Available online at www.sciencedirect.com
Composites: Part A 39 (2008) 176–187
www.elsevier.com/locate/compositesa
Titanium matrix composite lattice structures
Pimsiree Moongkhamklang *, Dana M. Elzey, Haydn N.G. Wadley
Department of Materials Science and Engineering, University of Virginia, 140 Chemistry Way, P.O. Box 400745, Charlottesville, VA 22904-4745, USA
Received 12 June 2007; received in revised form 31 October 2007; accepted 13 November 2007
Abstract
Cellular materials made from high temperature composites with efficient load supporting lattice topologies and small cell sizes would
create new options for light weight, high temperature structures. A method has been developed for fabricating millimeter cell size cellular
lattice structures with a square truss topology from 240 lm diameter Ti–6Al–4V coated SiC monofilaments. The compressive stiffness of
the lattice structures was well approximated by that of the monofilament fraction in the loading direction. The strength of the lattices was
controlled by elastic buckling and the results were accurately represented by an elastic buckling model. The post peak compressive deformation was accommodated by elastic buckling of the SiC fibers and plastic deformation of the titanium coating until the onset of monofilament fracture. The specific stiffness and strength of the lattices were found to be between 2 and 10 times that of other cellular
structures and thus appear to be promising candidates for high temperature, ultralight weight load supporting applications.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Cellular materials; A. Metal–matrix composites (MMCs); B. Mechanical properties
1. Introduction
Lightweight, multifunctional load supporting structures
based upon sandwich panel concepts have many applications [1–10]. Their cellular cores usually have either a prismatic (corrugations) or honeycomb topology and are
usually adhesively bonded to the face sheets [2–10]. The
cores are made of very low density materials such as
Nomex [3,4], polymer foams [5], or light metal constructions [6–9] that maintain the face sheet separation needed
for sandwich panel action at minimum parasitic mass [1].
Metallic core systems based upon light metals such as aluminum [6,7] and titanium [8,9] alloys are utilized where
high compressive strengths are needed to avoid local indentation. They can also be used for higher temperature applications provided metallurgical bonding is used to attach
the core to the face sheets [6–9]. The maximum use temperature of these structures is then limited by the creep rate of
the alloy system.
*
Corresponding author. Tel.: +1 434 982 5035; fax: +1 434 982 5677.
E-mail address: [email protected] (P. Moongkhamklang).
1359-835X/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compositesa.2007.11.007
While honeycomb topology systems usually offer significantly superior structural performance [1,2,10,11], their
closed-cell topology limits some potential multifunctional
applications [10]. They are also susceptible to corrosion
and suffer from delamination problems [2,9]. Stochastic
metal foam core systems with fully interconnected pores
have attracted interest because they provide multifunctional capabilities such as cross flow heat exchange
[11–14], dynamic load protection [11,15–17], and acoustic
damping [11,18]. However, their use in structural applications is severely constrained by their low elastic moduli
and indentation strengths [1,11].
Methods have recently begun to be developed for fabricating millimeter scale, open-cell metallic lattices from a
range of light metals and high temperature alloys [19–31].
The truss members in lattice materials can be topologically
configured to experience predominantly axial stresses
(i.e. tension or compression) when they are used in sandwich panels that are loaded in bending (i.e. the cores are
stretch dominated) [19,32–34]. This results in significantly
superior mechanical performance compared to stochastic
metal foams whose ligaments deform by bending [35].
P. Moongkhamklang et al. / Composites: Part A 39 (2008) 176–187
These lattice topologies also possess greater compressive
strength and therefore better resistance to indentation.
Numerous cell topologies have been fabricated including those with tetrahedral [19–23], pyramidal [21, 24–26],
3D-Kagomé [23,27], woven textile [28,29], and diamond
or square collinear [30,31] structures. Examples of these
lattices, configured as the cores of sandwich panels, are
schematically illustrated in Fig. 1. The textile and collinear
lattice structures exploit metallic wires for their fabrication
by a simple lay-up and transient liquid bonding process
[24,29–31].
