Composites Science and Technology 119 (2015) 26e33
Contents lists available at ScienceDirect
Composites Science and Technology
journal homepage: http://www.elsevier.com/locate/compscitech
Mechanical properties of carbon fiber composite octet-truss lattice
structures
Liang Dong*, Haydn Wadley
Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903, United States
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 16 June 2015
Received in revised form
1 September 2015
Accepted 22 September 2015
Available online 28 September 2015
Octet-truss lattice structures have been made from balanced [0/90] carbon fiber reinforced polymer
(CFRP) laminates using a simple snap-fit method. The lattice structures moduli and strengths have been
measured during [001] and [100] directions free compressions as a function of the lattice relative density.
Core failure occurred by either (i) Euler buckling ðr < 5%Þ or (ii) delamination dominated failure ðr > 5%Þ
of the struts. The measurements are shown to be well predicted by micromechanics models of these
composite strut failure modes. Snap-fit CFRP octet-truss lattice structures are found to exhibit mechanical properties competitive with other cellular materials and topologies. Their isotropic response
may provide new opportunities for ultra-lightweight multiaxial loaded structures.
© 2015 Elsevier Ltd. All rights reserved.
Keywords:
Octet-truss lattice
Elastic stiffness
Strength
Carbon fiber composite
1. Introduction
The octet-truss lattice structure first proposed by Fuller [1]
provides a method for filling 3-D space with a structurally efficient truss structure of an arbitrary cell size. This stretchdominated structure has a high nodal connectivity of 12 [2], and
an almost isotropic yield surface [3]. Recent alloy casting approaches have demonstrated the possibility of making octet-truss
lattices with strut lengths in the 5e10 mm range [3]. Wrought titanium alloy octet-truss lattices have also been recently fabricated
[4] while self-propagating waveguide or laser based stereolithographic methods, when combined with electroless nickel
plating or vapor deposition, have enabled fabrication of micrometer
scale structures [5e7].
Material property charts provide a useful way to compare the
mechanical properties of these low density materials. Fig. 1 compares the density dependent moduli and strengths of compressively loaded polymer and metal foams and lattice structures made
by investment cast of aluminum [3] and titanium alloys [8,9],
electrodeposition of Nie7P [5,6], carbon fiber composites via a
reversible assembly technique [10], photosensitive HDDA polymers
[6], and by the vapor deposition of alumina [6,7]. Recently reported
Tie6Ale4V octet-truss lattice structures [4], balsa wood [11],
* Corresponding author.
E-mail address: [email protected] (L. Dong).
http://dx.doi.org/10.1016/j.compscitech.2015.09.022
0266-3538/© 2015 Elsevier Ltd. All rights reserved.
polymer [12] and metallic [13] syntactic foams are also included in
these Ashby maps. Foams have a low nodal connectivity, and are
bending governed structures, and therefore compliant and weaker
than lattice topology counterparts. When made from high specific
strength materials, the octet-truss lattice is a highly weight efficient, multiaxial stress supporting structure, with a stiffness and
strength that scale linearly with the lattice relative density, r (the
density of the lattice structure divided by that of the material from
which it was made) [14] if the struts failed by plastic deformation.
Carbon fiber composites (CFRP) have a high specific strength
and stiffness and is therefore a promising material for making stiff
and potentially strong cellular structures. Here, we explore the
application of a simple “snap-fit” assembly method [15] for fabricating octet-truss cellular materials from CFRP laminate materials.
The [001] and [100] directions compressive properties of the octettruss lattices have been characterized as a function of the lattice
relative density and compared to micromechanical predictions.
