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Green laser powder bed fusion based fabrication and rate-dependent
mechanical properties of copper lattices
Sung-Gyu Kang
a,
⇑
, Ramil Gainov
b
, Daniel Heußen
c
, Sören Bieler
d
, Zhongji Sun
e
, Kerstin Weinberg
d
,
Gerhard Dehm
a
, Rajaprakash Ramachandramoorthy
a,
⇑
a
Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Straße 1, 40237 Düsseldorf, Germany
b
Institute of Mineral Resources Engineering, RWTH Aachen University, Wüllnerstraße 2, 52062 Aachen, Germany
c
Fraunhofer-Institut für Lasertechnik ILT, Steinbachstraße. 15, 52074 Aachen, Germany
d
Lehrstuhl für Festkörpermechanik, Universität Siegen, Paul-Bonatz-Straße 9-11, 57068 Siegen, Germany
e
Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Republic
of Singapore
highlights
Cu architectures with dense
microstructure and well-defined
complex geometries are achievable
through L-PBF with green laser.
Cu lattice structures exhibit
continuous plastic deformation with
strain hardening under compression.
Cu lattice structures show a
significant increase in strengths at a
dynamic strain rate of 1000/s.
Cu lattice structures exhibit a high
energy absorption capacity of 128 J/
mm
3
.
graphical abstract
article info
Article history:
Received 4 January 2023
Revised 12 April 2023
Accepted 19 May 2023
Available online 27 May 2023
Keywords:
Powder bed fusion
Copper
Lattice structures
Mechanical properties
Strain rate
abstract
Additive manufacturing of pure copper (Cu) via laser-powder bed fusion (L-PBF) is challenging due to the
low energy absorptivity under infra-red laser. As a result, 3-dimensional architectures, known for excel-
lent load-bearing and energy absorption capabilities, have not been fabricated in pure Cu, so far. This
study, for the first time, Cu lattice structures are fabricated through laser-powder bed fusion (L-PBF) with
green laser (k= 515 nm). Structural and microstructural analysis confirm that the lattice structures con-
sist of well-defined unit-cells and show dense microstructure. The deformation behavior is investigated
under a wide range of strain rates from 0.001 /s to 1000 /s. The stress–strain curves exhibit a smooth
and continuous deformation without any post-yield softening, which can be attributed to the intrinsic
mechanical properties of Cu. Correlated with post-mortem microscopy examination, the rate-
dependent deformation behavior of pure Cu lattice structures is investigated and rationalized. The cur-
rent work suggests that the complex Cu architectures can be fabricated by L-PBF with green laser and
are suitable for dynamic loading applications.
Ó2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
1. Introduction
Pure copper (Cu) exhibits excellent electrical/thermal conduc-
tivities and high ductility and has become an essential component
https://doi.org/10.1016/j.matdes.2023.112023
0264-1275/Ó2023 The Author(s). Published by Elsevier Ltd.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
⇑
Corresponding authors.
E-mail addresses: s.kang@mpie.de (S.-G. Kang), r.ram@mpie.de (R. Ramachan-
dramoorthy).
Materials & Design 231 (2023) 112023
Contents lists available at ScienceDirect
Materials & Design
journal homepage: www.elsevier.com/locate/matdes
in engineering applications. Advance in additive manufacturing
(AM) technology allows the fabrication of materials into complex
geometry which can be directly applied to engineering applica-
tions. To date, most AM-built structures are made by the laser-
powder bed fusion (L-PBF) technique, largely due to the process’s
refined surface finish and design freedom. However, it is currently
a challenge to fabricate pure Cu through the conventional L-PBF
route, which typically employs an infra-red laser with a
wavelength > 1000 nm. This is because the Cu energy absorptivity
drops significantly (<10 %) once the laser wavelength is
above 800 nm [1]. Together with this material’s high thermal
conductivity (400 W/m-K), it is difficult to maintain a stable melt
pool during fabrication. A preliminary study on the solid Cu parts
built via L-PBF reported a high density of internal fusion defects
agreeing with the previous hypotheses [2]. This problem can be
partially alleviated by increasing the laser power [3,4], decreasing
the spot size [5,6], and decreasing the powder size [7]. Recently, Qu
et al. successfully fabricated dense Cu structures via L-PBF with an
infra-red laser by systematically controlling the spot size, the layer
thickness, and the powder size [5,6]. With the optimized process
parameters and the concentrated energy, the Cu structures exhibit
enhanced strength and ductility without loss of thermal and elec-
trical conductivities. A more direct approach is to employ a laser
source with a lower wavelength. It has been recently reported that
the high energy absorptivity of Cu under a blue [8] or a green laser
[9,10] (wavelengths are 450 and 515 nm, respectively) allows fully
dense prints of Cu parts. Correspondingly, conceptual/theoretical
studies for Cu-based 3-dimensional architectures, utilizing their
mechanical, electrical, and thermal properties have been previ-
ously proposed [11-13], yet the fabrication and mechanical perfor-
mance of Cu-based architectures remain unexplored so far.
The lattice structures are widely known 3-dimensional archi-
tectures, composed of periodic solid frames and pores. Its periodic-
ity enables higher specific strength compared to unstructured
foams. Combined with large deformation until densification under
constant loads arising from the low relative density, the lattice
structures can exhibit a larger absorption capacity compared to
solid materials under compression [14-16]. The AM processes have
enabled several studies on lattice structures with envisioned appli-
cations in a variety of sectors including aerospace [17,18], bioma-
terials [19-23], mechanical band gap engineering [24-26], and
impact absorption [27-33]. The deformation characteristics of lat-
tice structures strongly depend on the geometry and the material.
