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Interlocking orthogrid: An efficient way to construct lightweight lattice-core sandwich composite structure
Composite Structures 176 (2017) 55–71
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Interlocking orthogrid: An efficient way to construct lightweight latticecore sandwich composite structure Shu Jiang a,b, Fangfang Sun a, Xirui Zhang a, Hualin Fan a,c,⇑ a Research Center of Lightweight Structures and Intelligent Manufacturing, State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b College of Mechanics and Materials, Hohai University, Nanjing 210098, China c Aerospace System Engineering Shanghai, Shanghai 201108, China
a r t i c l e
i n f o
Article history: Received 28 September 2016 Revised 12 March 2017 Accepted 11 May 2017 Available online 13 May 2017 Keywords: Sandwich structures Mechanical properties Mechanical testing
a b s t r a c t To construct weight efficient aerospace sandwich structures, interlocked orthogrid sandwich composite panels reinforced by carbon fibers were designed, made and tested. The orthogrid is weight efficient in flatwise compression for its strength is greater than usual three-dimensional (3D) lattice truss composite structures. Progressive crushing of the ribs endows the orthogrid long deformation plateau and great mean crushing force (MCF) while most of 3D lattice truss composite structures are usually brittle. Crushing models of lattice truss materials were developed to predict the MCF and it is found that the orthogrid composite has comparable or even better specific energy absorption (SEA) compared with 3D metallic lattice trusses. Forming continuous resin adhesive layers between the facesheets and the orthogrid, the orthogrid sandwich panel has stronger shear strength and is more weight efficient than usual 3D lattice truss sandwich panels jointed by adhesive joints in shear resistance. Through the research, it is concluded that interlocking orthogrid provides a simple but efficient way to construct lightweight sandwich composite. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Recently, lightweight lattice truss composite sandwich structures attract attentions of many researchers in aerospace science and technology [1], who try their best to propose efficient method to make these lattice structures, including corrugated lattice truss structure [2], octet-truss lattice structure [3,4], 3D honeycomb grid structure [5], pyramidal truss structure [6–9], octahedral stitched truss structure [10]. Usually, 3D lattice truss structures are looked as the most weight-efficient structure, such as Octet-trusses, pyramidal trusses and tetrahedral trusses. Obeying stretchingdominated deformation mechanism, the effective strength and the equivalent Young’s modulus are linear to their relative density. In-plane stretching service scenario is important for cellular lattice structure when it is applied as a dependent load-bearing structure, such as 3D space lattice structures [3], Iso-truss columns [11] and Isogrid cylindrical structures [12,13]. As these 3D lattice trusses are ⇑ Corresponding author at: Research Center of Lightweight Structures and Intelligent Manufacturing, State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. E-mail address: [email protected] (H. Fan). http://dx.doi.org/10.1016/j.compstruct.2017.05.029 0263-8223/Ó 2017 Elsevier Ltd. All rights reserved.
inserted into the core of a bended sandwich panel, it is found that the adhesive layer between the facesheets and the lattice trusses is dominant, more important than its compression strength in the case of lap shear and bending test scenarios. Thus, the weight efficiency is limited and the lattices face identical problems with traditional honeycombs and foams, which are assumed to be replaced by those stretching-dominated lattice structures. In other way, to construct a 3D lattice structure is so complex and expensive that the lattice cannot be produced at expected dimensions for engineering applications. All these shortcomings restrict the application of 3D lattice composite structure, although Li et al. [14] has successfully made 3D lattice-core sandwich cylinder, whose diameter is 625 mm. On the contrary, planar grid composite is easily made and inexpensive [15–18]. Interlocking method inspired by Han and Tsai [15] simplified the making process and reduced the cost. Using carbon fiber reinforced plastics (CFRP), Fan et al. [19–21] made Kagome grid-core sandwich panels. The Kagome grid is stretching-dominated in edgewise compression. But the in-pane stretching-domination is not important for a core structure when the panel is bended. Out-of-plane compression and shear behaviors are the most concerned. So in this paper, interlocking orthogrid, a simple way to construct efficient lightweight sandwich
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structure was proposed and mechanical properties of CFRP orthogrid panels were revealed. 2. Interlocked orthogrid To make the interlocked orthogrid, CFRP strips were firstly made by hot-pressing method. Prepreg carbon fiber (CFS15000) layers of [0°/90°]7 were placed into the mould and cured at 120 °C for 4 h. Each layer is about 0.15 mm. From the CFRP supplier, unidirectional carbon fiber (CFS15000) layered laminate has tensile strength of 819.1 MPa, tensile modulus of 82.1 GPa, shear strength of 18 MPa and fracture strain of 1.42%. CFRP strip with layers of [0°/90°] has compression strength of 294 MPa from our own measurement [2]. The rib has trapezoid cross section and changing thickness, varying from 2 mm to 1 mm linearly, as shown in Fig. 1. The strip width is 10 mm. Slots distribute along the strip with spacing of 20 mm. The maximum width of the slot is 1.5 mm and the depth
of the slot is 5 mm. The strips were then interlocked orthogonally to form the orthogrid. After that, the orthogrid was placed between two facesheets whose thickness is 1 mm. Adhesive, Epoxy resin YJ01, was applied to join the face sheet with seven layers of [0°/9 0°/0°/90°/0°/90°/0°] and the orthogrid. The sandwich panel was co-cured at room temperature for 12 h under a uniform compression force of 1.75 kN. After co-curing and removing the mould, the LTSP was fabricated. Through hot-pressing, a CFRP orthogrid sandwich panel was achieved. The relative density of the orthogrid, q , is
t d
q ¼ 2 ;
ð1Þ
where t is the mean thickness of the rib and d is the spacing between ribs. Usually, strength rs and Young’s modulus Es of the structure have following relations
rs ¼ Aq rM ; Es ¼ Bq EM
Fig. 1. (a) Rib structure, (b) orthogrid sandwich panel and (c) micro-fibers in the core pillar (Unit: mm).
ð2Þ
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with material strength rM and Young’s modulus EM . For orthogrid, A ¼ B ¼ 1 loaded from out-of-plane. For 3D lattices, these two coefficients are usually smaller than 0.5. For example, A ¼ 1=3 and B ¼ 1=6 for Octet-truss [22]. Usually 3D Kagome lattice is assumed as the strongest lattice material, but A ¼ 0:4. So that orthogrid is more weight-efficient when loaded from out-of-plane, as shown in Fig. 2, where buckling or node fracture is not considered. For lattice or orthogrid sandwich panels, the shear strength is usually controlled by the adhesions between the lattice core and the facesheets, rather than the shear strength of the lattice. 3. Flatwise compression behaviors 3.1. Flatwise compression strength
Fig. 2. Theoretical specific strength of orthogrid and typical 3D lattice truss materials.
Compression behaviors of the orthogrid were tested, as shown in Figs. 3 and 4. In compression, the sample dimensions are 100 mm 100 mm 12 mm. The weight of the sample is 56.5 g in average, while the pure orthogrid is 16.3 g. Accordingly, relative
Fig. 3. Out-of-plane compression (a) curves and failure modes of orthogrid sandwich panels (b) A1, (c) A2 and (c) A3.
Fig. 4. Details of the compression failure.