2. Lattice fabrication and laminate material properties
The as-received [0/90] CFRP laminate sheets (McMaster-Carr)
have a thickness t ¼ 1.59 mm, and a density 1.44 Mg/m3. They
contained 55 vol% 228 GPa carbon fiber in a vinyl ester matrix. The
laminate was comprised of 7 plies. The 2 surface plies were made
from plain weave fabrics while the 5 interior plies were unidirectional and laid up in a [0/90]5 arrangement (Supplementary
information S.1). The laminate sheets were fabricated in such a
L. Dong, H. Wadley / Composites Science and Technology 119 (2015) 26e33
Fig. 1. Material property charts showing (a) stiffness and (b) strength versus density
for octet-truss lattices and several other topology cellular structures.
way that the volume fraction of fibers along the laminate longitudinal direction (parallel to 0 unidirectional plies) is equivalent to
that of fibers along the laminate transverse direction (parallel to
90 unidirectional plies). However, the 0 unidirectional plies had a
volume approximately 1.5 times that of the 90 unidirectional plies.
This volume difference was compensated by different volumes of
warp and weft tows in the surface plies. Laminate sheets with
woven plies on the outer surfaces were selected for the present
study since they have better toughness and impact strength, and
are less susceptible to delamination during machining operations
such as drilling, side milling and slotting [16]. Thus, the use of
laminate sheets with woven surface plies was driven by a
manufacturing constraint: the need to avoid delamination failures
during fabrication and assembly of the lattice structures.
The CFRP octet-truss lattice structures were fabricated from the
as-received [0/90] CFRP laminate sheets in a three step process,
Fig. 2. The pyramidal truss row patterns, Fig. 2(a), and intermediate
faces, Fig. 2(c), were water jet and CNC mill cut separately from the
laminate sheets so that half the fibers were parallel to the struts
axes. Note that the strut axis was chosen to be parallel either to the
laminates longitudinal or transverse directions. We subsequently
27
use “longitudinal strut” and “transverse strut” to denote octet struts
with axes parallel to the longitudinal and transverse directions of
the laminate sheet from which they were cut. Rows of pyramidal
trusses were collinearly aligned and a second collinear array
attached to their top, forming a [0/90] arrangement; Fig. 2(b). The
pyramidal truss layers were then snap-fitted into the crosses of the
intermediate faces to form the octet-truss lattice; Fig. 2(d). A
HYSOL®E-120HP™ (Loctite®Brand, Westlakes, OH) high strength
epoxy was finally applied to the nodal regions of the assembled
structure. Octet-truss lattice structures were fabricated with a
relative density (octahedral cell relative density of the snap-fit
lattice) ranging from 1.7 to ~16% by allowing the strut length l,
defined in Fig. 2(a), to vary between 8 and 33 mm. All the lattice
structures had a strut thickness t ¼ 1.59 mm (t ¼ w) and node dimensions b ¼ 4.76 mm, c ¼ 2.24 mm, h ¼ 0.95 mm, htab ¼ 1.59 mm,
t0 ¼ 1.27 mm, m ¼ 2.77 mm, R ¼ 5.08 mm, and u ¼ 45 (the geometric design variables shown in Fig. 2(a) and (c)). The expression
used to calculate the relative density, r of the snap-fit octahedral
cell (Fig. 2(e)) is given in the Supplementary information S.2.
Photographs taken at several orientations of the assembled samples are shown in Fig. 3.
In order to predict lattice mechanical properties, the longitudinal and transverse compressive and tensile moduli and strengths of
the laminate material were first determined (Supplementary
information S.3), and the laminate material was experimentally
confirmed to be orthotropic material. Results are shown in Fig. 4(a)
and summarized in Table 1. The laminate compressive strengths
were different in different loading conditions due to different failure mechanisms: in CLC compression, failure was controlled by
plastic fiber micro-buckling, whereas the failure was dominated by
delamination in unclamped compression; as observed optically
(Fig. 4(c) and (d)) and confirmed by meXCT analysis (Fig. 4 (e) and
(f)). In both cases, kink bands formed in the plies whose fibers were
parallel to the loading direction. The damage modes (kink bands
and delamination) were both initiated within the plain weave
surface plies where fiber misalignment was the greatest. This initial
damage can disturb the subsequent loading condition in unclamped compression by introducing bending moments at the specimen
free ends, and stress concentrations can also trigger delamination
or matrix cracking near the damage zones prior to plastic fiber
micro-buckling of the interior unidirectional plies. In contrast, the
CLC test fixture eliminated the end effects, allowing the interior
unidirectional plies along the loading direction to fully contribute
the plastic fiber micro-buckling strength, and this resulted in a
higher compressive strength.