The strength of lattice core sandwich panels is governed
by the stress at which panel failure mechanisms are initiated under the various modes of loading (through thickness, longitudinal compression, bending, tension etc.)
[37–40]. These failure mechanisms are well established for
metallic materials and include face sheet yielding
[34,36,38], face sheet wrinkling [34,36,38], core shear
[28,37,38], core plastic yielding [34,36,38], fracture under
tension [33], and plastic buckling [27,33,34] of compressively loaded core truss members. Although the most common loading environments for sandwich panels are shear
and bending, the practical implementation of sandwich
panels is often limited by concentrated compressive stresses
at the loading points. In such cases, the core suffers local
yield or crushing (indentation) and can be accompanied
by face sheet stretching/tearing [11,36,37]. These are
affected by the compressive strength of the core and the cell
size (which controls the stretching periodicity) [34].
The compressive stiffness and strength of lattice structures could be significantly increased by the use of stiffer,
higher strength core materials. The highest specific strength
lattice structures fabricated to date have utilized Ti–6Al–
4V for the truss structures [26]. This alloy has a density
of 4.43 g/cm3, Young’s moduli in the range of 100–
120 GPa, and yield strengths of 750–1250 MPa [39]. A
Ti–6Al–4V coated SCS-6 SiC monofilament developed in
the 1990’s for titanium matrix composite (TMC) manufac-
177
ture [40–42] appears to be an even stronger (but less ductile) candidate material for lattice structures. For a 35%
fiber volume fraction, the axial Young’s modulus of the
monofilament is about 215 GPa and its ambient temperature tensile fracture strength exceeds 1800 MPa. Both are
approximately two times higher than that of Ti–6Al–4V
alloy, while the density of such a monofilament would be
3.93 g/cm3, roughly 12% less than that of Ti–6Al–4V.
These composite materials also offer much better creep
resistance than their all-metallic counterparts [43]. With
these considerations, cellular structures fabricated from
such composites might be attractive for high temperature
and/or weight sensitive structural applications.
The aim of the current paper is to report a method for
the fabrication of TMC lattice core sandwich panels. The
out-of-plane compressive behavior of the lattice structure
is investigated experimentally and the micromechanisms
of lattice deformation as a function of lattice relative density are identified. The mechanical properties are then compared to analytic estimates based upon the observed failure
modes. While these materials/structures have limited ductility, they appear to be one of the highest specific strength
cellular structures fabricated to date.
2. Lattice truss fabrication
Collinear lattice structures with a square orientation
(Fig. 1f) and a relative density, q, in the range of 5–17%
were fabricated from Ti–6Al–4V coated SCS-6 SiC monofilaments supplied by FMW Composite Systems, Inc.
(Clarksburg, WV). Each monofilament was approximately
240 lm in diameter and consisted of a 140 lm diameter SiC
(SCS-6) fiber surrounded by a 50 lm thick physical vapor
deposited Ti–6Al–4V coating, Fig. 2. The SCS-6 fibers were
made by chemical vapor deposition on carbon cylindrical
substrates (33 lm diameter fibers) [44,45]. The densities
of SCS-6 fiber, Ti–6Al–4V, and the composite monofilament are 3.00, 4.43, and 3.93 g/cm3, respectively.
Fig. 1. Examples of sandwich panel structures with open-cell, lattice core topologies. Metallic pyramidal, tetrahedral and kagomé core structures are made
by folding perforated metal sheets or by investment casting. The textile and collinear core structures are made by wire lay-up and brazing methods.
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Fig. 2. (a) Schematic and (b) cross-sectional micrograph of a Ti–6Al–4V coated SCS-6 SiC monofilament (35% fiber volume fraction).