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Fig. 5. Out-of-plane compression (a) curves and failure modes of orthogrid panels (b) D4 and (c) D5.
density of the orthogrid is 0.0815, smaller than the theoretical value, 0.12. The CFRP strip has layers of [0°/90°] and the compression strength is 294 MPa [2]. Theoretically, the strength of the orthogrid is 23.96 MPa. Attached with facesheets (Figs. 3 and 4), the strength of the orthogrid is about 21.7 MPa (Fig. 3), very close to the theoretical value. Without facesheets (Fig. 5), the strength is reduced to 13.5 MPa. The orthogrid is made up of CFRP laminate and the com-
pression strength of the CFRP laminate tightly relates to the end constraints. With facesheets, orthogrid ribs fail at fracture, companying with face sheet debonding, laminate delamination and fiber buckling, as shown in Fig. 4. Without facesheet constraints, orthogrid ribs tend to fail at delamination and buckling which greatly reduces the strength. As shown in Fig. 6, orthogrid has different deformation mode with most of 3D lattice truss composites. The CFRP octet-truss
Fig. 6. Compression behavior of orthogrid panel compared with (a) pyramidal honeycomb grid sandwich panel [5], (b) corrugated lattice truss sandwich panel [2] and (c) octet-truss panel [23].
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Fig. 7. Compression strengths of typical lattice truss composite structures [2].
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of the strut of the octet-truss greatly reduces the strength. The horizontal planar lattices have little contribution to the out-of-plane strength and reduce the weight efficiency. The CFRP corrugated lattice [2] is ductile but the relative density is increased to 0.2 to enlarge the adhesive area. Inclined struts of the corrugated lattice decrease its out-of-plane strength. As its relative density, 0.2, is about 2.45 times of the orthogrid, its strength is still much smaller than the orthogrid. The CFRP pyramidal honeycomb grid sandwich panel [5] has hybrid structure and the material cannot be fully utilized in compression. So its strength is much smaller, although its relative density is 0.12, greater than 0.0815, the relative density of the orthogrid. Through the comparisons in Fig. 7, the orthogrid is stronger than most of the 3D CFRP lattice truss composites. Even removing the facesheets, the orthogrid is still stronger. Only vertical components of the axial forces of the inclined struts resist the external compression load, so that 3D lattices have smaller strength and their weight efficiency will be reduced. 3.2. Energy absorption
[23] is brittle. As its relative density, 0.159, is about twice of the orthogrid, its strength is still much smaller than the orthogrid. According to Eq. (2), strength ratio of the octet-truss to the orthogrid is given by
rs jOctet-truss 1 ðq rM ÞjOctet-truss ¼ : rs jOrthogrid 3 ðq rM ÞjOrthogrid
ð3Þ
If they have identical CFRP strength and relative density, strength of the octet-truss truss is only 1/3 of the orthogrid. In experiment, rM jOctettruss 300 MPa in average [3] and rM jOrthogrid ¼ 294 MPa. Their strength ratio is 0.66 according to Eq. (3), close to the tested ratio, 0.57 and 0.8. Obviously, inclination
Different with most of 3D lattice composite structures, the orthogrid has ductile deformation, as shown in Figs. 3 and 5. In crushing, the delamination and fiber fracture are progressive and the mean crushing stress of all the orthogrid, rm , is close to the strength of naked orthogrid, rsn . Facesheet constraints only improve the strength rather than the mean crushing stress. The specific energy absorption (SEA) of the orthogrid, SEA, is given by
SEA ¼ rm ed ¼ rsn ed ¼ gq rM ed ;
ð4Þ
with
g¼
rsn ; rss
ð5Þ
Fig. 8. Compression behavior of orthogrid panel compared with (a) Ti-6Al-4V octet-truss lattice [4], (b) aluminum tetrahedral lattice [24] and (c) Ti-based Face-body-centred cubic lattice [25].
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Fig. 9. (a) Plastic deformation of aluminum tetrahedral lattice [24] and (b) specific energy absorption prediction.
Fig. 10. Edgewise compression behaviors of 100 mm long columns (a) with and (b) without end jackets.
Fig. 11. Details of the edgewise compression failure.
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Fig. 12. Edgewise compression behaviors of 200 mm long columns (a) with and (b) without end jackets.
where ed is the densification strain and its value is 0.6. And rss is the strength of sandwiched orthogrid. Here g ¼ 0:624. SEA of the orthogrid is 7.15 J/cm3, greater than most of 3D lattice truss composites. Even compared with metallic lattices absorbing energy through plastic deformation [4,24–26], the orthogrid has comparable or even better energy absorbing ability, as shown in Fig. 8. For Ti6Al-4V octet-truss lattice [4], its relative density is 0.126, greater than the orthogrid, and its MCF is 18.4 MPa, greater than 11.44 MPa, the MCF of the orthogrid. For aluminum tetrahedral lattice [24], its relative density is 0.085, a little greater than the orthogrid, and its MCF is 7.89 MPa, much smaller than 11.44 MPa, the MCF of the orthogrid. For Ti-based Face-body-centred cubic lattice [25], its relative density is 0.0685, smaller than the orthogrid, and
its deformation is brittle. Although Ti-based lattices have greater strength, when its topology is not optimally designed, its crushing-resistance must be greatly reduced. Energy absorption of Aluminum-based lattices is usually less than CFRP orthogrid. In crushing, there are three potential plastic hinges at the center and both ends of each metallic strut [24], as shown in Fig. 9. The total rotation of the plastic hinges is ð2x þ pÞ, where x is the inclination of the strut. The energy absorbed by an unit cell, Ep , is calculated by
Ep ¼ nM p ð2x þ pÞ;
ð6Þ
where n is the strut number in an unit cell. Mp is the full plastic moment of the strut and given by
Fig. 13. Edgewise compression behaviors of 300 mm long columns with end jackets.
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where ry is the yield strength (70 MPa) and ru is the ultimate strength (165 MPa) [24]. b and t denote the width and the thickness of the strut, respectively. The MCF, P m , is calculated by
Pm hed ¼ nM p ð2x þ pÞ:
ð9Þ
For tetrahedral lattice with b ¼ t, the SEA is given by
SEA ¼ rm ed ¼ ¼
ed Ph
t3 rp ð2x þ pÞ ¼ pffiffiffi 3 Au h 3L cos2 x sin x
1t q rp ð2x þ pÞ 2l
ð10Þ
with
q ¼ pffiffiffi
2t2
3L cos2 x sin x 2
;
ð11Þ
where l is the strut length. Accordingly, SEA ¼ 4:134 J=cm3 and
rm ¼ 7:8 MPa. The prediction is consistent with the test. The SEA
Fig. 14. Edgewise compression strength variation with column length.
Mp ¼ with
rp ¼
can also be expressed as
1 rp bt2 ; 4
ð7Þ
pffiffiffiffiffiffiffiffiffiffiffi ry ru ;
ð8Þ
SEA
rp
sp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffi 3 3 ¼ cos2 x sin xðq Þ2 ð2x þ pÞ: 8
ð12Þ
For tetrahedral lattice,
SEA=rp ¼ 1:224ðq Þ2 : 3
Fig. 15. Shear (a) test, (b) strength and failure of the sandwich panel (c) Q1 and (d) Q2.
ð13Þ
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Fig. 16. Bending behaviors of orthogrid sandwich panels with span of (a) 40 mm, (b) 60 mm,(c) 120 mm and (d) 160 mm.
SEA=rp is proportional to ðq Þ2 . As shown in Fig. 9, prediction given by Eq. (13) is consistent with the test of aluminum tetrahedral lattices [24], validating the plastic model. For orthogrid, SEA=rM is proportional to q . Orthogrid has better weight efficiency in energy absorption. 3
4. Edgewise compression behaviors Edgewise compression experiments were carried out at a loading rate of 0.2 mm/min. The compressed panels are 100 mm wide.
