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Design of composite lattice materials combined with fabrication approaches, Summaries of Materials science

The design and fabrication of composite lattice materials for lightweight structures. The authors propose two types of composite lattice materials with enhanced resistance to buckling: hollow lattice materials and hierarchical lattice materials with foam-core sandwich trusses. The mechanical performance of sandwich structures featuring the two types of lattice cores were tested and analyzed theoretically. The document also discusses the microstructural design of lattice materials to increase buckling resistance and specific properties while achieving ultra-low relative density.

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Design of composite lattice materials combined with
fabrication approaches
Jun Xu1, 2, 3, 4, Yaobo Wu1, 2, Xiang Gao1, 2, Huaping Wu5, Steven Nutt6, Sha Yin1, 2, 3*
1Department of Automotive Engineering, School of Transportation Science and Engineering, Beihang
University, Beijing, China, 100191
2Advanced Vehicle Research Center (AVRC), Beihang University, Beijing, China, 100191
3State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace
Engineering, Xi’an Jiaotong University, Xi’an, China, 710049
4State Key Laboratory for Automotive Safety and Energy, Tsinghua University, Beijing, China, 100084
5Key Laboratory of E&M (Zhejiang University of Technology), Ministry of Education & Zhejiang Province,
Hangzhou 310014, PR China
6Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles,
CA 90089-0241, USA
Abstract: Lattice materials can be designed through their microstructure while concurrently
considering fabrication feasibility. Here, we propose two types of composite lattice materials with
enhanced resistance to buckling: (a) hollow lattice materials fabricated by a newly-developed
bottom-up assembly technique and the previously developed thermal expansion molding
technique; (b) hierarchical lattice materials with foam-core sandwich trusses fabricated by
interlocking assembly process. The mechanical performance of sandwich structures featuring the
two types of lattice cores were tested and analyzed theoretically. For hollow lattice core material,
samples from two different fabrication processes were compared and both failed by nodal rupture
* Corresponding author: Prof. Sha Yin, E-mail: shayin@buaa.edu.cn. Tel: +86-10-82339921, Fax: +86-10-
82339923
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Design of composite lattice materials combined with

fabrication approaches

Jun Xu1, 2, 3, 4, Yaobo Wu1, 2, Xiang Gao1, 2, Huaping Wu^5 , Steven Nutt^6 , Sha Yin1, 2, 3* (^1) Department of Automotive Engineering, School of Transportation Science and Engineering, Beihang University, Beijing, China, 100191 (^2) Advanced Vehicle Research Center (AVRC), Beihang University, Beijing, China, 100191 (^3) State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, China, 710049 (^4) State Key Laboratory for Automotive Safety and Energy, Tsinghua University, Beijing, China, 100084 (^5) Key Laboratory of E&M (Zhejiang University of Technology), Ministry of Education & Zhejiang Province, Hangzhou 310014, PR China (^6) Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA 90089-0241, USA Abstract: Lattice materials can be designed through their microstructure while concurrently considering fabrication feasibility. Here, we propose two types of composite lattice materials with enhanced resistance to buckling: (a) hollow lattice materials fabricated by a newly-developed bottom-up assembly technique and the previously developed thermal expansion molding technique; (b) hierarchical lattice materials with foam-core sandwich trusses fabricated by interlocking assembly process. The mechanical performance of sandwich structures featuring the two types of lattice cores were tested and analyzed theoretically. For hollow lattice core material, samples from two different fabrication processes were compared and both failed by nodal rupture

  • (^) Corresponding author: Prof. Sha Yin, E-mail: shayin@buaa.edu.cn. Tel: +86-10-82339921, Fax: +86-10- 82339923

or debonding. In contrast, hierarchical lattice structures failed by shear buckling without interfacial failure in the sandwich struts. Calculations using established analytical models indicated that the shear strength of hollow lattice cores could be optimized by judicious selection of the thickness of patterned plates. Likewise, the shear strength of hierarchical foam-core truss cores could be maximized (with minimal weight) through design of truss geometry. The bottom-up assembly technique could provide a feasible way for mass-production of lattice cores, but the design about how to assembly is critical. Hierarchical lattice cores with foam sandwich trusses should be a relatively ideal choice for future lightweight material application.

