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Composites Science and Technology journal homepage: http://www.elsevier.com/locate/compscitech

Fabrication and mechanical behaviors of corrugated lattice truss composite sandwich panels Yang Hu a, b, Wanxin Li b, Xiyue An a, b, Hualin Fan b, * a b

College of Mechanics and Materials, Hohai University, Nanjing 210098, China State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 December 2015 Received in revised form 30 January 2016 Accepted 1 February 2016 Available online 3 February 2016

To get a strong, stiff and weight-efﬁcient structure, a novel carbon ﬁber reinforced composite (CFRC) lattice truss sandwich panel (LTSP) was designed and fabricated. The lattice core is made up of orthogonal corrugated lattice trusses (CLTs) and manufactured by mould pressing method. Compression and shearing experiments were carried out to reveal the strength and failure modes of the structure. A coupled compression-shear failure mode was observed in compression and the compression strength of the lattice truss structure is over 13 MPa. In shearing, the enlarged area of the node enhances the shear strength to 3.4 MPa. Structural models were built to evaluate the strength in compression and shearing. Failure maps were supplied to instruct optimal design of the CFRC LTSP. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Sandwich Structural composites Strength Failure criterion

1. Introduction Beneﬁted from light but strong carbon ﬁbers and stretchingdominated topology, CFRC lattice truss composite structure (LTCS) is weight-efﬁcient for its high speciﬁc stiffness and strength [1e3]. This structure has the potential to enhance innumerable applications ranging from aerospace structures to marine structures to civil infrastructure. In last two decades, Octet truss [1], tetrahedral truss [4], pyramidal truss [5], Kagome lattice [6], hierarchical lattice [7], woven lattice [8], IsoTruss® [9,10] and Isogrid [11e15] have been developed. Interlacing method [2,3], mould pressing method [4,16], cutting method [17], ﬁlament winding method [9e15] and woven method [8] have been developed to fabricate the LTCS. Usually shear strength of the CFRC LTSP is limited by the node failure. According to previous works [4,16], the shear strength is usually smaller than 1 MPa. To enhance the shear strength, nodes were epoxy bonded and buried in milled facesheet pockets [17]. Through this way, the shear strength can be greatly improved but the facesheet is severely damaged. Another efﬁcient way to enhance the anti-shear ability is enlarging the node area, such as corrugated topology for the lattice truss structure. In this paper, a novel CFRC LTSP was designed and

manufactured. To enhance the interfacial shear strength, corrugated lattice truss core structure was developed. Mould pressing method and co-curing scheme were applied to make the sandwich panel. Mechanical behaviors of the structure were revealed by experiments and theoretical analyses.

2. Structure and fabrication 2.1. Structure The sandwich panel has two facesheets and an orthogonal corrugated lattice truss structure performing as the core, as shown in Fig. 1. Compared with other lattice truss structures, corrugation design lets the skin and the core have enough adhesive area to guarantee the interfacial strength. The truss member has plate-like structure, whose width enlarges the adhesive area and improves the anti-shear resistance of the truss member. Bi-directional corrugation design avoids the cross-linking of the orthogonal members at the nodes. Simpliﬁed node structure greatly reduces stress concentration at the nodes. Relative density of the lattice truss structure, r*, is given by

r* ¼ 8btc * Corresponding author. E-mail address: [email protected] (H. Fan). http://dx.doi.org/10.1016/j.compscitech.2016.02.003 0266-3538/© 2016 Elsevier Ltd. All rights reserved.

1 c þa ; sin a cd2

(1)

where b (10 mm) and tc (2 mm) denote the width and thickness of

Y. Hu et al. / Composites Science and Technology 125 (2016) 114e122

115

Fig. 1. Corrugated lattice truss sandwich panel (CLSSP): (a) mould-pressing method, (b) corrugated strip cut from corrugated panel, (c) corrugated-truss core and (d) corrugated lattice truss sandwich panel.

the corrugated lattice strut, respectively. c (10 mm) is the thickness of the truss core of the sandwich panel. a (45 ) is the inclination of the corrugated strut and a (10 mm) is the adhesive length of the strut. Cell dimension, d, is 40 mm, as shown in Fig. 2. The relative density is designed to be 0.2 to avoid strut fracture and testify the shear failure strength of the adhesive layer enlarged by the corrugation topology.

was epoxy bonded with the CFRC facesheets with seven layers of [0 /90 /0 /90 /0 /90 /0 ], as shown in Fig. 1(d). 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.