3. Compression responses
The compressive stressestrain responses of the CFRP octet-truss
samples are measured (Supplementary information S.4) and shown
in Fig. 5(a) and (b). In all cases an initial linear response is observed
followed by a regime of nonlinear responses. Typically, the peak
stress was attained as strut failure was first observed. The stress
then decreased rapidly with increasing strain with serrations on the
stressestrain curve associated with a series of strut failures. Photographs of some of the lattice structures after testing are shown in
Fig. 5(c)e(g).
The lowest relative density sample ðr ¼ 1:7%Þ failed by struts
Euler buckling. Samples of higher densities failed by delamination
of the struts supporting compressive loads. Delamination typically
initiated near the ends of the struts and then propagated along the
strut axis. During [001] direction free compression, the intermediate faces supported tensile stresses and remained intact after the
tests (Fig. 5(c)e(e)) since the tensile strength of the laminate material is much higher than that in compression. During [100]
28
L. Dong, H. Wadley / Composites Science and Technology 119 (2015) 26e33
Fig. 2. Schematic illustration of the truss fabrication and “snap-fit” assembly method for making an octet-truss lattice from the [0/90] CFRP laminate sheets. The geometries of (a)
pyramidal truss and (b) intermediate face with relevant core design variables are identified. (e) An octahedral cell with a Cartesian co-ordinate system and miller index loading
directions.
Fig. 3. Photographs of snap-fit CFRP octet-truss specimens. (a) View in the [001] compression loading direction, (b) a side view showing the pyramidal trusses and (c) an isometric
view of a sample ðr ¼ 5:4%Þ. (d) An isometric view of a sample ðr ¼ 1:7%Þ with a higher strut slenderness ratio (l/t). (e) Shows a close-up of an assembled node at the side of the
r ¼ 5:4% sample. Sample size is defined by side length L(s), and height H(s).
direction free compression, intermediate faces struts supported
compressive loads, and eventually failed by delamination (Fig. 5(f)
and (g)). Nodal rotations were observed after the peak stress was
achieved and the loading symmetry at the nodes was broken.
Table 2 summarizes the compressive moduli and strengths of the
CFRP octet-truss specimens as a function of their relative densities
under both [001] and [100] directions free compressions.
4. Analytical models for compression responses
Deshpande et al. [3]. have analyzed an ideal octahedral cell
(cubic symmetry with vanishing node volume) made from isotropic
materials, and the results apply to the octet-truss lattice constructed by 3-D stacking of such an octahedral cell. For small t/l, the
contribution to overall lattice stiffness from struts bending is
L. Dong, H. Wadley / Composites Science and Technology 119 (2015) 26e33
29
Fig. 4. (a) Uniaxial stressestrain responses of the [0/90] CFRP laminate material along one of the fiber directions (“L” ¼ longitudinal; “T” ¼ transverse). Results from both the
Celanese compression (CLC) and unclamped compression are included. (b) The geometry of the laminate specimen used for unclamped compression testing. (c) Delamination
failure after unclamped compression. (d) Plastic fiber micro-buckling failure after CLC compression. m-XCT images of the laminate showing the failure modes after (e) unclamped
and (f) CLC compressions.
negligible compared to that from struts stretching [3], and thus the
DFA model assumed pin-joined struts to simplify the analysis. We
employed the same assumption for the analysis of the snap-fit CFRP
octet-truss lattice manufactured here.