Pure 60 mm long orthogrid panels failed at global buckling and the peak load is about 3.1 kN. The equivalent strength is only 3.1 MPa, much smaller than the flatwise compression strength. Global buckling decreases the strength. The sandwich panels are much stronger, as shown in Fig. 10. When the ends are constrained by steel jackets, the peak load of the panel is about 50 kN. The corresponding stress of the skin is about 270 MPa. Without end jackets, the peak load drops to 30 kN. The corresponding stress of the skin is about 170 MPa. As shown in Fig. 11, the panel failed at end crushing for one skin and the other skin failed at debonding and buckling. The debond-
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Fig. 17. Details of the failure of 40 mm span panel in bending.
Fig. 18. Flexural strength variation of orthogrid sandwich panels.
ing is restricted and the buckling wavelength is 60 mm but 100 mm when the column length is 200 mm or 300 mm. After the peak load, the load will drop to 30 kN, close to the strength of the column strength without end jackets. Only one skin stiffened by the orthogrid bears the load and the residual stress is close to a half of the peak load. Without end jackets the delamination initiates from the end and then induces skin debonding. The buckling wave length is about 100 mm. Similar phenomena were found in the compression tests of 300 mm long columns (Fig. 12) and 300 mm long columns (Fig. 13). End constraint effect is revealed by experiments and this will instruct the optimal design of orthogrid sandwich structures [27]. The experiments stressed the importance of the end flanges.
It is also found that column length has little influence to the compression strength, as shown in Fig. 14. In the experiments, the slenderness variation is not great and the columns fail at the same mode. Global buckling needs greater slenderness. 5. Shear behaviors 5.1. Shear strength For orthogrid panel, the shear strength, ss , depends on the shear strength of the orthogrid rib, sr , as
ss ¼ 0:5q : sr
ð14Þ
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Fig. 19. Shear failure modes of typical lattice composite structures with (a) bed-in nodes [6], (b) corrugated nodes [2] and (c) adhering nodes [7] and shear strength varying with (d) node area [2] and (e) relation to relative density.
For 3D lattice truss composites,
ss ¼ C q ; rm
ð15Þ
where C is smaller than 0.5. For example, C ¼ 1=6 for octet-truss [22]. So that the dimensionless shear strength of the orthogrid is usually higher. In most circumstances, shear failure of lattice-core composite sandwich panels is controlled by the interfacial property. In this way, shear strength of the orthogrid panel and most of 3D lattices is given by
ss ¼ q ; sa
ð16Þ
where sa is the shear strength of the adhesive layer. Eq. (16) can be expressed as
ss ¼ sa
Ad : Acell
ð17Þ
The shear strength is proportional to the adhesive area Ad in a unit cell (Acell ). Sometimes the shear strength is insensitive to the strength of the lattice strut. Lap compression shear experiments were carried out at a loading rate of 0.1 mm/min. The sample dimensions are 100 mm 100 mm 12 mm. In shear, the panel was divided into
Fig. 20. Failure criteria of bended orthogrid panels with 1 mm thick skins.
two parts from the adhesive layer. The sudden delamination led a brittle failure, as shown in Fig. 15. The shear strength varies from 1.8 MPa to 2.8 MPa. For specimen Q1, the facesheet is smooth. Through the failure map it is found that the shear failure occurs
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Fig. 21. Edgewise compression behaviors of 100 mm long orthogrid panels with 0.5 mm thick skins: (a) Stress, (b) strain and (c) failure modes.
at the interface between the facesheet and the adhesive film, not between the orthogrid and the adhesive film. It means that the actual adhesive area is much greater than the cross section area of the orthogrid. This phenomenon is quite different with other 3D lattice truss composite materials and endows the orthogrid has priority in shear resistance. In forming, the orthogrid is usually impressed into the resin film and the bonding is strong. To improve the bonding between the film and the skin, the facesheets of specimen Q2 and Q3 are pre-roughened before attached with the orthogrid. So that the resin film detached from the orthogrid and they have much greater shear strength. 5.2. Short-span bending behaviors Another way to evaluate the shear resistance of the sandwich panel is the short-span flexural behavior tested through threepoint bending experiments, as shown in Figs. 16 and 17. The span (L) varies from 40 mm to 160 mm. The width is 100 mm. The thickness is 12 mm. The facesheet thickness is 1 mm. For pure orthogrid, the peak load is only 2 kN when the span is only 40 mm. For orthogrid sandwich panels, the peak loads vary from 6.2 kN to 10 kN, almost independent of the span. When the span is 40 mm, the peak load is over 8 kN. The central facesheet firstly
delaminated from the orthogrid which was not destroyed, as shown in Fig. 16. Obviously, the shear resistance of the orthogrid is enhanced when sandwiched by two skins. Interfacial debonding failure controls the flexural behavior. After debonding, the load still increased slowly rather than decreased. The debonding did not develop and the panel was compressed and sheared. When the span is 60 mm, the debonding developed and the upper skin were completely detached from the orthogrid and the panel behaved as a stiffened before the lower skin fracture, supplying residual strength to the panel. When the span is over 80 mm, the delamination located at the one-fourth span. The delamination led an abrupt load drop. The panel was out of work when the facesheet was completely detached. Although the final failure modes are different, all the initial failures are induced by the shear failure of the adhesive layer and the peak load changes little as well as the residual load, as shown in Fig. 18. The peak load, P, can be simply evaluated by
P ¼ 2ss Bc;
ð18Þ
where B and c denote the width and thickness of the panel. Accordingly, the equivalent shear stress ss at failure varies from 2.6 MPa to 4.2 MPa, comparable to or a little greater than the shear strength
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Fig. 22. Edgewise compression behaviors of 200 mm long orthogrid panels with 0.5 mm thick skins: (a) Stress, (b) strain, (c) failure modes of D1 and (d) failure modes of D2.
derived from the lap compression shear experiments. The average value is 3.5 MPa. 5.3. Comparisons As shown in Fig. 19, the orthogrid has greater shear strength compared with lattice truss materials whose lattices are only adhered with the facesheets. The shear strength is proportional to the relative density as
ss ¼ K q :
ð19Þ
The coefficient K indicates the weight efficiency of the lattice in shear resistance. For orthogrid, K ¼ 33:1 in average. Given by experiments, K ¼ 27 for lattices with adhesive joints [3]. To enhance the shear strength, some researchers increased the adhesive area, such as corrugated lattice composites [2], but the weight efficiency is reduced to K ¼ 17. The orthogrid has better weight efficiency in shear resistance, as compared in Fig. 18.
