ORIGINAL RESEARCH
published: 31 July 2019
doi: 10.3389/fmats.2019.00169
Frontiers in Materials | www.frontiersin.org
1
July 2019 | Volume 6 | Article 169
Edited by:
Seunghwa Ryu,
Korea Advanced Institute of Science
and Technology (KAIST), South Korea
Reviewed by:
Dongchan Jang,
Korea Advanced Institute of Science
and Technology (KAIST), South Korea
Anastasiia O. Krushynska,
University of Groningen, Netherlands
*Correspondence:
Diego Misseroni
diego.misseroni@unitn.it
Specialty section:
This article was submitted to
Mechanics of Materials,
a section of the journal
Frontiers in Materials
Received:
14 January 2019
Accepted:
01 July 2019
Published:
31 July 2019
Citation:
Kudo A, Misseroni D, Wei Y and
Bosi F (2019) Compressive Response
of Non-slender Octet Carbon
Microlattices. Front. Mater. 6:169.
doi: 10.3389/fmats.2019.00169
Compressive Response of
Non-slender Octet Carbon
Microlattices
Akira Kudo
1
, Diego Misseroni
2
*
, Yuchen Wei
1
and Federico Bosi
3
1
Division of Engineering and Applied Science, California Ins
titute of Technology, Pasadena, CA, United States,
2
Department
of Civil, Environmental and Mechanical Engineering, Unive
rsity of Trento, Trento, Italy,
3
Department of Mechanical
Engineering, University College London, London, United Ki
ngdom
Lattices are periodic three-dimensional architected soli
ds designed at the micro and
nano-scale to achieve unique properties not attainable by t
heir constituent materials. The
design of lightweight and strong structured solids by addit
ive manufacturing requires the
use of high-strength constituent materials and non-slende
r geometries to prevent strut
elastic instabilities. Low slenderness carbon octet micro
lattices are obtained through
pyrolysis of polymeric architectures manufactured with st
ereolithography technique. Their
compressive behavior is numerically and experimentally in
vestigated when the relative
density
N
ρ
ranges between 10 and 50
%
, with specific stiffness and strength approaching
the limit of existing micro and nanoarchitectures. It is sho
wn that additive manufacturing
can introduce imperfections such as increased nodal volume
, non-cubic unit cell, and
orientation-dependent beam slenderness, all of which deep
ly affect the mechanical
response of the lattice material. An accurate numerical mod
eling of non-slender octet
lattices with significant nodal volumes is demonstrated to o
vercome the limitations of
classical analytical methods based on beam theory for the pr
ediction of the lattice
stiffness, strength and scaling laws. The presented numeri
cal results and experimental
methods provide new insights for the design of structural ca
rbon architected materials
toward ultra-strong and lightweight solids.
Keywords: architected materials, additive manufacturing, st
ructural metamaterials, pyrolyzed lattices, mechanics
1. INTRODUCTION
Additive manufacturing has become one of the most promising t
echnique to fabricate advanced
materials and microstructures that exhibit properties unatt
ained by homogeneous solids or
conventionally manufactured architectures. The available
3D printing techniques have recently
grown and comprise fused deposition modeling (FDM), direct ink w
riting (DIW), selective laser
sintering (SLS), stereolithography (SLA), etc. Similarly,
the selection of materials compatible
with these processes has expanded and include thermoelastic pol
ymers (
Carneiro et al., 2015
),
transparent glasses (
Nguyen et al., 2017
), oxide ceramics (
Wilkes et al., 2013
), metallic alloys
(
Schwab et al., 2016
), and composites (
Spierings et al., 2015; Ni et al., 2018; Quintanilla et al., 20
18
).
The precise micro- and nano-scale topology control achievabl
e through additive manufacturing
has allowed the development of unique functionalities to cat
alysis (
Essa et al., 2017
), batteries (
Xia
et al., 2016; Li et al., 2017
), scaffolds (
Maggi et al., 2017
), biomedical implants (
Murr et al., 2010
), and
Kudo et al.
Mechanics of Octet Carbon Microlattices
metamaterials (
Hengsbach and Lantada, 2014; Misseroni et al.,
2016; Bertoldi et al., 2017; Bilal et al., 2017
). In particular, the field
of architected material has benefited from the advancement o
f
small-scale manufacturing that enables the design of multi
stable
solids for energy storage (
Shan et al., 2015
), the evolution of
phononic bandgap behavior (
Sugino et al., 2015; Amendola
et al., 2018
) and the exploration of previously inaccessible
mechanical property combinations (
Bauer et al., 2016
). Examples
include structural metamaterials designed to achieve extr
emely
lightweight and strong solids through a hierarchical desig
n
(
Meza et al., 2015
) or novel highly deformable and recoverable
nanolattices made up of brittle materials (
Meza et al., 2014
).
Structured solids can be classified as rigid or non-rigid
architectures depending on their nodal connectivity, state
s of
self stress, and mechanisms (
Pellegrino and Calladine, 1986
).