Lattice structures were assembled from the monofilaments using a simple fixture (constructed of stainless steel
and spray coated with BN to prevent sticking) to align
the monofilaments in collinear layers, Fig. 3a. The orientation of consecutive layers was alternated to create a square
lattice truss topology structure. Fig. 4 shows a stacking
sequence and a unit cell of the lattice structure. Once
assembly of the TMC filament lay-up was complete, a dead
weight was used to apply a force of 3.7 102 N (equiva-
lent to an applied pressure of 1.5–5 MPa) to each contact
(truss–truss node). The assembly was diffusion bonded by
placing it in a vacuum furnace at a base pressure of
107 Torr. It was heated at 20 °C/min to 900 °C and then
held for 4 h under pressure, Fig. 3b. The lattice structures
were then removed from the tooling and cut, using wire
electro-discharge machining, to create samples that were
four cells high and six cells in length, Fig. 3c. The sample
width was approximately the same as the sample height,
Fig. 3. Fabrication of a TMC square lattice core sandwich panel: (a) assembly sequence to make a TMC lattice; (b) vacuum diffusion bonding of the core;
(c) sandwich panel lay-up; and (d) brazing of face sheets to the square orientated core.
P. Moongkhamklang et al. / Composites: Part A 39 (2008) 176–187
179
Fig. 5 shows nodal regions of the lattice structure after
the diffusion bonding step. It can be seen that excellent
metallurgical uniformity was achieved in the bonded
region. Equiaxed a-grains and an intergranular b-phase
microstructure was observed with an average grain size of
8 lm. During diffusion bonding, the spacing between consecutive layers and hence the macroscopic lattice width
decreased as the titanium alloy coating at the contact
points deformed and interdiffused. Fig. 4 schematically
shows a unit cell of the square lattice before and after diffusion bonding.
A diffusion bonding coefficient, b, can be introduced by
assuming the titanium alloy coating was redistributed similarly in each collinear layer (see Fig. 4). The b coefficient is
defined as w/wo, where w and wo are the unit cell widths
prior to and after the diffusion bonding process (Figs. 4b
and c), correspondingly. The unit cell volume of the diffusion bonded lattice can then be written:
V c ¼ wl2 ¼ bwo l2 ¼ b4al2 :
ð2Þ
Even though the titanium alloy coating is deformed at the
contacts, the volume occupied by the solid composite in the
unit cell remains the same as for the as laid-up unit cell.
The relative density of the diffusion bonded square lattice
structure, q, is therefore:
V s 2pa2 l 1 pa qo
ð3Þ
q¼
¼
¼
¼ :
V c b4al2 b 2l
b
Fig. 4. Representative unit cells of a square lattice: (a) three layer lattice;
(b) unit cell before diffusion bonding; and (c) unit cell of the diffusion
bonded structure (w < wo).
i.e. W H = 4l, where l, W, and H are the unit cell length,
the lattice width, and the lattice height, respectively.
The relative density of the as laid-up lattice,qo , is simply
the volume fraction of the unit cell occupied by solid truss
material:
qo ¼
V s 2pa2 l 2pa2 l pa
;
¼
¼
¼
2l
Vc
wo l2
4al2
Table 1 summarizes cell parameters and corresponding relative densities of the square lattices prior to and after diffusion bonding. For the diffusion bonding conditions
used here, b was 0.9–0.92, and the relative density of the
lattices therefore increased by 8–10% during the bonding
process.
After being cut to size, the lattices were brazed to 2 mm
thick Ti–6Al–4V face sheets using a TiCuNi-60Ò paste
braze alloy supplied by Lucas-Milhaupt, Inc. (Cudahy,
WI), Figs. 3c–d. This alloy powder had a nominal composition of Ti-15Cu-25Ni (wt%) and was held in a polymer
binder. The solidus and liquidus temperatures of the brazing alloy are 890 °C and 940 °C, respectively. The sandwich
panel samples were vacuum brazed by heating at 20 °C/min
to 550 °C, holding for 5 min (to volatilize and remove the
polymer binder), and finally heating to 975 °C for 30 min
at a base pressure of 107 Torr. Micrographs of a trussface sheet node made by the brazing technique are shown
in Fig. 6. It can be seen that the TiCuNi-60Ò braze provided good wettability to the SCS-6 fiber surface as well
as good penetration to the Ti–6Al–4V alloy coating and
face sheet. Photographs of sandwich panel samples of each
core relative density are shown in Fig. 7.