Others adopted bed-in joints for which the facesheet must be pre-slotted and this method greatly improves the shear strength. For bed-in octet-truss [3], K ¼ 37, while for bed-in pyramidal lattice [6], K ¼ 77. But this technique will be abandoned when the facesheet is thin because the pre-set slots introduce severe initial damages to the sandwich panel and will greatly weak the flexural of edgewise compression strength. For example, the buried depth (t0 ) is 2.54 mm when t0 ¼ 0:8t, where t is the strut thickness and is 3.175 mm [6]. For sandwich panel, the facesheet thickness must be much greater than 2.54 mm. When bed-in nodes are adopted, the facesheet must be thick enough, which limits the application of the bed-in method. As shown in Fig. 18, the orthogrid sandwich panel has comparable weight-efficiency to the bedin octet-truss in shear resistance and has no requirement to the skin thickness. Through the comparison, it is concluded that orthogrid sandwich panels have better interfacial shear resistance than usual 3D lattice truss sandwich panels. Bonding strength between truss
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Fig. 23. Edgewise compression behaviors of 300 mm long orthogrid panels with 0.5 mm thick skins: (a) Stress, (b) strain and (c) failure modes.
core and the facesheets can be significantly improved by grooves or bed-ins machined in the facesheets, but this method will greatly thicken the facesheet. In this research, as the thickness of the skin is only 1 mm or 0.5 mm, we did not consider this method. Grooves or bed-ins will greatly weaken the behavior of the ultra-thin skin. For metallic lattice sandwich panels, the shear strength usually depends on the compression behaviors of the struts because the welded joints usually have strong shear-resistance. 6. Discussions 6.1. Bending design consideration In 160 mm span bending, the skin stress is about 290 MPa, close to the skin failure strength. The peak load determined by the skin failure is
Fig. 24. Edgewise compression strength variation of column length.
P¼4
Bt f ðc þ tf Þ rf ; L
ð20Þ
where rf , tf ,and L denote he skin failure strength, the skin thickness and the span, respectively. Critical span changing from shear failure to skin failure is given by
L¼2
t f ðc þ tf Þ c
rf : ss
ð21Þ
So we can give a design curve for this sandwich as shown in Fig. 20. It is found that using shear failure criterion and skin failure criterion, the flexural strength of the orthogrid sandwich panel can be well predicted. This method will be validated by more experimental results changing the skin thickness. 6.2. Skin thickness effects To further make clear the structural responses of the orthogrid sandwich panel, the skin thickness is lessened to 0.5 mm. The orthogrid keeps unchanged. The thickness of the panel now is 11.0 mm. In the experiments, strain gauges were adhered onto the skin surface to measure the strain which will be applied to explain the fatal failure mode of the orthogrid sandwich panel. Edgewise compression behaviors of the orthogrid sandwich panels were revealed, as shown in Figs. 21–23. Monocell buckling of the skin was observed when the stress is not high enough. In experiments, the monocell buckling load is close to 5.5 kN. The monocell buckling will not induce fatal failure, and then debonding or instability induced by skin dimpling or fracture was observed in succession. Peak load of the panels changes from 19.7 kN to 32 kN, as shown in Fig. 24. Column length has influence to the edgewise compression strength. The skin failure strength is about 270 MPa in average, close to the result tested from the panel with 1.0 mm thick skins. It is validated that skin failure stress in this research is 270 MPa. Three-point bending experiments were performed, as shown in Figs. 25 and 26, where the span changes from 40 mm to 200 mm. In bending, monocell cell buckling was observed firstly and this
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Fig. 25. Flexural behaviors of orthogrid panels with 0.5 mm thick skins with span of (a) 40 mm, (b) 60 mm, (c) 80 mm and (d) 120 mm.
damage will induce skin fracture or final debonding. Monocell buckling is not fatal and flexural strength of the panel is decided by the skin failure stress as the peak load decreases with increasing spans, as shown in Fig. 27. It is interesting that the shear failure criterion and the skin failure criterion consistently predict the peak load of the panel with 0.5 mm thick skins. Critical span transferring shear failure to skin flexural failure is 77 mm. Compared with panels composed of identical orthogrid and 1.0 mm skins, thinner skins make orthogrid sandwich panels more prone to flexural failure.
7. Conclusions Through the research, it is found that interlocking orthogrid is a simple way to construct efficient lightweight sandwich structure. According to the experiments, it is concluded that: 1) The orthogrid has greater strength and better weight efficiency in compression compared with 3D lattice truss composites.
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Fig. 26. Flexural behaviors of orthogrid panels with 0.5 mm thick skins with span of (a) 160 mm and (d) 200 mm.
3) The shear resistance usually depends on the adhesion area. The orthogrid panel has continuous ribs and a continuous adhesive layer between the orthogrid and the facesheet, which endows the orthogrid sandwich panel have better shear resistance than usual 3D lattice truss composites joined by adhering nodes. 4) Shear failure and skin flexural failure controls the flexural strength of the panel. Monocell buckling may be the initial failure when the skin is thin enough but it will not decide the strength. Debonding is the final failure style of the panel but usually it is induced by skin failure and observed in postfailure stage if the adhesive layer has good quality. Thinner skins make orthogrid sandwich panels more prone to skin flexural failure.
Acknowledgments
Fig. 27. Failure criteria of bended orthogrid panels with 0.5 mm thick skins.
2) Compared with the brittle failure mode of 3D lattice truss composites, the orthogrid has ductile deformation and keeps high MCF. The SEA of the orthogrid composites is comparable to or even greater than metallic lattice truss structure.
Supports from the National Natural Science Foundation of China (11372095, 11672130) and State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-0215G01) are gratefully acknowledged. References [1] Fan HL, Zeng T, Fang DN, et al. Mechanics of advanced fiber reinforced lattice composites. Acta Mech Sin 2010;26:825–35.
S. Jiang et al. / Composite Structures 176 (2017) 55–71 [2] Hu Y, Li WX, An XY, et al. Fabrication and mechanical behaviors of corrugated lattice truss composite sandwich panels. Compos. Sci. Technol. 2016;125:114–22. [3] Dong L, Wadley H. Shear response of carbon fiber composite octet-truss lattice structures. Compos Part A 2016;81:182–92. [4] Dong L, Deshpande V, Wadley H. Mechanical response of Ti–6Al–4V octet-truss lattice structures. Int J Solids Struct 2015;60–61:107–24. [5] Xiong J, Vaziri A, Ghosh R, et al. Compression behavior and energy absorption of carbon fiber reinforced composite sandwich panels made of threedimensional honeycomb grid cores. Extreme Mech Lett 2016;7:114–20. [6] George T, Deshpande VS, Wadley HNG. Mechanical response of carbon fiber composite sandwich panels with pyramidal truss cores. Composites Part A 2013;47:31–40. [7] Xiong J, Ma L, Pan S, et al. Shear and bending performance of carbon fiber composite sandwich panels with pyramidal truss cores. Acta Mater 2012;60:1455–66. [8] Sun YG, Gao L. Mechanical behavior of all-composite pyramidal truss cores sandwich panels. Mech Mater 2013;65:56–65. [9] Chen MJ, Zhu XL, Lei HS, et al. Effect of defect on the compressive response of sandwich structures with carbon fiber pyramidal truss cores. Int J Appl Mech 2015;7(1):1550004. [10] Che L, Xu G, Zeng T, et al. Compressive and shear characteristics of an octahedral stitched sandwich composite. Compos Struct 2014;112:179–87. [11] Lai CL, Wang JB, Liu C, et al. A flexible tooling and local consolidation process to manufacture 1D lattice truss composite structure. Compos Sci Technol 2015;113:63–70. [12] Fan HL, Fang DN, Chen LM, et al. Making and testing of a CFRC sandwich cylinder with Kagome cores. Compos Sci Technol 2009;69:2695–700. [13] Han YS, Wang P, Fan HL, et al. Free vibration of CFRC lattice-core sandwich cylinder with attached mass. Compos Sci Technol 2015;118:226–35. [14] Li WX, Sun FF, Wang P, et al. A novel carbon fiber reinforced lattice truss sandwich cylinder: fabrication and experiments. Compos Part A 2016;81:313–22.