The octahedral cell designed in the present study contains extra
nodal masses, as shown in Fig. 2(e), and has a transverse isotropic
symmetry due to its nodal geometry. The linear elastic stress, s and
strain, ε tensor relationship takes the form (with Cartesian indices);
2
Cxxxx
Cxxyy
3 6
6 Cxxyy Cxxxx
sxx
6
6 syy 7 6
Cxxzz Cxxzz
6
7 6
6 szz 7 6
6
7¼6
6 syz 7 6
0
0
6
7 6
4 sxz 5 6
6 0
0
6
sxy
6
4
0
0
2
3
εxx
6 εyy 7
6
7
6 εzz 7
7
6
6 εyz 7
6
7
4 εxz 5
εxy
2
Cxxzz
0
0
Cxxzz
0
0
Czzzz
0
0
0
Cyzyz
0
0
0
Cyzyz
0
0
0
0
3
7
7
7
7
7
0
7
7
7
0
7
7
7
0
7
7
Cxxxx Cxxyy 5
2
0
(1)
with the principal material axes (x,y,z) are defined in Fig. 2(e).
There are five independent elastic stiffness constants, Cij (the
contracted indices i and j are ordered pairs of Cartesian indices),
fC11 ; C12 ; C13 ; C33 ; C44 g, equivalent to fCxxxx ; Cxxyy ; Cxxzz ; Czzzz ;
Cyzyz g with contracted indices. In [001] direction free (or confined)
compression, 1=Szzzz (or Czzzz ) is determined, while in [100] direction free (or confined) compression, 1=Sxxxx (or Cxxxx ) is
determined.
The octahedral cell shown in Fig. 2(e) contains 4 longitudinal
and 4 transverse struts that are loaded in compression. The unit cell
compressive stiffness therefore depends on both the longitudinal
and transverse struts compressive moduli, whereas the unit cell
compressive strength will be governed by the compressive strength
of the (weakest) transverse struts. Since the longitudinal struts
have higher moduli than the transverse struts, these octet struts
will suffer different displacements when the octahedral cell is under free compression, and static equilibrium is achieved by
(compensating) nonuniform nodal displacements. However, the
requirement for static equilibrium dictates that all the octet struts
have the same internal stress when the octahedral cell is under free
compression. To simplify the analysis, we assumed that all the
struts have the same compressive, ECave and tensile, ETave moduli,
where ECave ð¼ 1=2ðECL þ ECT Þ 26GPaÞ and ETave ð¼ 1=2ðETL þ ETT Þ 60GPaÞ are the averages of longitudinal, and transverse compressive and tensile moduli of the laminate material, respectively.
4.1. Compressive modulus
As shown in Supplementary information S5, the octahedral cell
compressive modulus Ezz under [001] direction free compression is
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L. Dong, H. Wadley / Composites Science and Technology 119 (2015) 26e33
Table 1
The measured properties of the as-received [0/90] CFRP laminate along both the longitudinal and transverse directions. Standard deviations are given based on multiple
measurements for each mechanical property.
Compressive modulus
(Unclamped)
Longitudinal direction (L)
Transverse direction (T)
Compressive modulus
(CLC)
Micro-buckling
strength (CLC)
Delamination strength
(Unclamped)
Tensile strength
Tensile modulus
ECðUCÞ (GPa)
ECðCLCÞ (GPa)
smb (MPa)
sdl (MPa)
sT (MPa)
ET (GPa)
32.5 ± 1.8 (15 times)
19.8 ± 2.3 (15 times)
33.6 ± 2.1 (7 times)
20.5 ± 1.4 (7 times)
640 ± 36 (7 times)
428 ± 42 (6 times)
457 ± 76 (21 times)
305 ± 63 (28 times)
949 ± 34 (6 times)
497 ± 10 (5 times)
76 ± 3.5 (7 times)
45 ± 1.9 (5 times)
2Eave Eave t 2 H½001
Ezz ¼ aveT C ave lA½001
EC þ 2ET
(2)
where H½001 ¼ 2ðl sin u þ h þ 2htab Þ is the [001] direction octahedral cell height, A½001 ¼ ð2l cos u þ b þ cÞ2 =2 is the cross-sectional
area perpendicular to the [001] direction.
