Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2018.
Supporting Information
for
Adv. Funct. Mater.,
DOI: 10.1002/adfm.201806772
Discrete-Continuum Duality of Architected Materials: Failure,
Flaws, and Fracture
Arturo J. Mateos, Wei Huang, Yong-Wei Zhang,* and Julia R.
Greer*
Supporting Information
Discrete-continuum duality of architected materials: failure, flaws, and
fracture
Arturo J. Mateos
a
, Wei Huang
b
, Yong-Wei Zhang
c
, and Julia R. Greer
a
a
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125;
b
School of Aeronautics, Northwestern Polytechnical University, Xi’an,
China, 710072;
c
Institute of High Performance Computing, A*STAR, Singapore, 138632
1. Fabrication
A multi step fabrication process is employed to fabricate nanomechanical tensile specimens; as illustrated in
Fig.
S1. Fabrication of all samples starts with the writing of a polymer sample made out of photoresist (IP-
Dip) using two-photon lithography (TPL) direct laser writing (DLW) in a Photonic Professional lithographic
system (Nanoscribe GmbH). Samples are written using laser powers in a range from 15-20
mW
and a
writing speed of 20000-50000
μm/s
. The laser power is used to control the effective diameter of the tubes,
and the speed varies slightly during the writing process to control the quality of the supporting structures.
Fig. S1.
Complete step-by-step fabrication process employed to create hollow tube tensile specimens.
The resulting polymeric sample is then critically-point dried with a Autosamdri 931 (Tousimis) and
conformally coated with
50
nm
of aluminum oxide (alumina) using atomic layer deposition (ALD). Deposition
is done at
150
◦
C
in a Cambridge Nanotech S200 ALD system using the following steps: H2O is pulsed for
15ms, the system is purged for 20s, trimethyl aluminum (TMA) is pulsed for 15ms, the system is purged for
20s, and the process is repeated. The carrier gas is nitrogen, which is used at a flow rate of
20
sccm
. The
process was repeated for 500 cycles to obtain the desired thickness coating. The thickness of the coatings
was verified using spectroscopic ellipsometry with an alpha-SE Ellipsometer (J.A. Wollam Co., Inc.).
After deposition, a focused ion beam (FIB) (Versa 3D DualBeam, FEI) is used to mill away auxiliary
beams of the sample to expose the polymer to air, as shown in Fig.
S2. Once the polymer is exposed,
samples are placed into a SP100 oxygen plasma system (Anatech Ltd.) for 50-80 hours at a pressure of
100
mTorr
and at
100
W
of power in order to remove the polymer from the gauge section. It is possible to
determine whether the polymer has been fully etched away by looking for any contrast change in the beams
using a scanning electron microscope, as shown in Fig.
S3. For tensile specimens, it is crucial to regularly
measure the etching profile to prevent structural damage of the supporting structures.
Fig. S2.
Focused Ion Beam (FIB) milling is employed to expose the polymeric core by removing sacrificial beams.
Etching profile.
To expose the polymer core and etch it away, auxiliary struts were milled by focused-ion
beam (FIB) milling to provide an opening for oxygen plasma to ash the polymer using a SP100 oxygen
plasma system (Anatech Ltd.) (Figs.
S2-S3). The addition of auxiliary struts enables the exposure of the
internal polymer with minimal ion bombardment to sacrificial material and no damage in critical regions of
the sample, such as the vicinity of the notch root. Excessive ion bombardment could induce material and
geometric defects, such as changes in the material composition and introduce external flaws in the form of
missing struts or nodes. The final sample consists of a ceramic hollow-tube gauge section supported by
polymer-alumina composite structures.
Sample Survival Rate.
There are several critical steps in the fabrication process that reduced the sample
survival rate. More than 1000 samples were successfully written on silicon substrates but
∼
114
samples
were used during the analysis of this work. Most samples were successfully developed, critically point dried,
and coated with ALD alumina. Sacrificial beams and a pre-defined notch allowed for a high survival rate
after focused ion beam milling; which enabled identical samples regardless of the presence of a notch or
notch orientation. The survival rate after the etching process was low (
∼
10%
) making this the critical step
in the fabrication process. The low survival rate is mostly due to the high probability of finding an unwanted
defect in the alumina thin film which lets
O
2
plasma etch the substrate at undesirable locations. For
example, if a defect (in the form of a crack or void) is located at the interface between the bottom support
and the substrate, then etching will simultaneously start at the gauge section and at the bottom support.
Since the etching rate is higher for the support compared to the tortuous paths of the gauge section, then
the support will be completely hollowed out before the gauge section is ready for the tension experiment. A
Mateos et al.
Page 2
Fig. S3.
Etching profile. Sacrificial beams are removed from both sides of the gauge section to expose the polymer core to oxygen plasma. The duration of the etching
process depends on the number of openings and the distance between the openings and the wavefront of polymer. Afterwards, the gauge section consists of hollow alumina
tubes.
visual inspection of the supports with a microscope does not necessarily allow the determination of failed
samples, which leads to evaluating the integrity of the samples during the testing phase. The minimum
hours required to fabricate an tension specimen with an architected gauge section is
>
84.5
hr/sample
, as
listed in Table
S1.
Table S1. Duration of each step during the fabrication process and testing phase.
#
Process
Duration
Approx. survival rate
1
Substrate preparation
1
hr/sample
99%
2
Two-photon lithography
4
hr/sample
90%
3
Resin development
0.5
hr/sample
90%
4
Critical point drying
1
hr/sample
90%
5
Thin film deposition
6
hr/sample
90%
6
Focused ion beam milling
1
hr/sample
90%
7
O
2
plasma etching
>
70
hr/sample
10%
8
Tension experiment
1
hr/sample
80%
TOTAL
>
84.5
hr/sample
10%
Mateos et al.