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[15] Han D, Tsai SW. Interlocked composite grids design and manufacturing. J Compos Mater 2002;37(4):287–316. [16] Li GQ, Muthyala VD. Impact characterization of sandwich structures with an integrated orthogrid stiffened syntactic foam core. Compos Sci Technol 2008;68(9):2078–84. [17] Li JH, Hunt JF, Gong SQ, et al. Simplified analytical model and balanced design approach for light-weight wood-based structural panel in bending. Compos Struct 2016;136:16–24. [18] Sun Z, Shi SS, Guo X, et al. On compressive properties of composite sandwich structures with grid reinforced honeycomb core. Compos Part B 2016;94:245–52. [19] Fan HL, Meng FH, Yang W. Mechanical behaviors and bending effects of carbon fiber reinforced lattice materials. Arch Appl Mech 2006;75:635–47. [20] Fan HL, Meng FH, Yang W. Sandwich panels with Kagome lattice cores reinforced by carbon fibers. Compos Struct 2007;81(4):533–9. [21] Fan HL, Yang L, Sun FF, et al. Compression and bending performances of carbon fiber reinforced lattice-core sandwich composites. Compos Part A 2013;52:118–25. [22] Fan HL, Yang W. An equivalent continuum method of lattice structures. Acta Mech Solida Sin 2006;19(2):103–13. [23] Dong L, Wadley H. Mechanical properties of carbon fiber composite octet-truss lattice structures. Compos Sci Technol 2015;119:26–33. [24] Kooistra GW, Deshpande VS, Wadley HNG. Compressive behavior of age hardenable tetrahedral lattice truss structures made from aluminium. Acta Mater 2004;52:4229–37. [25] Ullah I, Brandt M, Feih S. Failure and energy absorption characteristics of advanced 3D truss core structures. Mater Des 2016;92:937–48. [26] Sun FF, Lai CL, Fan HL. Crushing mechanism of hierarchical lattice structure. Mech Mater 2016;97:164–83. [27] Jiang S, Sun FF, Fan HL. Fabrication and testing of composite orthogrid sandwich cylinder. Compos Sci Technol 2017;142:171–9.
Contents lists available at ScienceDirect
Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Interlocking orthogrid: An efficient way to construct lightweight latticecore sandwich composite structure Shu Jiang a,b, Fangfang Sun a, Xirui Zhang a, Hualin Fan a,c,⇑ a Research Center of Lightweight Structures and Intelligent Manufacturing, State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b College of Mechanics and Materials, Hohai University, Nanjing 210098, China c Aerospace System Engineering Shanghai, Shanghai 201108, China
a r t i c l e
i n f o
Article history: Received 28 September 2016 Revised 12 March 2017 Accepted 11 May 2017 Available online 13 May 2017 Keywords: Sandwich structures Mechanical properties Mechanical testing
a b s t r a c t To construct weight efficient aerospace sandwich structures, interlocked orthogrid sandwich composite panels reinforced by carbon fibers were designed, made and tested. The orthogrid is weight efficient in flatwise compression for its strength is greater than usual three-dimensional (3D) lattice truss composite structures. Progressive crushing of the ribs endows the orthogrid long deformation plateau and great mean crushing force (MCF) while most of 3D lattice truss composite structures are usually brittle. Crushing models of lattice truss materials were developed to predict the MCF and it is found that the orthogrid composite has comparable or even better specific energy absorption (SEA) compared with 3D metallic lattice trusses. Forming continuous resin adhesive layers between the facesheets and the orthogrid, the orthogrid sandwich panel has stronger shear strength and is more weight efficient than usual 3D lattice truss sandwich panels jointed by adhesive joints in shear resistance. Through the research, it is concluded that interlocking orthogrid provides a simple but efficient way to construct lightweight sandwich composite. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction Recently, lightweight lattice truss composite sandwich structures attract attentions of many researchers in aerospace science and technology [1], who try their best to propose efficient method to make these lattice structures, including corrugated lattice truss structure [2], octet-truss lattice structure [3,4], 3D honeycomb grid structure [5], pyramidal truss structure [6–9], octahedral stitched truss structure [10]. Usually, 3D lattice truss structures are looked as the most weight-efficient structure, such as Octet-trusses, pyramidal trusses and tetrahedral trusses. Obeying stretchingdominated deformation mechanism, the effective strength and the equivalent Young’s modulus are linear to their relative density. In-plane stretching service scenario is important for cellular lattice structure when it is applied as a dependent load-bearing structure, such as 3D space lattice structures [3], Iso-truss columns [11] and Isogrid cylindrical structures [12,13]. As these 3D lattice trusses are ⇑ Corresponding author at: Research Center of Lightweight Structures and Intelligent Manufacturing, State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. E-mail address: [email protected] (H. Fan). http://dx.doi.org/10.1016/j.compstruct.2017.05.029 0263-8223/Ó 2017 Elsevier Ltd. All rights reserved.
inserted into the core of a bended sandwich panel, it is found that the adhesive layer between the facesheets and the lattice trusses is dominant, more important than its compression strength in the case of lap shear and bending test scenarios. Thus, the weight efficiency is limited and the lattices face identical problems with traditional honeycombs and foams, which are assumed to be replaced by those stretching-dominated lattice structures. In other way, to construct a 3D lattice structure is so complex and expensive that the lattice cannot be produced at expected dimensions for engineering applications. All these shortcomings restrict the application of 3D lattice composite structure, although Li et al. [14] has successfully made 3D lattice-core sandwich cylinder, whose diameter is 625 mm. On the contrary, planar grid composite is easily made and inexpensive [15–18]. Interlocking method inspired by Han and Tsai [15] simplified the making process and reduced the cost. Using carbon fiber reinforced plastics (CFRP), Fan et al. [19–21] made Kagome grid-core sandwich panels. The Kagome grid is stretching-dominated in edgewise compression. But the in-pane stretching-domination is not important for a core structure when the panel is bended. Out-of-plane compression and shear behaviors are the most concerned. So in this paper, interlocking orthogrid, a simple way to construct efficient lightweight sandwich
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structure was proposed and mechanical properties of CFRP orthogrid panels were revealed. 2. Interlocked orthogrid To make the interlocked orthogrid, CFRP strips were firstly made by hot-pressing method. Prepreg carbon fiber (CFS15000) layers of [0°/90°]7 were placed into the mould and cured at 120 °C for 4 h. Each layer is about 0.15 mm. From the CFRP supplier, unidirectional carbon fiber (CFS15000) layered laminate has tensile strength of 819.1 MPa, tensile modulus of 82.1 GPa, shear strength of 18 MPa and fracture strain of 1.42%. CFRP strip with layers of [0°/90°] has compression strength of 294 MPa from our own measurement [2]. The rib has trapezoid cross section and changing thickness, varying from 2 mm to 1 mm linearly, as shown in Fig. 1. The strip width is 10 mm. Slots distribute along the strip with spacing of 20 mm. The maximum width of the slot is 1.5 mm and the depth
of the slot is 5 mm. The strips were then interlocked orthogonally to form the orthogrid. After that, the orthogrid was placed between two facesheets whose thickness is 1 mm. Adhesive, Epoxy resin YJ01, was applied to join the face sheet with seven layers of [0°/9 0°/0°/90°/0°/90°/0°] and the orthogrid. The sandwich panel was co-cured at room temperature for 12 h under a uniform compression force of 1.75 kN. After co-curing and removing the mould, the LTSP was fabricated. Through hot-pressing, a CFRP orthogrid sandwich panel was achieved. The relative density of the orthogrid, q , is
t d
q ¼ 2 ;
ð1Þ
where t is the mean thickness of the rib and d is the spacing between ribs. Usually, strength rs and Young’s modulus Es of the structure have following relations
rs ¼ Aq rM ; Es ¼ Bq EM
Fig. 1. (a) Rib structure, (b) orthogrid sandwich panel and (c) micro-fibers in the core pillar (Unit: mm).