From the geometrical point of view, the strength of the lattices can
be tuned by controlling the orientation of load-bearing solid
frames, density, and connectivity. To date, various lattice geome-
tries such as open-cell truss lattices [27,29,34,35], closed-cell plate
lattices [36-38], triply periodic minimal surface structures [39-41],
and shell structures [42,43], have been investigated both experi-
mentally and computationally. From the material point of view,
previous studies have shown that the intrinsic mechanical proper-
ties of the material strongly affect the deformation characteristics
of lattice structures. The microlattice structures made of brittle
materials such as alumina [43-46] and pyrolytic carbon [36] show
high strength but low plasticity. On the other hand, the macroscale
lattice structures made of metals such as Ti- [47-50], Al- [51], and
Fe-alloys [52,53] show continuous deformation with large plastic
strains, leading to superior energy absorption capacity as com-
pared to random foam structures. It suggests that lattice structures
made of pure Cu can also exhibit unique load-bearing and energy
absorption capabilities, along with Cu’s inherent thermal and elec-
trical properties.
To evaluate the load-bearing and the energy absorption capabil-
ities of lattice structures, the deformation behavior needs to be
investigated at a wide range of strain rates. This is because the
strength of bulk metallic materials show a distinctive strain rate
dependency, governed by the dislocation movements [54]. Like-
wise, lattice structures made of such materials are also subjected
to the influence of different strain rates during plastic deforma-
tions. However, due to the experimental complexities and the
requirement of different testing devices, the deformation behavior
of previously designed lattice structures was mainly studied either
at quasi-static (0.001 /s) [55,56] or dynamic strain rates (1000 /s)
[57,58]. Therefore, this is currently a knowledge gap on mechanical
behavior of lattice structures across the full range of strain rates,
i.e., including the quasi-static, the intermediate (0.01 100 /s),
and the dynamic strain rates (>1000 /s). Such data is critical to
thoroughly understand the deformation behavior of lattice struc-
tures and propose future design guidelines for lattice structure
adoptions.
In this study, for the first time, we demonstrate that complex
lattice structures made of pure Cu can be fabricated successfully
via L-PBF with a green laser. The structural and microstructural
analysis confirms that pure Cu lattice structures show well-
defined geometries close to the original designs and dense
microstructure. Systematic mechanical testing at a wide range of
strain rates from 0.001 to 1000/s reveals that different lattice archi-
tectures (octet and cuboctahedron) show different deformation
characteristics. But more importantly, the pure Cu lattice struc-
tures deform continuously during compression without post-
yield softening which is commonly the response of lattice struc-
tures with similar geometries made of other materials. Combined
with post-mortem structural and microstructural analysis, the
deformation mechanisms and the mechanical performance of Cu
lattice structures were identified. We believe that this study will
expand the applicability of additively manufactured pure Cu struc-
tures and will provide a guideline for the fabrication of metallic lat-
tices for dynamic applications.
2. Experimental methods
2.1. Sample preparation
The deformation of strut-based lattice structures is primarily
dictated by the nodal connectivity according to Maxwell’s criteria
[59],
M¼b3jþ6ð1Þ
where band jare the number of struts and intersections (nodes) in
the unit cell. For the structure with high nodal connectivity (M0),
the deformation is dominated by the stretching of struts. For the
structure with low nodal connectivity (M<0), the deformation is
dominated by the bending of struts [14]. Accordingly, we selected
an octet-truss structure with M¼0 (denoted as Oct) and a cubocta-
hedron structure with M¼6 (denoted as Cub) as unit cells of the
lattice structures (Fig. 1(a, b)). The unit-cell length and the strut
diameter were chosen as 1.5 mm and 300
l
m, respectively. The rel-
ative densities of Oct and Cub structures are 0.38 and 0.21, respec-
tively. Each lattice structure was designed to have 80-unit cell
repetitions: A 4-repetition of unit cells along the z-axis, and a 20-
repetition of unit cells in a cross-section perpendicular to the z-
axis. In the cross-section perpendicular to the z-axis, we discretized
the unit-cell geometry and arranged them symmetrically, optimiz-
ing the lattice geometry for the mechanical test (Fig. S1). Additional
plates at the top and the bottom of the lattice structure were intro-
duced to ensure uniform deformation under loading along the z-
axis. Computer-aided design (CAD) files of the Cub and the Oct
structures were designed for the following fabrication process.
We utilized the L-PBF process with both green laser and infra-
red laser beams (k= 515 and 1064 nm) for the sample fabrication.
The pure Cu (electrolytic tough-pitch) powder with a diameter of
S.-G. Kang, R. Gainov, D. Heußen et al. Materials & Design 231 (2023) 112023
2
16–63
l
m (Nanoval GmbH) was used. Before the lattice fabrica-
tion, the L-PBF parameters, such as laser power, scan speed, layer
thickness, and beam diameter were determined after a sequential
process parameter optimization by fabricating the test cuboidal
samples (10 mm 10 mm 10 mm) with varying parameters
to maximize the density. Afterwards, vector parameters such as
beam compensation and gap between vector contours were opti-
mized on the lattice structures. For the lattice fabrication with
the green laser, laser power, scan speed, and beam diameter were
set as 600 W, 1000 mm/s, and 160
l
m, respectively. For the lattice
fabrication with the infra-red laser, laser power, scan speed, and
beam diameter were set as 600 W, 800 mm/s, and 80
l
m, respec-
tively. In both cases, a layer thickness was set as 20
l
m. For the lat-
tice part, due to the small strut diameter, only the contour laser
scanning was adopted (contour fill). A gap of 80
l
m was intro-
duced between each contour. For the top and bottom plates, a
hatch spacing of 100
l
m was adopted. The LPBF process was con-
ducted under inert gas (Ar) flow (<100 ppm residual oxygen). The
parameters of the LPBF process with two different laser beam
sources are summarized in Table 1.