Keywords: Sandwich structure; Lattice materials; Fiber composites; Mechanical properties; Structural design; Mass production.

1. INTRODUCTION

Lattice materials are regarded as viable lightweight and multifunctional candidates for the next generation of efficient structures due to their superior specific strength and stiffness [1-3], large interconnected open space [4-5], and energy absorption capability [6-8]. Selection of fiber composites as constituent materials for lattice cores can lead to specific mechanical properties that surpass those of metallic counterparts in engineered systems [9]. Various reports have documented efforts over the past decade to explore fiber reinforced lattice composites [10-15], and these efforts encompass techniques for producing lattice core structures, such as hot press molding, weaving [16, 17], interlocking [18] and additive assembly manufacturing [19].

Microstructural design of lattice materials can be an effective pathway to increase buckling resistance and thus specific properties while achieving ultra-low relative density. In particular, design of truss cross-section has been proven to be an effective strategy. For example, pyramidal

Lattice materials produced by mass-production approaches is a largely underdeveloped domain in the technology of core materials, despite the critical role it plays in adaptation. Thus, the objective of this work is to seek simpler methods for large-volume production of two types of composite lattice cores cited above, and then evaluate the process by structural overall performance. First, we describe a flexible bottom-up assembly method for hollow lattice cores. This mold-free technique shares the same processing idea as the micro/nano additive manufacturing method. In addition, we describe a vacuum bag only process combined with interlocking assembly method for producing foam-core hierarchical lattice cores, so as to increase the interfacial properties of foam sandwich trusses. The mechanical performance of the two types of structures is discussed and analyzed. Finally, theoretical models are employed for prediction of properties and further optimization, which provides a means to evaluate the fabrication approach as well.

2. EXPERIMENTAL

2.1. Fabrication of composite lattice core sandwich structures with hollow trusses

A flexible and mold-free, bottom-up assembly method is proposed to fabricate hollow composite lattice cores besides the previously developed thermal expansion molding method. For the bottom-up fabrication technique, trusses and perforated sheets were used for positioning as basic elements. Unidirectional pultruded composite rods (solid and hollow) were used for truss elements. Pre-drilled laminates were used to situate trusses and guide truss insertion. The perforated guide plates featured custom designed patterns, as shown in Figures 1a-b. Two- dimensional perforated guide plates with inclined holes were produced, and the representative unit cell of this intermediate layer (between facesheets and lattice core) is shown schematically in

Figure 1c. A patterned composite plate made from woven fiber-glass is shown in Figure 1d. The relative density of the patterned plate after perforation can be expressed as

(1)

where is related to the geometry of the pyramidal lattice structure; is the

edge dimension of the square hole in the perforated sheet, and =45o^ is the inclination angle. Note that due to the limitations of laboratory processing conditions in this study, elliptical through- thickness holes of diameter were drilled in the lattice sheets by projection of inclined tubes.

An illustration showing the insertion of trusses is shown in Figure 2a. Before insertion, hollow trusses were cut to specific lengths with ends at angle according to the final truss configuration. During the process, we first inserted trusses into four corners, then into arrays along lattice sheet edges, and finally the middle array of holes. Figure 2b shows the assembled hollow lattice core, and the 2-D planar lattice sheet functioning as attachment to the hollow lattice core. In the following section, we describe how the core assemblies were co-bonded with two carbon fiber composite facesheets (3234/T700, Beijing Institute of Aeronautical Materials, China) using epoxy film adhesive to form the hollow lattice core sandwich structures in Figure 2c.

The 2-D lattice sheets can be considered as intermediate layers connecting the facesheets and the hollow lattice cores. A schematic of the representative unit cell, including patterned plate, is shown in Figure 2d, and defines the relevant geometric parameters of the lattice structure. The

relative density is given by the ratio of the solid volume to that of the unit cell:

2 2 2

rint = m^ -^2 n^ - m^ p 2 do / sinw

m = ( 2 l 1 cos w+ 2 l 2 ) n

w

d 0

w

r

0.09 MPa), and bagged samples were debulked for 1h at room temperature to remove trapped air. After the room-temperature vacuum hold, samples were cured according to the recommended cure cycle (Figure 3b), then cooled to room temperature.