ð2Þ
S. Jiang et al. / Composite Structures 176 (2017) 55–71
57
with material strength rM and Young’s modulus EM . For orthogrid, A ¼ B ¼ 1 loaded from out-of-plane. For 3D lattices, these two coefficients are usually smaller than 0.5. For example, A ¼ 1=3 and B ¼ 1=6 for Octet-truss [22]. Usually 3D Kagome lattice is assumed as the strongest lattice material, but A ¼ 0:4. So that orthogrid is more weight-efficient when loaded from out-of-plane, as shown in Fig. 2, where buckling or node fracture is not considered. For lattice or orthogrid sandwich panels, the shear strength is usually controlled by the adhesions between the lattice core and the facesheets, rather than the shear strength of the lattice. 3. Flatwise compression behaviors 3.1. Flatwise compression strength
Fig. 2. Theoretical specific strength of orthogrid and typical 3D lattice truss materials.
Compression behaviors of the orthogrid were tested, as shown in Figs. 3 and 4. In compression, the sample dimensions are 100 mm 100 mm 12 mm. The weight of the sample is 56.5 g in average, while the pure orthogrid is 16.3 g. Accordingly, relative
Fig. 3. Out-of-plane compression (a) curves and failure modes of orthogrid sandwich panels (b) A1, (c) A2 and (c) A3.
Fig. 4. Details of the compression failure.
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Fig. 5. Out-of-plane compression (a) curves and failure modes of orthogrid panels (b) D4 and (c) D5.
density of the orthogrid is 0.0815, smaller than the theoretical value, 0.12. The CFRP strip has layers of [0°/90°] and the compression strength is 294 MPa [2]. Theoretically, the strength of the orthogrid is 23.96 MPa. Attached with facesheets (Figs. 3 and 4), the strength of the orthogrid is about 21.7 MPa (Fig. 3), very close to the theoretical value. Without facesheets (Fig. 5), the strength is reduced to 13.5 MPa. The orthogrid is made up of CFRP laminate and the com-
pression strength of the CFRP laminate tightly relates to the end constraints. With facesheets, orthogrid ribs fail at fracture, companying with face sheet debonding, laminate delamination and fiber buckling, as shown in Fig. 4. Without facesheet constraints, orthogrid ribs tend to fail at delamination and buckling which greatly reduces the strength. As shown in Fig. 6, orthogrid has different deformation mode with most of 3D lattice truss composites. The CFRP octet-truss
Fig. 6. Compression behavior of orthogrid panel compared with (a) pyramidal honeycomb grid sandwich panel [5], (b) corrugated lattice truss sandwich panel [2] and (c) octet-truss panel [23].
S. Jiang et al. / Composite Structures 176 (2017) 55–71
Fig. 7. Compression strengths of typical lattice truss composite structures [2].
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of the strut of the octet-truss greatly reduces the strength. The horizontal planar lattices have little contribution to the out-of-plane strength and reduce the weight efficiency. The CFRP corrugated lattice [2] is ductile but the relative density is increased to 0.2 to enlarge the adhesive area. Inclined struts of the corrugated lattice decrease its out-of-plane strength. As its relative density, 0.2, is about 2.45 times of the orthogrid, its strength is still much smaller than the orthogrid. The CFRP pyramidal honeycomb grid sandwich panel [5] has hybrid structure and the material cannot be fully utilized in compression. So its strength is much smaller, although its relative density is 0.12, greater than 0.0815, the relative density of the orthogrid. Through the comparisons in Fig. 7, the orthogrid is stronger than most of the 3D CFRP lattice truss composites. Even removing the facesheets, the orthogrid is still stronger. Only vertical components of the axial forces of the inclined struts resist the external compression load, so that 3D lattices have smaller strength and their weight efficiency will be reduced. 3.2. Energy absorption
[23] is brittle. As its relative density, 0.159, is about twice of the orthogrid, its strength is still much smaller than the orthogrid. According to Eq. (2), strength ratio of the octet-truss to the orthogrid is given by
rs jOctet-truss 1 ðq rM ÞjOctet-truss ¼ : rs jOrthogrid 3 ðq rM ÞjOrthogrid
ð3Þ
If they have identical CFRP strength and relative density, strength of the octet-truss truss is only 1/3 of the orthogrid. In experiment, rM jOctettruss 300 MPa in average [3] and rM jOrthogrid ¼ 294 MPa. Their strength ratio is 0.66 according to Eq. (3), close to the tested ratio, 0.57 and 0.8. Obviously, inclination
Different with most of 3D lattice composite structures, the orthogrid has ductile deformation, as shown in Figs. 3 and 5. In crushing, the delamination and fiber fracture are progressive and the mean crushing stress of all the orthogrid, rm , is close to the strength of naked orthogrid, rsn . Facesheet constraints only improve the strength rather than the mean crushing stress. The specific energy absorption (SEA) of the orthogrid, SEA, is given by
SEA ¼ rm ed ¼ rsn ed ¼ gq rM ed ;
ð4Þ
with
g¼
rsn ; rss
ð5Þ
Fig. 8. Compression behavior of orthogrid panel compared with (a) Ti-6Al-4V octet-truss lattice [4], (b) aluminum tetrahedral lattice [24] and (c) Ti-based Face-body-centred cubic lattice [25].
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Fig. 9. (a) Plastic deformation of aluminum tetrahedral lattice [24] and (b) specific energy absorption prediction.
Fig. 10. Edgewise compression behaviors of 100 mm long columns (a) with and (b) without end jackets.
Fig. 11. Details of the edgewise compression failure.
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Fig. 12. Edgewise compression behaviors of 200 mm long columns (a) with and (b) without end jackets.
where ed is the densification strain and its value is 0.6. And rss is the strength of sandwiched orthogrid. Here g ¼ 0:624. SEA of the orthogrid is 7.15 J/cm3, greater than most of 3D lattice truss composites. Even compared with metallic lattices absorbing energy through plastic deformation [4,24–26], the orthogrid has comparable or even better energy absorbing ability, as shown in Fig. 8. For Ti6Al-4V octet-truss lattice [4], its relative density is 0.126, greater than the orthogrid, and its MCF is 18.4 MPa, greater than 11.44 MPa, the MCF of the orthogrid. For aluminum tetrahedral lattice [24], its relative density is 0.085, a little greater than the orthogrid, and its MCF is 7.89 MPa, much smaller than 11.44 MPa, the MCF of the orthogrid. For Ti-based Face-body-centred cubic lattice [25], its relative density is 0.0685, smaller than the orthogrid, and
its deformation is brittle. Although Ti-based lattices have greater strength, when its topology is not optimally designed, its crushing-resistance must be greatly reduced. Energy absorption of Aluminum-based lattices is usually less than CFRP orthogrid. In crushing, there are three potential plastic hinges at the center and both ends of each metallic strut [24], as shown in Fig. 9. The total rotation of the plastic hinges is ð2x þ pÞ, where x is the inclination of the strut. The energy absorbed by an unit cell, Ep , is calculated by
Ep ¼ nM p ð2x þ pÞ;
ð6Þ
where n is the strut number in an unit cell. Mp is the full plastic moment of the strut and given by
Fig. 13. Edgewise compression behaviors of 300 mm long columns with end jackets.