To reduce the surface roughness of as-fabricated lattice struc-
tures, a chemical etching step was conducted on every specimen
before mechanical testing (Fig. S2). The Cub and Oct copper struc-
tures were immersed into a chemical etchant (5 g FeCl
3
+10ml
HCl + 100 ml H
2
O) for 200 sec [60-62].
2.2. Rate-dependent compression tests
The mechanical properties of Cu lattice structures across six
orders of strain rate magnitude were investigated. To explore such
a wide range of strain rates, we utilized a combination of a
dilatometer (DIL 805A/D, TA instruments) (0.001/s – 10/s) and a
split-Hopkinson pressure bar (SHPB) testing setup (1000/s) at
room temperature. The SHPB testing setup consists of two bars
with a length and diameter of 1800 mm and 20 mm. Both the inci-
dent bar and the transmission bar are made of aluminum. The stri-
ker has a length of 500 mm and is made of the same material as the
bars. With strain gages placed centrally on the bars, the signals can
be recorded at a sampling rate of 1 M samples per second. Striker
speeds between 8 and 14 m/s were used to achieve the required
high strain rates and strains.
Before the compression test, the top and bottom surfaces of
each specimen were mechanically polished. The structures were
compressed to 25 and 50 % engineering strains at strain rates of
0.001, 0.01, 0.1, 1, 10, and 1000 /s. We evaluated the nominal stress
and strain by dividing the load by the effective cross-sectional area
of the lattice structure and by dividing the displacement by the
height of the sample, respectively. The structural and microstruc-
tural analyses were conducted before and after the mechanical test
to explore the deformation mechanisms involved.
2.3. Structural analysis
2D and 3D structural analysis of additively manufactured metal
parts can be effectively studied using computed tomography (CT)
[63,64]. ProCon CT-Alpha industrial X-ray CT equipment was used
for the non-destructive structural analysis of the Cu lattice struc-
tures. This CT system includes a high-precision setup, leading to
fine and stable geometric positioning within the 3D space using a
5-axis of x-y-z-rotation-tilting system with a reproducible
accuracy <1
l
m and resulting in a resolution of up to around
2
l
m for appropriate contrast images. The detector system XRD
1611 AP3 has 4064 4064 pixels, with each pixel dimension
of 100
l
m. The X-ray tube XWT-240-TCHE Plus by X-ray WorkX
Fig. 1. Geometry of lattice structures made of pure Cu.(a) Computer-aided design of unit-cells and lattice structures. (b) Optical photographs of pure Cu lattice structures
fabricated by L-PBF with green laser beam. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1
Process parameters of L-PBF with green and infra-red laser.
Laser type Laser power (W) Scan speed (mm/s) Beam diameter (
l
m) Layer thickness (
l
m) Hatch distance (
l
m)
Green 600 1000 160 20 100
Infra-red 600 800 80 20 100
S.-G. Kang, R. Gainov, D. Heußen et al. Materials & Design 231 (2023) 112023
3
GmbH has an anode made of tungsten target material. This X-ray
tube reaches a maximum of 240 kV, leading to increased penetra-
tion of high-density samples. Software VG Studio MAX 3.5 of Vol-
ume Graphics GmbH (Heidelberg, Germany) was used for the 3D
reconstruction and analysis of the MicroCT scans.
In this study, CT investigations were carried out using high-
power X-ray tube mode to reach appropriate statistics within a
short time. The parameters were optimized to observe the internal
structure of Cu lattice structures. The parameter values for 3D
image exposition were as follows: voltage of about 150 kV and cur-
rent of about 200
l
A during a measurement time of approximately
30–40 min. The voxel size for the samples investigated was around
30
l
m and filters with tin plates of 1 mm thickness were used.
These optimized parameters were kept constant for all the investi-
gated samples to ensure stable and comparable CT results.
2.4. Microstructural analysis
We characterized the microstructure of Cu lattice structures
before and after the deformation. The cross-section of specimens
parallel to the building direction was polished with colloidal silica.
A field-emission scanning electron microscope (FE SEM, Sigma,
ZEISS) equipped with an electron backscattering diffraction (EBSD,
TSL) detector was used for obtaining the microstructure. A critical
misorientation angle for grain boundaries was set as 15°, to distin-
guish between low-angle grain boundary (LAGB) and high-angle
grain boundary (HAGB).
2.5. Finite element analysis
Stress distribution in the lattice structures under compression
load was examined through finite element analysis (COMSOL Mul-
tiphysics). Based on the CAD design of Oct structure, a 3-
dimensional model was constructed. Due to the high computa-
tional cost, only the elastic deformation of Oct structure was con-
sidered. Density, elastic modulus and Poisson’s ratio of Cu were set
as 8960 kg/m
3
, 120 GPa and 0.34, respectively. To describe the
deformation under compression, the bottom plate of the structure
was fixed, and the top plate was set to move downward by the pre-
scribed displacement. The Oct CAD model was subsequently
meshed using triangular elements. There were 187,393 elements
and 840,294 degrees of freedom in the model.