If we define Es ¼ ECave , Equation (2) can be expressed in the form
of relative compressive modulus as
t 2 H½001
t 2 H½001
2Eave
Ezz
¼ ave T ave ¼ KE
Es
lA
lA½001
EC þ 2ET
½001
(3)
with KE ¼ 2ETave =ðECave þ 2ETave Þ. It is noted here that Equations (2)
and (3) were derived assuming free compression; in lateral
confined compression KE ¼ 1.
Similarly, it can be shown that the unit cell compressive
modulus Exx under [100] direction free compression is
Fig. 5. Compressive stressestrain responses of CFRP octet-truss samples of various relative densities. (c), (d) and (e) show the failure mechanisms under [001] direction free
compression: (c) Pyramidal strut delamination in the r ¼ 5:4% specimen, and (d) a higher magnification view of the delamination. (e) Euler buckling initiated strut fracture in the
lowest density ðr ¼ 1:7%Þ specimen. (f) Failure mechanism under [100] direction free compression ðr ¼ 5:4%Þ, and (g) a higher magnification view of a delaminated intermediate
face strut.
L. Dong, H. Wadley / Composites Science and Technology 119 (2015) 26e33
31
Table 2
Relative densities, experimental and unit cell compressive moduli and compressive strengths under [001] and [100] directions compression of the manufactured snap-fit CFRP
octet-truss specimens.
Length
(l, mm)
Relative
density ðrÞ
Sample compressive
stiffness (GPa)
[001]
33.020
16.891
12.014
9.728
8.433
1.7%
5.4%
9.4%
13.0%
15.9%
0.075
0.295
0.556
0.753
0.983
Exx ¼ Unit cell compressive
stiffness (GPa)
Sample compressive
strength (MPa)
[100]
[001]
[100]
[001]
[100]
[001]
[100]
0.107
0.301
0.546
0.773
1.033
0.060
0.237
0.447
0.606
0.792
0.079
0.230
0.422
0.602
0.811
0.73
4.39
7.98
9.90
11.39
0.75
4.01
7.01
9.53
10.95
0.60
3.69
6.81
8.54
9.89
0.57
3.14
5.60
7.71
8.95
t 2 H½100
2ETave ECave
ave
ave
lA½100
EC þ 2ET
5. Comparison of measurements and predictions
(4)
and the corresponding relative compressive modulus
t 2 H½100
t 2 H½100
2Eave
Exx
¼ ave T ave ¼ KE
Es
lA½100
lA½100
EC þ 2ET
(5)
pffiffiffi
where, H½100 ¼ 2pl ffiffiffi
þ b þ c, is the
pffiffiffi[100] direction octahedral cell
height, A½100 ¼ ð 2l þ b þ cÞðl= 2 þ h þ 2htab Þ is the crosssectional
area
perpendicular
to
the
[100]
direction,
KE ¼ 2ETave =ðECave þ 2ETave Þ. Again, KE ¼ 1, in the case of [100] direction lateral confined compression.
4.2. Compressive strength
The octahedral cell compressive strength under [001] direction
free compression is given by (Supplementary information S.5)
spk
zz ¼
pffiffiffi
2 2t 2
sc
A½001
(6)
where, sc is the collapse strength of a single strut. If we define ss ¼
save
, where save
¼ 1=2ðsLmb þ sTmb Þ 535MPa, the average of
mb
mb
laminate longitudinal and transverse compressive strengths,
Equation (6) can be expressed in the form of a relative compressive
strength
pffiffiffi
spk
2 2t 2 sc
t 2 sc
zz
¼ ave
¼ Ks
ss
smb A½001
A½001
(7)
pffiffiffi
Where, Ks is a constant ¼ 2 2=save
.
mb
Similarly, it can be shown that the [100] direction unit cell
compressive strength is
spk
xx
pffiffiffi
2 2t 2
¼
sc
A½100
(8)
the relative compressive strength in this direction is
pffiffiffi
pk
sxx
2 2t 2 sc
t 2 sc
¼ ave
¼ Ks
ss
smb A½100
A½100
Unit cell compressive
strength (MPa)
(9)
pffiffiffi
where, Ks is a constant ¼ 2 2=save
.
mb
During either [001] or [100] direction compression, a CFRP
octet-truss lattice can collapse by either (i) Euler buckling (ii)
delamination or (iii) plastic fiber micro-buckling of the struts. The
collapse strength of a single strut due to different collapse mechanisms can be found in Supplementary information S.6.