(2) Interlocking assembly method for the hierarchical composite lattice cores Laminated sandwich panels were cut into strips and then grooved to produce the geometries indicated above. Strips were subsequently joined by slot insertion at the nodes to form the lattice cores, and the nodes were secured with epoxy adhesive as introduced in a former publication [26]. The lattice cores with foam sandwich struts were bonded with two laminates, forming the corresponding sandwich structures, as shown in Figure 3c, for subsequent testing. The effective density of the representative unit cell shown in Figure 3d is deduced as

(3)

where and b are length and width of the sandwich strut; is the length of the horizontal trusses

which connects the inclined struts at the pyramidal node and is the inclination angle between the struts and the base of the unit cell. The thickness and density of the foam core in the sandwich strut is and , while the facesheet thickness and density is and. Here, = 16.97 mm,

= 12 mm, b = 3 mm, = 0.4 mm, = 4 mm, = 0.052 g/cm^3 , = 1.8 g/cm^3. Thus, the

effective density of the hierarchical core is 0.0353 g/cm^3.

2.3. Mechanical testing method

( )

1 2 eff 2 1 2 1

2 tan 2 2 cos tan 2 sin

b l l b t (^) f f tc c l l b l b

w r r
r w
w w

éê (^) + - ùú + = ë^ û éê (^) + - ùú + ë û l 1 l 2

w
t c r c t^ f r f l 1 l 2
t f tc r c r f

For hollow lattice cores, the compressive properties can be referred to Ref. [22], and only shear tests were performed here. For compression tests, hierarchical lattice cores with 33 cells were prepared, and through-thickness tests were performed following the guidelines of ASTM C365/C365M as shown in Figure 4a. For shear tests, samples with 24 unit cells were prepared in accordance with ASTM C273/C273M-06. Composite lattice core sandwich structures with hollow trusses and foam sandwich trusses were both tested on a hydraulic servo testing machine (MTS

  1. with a 100 kN load cell using a single-lap shear configuration in Figure 4b at an applied nominal shear strain rate of 1 mm/min. The measured load cell force was used to calculate the shear stress while the relative sliding of the two faces of sandwich plates was measured using a laser extensometer. The shear strain was calculated from the sliding displacement.

3. THEORETICAL ANALYSIS

3.1. Effective shear properties of composite lattice cores with hollow trusses

Analysis of the effective shear properties of hollow truss composite pyramidal lattice structure was undertaken by considering the deformation of a single tube from a unit cell, as sketched in Figure 5. Note that trusses produced by the bottom-up technique are constrained by both the facesheets and the intermediate layers (if perfectly bonded), and thus the boundary constraint coefficients k are assumed to be k = 2 for the two techniques described above.

3.1.1. Shear stiffness An imposed in-plane displacement in the x -direction gives rise to a shear angle and a

resultant force. Two truss members will be loaded in compression, while the other two will be

d x g xz
F xz

If trusses fail by node rupture, shear failure mechanisms are different for structures produced by the two techniques.

(1) Samples produced by thermal expansion molding. The progressive failure process starts at the node ends where the truss fibers are twisted and embedded into the face sheet. The transverse shear strength of a lattice core with hollow trusses can be derived as

(6)

where is the peak load of a sandwich plate with a single inclined truss (produced by the same

fabrication process) in transverse shear loading. Note that the value of is correlated only to the

fabrication details at the truss ends.