3. Results and discussion
3.1. Structural analysis
The Cu lattice structures in this study show well-defined open-
pore channels and nodal connectivity. As-fabricated lattice struc-
tures have rough surfaces originating from the unmelted powder
adhesion, which may induce strong stress concentrations and facil-
itate subsequent crack initiation during deformation [65-67].
Therefore, chemical etching was conducted on the lattice struc-
tures. Fig. S2 shows the reduction of unmelted powders on the sur-
face after the chemical etching. Fig. 1 (b) shows the optical
photographs of undeformed Oct and Cub structures after the
chemical etching. Visual inspection shows that the open-pore
channels are clearly distinguished, and they are consistent with
the pre-defined CAD design. Detailed geometries and the nodal
connectivity of lattice structures can be obtained from the tomo-
graphic analysis (Fig. 2). Fig. 2 (a, b) are the 3-dimensional recon-
struction slice of each structure viewed from a specific angle
where the Oct and Cub structures can be easily distinguished (de-
tailed CT 3-dimensional reconstructions of lattice structures are
shown in Movies M1 and M2). Importantly, the horizontal and
the inclined struts are almost identical to the original CAD designs
that constitute and differentiate the lattice structures from each
other. The geometrical feature sizes of each structure were also
evaluated from the reconstructions. From the 3-dimensional
reconstruction, the unit-cell length and the strut diameter of Oct
and Cub structures are 1.46 (±0.02) and 1.49 (±0.01) mm, 328
(±27) and 347 (±16)
l
m, respectively. Compared to the original
designs (1.5 mm of unit-cell length and 300
l
m of strut diameter),
the printed parts show only 2 and 13 % difference in the unit-cell
length and the strut diameter of Oct and Cub structures.
Both structures show rough surfaces with spherical agglomer-
ates as confirmed by the surface SEM images (Fig. S2). The spheri-
cal agglomerates may stem from a balling effect induced by less
optimized process parameters [68,69]. Moreover, the fabrication
of 3-dimensional structures with open-pore channels through L-
PBF leads to uncontrolled and inhomogeneous powder adhesion
on the beam surfaces and resultant rough surfaces [70-72]. The
high thermal conductivity of Cu leads to further unmelted powder
adhesion to the melt pool during solidification due to insufficient
remelting [5,73].
The presence of internal pores in both structures was confirmed
via experimental X-ray CT investigation. Fig. 2 (c, d) shows a CT
analysis of the porosity distribution in lattice structures. The CT
study provided detailed 3-dimensional pore distributions in the
lattice structures, as shown in Movies M1 and M2. In both cases,
the volume of closed pores is mostly below 0.01 mm
3
, but there
are also a few large pores with a volume of 0.03 0.05 mm
3
.
The closed pores with sizes below 0.01 mm
3
are most probably
due to the lack of powder fusion [74,75]. Notably, there are more
small pores in the Cub structure than in the Oct structure. It is
known that structures with low inclination angles fabricated by
the L-PBF process tend to exhibit high porosity [76]. It is attributed
to a different cooling rate in the upper part and lower part of the
strut with a low inclination angle. The excess energy in the lower
part may lead to an instability of the melt pool. The Cub structure
shows a higher volume fraction of horizontal struts (33 %) com-
pared to the Oct structure (25 %). Furthermore, the Oct structure
shows higher nodal connectivity which may lead to a relatively
uniform cooling rate in the horizontal struts. Of the large pores
in both structures, most of them are located in the lower half of
the structure. Given that the bottom plate of the lattice structure
was in direct contact with a base substrate, the cooling rate at
the bottom plate may be slightly higher than that at the lattice
structure and the top plate. Such a higher cooling rate may reduce
the heat absorption of material during fabrication, leading to the
formation of pores.
Even with the surface roughness and the internal pores, the lat-
tice structures in this study which are fabricated by green laser
irradiation show considerably fewer fusion defects compared to
the previously studied pure Cu structures which were fabricated
by using a conventional L-PBF process with infra-red laser [4,77-
83]. As a direct comparative study, we also fabricated the Oct
structure by using the conventional L-PBF process with an infra-
red laser (Fig. S3 (a, b)). Notably, the Oct structure fabricated with
the infra-red laser shows a relatively smooth surface than the one
fabricated by the green laser. It can be attributed to the different
beam diameters used: 160
l
m for green laser and 80
l
m for
infra-red laser. It has been previously reported that a laser beam
with a large diameter may induce balling and a large re-heated
zone, leading to a rough surface of the printed part [84,85]. Despite
the relatively smooth surface, due to the low energy absorption,
the Oct structure fabricated by infra-red laser exhibits even larger
fusion defects, and the defects/cracks are distributed throughout
the structure (Fig. S3)[2]. To summarize, the high energy absorp-
tion of Cu from the green laser during the L-PBF process is the
S.-G. Kang, R. Gainov, D. Heußen et al. Materials & Design 231 (2023) 112023
4
key to obtaining a well-defined geometry and a low defect density
in lattice structures.
3.2. Microstructural analysis
The materials fabricated by L-PBF typically show unique
microstructures such as columnar dendritic structures [86-88],
elongated grains [89-91], strong texture [92-94], and dislocation
cell structures [95-97] along the building direction due to the
repetitive rapid heating and cooling. Hence, we examined the
microstructure in the cross-section along the building direction
of each lattice structure. Fig. 3 shows the microstructure of the rep-
resentative unit cross-section in the undeformed Oct structure.