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where ry is the yield strength (70 MPa) and ru is the ultimate strength (165 MPa) [24]. b and t denote the width and the thickness of the strut, respectively. The MCF, P m , is calculated by
Pm hed ¼ nM p ð2x þ pÞ:
ð9Þ
For tetrahedral lattice with b ¼ t, the SEA is given by
SEA ¼ rm ed ¼ ¼
ed Ph
t3 rp ð2x þ pÞ ¼ pffiffiffi 3 Au h 3L cos2 x sin x
1t q rp ð2x þ pÞ 2l
ð10Þ
with
q ¼ pffiffiffi
2t2
3L cos2 x sin x 2
;
ð11Þ
where l is the strut length. Accordingly, SEA ¼ 4:134 J=cm3 and
rm ¼ 7:8 MPa. The prediction is consistent with the test. The SEA
Fig. 14. Edgewise compression strength variation with column length.
Mp ¼ with
rp ¼
can also be expressed as
1 rp bt2 ; 4
ð7Þ
pffiffiffiffiffiffiffiffiffiffiffi ry ru ;
ð8Þ
SEA
rp
sp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffi 3 3 ¼ cos2 x sin xðq Þ2 ð2x þ pÞ: 8
ð12Þ
For tetrahedral lattice,
SEA=rp ¼ 1:224ðq Þ2 : 3
Fig. 15. Shear (a) test, (b) strength and failure of the sandwich panel (c) Q1 and (d) Q2.
ð13Þ
S. Jiang et al. / Composite Structures 176 (2017) 55–71
63
Fig. 16. Bending behaviors of orthogrid sandwich panels with span of (a) 40 mm, (b) 60 mm,(c) 120 mm and (d) 160 mm.
SEA=rp is proportional to ðq Þ2 . As shown in Fig. 9, prediction given by Eq. (13) is consistent with the test of aluminum tetrahedral lattices [24], validating the plastic model. For orthogrid, SEA=rM is proportional to q . Orthogrid has better weight efficiency in energy absorption. 3
4. Edgewise compression behaviors Edgewise compression experiments were carried out at a loading rate of 0.2 mm/min. The compressed panels are 100 mm wide.
Pure 60 mm long orthogrid panels failed at global buckling and the peak load is about 3.1 kN. The equivalent strength is only 3.1 MPa, much smaller than the flatwise compression strength. Global buckling decreases the strength. The sandwich panels are much stronger, as shown in Fig. 10. When the ends are constrained by steel jackets, the peak load of the panel is about 50 kN. The corresponding stress of the skin is about 270 MPa. Without end jackets, the peak load drops to 30 kN. The corresponding stress of the skin is about 170 MPa. As shown in Fig. 11, the panel failed at end crushing for one skin and the other skin failed at debonding and buckling. The debond-
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Fig. 17. Details of the failure of 40 mm span panel in bending.
Fig. 18. Flexural strength variation of orthogrid sandwich panels.
ing is restricted and the buckling wavelength is 60 mm but 100 mm when the column length is 200 mm or 300 mm. After the peak load, the load will drop to 30 kN, close to the strength of the column strength without end jackets. Only one skin stiffened by the orthogrid bears the load and the residual stress is close to a half of the peak load. Without end jackets the delamination initiates from the end and then induces skin debonding. The buckling wave length is about 100 mm. Similar phenomena were found in the compression tests of 300 mm long columns (Fig. 12) and 300 mm long columns (Fig. 13). End constraint effect is revealed by experiments and this will instruct the optimal design of orthogrid sandwich structures [27]. The experiments stressed the importance of the end flanges.
It is also found that column length has little influence to the compression strength, as shown in Fig. 14. In the experiments, the slenderness variation is not great and the columns fail at the same mode. Global buckling needs greater slenderness. 5. Shear behaviors 5.1. Shear strength For orthogrid panel, the shear strength, ss , depends on the shear strength of the orthogrid rib, sr , as
ss ¼ 0:5q : sr
ð14Þ
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Fig. 19. Shear failure modes of typical lattice composite structures with (a) bed-in nodes [6], (b) corrugated nodes [2] and (c) adhering nodes [7] and shear strength varying with (d) node area [2] and (e) relation to relative density.
For 3D lattice truss composites,
ss ¼ C q ; rm
ð15Þ
where C is smaller than 0.5. For example, C ¼ 1=6 for octet-truss [22]. So that the dimensionless shear strength of the orthogrid is usually higher. In most circumstances, shear failure of lattice-core composite sandwich panels is controlled by the interfacial property. In this way, shear strength of the orthogrid panel and most of 3D lattices is given by
ss ¼ q ; sa
ð16Þ
where sa is the shear strength of the adhesive layer. Eq. (16) can be expressed as
ss ¼ sa
Ad : Acell
ð17Þ
The shear strength is proportional to the adhesive area Ad in a unit cell (Acell ). Sometimes the shear strength is insensitive to the strength of the lattice strut. Lap compression shear experiments were carried out at a loading rate of 0.1 mm/min. The sample dimensions are 100 mm 100 mm 12 mm. In shear, the panel was divided into
Fig. 20. Failure criteria of bended orthogrid panels with 1 mm thick skins.
two parts from the adhesive layer. The sudden delamination led a brittle failure, as shown in Fig. 15. The shear strength varies from 1.8 MPa to 2.8 MPa. For specimen Q1, the facesheet is smooth. Through the failure map it is found that the shear failure occurs
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Fig. 21. Edgewise compression behaviors of 100 mm long orthogrid panels with 0.5 mm thick skins: (a) Stress, (b) strain and (c) failure modes.
at the interface between the facesheet and the adhesive film, not between the orthogrid and the adhesive film. It means that the actual adhesive area is much greater than the cross section area of the orthogrid. This phenomenon is quite different with other 3D lattice truss composite materials and endows the orthogrid has priority in shear resistance. In forming, the orthogrid is usually impressed into the resin film and the bonding is strong. To improve the bonding between the film and the skin, the facesheets of specimen Q2 and Q3 are pre-roughened before attached with the orthogrid. So that the resin film detached from the orthogrid and they have much greater shear strength. 5.2. Short-span bending behaviors Another way to evaluate the shear resistance of the sandwich panel is the short-span flexural behavior tested through threepoint bending experiments, as shown in Figs. 16 and 17. The span (L) varies from 40 mm to 160 mm. The width is 100 mm. The thickness is 12 mm. The facesheet thickness is 1 mm. For pure orthogrid, the peak load is only 2 kN when the span is only 40 mm. For orthogrid sandwich panels, the peak loads vary from 6.2 kN to 10 kN, almost independent of the span. When the span is 40 mm, the peak load is over 8 kN. The central facesheet firstly
delaminated from the orthogrid which was not destroyed, as shown in Fig. 16. Obviously, the shear resistance of the orthogrid is enhanced when sandwiched by two skins. Interfacial debonding failure controls the flexural behavior. After debonding, the load still increased slowly rather than decreased. The debonding did not develop and the panel was compressed and sheared. When the span is 60 mm, the debonding developed and the upper skin were completely detached from the orthogrid and the panel behaved as a stiffened before the lower skin fracture, supplying residual strength to the panel. When the span is over 80 mm, the delamination located at the one-fourth span. The delamination led an abrupt load drop. The panel was out of work when the facesheet was completely detached. Although the final failure modes are different, all the initial failures are induced by the shear failure of the adhesive layer and the peak load changes little as well as the residual load, as shown in Fig. 18. The peak load, P, can be simply evaluated by
P ¼ 2ss Bc;
ð18Þ
where B and c denote the width and thickness of the panel. Accordingly, the equivalent shear stress ss at failure varies from 2.6 MPa to 4.2 MPa, comparable to or a little greater than the shear strength
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Fig. 22. Edgewise compression behaviors of 200 mm long orthogrid panels with 0.5 mm thick skins: (a) Stress, (b) strain, (c) failure modes of D1 and (d) failure modes of D2.