The manufactured samples have extra edge struts that belong to
the unit cells of a larger area sample. These edge struts of partial
unit cells contribute both stiffness and strength to the samples
mechanical response. The measured compressive properties were
thus adjusted to account for the edge effect in order to make
comparison with modeled properties. The properties of a lattice
without extra edge struts are subsequently defined as the unit cell
stiffness or strength (Supplementary information S.7), and are
summarized in Table 2.
The measured unit cell compressive elastic moduli in both [001]
and [100] directions are plotted against the relative density, r, in
Fig. 6(a) and (b), and the compressive strength data in Fig. 6(c) and
(d). The model predictions are also plotted on all the figures. The
relative moduli and strengths were normalized by the average
compressive modulus Es ¼ ECave ð26GPaÞ and strength governed by
plastic fiber micro-buckling failure, ss ¼ save
ð535MPaÞ of the
mb
laminate material. The delamination and plastic fiber microbuckling models used conservative transverse compressive
strengths, sTdl ðminÞ ¼ 240MPa and sTmb ðminÞ ¼ 386MPa, of the
laminate material for predictions. An average compressive modulus
ECave ð26GPaÞ of compression struts was used for the Euler buckling
failure model predictions.
In Fig. 6(a) and (b), results are shown for the relative
compressive moduli in both laterally confined compression (Czzzz/
Es, equivalent to C33/Es for [001] compression and Cxxxx/Es,
equivalent to, C11/Es for [100] compression) and free compression
((1/Szzzz)/Es, that is (1/S33)/Es for [001] compression and (1/Sxxxx)/
Es, or (1/S11)/Es for [100] compression) using Es ¼ ECave ð26GPaÞ. The
unit cell data is found to be well predicted by the free compression
models for [001] direction compression, but is slight underestimated by the free compression model in the case of [100] direction compression. In [100] direction free compression, the
unmodelled flexural stiffness of the intermediate faces provided
lateral constraint in such a loading configuration. Also, the nodal
design of the intermediate faces improved the nodal rotational
stiffness, and k was therefore likely to lie between 1 and 2 for the
actual struts end conditions.
The experimental data of relative compressive strengths
(Fig. 6(c) and (d)) follow the Euler buckling model at low relative
density (r < 0:054), and are then consistent with the delamination
model when r > 0:054. However, the model predicted a failure
mode transition from Euler buckling to delamination near rz0:07
rather than the measured transition near rz0:054. This is attributed to k ¼ 1 pin-joined struts model assumption; whereas, the
precise rotational stiffness of the designed nodes lies between 1
and 2. Due to insufficient node constraint, the plastic fiber microbuckling failure mode of the struts was not activated, and the
lattice properties are inferior to the corresponding model
predictions.
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L. Dong, H. Wadley / Composites Science and Technology 119 (2015) 26e33
6. Comparisons with other materials
The measured [001] direction unit cell compressive responses of
the snap-fit CFRP octet-truss lattices were included in the material
property charts shown in Fig. 1. The properties of the snap-fit CFRP
octet-truss lattices are clearly superior to the counterparts made via
the reversible assembly technique [10], and lattices made by investment casting using aluminum [3] and titanium alloys [8,9].
They also out-perform electrodeposition deposited Nie7P [5],
photosensitive HDDA polymers and vapor deposited alumina (with
solid trusses) [6], and are quite competitive with the Tie6Ale4V [4]
and Al2O3-polymer hybrid octet-truss lattices [7].