Consistent with the structural analysis using microCT, the cross-
section shows the well-defined and fully dense struts and nodes.
From the inverse pole figure (IPF) maps along the building direc-
tion and the corresponding pole figure maps in Fig. 3 (a), the
microstructural characteristics of lattice structures were identified.
Firstly, the grains are elongated but no solidification dendrites are
identified. The size of solidification dendrite typically varies from
300 nm to 1
l
m[98], and no such feature is observed in the current
study, as shown in the high-magnification EBSD maps Fig. 3(a). The
absence of the dendritic structure indirectly reflects the high purity
of our copper powder feedstock, that the material solidifies in a
planar solidification mode without partitioning-induced interface
protrusion or turbulence. Secondly, there is no strong crystallo-
graphic texture in the material. The pole figure maps along the
building direction in Fig. 3 (a) indicate that there is no apparent
preferential texture. Metallic materials fabricated by the L-PBF pro-
cess are known to show a strong crystallographic texture along the
building direction, as the grain grows parallel to the temperature
gradient [92-94]. For bulk copper, {100} or {11 0} texture along
the building direction has been reported previously [60]. However,
for the lattice structures, the unmelted or partially melted particles
act as nucleation sites for new grains, which hinders the texture
development along the building direction [99]. The elongated
grains along the cooling direction are also responsible for the weak
texture. Due to the different axial directions of struts, the temper-
ature gradient during the L-PBF process is not always parallel to
the building direction. Moreover, multiple re-melting and solidifi-
cation cycles can introduce randomness in the crystallographic
texture [60]. The small difference between the gap of each contour
scan (80
l
m) and the laser beam diameter (160
l
m) used for the
lattice fabrication process leads to additional re-melting and solid-
ification. Thirdly, we hypothesize that there are residual stresses at
the node of the lattice structure. The grain boundary map and Ker-
nel average map in Fig. 3 (b) indicate the presence of residual stres-
ses in the solidified materials [100,101]. At the nodes of the lattice
structure, there is a high density of low-angle grain boundaries and
high local misorientation. Thermal stress at the node may not have
been completely relieved, as the volume change is limited by the
surrounding truss components. The misorientation angle distribu-
Fig. 2. Tomographic analysis of pure Cu lattice structures. (a, b) 3-dimensional reconstruction of lattice structures. (c, d) Porosity distribution map of lattice structures.
S.-G. Kang, R. Gainov, D. Heußen et al. Materials & Design 231 (2023) 112023
5
tion in Fig. 3 (c) confirms a high fraction of LAGB, while for HAGB
(>15°), the distribution follows that of random misorientation.
Lastly, the average grain size (measured by the equivalent circle
diameter method) of the lattice structure is 30 ± 19
l
m. The grain
size distribution in Fig. 3 (d) implies a large fraction of small size
grains (<15
l
m). As shown in Fig. 3 (a, b), the small grains are
mostly located at the outer surface of the structure (thickness of
small grain layer is 38 ± 10
l
m). These grains may come from
unmelted or partially melted powders remaining after the chemi-
cal etching. The chemical etching was conducted on the as-
fabricated lattice structures to partially alleviate the surface rough-
ness which may lead to early yielding or crack formation during
deformation. Nevertheless, some unmelted powder remains even
after chemical etching. However, it is expected that these partially
attached powders with small grains on the surface are unlikely to
significantly contribute to the strength of the lattice structures. We
also investigated the microstructure of the Cub structure as shown
in Fig. S4. Similarly, the Cub structure shows elongated grains
without strong texture, LAGB at the node, and average grain size
of 30 ± 20
l
m. As such, it could be concluded that a nominal
change in the design/geometry does not significantly affect the
microstructure of the Cu lattices.
3.3. Deformation behavior
To investigate the applicability of the Cu lattice structure in
dynamic applications, we conducted compression tests at various
strain rates. Fig. 4 (a, b) shows the engineering stress–strain curves
of Oct and Cub structures, respectively, at 0.001, 0.01, 0.1, 1, 10,
and 1000 /s. Several distinct deformation characteristics can be
observed in the stress–strain curves. Firstly, at every strain rate,
the Oct structure shows about 1.5-times higher stress level than
the Cub structure. The difference in stress level stems from the
deformation mechanism of each structure. As mentioned above,
the deformation of the lattice structure is governed by the connec-
tivity of struts. Hence, the Oct structure with higher connectivity is
stiffer and stronger than the Cub structure with lower connectivity.
Furthermore, the higher relative density of the Oct structure than
Fig. 3. Microstructure of representative unit cross-section in Oct structure. (a) Inverse pole figure and corresponding pole figure maps along building direction. (b) Grain
boundary map and Kernal average misorientation map. (c) Misorientation angle distribution. (d) Grain size distribution plots.