(2) Samples produced by bottom-up assembly Truss pullout occurs readily at truss-sheet junctions as shown in Figure 6b. The interface between lattice trusses and facesheet is identified as Interface 1, while the interface between lattice trusses and intermediate layers will be called Interface 2. Truss peel-off occurs only when the shear force triggers debonding at both Interface 1 and Interface 2, and thus the shear forces from Interface 1 and 2 will contribute to the shear strength of the entire structure. Thus, the shear strength of lattice structures is expressed as

(7)

1 22

( cos 2 )
F nr

t = l w+ l

F nr
F nr
t = t r n h + 4 t^^ n (^ d d^ o^ o 2 r - h^ cos di 2 )w t int

where is the adhesive shear strength between the plate and the trusses, and is the thickness

of the patterned plates. The first term in Eq.7 bodies the adhesive shear force in Interface 1, while the second item expresses the shear force in Interface 2. However, due to the limits of the laboratory fabrication methods for producing the holes in this study, only the adhesive shear force in Interface 1 contributes to the overall shear strength.

3.2. Effective shear properties of composite lattice cores with foam sandwich trusses

Theoretical deduction about the out-of-plane compressive properties for hierarchical lattice cores can be referred to Ref. [26], and the shear performance can be analyzed in a similar way.

3.2.1. Shear stiffness The shear stiffness of the hierarchical lattice cores with foam sandwich trusses can be given by

where is compressive stiffness of the foam core sandwich strut, is

shear stiffness, and is the bending stiffness. For the selected foam (Rohacell

55WF-HT) in this paper, the measured density , Young’s modulus ,

shear modulus , and shear strength.

3.2.2 Shear strength

t (^) n t int

1 2 2 (^2 1 13 ) 1 2

( sin ) cos sin cos tan (^2) sand (^12) sand sand

G l^ b l l b l^ l^ l A (^) D A

w w w
w w

éê ùú = +^ ê^ + ú éê (^) + - ùú êê^ + úú ë û ë û Asand = 2 E bteqf f Ssand = G btc c (^13) sand 6 D^ I = E eqf t bf

r c = 52 g/m k^3 Ec =75MPa
Gc = 28.125MPa t c =0.8MPa

(c) Shear failure of foam core Shear force applied on a strut will induce shear failure of the foam core. The maximum shear force in the foam strut is , is the foam shear strength. Then, the shear strength of the

lattice sandwich cores is

(d) Euler buckling of sandwich struts Struts are likely buckle when compressed. The Euler buckling load of foam sandwich struts

with a fixed boundary condition is , and the shear strength is given by

(e) Shear buckling of sandwich struts

( ) (^13 ) (^2 2 ) 1 2

= cos^1 sin cos cos tan cos^1 2 12

f c c f sand sand sand

E E G bt l l b A l D S

t^ w w j w w^ w

éê ùú ê ê (^) + úú é (^) + - ù (^) ê æç^ + ö÷ú êë úû (^) êë (^) è øúû

F s = t c ct b^ t c

2 12 2 2 1 2

cos ( 1 ) = sin^ 1+ 12 cos cos tan sin 2

c ct b A^ sand D^ lsand^ Ssand l l b

t w^ w t w w j w

éê (^) + ùú êê úú éê (^) + - ùú ê ú ë û ë û

Fa = 4 π 2 Dsand / l 12

2 2 2 2 2 12 1 1 2

= 4 cos^1 sin cos cos tan cos^1 2 12

sand sand sand sand

D

l l l b A l D S

t^ p w w
j w w^ w

éê ùú ê ê (^) + úú é (^) + - ù (^) ê æç^ + ö÷ú êë úû (^) êë (^) è øúû

Shear buckling will possibly occur when compressive force reaches the critical load at

. The shear strength can be expressed as

(f) Debonding Debonding can occur when the shear strength at the facesheet-lattice core interface is exceeded. The shear strength is related to the bond area as

(14)

3.3. Optimal design

3.3.1. Composite lattice cores with hollow trusses Based on the analysis described above, we can design nodal properties (and thus shear performance) using the bottom-up assembly technique for a specific truss configuration by selection of an appropriate patterned plate (e.g., length n , thickness ). Analytical models showed

that nodal or interfacial strength can be increased by increasing the thickness of the patterned plates. When the thickness is increased to a specific value, we assume that the shear force contributed by adhesive shear from Interfaces 1 and 2 is equal to the truss failure force. Optimal design involves competition between truss failure and nodal debonding, and thus the shear strength