ð1Þ
where Vc, Vs, wo, a, and l are the unit cell volume, the volume occupied by the solid trusses, the cell width, the filament radius, and the cell length, respectively.
3. Experimental compressive response
The square lattice structures were tested at ambient temperature in compression with a displacement rate of
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Fig. 5. Diffusion bonded truss–truss nodes: (a) exterior deformation of the metal coating at the nodes; (b) cross-section of a pair of nodes; and (c) diffusion
bonded region between a pair of monofilaments.
Table 1
Cell/lattice parametersa and corresponding relative densities prior to and after core diffusion bonding (T = 900 °C, t = 4 h, P = 1.5–5 MPa)
Center-to-center cell
length, l (mm)
1.26
1.88
2.51
3.77
a
Prior to diffusion bonding
After diffusion bonding
b (w/w0)
Relative density, qo ð%Þ
Core width, Wo (mm)
Core width, W (mm)
Relative density, q ð%Þ
15.0
10.0
7.5
5.0
6.03
9.05
12.06
18.10
5.43 ± 0.015
8.35 ± 0.025
10.91 ± 0.043
16.75 ± 0.147
16.7 ± 0.05
10.8 ± 0.03
8.3 ± 0.03
5.4 ± 0.05
0.90 ± 0.003
0.92 ± 0.003
0.90 ± 0.004
0.92 ± 0.008
The monofilament diameter was 240 lm for all samples. The center-to-center cell length l is unaffected by diffusion bonding.
Fig. 6. Truss-face sheet interface for a square oriented lattice structure after the brazing treatment: (a) SEM micrograph; (b) optical microscope crosssectional micrograph; and (c) SEM cross-sectional micrograph.
Fig. 7. Photographs showing TMC square lattice core sandwich structures.
0.02 mm/min (see Table 2 for corresponding strain rates).
The measured load cell force was used to calculate the
nominal stress applied to the sandwich, and the nominal
through thickness strain was obtained from a laser extensometer positioned about the sample centerline. The gage
length for strain measurement for the compression samples
was the core height, H (see Table 2).
The through thickness, compressive stress–strain
responses for square lattice structures at each q are shown
in Fig. 8. All the cellular structures deformed in an elastic–
brittle manner with a variable degree of post peak strength
retention that decreased with increasing relative density.
The stiffnesses and peak strengths are plotted against q in
Figs. 9a and b. The stiffness exhibited a linear dependence
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181
Table 2
Compression test parameters
Sample relative density,
q ð%Þ
Core height,
H (mm)
Strain rate,
e_ (105 s1)
16.7
10.8
8.3
5.4
6.20 ± 0.031
9.38 ± 0.010
12.66 ± 0.015
19.26 ± 0.022
5.38 ± 0.027
3.56 ± 0.004
2.68 ± 0.003
1.73 ± 0.002
Fig. 8. Compressive stress–strain response for square lattice truss structures with q ¼ 16:7; 10:8; 8:3; and 5:4%.
3
upon q, while the strength appeared to depend on ðqÞ .
Figs. 10 and 11 show stress–strain responses and photographs of the lattice taken during the compression of samples with high (q ¼ 16:7%) and low (q ¼ 5:4%) lattice
relative densities, correspondingly. As the samples were
compressed, trusses parallel to the loading direction
deformed elastically and then buckled cooperatively as a
consequence of being joined by the horizontal trusses.
The peak stress in the stress–strain curve coincided with
the onset of this buckling instability. Unload/reload tests
indicated that prior to the peak compressive strength the
strain was fully recoverable, indicating that the strength
of these structures is controlled by elastic buckling of the
vertical trusses. Note that Fig. 8 indicates that the lower
the relative density (the more slender the trusses) the lower
the strength and the smaller the core strain at the onset of
elastic buckling.