S.-G. Kang, R. Gainov, D. Heußen et al. Materials & Design 231 (2023) 112023
6
that of the Cub structure results in a higher stress level. Secondly,
there is no post-yield softening in the stress–strain curves of the
Oct structure. Previous studies on the Oct structure made of Ti-
6Al-4 V, Al-Si10-Mg, stainless steels, and polymer report post-
yield softening during deformation [14,47,48,51,53,102]. This
deformation behavior originates from the high connectivity of
the structure which leads to an abrupt buckling or fracture of
struts. The deformation process also depends on the exact dimen-
sions and the material choice. The buckling of the strut is known to
occur in slender struts [103,104]. Tancogne-Dejean et al. computa-
tionally demonstrated that the Oct structures with high strut
aspect ratio are prone to buckling under compressive stress
[104]. They identified that there was no buckling deformation in
the Oct structures with strut aspect ratio lower than 5. For the lat-
tice structures in this study, the aspect ratio is 3.54, hence the
struts are not favorable for buckling deformation. In addition, Cu
which typically possesses high ductility may enable a gradual plas-
tic deformation in the struts. Therefore, the post-yield softening of
the Cu Oct structure is less probable despite the high strut connec-
tivity. We observed a continuous and smooth hardening behavior
in both Oct and Cub Cu structures during deformation and it can
be attributed to the intrinsic mechanical properties of Cu and the
relative density of Oct and Cub structure. It has been reported that
coarse-grained Cu with a grain size of 10–50
l
m shows a high
strain hardening exponent and high hardening capability
[105,106].Fig. S5 shows tensile stress–strain curves obtained from
dog bone shaped specimens oriented along the building direction
of L-PBF. The L-PBFed Cu in this study shows a higher hardening
exponent (n = 0.27 ± 0.01) and failure strain (46 ± 3 %) compared
to Ti- [47,48] and Al- [51] alloys previously used for the lattice fab-
rication. This intrinsic material property could also be a contribut-
ing factor toward the continuous and smooth hardening-based
deformation of the Cu lattices. However, if the relative density of
the lattice structure (even if it shows bending-dominated deforma-
Fig. 4. Mechanical properties of pure Cu lattice structures. (a, b) Nominal compressive stress–strain curves of Oct and Cub structures at wide range of strain rates. Comparison
of (c) 2 % offset yield stress, (d) 20 % flow stress, and (e) absorbed energy of Oct and Cub structures under compressive deformation.
S.-G. Kang, R. Gainov, D. Heußen et al. Materials & Design 231 (2023) 112023
7
tion) is below 10%, then the post-yield softening may occur even in
the ductile pure Cu lattice structures. Fu et al. investigated the
deformation behavior of TPMS lattice structures, a bending-
dominated structure, with various relative densities and found that
the post-yield softening occurred in the structures with a relative
density of 10% or less due to the shear band formation [29,107].
As such, it can be deduced that the relative densities of the pure
Cu lattice structures (0.38 and 0.21 for Oct and Cub structures,
respectively) in this study also contribute to the continuous and
smooth deformation characteristics. Third, the lattice structures
show a clear strain rate dependency under compression. Both the
structures show similar yield and flow stress levels even when
the strain rate is increased from 0.001 /s to 1 /s. At 10 /s though,
the flow stress slightly increases, and at 1000 /s, both the yield
and flow stress drastically increase. For the quantitative analysis
of the lattice performance, we evaluated the 2% offset yield stress
(
r
y
), the flow stress at 20 % strain (
r
0:2
), and the energy absorption
capacity (U
A
) of each structure compressed at various strain rates.
Fig. 4 (c, d) shows the comparison of
r
y
and
r
0:2
. The strain rate
sensitivity (m) was calculated based on the flow stress as below:
m¼@ln
r
f
@ln _
e
ð2Þ
where
r
f
is the flow stress and _
eis the strain rate. In order to eval-
uate min the plastic deformation regime, the flow stresses at 0.2
strain were selected. It was reported that the cellular materials with
relative density higher than 0.4 commonly exhibits msimilar to the
base material. On the other hand, it was reported that the cellular
materials with relative density lower than 0.4 shows increased m
due to the micro-inertia effect [108-110]. For the Oct and Cub lat-
tices, mwere calculated as 0.016 and 0.028 respectively. The mof
Oct structure (relative density of 0.38) is analogous to the polycrys-
talline bulk Cu (m ¼0:0158) [111,112]. The Cub lattice with relative
density of 0.21 shows increased mcompared to the Oct lattice. The
sharp increase in
r
y
and
r
0:2
at 1000 /s can be attributed to a tran-
sition in the deformation mechanisms. It was reported previously
that the polycrystalline Cu shows distinctive strain rate sensitivity
in compressive strength, especially at high strain rates [111,112].
At dynamic strain rates (>100 /s), the dislocation motion is affected
by the phonon vibration and the viscous-drag effect of dislocation
by phonons during the plastic deformation leads to a sharp increase
in the
r
y
and
r
f
[113]. Consequently, there is a clear increase in
r
y
and
r
0:2
when the strain rate is increased from 10 /s to 1000 /s, sug-
gesting a possible viscous-drag effect in the Cu lattice structures.
The U
A
, as shown in Fig. 4 (e), can be obtained as follows:
U
A
¼Z
e
d
0
r
d
e
ð3Þ
where the
r
,e, and e
d
are the stress, strain, and densification strain.
The e
d
is the critical strain where the open pore channels are closed,
and at e>e
d
the flow stress drastically increases. The lattice struc-
tures in this study show continuous hardening during compression,
obscuring trivial identification of e
d
. From the microCT scan image
of the Cub structure, it can be seen that densification occurred at
samples compressed up to 50% strain (Fig. S6). To quantitatively
determine e
d
from the stress–strain curves, the second derivative
was taken to obtain the concavity of the curve. The strain where
the second derivative becomes positive and drastically increases
is selected as e
d
(Fig. S7). The densification strain of Oct and Cub
structures was identified as 41 % and 45 %, respectively. The differ-
ence in densification strain stems from the different relative densi-
ties of structures. Fig. 4 (e) clearly shows that U
A
of Oct structure is
significantly higher than that of Cub structure due to the higher
stress level, originating from differences in the nodal connectivity
and the relative density. Furthermore, there are sharp increases in
U
A
of Oct and Cub structure at 1000 /s strain rate, which can be
attributed to the viscous drag effect.