F a = G t bc c

2 (^2 2 ) 1 2

= cos^1 sin cos cos tan cos^1 2 12

c c sand sand sand

G t b l l b A l D S

t^ w w j w w^ w

éê ùú ê ê (^) + úú é (^) + - ù (^) ê æç^ + ö÷ú êë úû êë (^) è øúû

2 2 2 1 2

2 cos tan 2
n^ l b^ b
l l b
t t w
w
éê + - ùú
ë û

t int

and

(17)

4. RESULTS AND DISCUSSION

4.1. Composite lattice cores with hollow trusses

The shear stress-strain curves and the representative failure modes of three hollow lattice core sandwich structures with different relative densities fabricated by the bottom-up assembly technique are shown in Figure 6. The stress increases linearly before reaching the peak, associated with node debonding at the truss and interlayer interface, followed by stress fluctuations and a sharp drop, which corresponds to node failure at truss ends. The shear strength for the three structures increases with core density, but the corresponding failure mode (tube-facesheet debonding) remains the same, as shown in Figure 6b.

Figure 7 shows the shear behavior of sandwich structures with similar truss geometries produced using thermal expansion molding. The curves in Figure 7a differ from those in Figure 6a, exhibiting nonlinear behavior prior to the peak stress, followed by a gradual decline in (fluctuating) stress associated with progressive node rupture. For structures with relative density of 1.07%, trusses in compression failed by crushing, while trusses in tension failed by node rupture. However, lattice structures with relative density of 2.21% and 4.53% both failed exclusively by node rupture.

4.2. Composite lattice cores with foam sandwich trusses

l 2 = tc^ G t n^ c^^ coscos wj + 2 b

The measured compressive stress-strain curves are plotted in Figure 8a along with theoretical prediction. The nominal compressive stress increases almost linearly with the nominal strain and reaches a peak. Shear buckling of sandwich lattice struts happened at the peak stress with a failure strain of 0.026 following with a sharp stress drop. The measured shear stress-strain curve of the hierarchical lattice cores with foam sandwich trusses is plotted in Figure 8b. After an initial increase, the shear stress reaches a peak, followed by a sharp drop and a long stress plateau. The governing failure mode observed in the shear tests is also shear buckling of sandwich struts.

The measured compressive strength differs from predicted value by 11%. Also, the shear strength value obtained from the theoretical models is included in Figure 8b. The deviation between measured shear strength and predicted shear strength can be attributed to sample misalignment, and the adhesive layer may introduce relative displacement of the loading plates. The measured shear strength differs from predicted values by 14%. The difference can be attributed to fabrication defects and actual geometries departing from ideal ones ( tc in the obtained sandwich strut is about 3 mm here).

4.3. Comparison

A comparison between analytical predictions and experimental results is summarized in Table 4 for hollow lattice cores fabricated by thermal expansion molding (Variant 1), bottom-up assembly (Variant 2) and for hierarchical lattice cores with foam sandwich trusses (Variant 3). From the analytical results in Table 4, for hollow lattice cores, we can assume that when hole of the patterned plate and rod are assembled (snug) and the adhesion area is sufficiently large, the corresponding shear strength could be guaranteed. Thus, the bottom-up assembly technique

occurred. The mechanical models accurately predict the shear properties of the enhanced lattice materials, and optimized truss geometries of foam sandwich struts are deduced.

The bottom-up assembly technique provides a feasible way for mass-production of hollow lattice cores, but the design about how to assembly could be improved in future work. Also, alternative cellular materials, such as foams, with strength exceeding shear strength of adhesives, may provide additional choices for patterned plates in hollow lattice cores. The structural efficiency of the two types of lattice cores considered in the present study is the same after optimization. Combined with fabrication process, hierarchical lattice cores with foam sandwich trusses should be a better choice to future lightweight material application.

Acknowledgements : This work is financially supported by the National Natural Science Foundation of China under grant No. 11402012, Young Elite Scientist Sponsorship Program by CAST, Opening fund of State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University (SV2015-KF-07, SV2016-KF-20), Opening fund of State Key Laboratory for Automotive Safety and Energy, Tsinghua University (Grant No. KF16142), and Beijing Municipal Science & Technology Commission (Grant No.Z161100001416006).

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