crystals
, Vol.
177
,
Springer Science & Business Media, London, New York
.
32.
Dowling
,
N.
,
2013
,
Mechanical Behavior of Materials: Engineering Methods for Deformation Fracture and Fatigue
,
Pearson
,
Boston, MA
.
33.
Findley
,
W. N.
,
1959
, “
A Theory for the Effect of Mean Stress on Fatigue of Metals Under Combined Torsion and Axial Load or Bending
,”
ASME J. Eng. Ind.
,
81
(
4
), pp.
301
305
.
34.
Socie
,
D. F.
,
1987
, “
Multiaxial Fatigue Damage Models
,”
ASME J. Eng. Mater. Technol.
,
109
, pp.
293
298
.
35.
Brown
,
M.
, and
Miller
,
K.
,
1979
, “
High Temperature Low Cycle Biaxial Fatigue of Two Steels
,”
Fatigue Fract. Eng. Mater. Struct.
,
1
(
2
), pp.
217
229
.
36.
Liu
,
J.
,
Lv
,
X.
,
Wei
,
Y.
,
Pan
,
X.
,
Jin
,
Y.
, and
Wang
,
Y.
,
2020
, “
A Novel Model for Low-Cycle Multiaxial Fatigue Life Prediction Based on the Critical Plane-Damage Parameter
,”
Sci. Prog.
,
103
(
3
), p.
0036850420936220
.
37.
Socie
,
D.
, and
Marquis
,
G.
,
1999
,
Multiaxial Fatigue, R-234
,
SAE International Publisher
,
New York
.
38.
Jesus
,
J.
,
Borrego
,
L.
,
Ferreira
,
J. M.
,
Costa
,
J.
, and
Capela
,
C.
,
2021
, “
Fatigue Behavior of Ti6Al4V Alloy Components Manufactured by Selective Laser Melting Subjected to Hot Isostatic Pressing and Residual Stress Relief
,”
Fatigue Fract. Eng. Mater. Struct.
,
44
(
7
), pp.
1916
1930
.
39.
Carrion
,
P.
, and
Shamsaei
,
N.
,
2019
, “
Fatigue Behavior of LB-PBF Ti-6Al-4VParts Under Mean Stress and Variable Amplitude Loading Conditions
,”
2019 Annual International Solid Freeform Fabrication Symposium
,
Austin, TX
,
Aug. 12–14
.
40.
Dowling
,
N.
,
2009
, “
Mean Stress Effects in Strain-Life Fatigue
,”
Fatigue Fract. Eng. Mater. Struct.
,
32
(
12
), pp.
1004
1019
.
41.
Apetre
,
N.
,
Arcari
,
A.
,
Dowling
,
N.
,
Iyyer
,
N.
, and
Phan
,
N.
,
2015
, “
Probabilistic Model of Mean Stress Effects in Strain-Life Fatigue
,”
Proc. Eng.
,
114
, pp.
538
545
.
42.
Kalnins
,
A.
,
July 25–29, 2004
,
Fatigue analysis in pressure vessel design by local strain approach: Methods and software requirements
,
Proceedings of the ASME/JSME 2004 Pressure Vessels and Piping Conference
,
San Diego, CA
, Pressure Vessel and Piping Codes and Standards, Vol. 4675, pp.
13
21
.
43.
Neuber
,
H.
,
1961
, “
Theory of Stress Concentration for Shear Strained Prismatic Bodies With Arbitrary Nonlinear Stress–Strain Law
,”
ASME J. Appl. Mech.
,
28
(
4
), pp.
544
550
.
44.
Manson
,
S.
, and
Hirschberg
,
M.
,
1966
, “
Crack Initiation and Propagation in Notched Fatigue Specimens
,”
Proceedings of the First International Conference on Fracture
,
Sendai, Japan
, Sept. 12–17, pp.
479
498
.
45.
Afroz
,
L.
,
Das
,
R.
,
Qian
,
M.
,
Easton
,
M.
, and
Brandt
,
M.
,
2022
, “
Fatigue Behaviour of Laser Powder Bed Fusion (l-PBF) Ti–6Al–4V, Al-Si-Mg and Stainless Steels: A Brief Overview
,”
Int. J. Fract.
,
235
(
1
), pp.
3
46
.
46.
Susmel
,
L.
,
2008
, “
The Theory of Critical Distances: A Review of Its Applications in Fatigue
,”
Eng. Fract. Mech.
,
75
(
7
), pp.
1706
1724
.
You do not currently have access to this content.