In the highest relative density lattice (with q ¼ 16:7%),
the trusses had a relatively low aspect ratio, and fracture
of the monofilament was observed instantaneously with
buckling (Fig. 10). Fig. 11 shows clearly that for the lattices
with lower relative densities (more slender trusses), the
trusses continued to buckle cooperatively as the strain
progressed beyond the load peak. The buckling half
wavelength was equal to the core height. This bucklingaccommodated straining was accompanied by a significant
decrease in applied stress, i.e. core softening. As compres-
Fig. 9. Experimental data for (a) out-of-plane compressive stiffness and
(b) out-of-plane compressive strength of the TMC square truss cores.
sion continued, the truss nodes were subjected to increasingly significant shear forces and eventually debonded.
Fig. 12 shows micrographs of a vertical truss after the compression test where shear debonding has occurred. In addition to debonding at the nodal contact, fracture of the
metallic coating and fiber also occurred in this case.
While the peak compressive strengths appear to be simply controlled by the elastic buckling instability, the post
peak stress behavior is controlled by less obvious mechanisms. From Fig. 11, it is clear that the unloading paths
were not parallel to the initial elastic response and did
not return to zero strain. This is indicative of inelastic
deformation of the metallic coating. It appears that after
the onset of the buckling instability, the SCS-6 fiber contin-
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P. Moongkhamklang et al. / Composites: Part A 39 (2008) 176–187
Fig. 10. Compressive stress–strain response and corresponding photographs of a square lattice truss structure with q ¼ 16:7%: (a) prior to initial loading;
(b) prior to peak load; (c) immediately after the peak load; and (d) after the peak load. Events (b)–(d) occurred within a few seconds.
Fig. 11. Compressive stress–strain response and corresponding photographs of a square oriented lattice truss structure with q ¼ 5:4%: (a) prior to initial
loading; (b) after the peak load and prior to first unloading; (c) following first unloading; (d) prior to second unloading; (e) following second unloading; (f)
prior to third unloading; (g) following third unloading; (h) prior to fourth unloading; and (i) following fourth unloading.
P. Moongkhamklang et al. / Composites: Part A 39 (2008) 176–187
183
where Es is the axial Young’s modulus of the parent material. The axial Young’s modulus of the TMC monofilament
can be estimated by the rule of mixtures:
Es ¼ ð1 f ÞEm þ fEf ;
ð5Þ
where f is the volume fraction of the SCS-6 fiber, and Em
and Ef are the Young’s moduli of the Ti–6Al–4V matrix
and SCS-6 fiber, respectively. For Ef = 400 GPa [44,45],
Em = 115 GPa [39], and f = 0.35, Eq. (5) gives Es =
215 GPa.
A comparison between the measured and predicted stiffness (plotted as non-dimensional compressive stiffness,
P ¼ Ec =ðEs qÞÞ as a function of the lattice relative density
is shown in Fig. 13a. While most of the experimental data
lie within 30% of the predicted value, some data lie well
Fig. 12. Nodal shear and coating/fiber fracture near the nodes of a
compressively loaded square lattice truss structure with q ¼ 10:8%.
ued to buckle elastically, while Ti–6Al–4V coating
deformed plastically to accommodate the bending strain
and node shear. At the highest core strains, beyond the
elastic limit of the SCC-6 fiber and ductility of the Ti alloy
coating, truss node debonding, coating fracture, and eventually SCS-6 fiber fracture accommodated the imposed
strain and were responsible for the core softening.
The reloading behavior of these structures also revealed
interesting effects, Fig. 11. In particular, it can be seen that
when the lattice structure was reloaded, it followed a different stress–strain path to that during unloading. During
unloading, the applied stress at a fixed core strain was less
than that during the subsequent reloading cycle. This
appears to be a result of elastic SiC fiber spring back and
the release of the stored elastic energy in the fiber.
4. Discussion
Simple micromechanical arguments can be used to rationalize the initial loading modulus and peak strength of the
composite cellular materials tested here.