Page 3
2. Center-notched tension design for architected materials
Adequate consideration of sample design must be taken into account for a proper tensile test, at any length
scale. The sample design must prevent induced stress concentrations and premature failure initiation sites,
introduced by the required supporting structures bracing the gauge section. The nanolattices in this work
were designed to emulate conventional conditions for fracture experiments in monolithic materials, where
samples take a dog-bone shape with a central gauge section of uniform width. The gauge section is braced
by a bottom support attached to the substrate and a top support that engages with a custom-made tension
grip in an in-situ nanomechanical instrument (InSEM, Nanomechanics Inc.). The supports were designed
to minimize the stress concentrations and premature failure initiation at their interfaces with the gauge
section. The gauge section contains 918 octet unit cells (27 (height, H) x 17 (width, W) x 2 (thickness, B)).
The as-fabricated dimensions consist of an average unit cell length of
4
.
72
±
0
.
03
μm
, an average outer tube
radius of
491
nm
±
62
nm
with eccentricity of 1.1, and alumina tube wall thicknesses of
50
nm
.
The gauge section geometry was generated using MATLAB scripts and the supporting structures were
designed using a CAD model generated with Solidworks (Dassault Systèmes). These CAD models were
also used to determine the relative density of the samples. The notch geometry was designed to resemble
naturally occurring cracks in lattices. For materials with lattice architectures, notches come in the form of
a combination of structural imperfections; such as unconnected or broken struts and missing nodes. We
fabricated some of the samples to contain a pre-defined through-thickness notch, which was composed of
a collection of omitted tubes with relative notch lengths of
2
a/W
= 0
.
45
and notch orientations varying
from 0 to 90 degrees with respect to the direction of loading. Notch orientations are related to the
in-plane cubic symmetry of the octet ranging from 0 to 90 degrees; that is,
β
=
arctan
(
i
)
·
(
180
π
)
where
i
= [0
,
0
.
5
,
1
,
2
,
8
,
∞
]
. The addition of the notch to the pre-defined gauge section designs provides consistent
means of fabricating nearly identical samples. The designs were used as input to the lithographic instrument.
A visual representation of the notch generating scripts is provided with
Video S3
.
Mateos et al.
Page 4
90.0
°
63.4
°
45.0
°
26.6
°
7.1
°
A
0.0
°
B
C
Fig. S4.
Center-notch geometry generated by MATLAB scripts. (A) Architected gauge sections of notched samples contain a pre-defined through-thickness notch composed
of a collection of omitted tubes and nodes with relative notch lengths of
2
a/W
= 0
.
45
and notch orientations varying from 0 to 90 degrees with respect to the direction of
loading. (B-C) Close-up MATLAB image of notch oriented at 63.4 degrees and corresponding SEM image of final sample.
3. Nanomechanical experimental setup
Uniaxial tension experiments were conducted in an in-situ nanomechanical instrument (InSEM, Nanome-
chanics Inc.) to observe global and local failure behavior. Samples were subjected to an applied tensile
load at a quasi-static strain rate of
10
−
3
s
−
1
by engaging with a custom-made tension grip. The tension
grip was machined on the head of a
0
.
8
mm
stainless steel screw by electrical discharge machining, see Fig.
S5.
Video S1
and
Video S2
show the in-situ mechanical data and its corresponding real-time video of the
deformation of an unnotched and notched specimen.
Mateos et al.
Page 5
Fig. S5.
Custom tension grip used to test nano-architected tensile samples.
4. Data Analysis Methods
To correctly measure the uniaxial tensile properties of a material, special techniques must be adopted in order
to avoid damaging samples and compromising the area of interest. However, the additional material that
must be used to grip, support, or adhere the sample, will lie in the loading path and influence the recorded
strain measurements. The contributions from these sources must be accounted for to accurately report
the strains of the area of interest. The extension from outside the gauge section must be determined and
subtracted from the total measured extension. The total measurement of the stiffness for the nanomechanical
experiments can be viewed as the effective stiffness of springs in series, as illustrated in Fig.
S6A and
quantified as
1
K
eff
=
1
K
+
1
K
s
[1]
where
K
eff
is the effective stiffness recorded by the nanomechanical instrument,
K
is the stiffness of the
gauge section, and
K
s
is the stiffness outside of the gauge section, as shown in Fig.
S6B. Since compliance
is the inverse of stiffness, Eq.
1 can be written as
C
eff
=
C
+
C
s
[2]
Additional experiments on samples without the gauge section were performed to determine
C
s
. Samples
were fabricated without the hollow gauge section, as shown in Fig.
S6C. Two layers of alumina-polymer
core-shell composite octet unit cells make up the central section of these samples to resemble the few
composite unit cells in samples with complete hollow gauge sections. The average compliance of multiple
samples was determined and subtracted from the displacement and subsequent strain calculations for each
unnotched and notched sample. The corrected displacements were then normalized by the gauge section
length to determine engineering strains. The corresponding loads for all samples were converted to stresses,
defined as
σ
=
P/A
;
P
is the measured load and
A
is the total cross-sectional area perpendicular to the
load.
Displacements and strains of the gauge section could also be calculated using the observed length change
with the real-time deformation video recorded by the scanning electron microscope. However, since the
window frame of the video must account for the entire gauge section (
∼
120
μm
in length) and total strain
Mateos et al.
Page 6