We further investigated the structural evolution in the
deformed lattices. Fig. 5 shows the MicroCT scan images of unde-
formed and compressed Oct and Cub structures at 0.001, 1, and
1000 /s strain rates at 25% strain. The images were obtained at
the central cross-section of structures. The scan images of unde-
formed Oct and Cub structures (Fig. 5 (a, b)) show well-defined
open-pore channels and struts. Notably, there are also low contrast
areas at the bottom layers of each lattice structure (denoted by yel-
low arrows), which most probably originate from the residual
unmelted powders [114]. The open-pore channels also can be iden-
tified in the scan images of compressed structures at 0.001 /s (Fig. 5
(c, d)), meaning that the structures are not densified yet at a strain
of 25%. This remains the same for other compressed structures at
higher strain rates of 1 /s (Fig. 5 (e, f)) and 1000 /s (Fig. 5 (g)). More-
over, the scan images of compressed Oct and Cub structures com-
monly show that the structures were compressed homogeneously,
suggesting that there was no localized deformation. In previous
studies on the lattice structures, a localized shear band formation
in the structure during compression was reported [115-117]. The
shear bands crossing the entire structure are typically formed with
a crack initiation or severe deformation of the strut, decreasing the
energy absorption capacity. This localized deformation can be sup-
pressed by improving the ductility of materials of lattice structures
and increasing the relative density of the structure
[29,65,107,117]. Hence, it can be deduced that the ductile nature
of pure Cu and the relative density of the lattice structure enables
homogeneous deformation across six orders of strain rate magni-
tudes and results in robust energy absorption by the pure Cu lattice
structures.
We also investigated the possible microstructural evolution in
the deformed lattice structures. Especially because the deforma-
tion at dynamic strain rates is known to introduce unique
microstructures such as a strong shear localization and dynamic
recrystallization to materials [118,119]. To investigate the
microstructural change, we examined the cross-section along the
building direction of Oct structures compressed at quasi-static
and dynamic conditions and compared the microstructures
(Fig. 6). The post-mortem microstructure analysis confirms that
there is no severe inhomogeneous deformation induced during
dynamic compression. In the grain boundary map of deformed
materials, the LAGB indicates plastic deformation [100].Fig. 6 (a)
shows the grain boundary map overlayed with the image quality
map of the representative unit cross-section of the Oct structure
compressed at 0.001 /s and 1000 /s, respectively. Notably, there
is no clear difference in the grain boundary maps, suggesting that
dynamic compression may not induce inhomogeneous deforma-
tion. Instead, compared to the microstructure of the undeformed
Oct structure in Fig. 3(b), regardless of the strain rate, the com-
pressed structures show increased LAGB at the points where the
strut and the node are connected. This LAGB may originate from
the stress concentration and resulting deformation under compres-
sive load. As confirmed by the finite element analysis (Fig. S8),
when the structure is compressed, the stress is concentrated at
these connecting points. Consistently, the corresponding KAM
maps (Fig. 6 (b)) show high local misorientation at the strut-
node connecting area. Fig. 6 (d) shows that there is no apparent
change in misorientation angle distribution with strain rate. Com-
pared to the distribution of undeformed Oct structure in Fig. 3(b),
the compressed structures again show an increase in the low-angle
grain boundaries (<15°) which can be attributed to the plastic
deformation[100].
We hypothesize that dynamic recrystallization was unlikely to
occur in these Cu architectures during dynamic compression.
Fig. 6 (c) shows grain orientation spread (GOS) maps overlayed
S.-G. Kang, R. Gainov, D. Heußen et al. Materials & Design 231 (2023) 112023
8
with the image quality map of the Oct structure compressed at
0.001 /s and 1000 /s. To separate the recrystallized grains from
the deformed grains, a GOS cutoff of one degree was taken. There
is no clear difference between the Oct structures compressed at
0.001 /s and 1000 /s. Moreover, there is no apparent indication that
the recrystallization occurred at the strut-node connections, where
the stress is concentrated. The grain size distribution in Fig. 6 (e)
shows no difference between structures compressed at 0.001 /s
and 1000 /s. It is also supported by no softening in the stress–strain
curves (Fig. 4 (a, b)), a typical signature of dynamic recrystalliza-
tion. It was reported that the adiabatic temperature rise during
deformation at a high strain rate induces dynamic recrystallization
of bulk Cu at a dynamic strain rate of 10000 /s [120,121]. With a
relatively low dynamic strain rate (1000 /s) and pore channels in
the lattice structure made of thermally conductive Cu, the adia-
batic temperature rise required for the dynamic recrystallization
may not be reached.