4.1. Compressive stiffness
Under out-of-plane compression, only half of the trusses
(the vertical trusses) carry load. Prior to buckling of the
compressively loaded columns, the elastic modulus, Ec, of
the collinear lattice is simply [46]:
1
Ec ¼ Es q;
2
ð4Þ
Fig. 13. Analytical prediction and experimental data for (a) dimensionless
stiffness and (b) strength of TMC square lattices.
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P. Moongkhamklang et al. / Composites: Part A 39 (2008) 176–187
below the prediction. Such discrepancies have been frequently reported for cellular materials [20–31] and the origin of the effect appears to result from imperfections
introduced in the fabrication process. The discrepancy
observed here is believed to be a consequence of small variations in the length of the load–carrying trusses (core
height) due to the cutting process. During initial loading
the applied load would then be disproportionately shared
between the trusses. The compressive platen would apply
the load onto longer trusses first. Because the platen moved
with a constant rate, lower load would then be required than
if all the trusses were load carrying. As compression proceeds, the load would be applied onto more and eventually
all trusses. This makes the initial slope of the stress–strain
plot (where a constant load supporting area is assumed) relatively low, but it continues to increase until the applied
load is proportionately shared among all the trusses.
4.2. Compressive strength
The peak compressive strengths of the TMC square collinear cores can be estimated by analyzing the failure
modes of truss members as individual axially loaded columns. It is assumed that the lattice collapses by elastic
buckling of the constituent struts over the full height of
the sandwich core as schematically illustrated in Fig. 14.
If the vertical trusses are not joined together by horizontal
trusses, the buckling stress acting on each vertical truss can
be described by the elastic bifurcation stress, rcr, of a compressively loaded circular column [47,48]:
2
p2 k 2 E s a
rcr ¼
;
ð6Þ
lb
4
where Es is the column elastic modulus, a the column radius and lb the length of the column between two supporting ends. The factor k depends upon the rotational stiffness
of the end nodes with k = 1 corresponding to a freely rotating pin-joint and k = 2 corresponding to built in nodes
which cannot rotate [47,48]. For the square lattices, the
trusses length was H (the core height) and we assume
k = 2. Using this expression for the predicted critical
strength of individual truss members, the mechanical properties of the sandwich panel that has no interaction among
the truss members can be globalized and the compressive
collapse strength of a core structure, r0pk , can be expressed
by [21]:
r0pk ¼ Rrcr q;
ð7Þ
where R is a lattice topology dependent scaling factor.
The scaling factor R = 1/2(sin2x1 + sin2x2) accounts for
the fact that trusses oriented in the loading direction are
the most efficient for load bearing, while those that are
inclined are limited by force resolution considerations
[49]. For square truss samples, half of the trusses have
x1 = 0° and another half have x2 = 90° so the effective
value of R ¼ 0:5.
By substituting Eq. (6) into Eq. (7), the peak compressive strength of a square lattice truss structure failing by
elastic buckling is then:
p2 E s a 2
r0pk ¼
q:
ð8Þ
2 H
Substituting H = nl (where n = number of unit cells along
the height of the core), Eqs. (1) and (3) into Eq. (8) gives
a relation between core strength, lattice relative density,
and the number of cells in the principle loading direction:
r0pk ¼
2Es 3 2Es b2 3
q ¼
q:
n2 b o
n2
ð9Þ
However, since the vertical trusses are joined together and
hence are forced to buckle cooperatively, an additional
shear stress at the truss nodes is also present (as suggested
by experiment, see Fig. 12). This cooperative buckling
mode is similar to the shear buckling mode of a fiber composite material modeled by Rosen [50]. In Rosen’s model,
adjacent fibers buckle with the same wavelength and in
phase with one another. The deformation of the matrix
material between adjacent fibers is assumed to be primarily
a shear deformation. Rosen found that the compressive
strength of a fiber composite rc due to (cooperative) shear
buckling is:
rc ¼
Fig. 14. Sketches of (a) an undeformed square lattice core and (b) its
expected buckling mode under compression.