derived from the lap compression shear experiments. The average value is 3.5 MPa. 5.3. Comparisons As shown in Fig. 19, the orthogrid has greater shear strength compared with lattice truss materials whose lattices are only adhered with the facesheets. The shear strength is proportional to the relative density as
ss ¼ K q :
ð19Þ
The coefficient K indicates the weight efficiency of the lattice in shear resistance. For orthogrid, K ¼ 33:1 in average. Given by experiments, K ¼ 27 for lattices with adhesive joints [3]. To enhance the shear strength, some researchers increased the adhesive area, such as corrugated lattice composites [2], but the weight efficiency is reduced to K ¼ 17. The orthogrid has better weight efficiency in shear resistance, as compared in Fig. 18.
Others adopted bed-in joints for which the facesheet must be pre-slotted and this method greatly improves the shear strength. For bed-in octet-truss [3], K ¼ 37, while for bed-in pyramidal lattice [6], K ¼ 77. But this technique will be abandoned when the facesheet is thin because the pre-set slots introduce severe initial damages to the sandwich panel and will greatly weak the flexural of edgewise compression strength. For example, the buried depth (t0 ) is 2.54 mm when t0 ¼ 0:8t, where t is the strut thickness and is 3.175 mm [6]. For sandwich panel, the facesheet thickness must be much greater than 2.54 mm. When bed-in nodes are adopted, the facesheet must be thick enough, which limits the application of the bed-in method. As shown in Fig. 18, the orthogrid sandwich panel has comparable weight-efficiency to the bedin octet-truss in shear resistance and has no requirement to the skin thickness. Through the comparison, it is concluded that orthogrid sandwich panels have better interfacial shear resistance than usual 3D lattice truss sandwich panels. Bonding strength between truss
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Fig. 23. Edgewise compression behaviors of 300 mm long orthogrid panels with 0.5 mm thick skins: (a) Stress, (b) strain and (c) failure modes.
core and the facesheets can be significantly improved by grooves or bed-ins machined in the facesheets, but this method will greatly thicken the facesheet. In this research, as the thickness of the skin is only 1 mm or 0.5 mm, we did not consider this method. Grooves or bed-ins will greatly weaken the behavior of the ultra-thin skin. For metallic lattice sandwich panels, the shear strength usually depends on the compression behaviors of the struts because the welded joints usually have strong shear-resistance. 6. Discussions 6.1. Bending design consideration In 160 mm span bending, the skin stress is about 290 MPa, close to the skin failure strength. The peak load determined by the skin failure is
Fig. 24. Edgewise compression strength variation of column length.
P¼4
Bt f ðc þ tf Þ rf ; L
ð20Þ
where rf , tf ,and L denote he skin failure strength, the skin thickness and the span, respectively. Critical span changing from shear failure to skin failure is given by
L¼2
t f ðc þ tf Þ c
rf : ss
ð21Þ
So we can give a design curve for this sandwich as shown in Fig. 20. It is found that using shear failure criterion and skin failure criterion, the flexural strength of the orthogrid sandwich panel can be well predicted. This method will be validated by more experimental results changing the skin thickness. 6.2. Skin thickness effects To further make clear the structural responses of the orthogrid sandwich panel, the skin thickness is lessened to 0.5 mm. The orthogrid keeps unchanged. The thickness of the panel now is 11.0 mm. In the experiments, strain gauges were adhered onto the skin surface to measure the strain which will be applied to explain the fatal failure mode of the orthogrid sandwich panel. Edgewise compression behaviors of the orthogrid sandwich panels were revealed, as shown in Figs. 21–23. Monocell buckling of the skin was observed when the stress is not high enough. In experiments, the monocell buckling load is close to 5.5 kN. The monocell buckling will not induce fatal failure, and then debonding or instability induced by skin dimpling or fracture was observed in succession. Peak load of the panels changes from 19.7 kN to 32 kN, as shown in Fig. 24. Column length has influence to the edgewise compression strength. The skin failure strength is about 270 MPa in average, close to the result tested from the panel with 1.0 mm thick skins. It is validated that skin failure stress in this research is 270 MPa. Three-point bending experiments were performed, as shown in Figs. 25 and 26, where the span changes from 40 mm to 200 mm. In bending, monocell cell buckling was observed firstly and this
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Fig. 25. Flexural behaviors of orthogrid panels with 0.5 mm thick skins with span of (a) 40 mm, (b) 60 mm, (c) 80 mm and (d) 120 mm.
damage will induce skin fracture or final debonding. Monocell buckling is not fatal and flexural strength of the panel is decided by the skin failure stress as the peak load decreases with increasing spans, as shown in Fig. 27. It is interesting that the shear failure criterion and the skin failure criterion consistently predict the peak load of the panel with 0.5 mm thick skins. Critical span transferring shear failure to skin flexural failure is 77 mm. Compared with panels composed of identical orthogrid and 1.0 mm skins, thinner skins make orthogrid sandwich panels more prone to flexural failure.
7. Conclusions Through the research, it is found that interlocking orthogrid is a simple way to construct efficient lightweight sandwich structure. According to the experiments, it is concluded that: 1) The orthogrid has greater strength and better weight efficiency in compression compared with 3D lattice truss composites.
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Fig. 26. Flexural behaviors of orthogrid panels with 0.5 mm thick skins with span of (a) 160 mm and (d) 200 mm.
3) The shear resistance usually depends on the adhesion area. The orthogrid panel has continuous ribs and a continuous adhesive layer between the orthogrid and the facesheet, which endows the orthogrid sandwich panel have better shear resistance than usual 3D lattice truss composites joined by adhering nodes. 4) Shear failure and skin flexural failure controls the flexural strength of the panel. Monocell buckling may be the initial failure when the skin is thin enough but it will not decide the strength. Debonding is the final failure style of the panel but usually it is induced by skin failure and observed in postfailure stage if the adhesive layer has good quality. Thinner skins make orthogrid sandwich panels more prone to skin flexural failure.
Acknowledgments
Fig. 27. Failure criteria of bended orthogrid panels with 0.5 mm thick skins.
2) Compared with the brittle failure mode of 3D lattice truss composites, the orthogrid has ductile deformation and keeps high MCF. The SEA of the orthogrid composites is comparable to or even greater than metallic lattice truss structure.
Supports from the National Natural Science Foundation of China (11372095, 11672130) and State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-0215G01) are gratefully acknowledged. References [1] Fan HL, Zeng T, Fang DN, et al. Mechanics of advanced fiber reinforced lattice composites. Acta Mech Sin 2010;26:825–35.
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