The former includes octet lattices and shows a stretching
dominated behavior, while the latter mostly presents a bendi
ng
dominated response as demonstrated by pyramidal lattices. Th
e
response of architected materials has been extensively analy
zed
through the investigation of their constituent unit cells u
sing
beam theory to obtain the lattice effective stiffness and streng
th
scaling laws (
Gibson and Ashby, 1997; Deshpande et al., 2001
).
These analytical tools have been proven to well predict the
mechanical response of several lattices when the relative de
nsity
N
ρ
is lower than 0.1 and the strut slenderness ratio
r
/
l
does not
exceed 0.06 (
Meza et al., 2017
). However, some computational
and experimental studies (
Schaedler et al., 2011; Meza et al.,
2015; Bauer et al., 2016
) have recently reported deviations
from the classical scaling laws due to non-slender struts and
the influence of the node geometry (
Portela et al., 2018
),
thus proposing different scaling laws. The difficult micro- and
nano-scale fabrication of slender structured solids that o
bey to
classical scaling laws motivates the investigation of non-
slender
architectures with pronounced nodal volume caused by an
imperfect 3D printing. Therefore, the study of their mechanic
al
properties is fundamental for the design of stronger lattices
that
do not suffer from strut elastic instabilities.
One of the most promising materials to fabricate extremely
lightweight and resistant architected solids is carbon, wh
ich
has recently become compatible with additive manufacturing
processes. Direct ink writing (DIW) with printable inks that
contain graphene, carbon nanotube, and graphene oxide (
Fu
et al., 2017
) has been employed for the realization of flexible,
conductive, and chemically stable prototypes (
Sun et al., 2013;
Zhu et al., 2015; Yao et al., 2016; Zhang et al., 2016
),
while 3D-printed carbon fiber reinforced composites have
been manufactured by means of FDM (
Lewicki et al., 2017;
Anwer and Naguib, 2018
). Carbon nano- and micro-lattices are
another form of 3D printed carbon which have demonstrated
elevated structural performances. Architected carbon mate
rials
are obtained by pyrolyzing 3D-printed precursor, especially
polymer lattices prepared by photocuring techniques. Carbon
nanolattices fabricated through two-photon lithography hav
e
shown a strength comparable with the theoretical strength of
flaw insensitive glassy carbon (
Bauer et al., 2016
). This printing
technique solidifies the polymeric precursor solution point-
by-point at a submicron scale in a prolonged process, thus
preventing the production of micro- and nano-architectures
at a large scale. Carbon microlattices produced by self-
propagating photopolymer waveguides (
Jacobsen et al., 2011
)
and stereolithography (SLA) (
Chen et al., 2017
) overcome the
scalability difficulties toward faster manufacturing of lar
ger
scale lattices. However, their mechanical performances are
still limited, and the development of enhanced architected
solids demands further understanding of the influence of the
manufacturing-induced imperfection on the mechanics of 3D-
printed carbon lattices.
The aim of this work is to manufacture stiff and strong
non-slender octet carbon microlattices through digital ligh
t
processing stereolithography (DLP-SLA), and to analyticall
y,
computationally, and experimentally investigate their
compressive mechanical properties and scaling laws. We show
that DLP-SLA 3D printing and pyrolysis techniques can affect
the designed lattice architecture introducing undesired f
eatures
as increased nodal volume, non-cubic unit cell and different st
rut
slenderness depending on the beam orientation with respect
to the printing direction. We investigate the influence of the
se
factors on the compressive stiffness and strength of non-slend
er
lattices with relative density
N
ρ
that ranges between 10 and 50%.
We prove the inappropriateness of classical analytical tools bas
ed
on beam theory and the derived expressions for non-slender
architectures with negligible effective Poisson’s ratio, du
e to
the topological features that are not accounted for in these
formulations. We develop computational models that faithfu
lly
predicts the experimental lattice response by reproducing the
manufactured geometry and we demonstrate that an accurate
numerical modeling of non-slender octet lattices with signi
ficant
nodal volumes allows to identify the deviation from classica
l
scaling laws and enables a proper design of advanced structura
l
DLP-SLA 3D printed carbon architectures.
2. MATERIALS AND METHODS
2.1. Sample Fabrication
Three sets (
A
,
B
, and
C
) of carbon octet microlattices were
manufactured by pyrolyzing polymeric lattices fabricated wit
h
a DLP-SLA Autodesk Ember 3D printer that employs a PR-48
transparent photoresist resin. The periodic polymeric 3D printe
d
specimens consisted of a 10
×
3
×
6 (length
×
width
×
height)
tassellation of 900
m octet unit cell with three different strut
radii of
r
A
=
52.8
m,
r
B
=
71.4
m, and
r
C
=
90.0
m (
Figure 1
). The microlattices presented a theoretical relative
density
N
ρ
A
=
0.16,
N
ρ
B
=
0.27,
N
ρ
C
=
0.40, and a beam slenderness
ratio of