Gm
þ vf rcr ;
1 vf
ð10Þ
where Gm, vf, and rcr are the shear modulus of the matrix,
the volumetric fraction of the fibers, and the buckling
strength of the fibers. The first term on the right-hand side
of Eq. (10) is the contribution to the composite compressive strength from matrix shear and the remaining term is
the contribution to the compressive strength associated
P. Moongkhamklang et al. / Composites: Part A 39 (2008) 176–187
185
with the finite-bending resistance of the fibers. Fleck [51]
subsequently argued that the matrix shear contribution,
Gm/(1vf), should be replaced by the in-plane shear modulus of the composite when the compressive strength of the
composite material is to be estimated.
Using this composite analogy, the cooperative buckling
strength of a square lattice is then controlled by the resistance to lattice buckling (Eq. (9)) and the resistance to lattice shear given by the in-plane shear modulus of the lattice
structure, G:
rpk ¼ G þ r0pk :
ð11Þ
An analytical expression of the in-plane shear modulus of
square lattice G has been recently derived by Hutchinson
[52]. He finds that the structure investigated here has a
shear modulus:
G¼
1
Es q3 :
16
ð12Þ
By substituting Eqs. (12) and (9) into Eq. (11), the peak
compressive strength of a square lattice truss structure that
fails by cooperative elastic buckling then becomes:
1 2b2
þ
ð13Þ
rpk ¼
Es q3 :
16 n2
A comparison between the measured and predicted compressive peak strength (plotted as non-dimensional peak
compressive strength, R ¼ rpk =ðEs q3 Þ against qÞ of the
TMC square collinear cores is shown in Fig. 13b. The cooperative elastic buckling model is seen to capture the peak
compressive strengths of these square lattices well. The
analytically predicted strength coefficient is 0.13. Most of
the experimental data lie within 20% of this estimate.
4.3. Comparisons with other cellular structures
The highest specific strength lattice structures previously
reported [19–31] utilized a Ti–6Al–4V alloy for the truss
structure. The specific strength of such lattices was found
to be approximately 100 kN m/kg [26]. The specific
strength of the titanium composite lattices studied here
was 185 kN m/kg. These TMC lattices therefore appear
to be the highest specific strength cellular materials
reported to date.
The titanium composite lattices investigated here are
expected to retain good dimensional stability during loading at temperature up to 500 °C (above this, creep of the
metallic component becomes significant). The stiffness
and peak strength of the square TMC lattice structures
can be compared with those of similar lattices made from
stainless steel [30] and ceramic foams [53–62] whose service
temperatures also extend to 500 °C and above, Fig. 15.
Examination of the figure indicates that the higher relative
density TMC lattices possess a higher specific stiffness and
strength than any of the other structures/materials. These
materials may therefore provide interesting high tempera-
Fig. 15. (a) Stiffness and (b) compressive strength versus density for TMC
and stainless steel collinear lattice structures. Data for ceramic foams
having service temperature of 500 °C and above is also included.
ture multifunctional opportunities provided their limited
ductility is not a significant constraint.
5. Conclusions
1. A method for making titanium sandwich panels with
millimeter-scale titanium matrix composite (TMC) lattice cores has been developed. The method involves laying up linear arrays of TMC monofilaments, alternating
the direction of consecutive layers, and using diffusion
bonding to join the nodes. The relative density of the
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lattice was controlled by the diameter of the TMC
monofilaments, the spacing between the filaments in
each collinear layer (cell length), and the degree of diffusion bonding.
2. The out-of-plane modulus of square TMC lattice structures has been shown to scale linearly with q. The compressive peak strength was controlled by cooperative
elastic buckling and varied with ðqÞ3 .
3. The specific strength and stiffness of the lattices significantly exceeds that of other lattice structures fabricated
to date.
4. These TMC lattices appear promising candidates for elevated temperature, multifunctional applications.
Acknowledgements
The authors are grateful to Norman Fleck at the University of Cambridge and Vikram Deshpande at the University of California at Santa Barbara for helpful
discussions of the interpretation of this work. The study
was supported by the Office of Navel Research (ONR)
and monitored by Drs. David Shifler and Steve Fishman
under Grant Number N00014-01-1-1051.
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