The specific compressive strength and energy absorption capac-
ity of Cu Oct and Cub structures in this study were compared to Oct
structures made of Cu [122-124], Ti alloy [47,48], Al alloy [51],
stainless steel [52,53], and alumina [43-45] from previous reports
and are summarized in Fig. 7. As shown in Fig. 7 (a), the compres-
sive strengths of the Oct and Cub structures at 0.001 /s in this study
are in an analogous trend to the previous studies on the pure Cu
micro-and nano-scale structures [122-124]. Notably, in these small
structures, the material size effect may play a significant role in the
mechanical properties. However, in the case of the nano-foams, the
absence of periodicity reduces the load-bearing capability of the
Fig. 5. Cross-sectional microCT images of Oct (left) and Cub (right) structures. (a, b) MicroCT images before compression. Yellow arrows indicate the unmolten powders
which have negligible effect on the mechanical properties. (c-g) MicroCT images after compression to 25 % engineering strain at strain rates of 0.001, 1, and 1000 /s. (h)
Schematics of cross-section of interest in each structure. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this
article.)
S.-G. Kang, R. Gainov, D. Heußen et al. Materials & Design 231 (2023) 112023
9
structure [123,124]. In the case of the microscale Oct structure, due
to the grain size which is comparable to the strut diameter, it
shows a single crystalline-like deformation behavior [122]. Hence,
even though the macroscale lattice structures of this study are 2–3
orders of magnitude larger than the microlattices tested in previ-
ous studies, they exhibit comparable strength due to the combina-
tion of polycrystalline microstructure and ordered architecture.
Further, the alumina hollow Oct structures show extremely
high specific strength (10 times higher than the Cu lattice struc-
tures) due to the low density and the high compressive strength
(Fig. 7 (a)) [43-45]. However, due to its intrinsic brittleness, the
energy absorption capacity is as low as the metal foams as shown
in Fig. 7 (b). On the other hand, the Cu Oct and Cub structures, due
to their ductile nature, show high energy absorption capacity, out-
performing the strong alumina structures. Moreover, as the Cu lat-
tice structures show continuous strain hardening without post-
yield softening, the energy absorption capacity is comparable to
that of lattice structures made of high-strength alloys. Clearly,
the Oct structures made of Ti-, Al- alloys and stainless steels show
higher compressive strength than the pure Cu Oct structures, but
their energy absorption capacity is similar to or lower than pure
Cu Oct structures. As such, the current study on the lattice struc-
tures made of Cu and their mechanical properties at a wide range
of strain rates provides evidence for the applicability of ductile
metals as appropriate structural materials for dynamic energy
absorption.
It should be mentioned that the lattice structures of Cu alloys
can be fabricated via L-PBF with infra-red laser. As Cu alloys tend
to have intrinsically higher strength than pure Cu, architectures
built using Cu alloys could possess superior compressive strength
Fig. 6. Microstructure of representative unit cross-section in Oct structure after compression. (a, b) Grain boundary map. (c) Misorientation angle distribution and (d) grain
size distribution plots.
S.-G. Kang, R. Gainov, D. Heußen et al. Materials & Design 231 (2023) 112023
10
and energy absorption capacity. For example, Ma et al. fabricated
the triply periodic minimal surface (TPMS) lattice structures of
Cu-Cr-Zr (CCZ) alloy and investigated their deformation behavior
[125]. During the deformation, the CCZ alloy structures didn’t show
post-yield softening. This can be attributed to the TPMS geometry
of the lattice structure, which is known to be dominated by the
bending of struts, and the bending-dominated deformation leads
to continuous deformation without post-yield softening as shown
from the pure Cu Cub structure in this study. Accordingly, as a fur-
ther study, it is worth fabricating the Oct structures made of Cu
alloy and exploring their deformation behavior and energy absorp-
tion capacity. However, beyond the strength, pure Cu has much
higher conductivity and ductility than Cu alloys. Thus, the pure
Cu lattice structures can be utilized in fields requiring high electri-
cal/thermal conductivity, along with mechanical robustness such
as packaging materials for electrical devices and electrodes for
battery.
In the future, the surface roughness of lattice structures, which
may lower their mechanical performance, can be further improved
by parameter optimization via high-throughput screening [126],
by adopting a multi-beam exposure strategy for lattice fabrication
[127,128] or by conducting additional post-treatment such as laser
polishing [129]. In summary, this study shows the feasibility of Cu
3-dimensional architectures in future multifunctional applications
that require excellent mechanical, electrical, and thermal proper-
ties simultaneously.
4. Conclusion
We fabricated pure Cu lattice structures with different nodal
connectivities using a green laser beam LPBF process. The struc-
tural and microstructural analysis demonstrate that the Cu lattice
structures possess well-defined open-pore channels with low
defect density. The mechanical properties under compression were
investigated at a wide range of strain rates (0.001 - 1000 /s). The
appropriate geometrical dimensions of the lattices prevented
buckling deformation of the strut and the copper with its high duc-
tility enabled continuous plastic deformation with strain harden-
ing and prevented post-yield softening. Therefore, a high energy
absorption capacity was identified, demonstrating the applicability
of Cu lattice architectures as structural materials that can sustain
dynamic loadings.
Data availability
Supplementary information to this article can be found online
Declaration of Competing Interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared
to influence the work reported in this paper.
Acknowledgements
SGK gratefully acknowledges funding by the National Research
Foundation of Korea (NRF, No. NRF-2020R1A6A3A03039038). The
authors would like to thank Michael Adamek for his assistance
with the mechanical test. ZS acknowledges financial support from
the Career Development Fund (Grant reference No.: C222812017),
A*STAR, Singapore.
Appendix A. Supplementary data
Supplementary data to this article can be found online at
https://doi.org/10.1016/j.matdes.2023.112023.
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