For densities lower than 0.04 Mg/m3 (where Euler buckling
dominates), the compressive strengths of the snap-fit CFRP octettruss lattices are inferior to electrodeposited alumina and Nie7P
octet-truss lattices with hollow trusses [6] due to a lower second
area moment of the solid struts. Even so, it is evident that the
predicted compressive moduli of the snap-fit CFRP octet-truss lattices are superior to the hollow truss Nie7P octet-truss lattices [6]
and very competitive with the hollow truss alumina octet-truss
lattices [6] in the lower density range (<0.04 Mg/m3).
The model predictions clearly reveal the potential of CFRP octettruss lattices for filling gaps in material property space. The mechanical properties of a cellular material are determined by its
relative density, by its parent material mechanical properties and
by the cell topology. The strength of a stretch-dominated cellular
lattice, spk , can be expressed in the general form [17];
spk ¼ Sss r
(10)
where, ss is the strength of the solid material from which the lattice
is made, r is the relative density of the lattice and S is a lattice
topology dependent “strength coefficient”. The gap between the
linear extrapolation of lattice property data points and solid material property is attributed to this topology dependent strength
coefficient S (since when, r ¼ 1, spk ¼ Sss ). For an octet-truss lattice, if the node volume vanishes, S ¼ 1=3 [3]; but in the case of the
snap-fitted octet-truss lattice designed in the present study, extra
node mass was present, and so the topology dependent strength
coefficient becomes a function of the node geometry, and for the
cases investigated here was less than 1/3.
The minimum cell size that can be produced by the snap-fit
route was dictated by the precision of the machining operation,
by the variability in laminate thickness and by the tools used for
the assembly of the lattice. If one seeks to make samples of
similar relative density to those reported here, but with a smaller
cell size, it would be necessary to keep the width to length ratio
of the struts fixed. This in turn would require a reduction in the
thickness of the starting laminate (in proportion to the reduction
in cell length). If the thickness of the plies used to fabricate the
laminate remained fixed, this would require a reduction in the
number of plies. However, recently developed very thin ply
composite laminates could enable significantly thinner laminates
to be used [18].
Fig. 6. Comparisons between measured (symbols) and predicted relative compressive moduli and strengths of the snap-fit CFRP octet-truss lattices as a function of the relative
density. Error bars represent the maximum and minimum values obtained from 3 experiments.
L. Dong, H. Wadley / Composites Science and Technology 119 (2015) 26e33
It is possible that the delamination failure mode could be suppressed with the use of a higher shear strength matrix [19], or by a
stitching [20] or 3D weaving/braiding approach [21,22] to improve
the delamination resistance and increase the fraction of fibers in
the load carrying directions. Finally, if these strategies delay the
onset of buckling and delamination failure modes, the use of
nanoscopic reinforcements of the polymer matrix [23,24], might
enable the stress at which the plastic fiber micro-buckling failure
mechanism is activated to be raised.
7. Conclusion remarks
CFRP octet-truss lattice structures made from [0/90] CFRP
laminate sheets with relative densities ðrÞ in the range 1.7e16%
have been successfully manufactured by employing a simple snapfitting method. The lattice structures moduli and strengths have
been characterized under both [001] and [100] directions free
compressions as a function of the relative density ðrÞ. The failure
mechanism changed from Euler buckling to delamination of
compression struts at a relative density of about 0.054. The
compressive moduli and strengths of the lattice structures are well
predicted by a micromechanics model adapted to account for extra
node volume.
The CFRP octet-truss lattices exhibit mechanical properties
competitive with other isotropic materialecell topology combinations, and appear to be a promising candidate for ultra-lightweight
load bearing applications. However, the current designs undergo
delamination failures of the struts and do not achieve the full potential of composite cores as predicted by the plastic fiber microbuckling failure models.
Acknowledgments
We are grateful to the DARPA MCMA program (Grant Number
W91CRB-10-1-005) for the financial support of this research (Program manager, Dr. Judah Goldwasser).
Appendix A. Supplementary information
Supplementary information related to this article can be found
at http://dx.doi.org/10.1016/j.compscitech.2015.09.022.
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