2.2. Fabrication

3.1. Flatwise compression

T700/Epoxy-resin carbon ﬁbers were applied to fabricate the structure. Tensile strength of the carbon ﬁber is 4300 MPa and the Young's modulus is 240 GPa. In fabrication, mould-pressing method was applied to make the LTSP, as shown in Fig. 1. The CFRC LTSP was solidiﬁed using twice co-curing scheme. Corrugated mould was ﬁrstly designed, as shown in Fig. 1(a). Prepreg carbon ﬁber layers of [0 /0 /±45 /0 /0 / ± 45 /0 ]s were placed into the mould and then pressed and solidiﬁed in a hotpress to form a corrugated panel. The corrugated panel was cured at 120 C for 4 h. Then the cured panel was cut into narrow strips, as shown in Fig. 1(b). The strips were woven periodically to form the lattice truss structure, as shown in Fig. 1(c). Then the lattice truss

Flatwise compression experiments were carried out at a loading rate of 0.2 mm/min, as shown in Fig. 3, where two failure modes and two typical deformation curves were observed. For A1 and A2, the compression strength is 10.1 MPa and 9.8 MPa, respectively. These two panels fail at adhesive shear failure and truss member compression failure successively. When loaded to about 96.6 kN or 6.7 MPa, the adhesive layer between y-axis directional corrugated trusses and the skin delaminated, induced by the interlayer shear stress. The bonded x-axis directional corrugated trusses were still compressed to over 140 kN and then failed at strut compression. Delamination of the laminated strut controls the strut strength in compression. The failure is ductile as the deformation has plateau

3. Experiments

Fig. 2. Geometrical dimensions (unit: mm) of unit cell of CLSSP.

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Fig. 3. Compression curves of (a) A1, A2, (b) A3, A4 and (c) failure maps of A1.

and densiﬁcation stages. Through the experiments, it can be deduced that if the sandwich panel fails entirely at strut compression failure, the compression strength should be about 20.2 MPa. For A3 and A4, the compression strength is 13.6 MPa and 13.2 MPa, respectively. These two panels fail at shear failure of the adhesive layer. The corrugated struts along y-axis and x-axis delaminated from the skin simultaneously. The shear failure is brittle. Shear strength is about twice of the initial shear failure stress of A1 and A2 (6.7 MPa), corresponding to the ratio of the shear failure areas, 2.0.

strut are given by

dz 2 12EI sin a; Q ¼ 3 dz sin3 a cos a; M c c 6EI 2 ¼ 2 dz sin a cos a; c

N ¼ EA

where E, A and I are the Young's modulus, the cross section area, the second moment of area of the strut, respectively. Compression stress, sz, is given by

sz ¼

3.2. Shear

(3)

8 8 t2 ðN sin a Q cos aÞ ¼ Ebtc sin3 a 1 c2 cos2 a εz : Au Au c (4)

Shear experiments were carried out at a loading rate of 0.1 mm/ min, as shown in Fig. 4. In shear, the panel was divided into two parts from the adhesive layer. The sudden delamination led a brittle failure. The shear strength (ts) is 3.3 MPa for S1 and 3.5 MPa for S2, about one fourth of the shear-controlled compression strength of the CLT. In shear tests, the two specimens have close shear strength but the shear deformations have great difference, induced by the test method. It must be pointed out that the shear deformation measured directly through the displacement of the load platen of the test machine is not the true shear deformation of the sandwich panel.

Ez ¼

tc2 2 1 cos a E: c2 ðc cot a þ aÞ2 2btc sin3 a

(5)

Stress of the strut, sb, is given by

sb ¼

N M tc tc þ ¼ Eεz sin2 a 1 þ 3 cos a : A I 2 c

(6)

Equivalent compression strength of the lattice, szf, is given by

4. Failure analyses

szf ¼

4.1. Compression model Under vertical displacement, dz, displacements along the strut, dN, and transverse to strut, dQ, are given by Ref. [18].

dN ¼ dz sin a; dQ ¼ dz cos a:

where the compression strain, εz, is εz ¼ dz/c and the area of unit lattice cell, Au, is Au ¼ 4(ccota þ a)2. Equivalent compression modulus of the lattice, Ez, is given by

(2)

Axial force, N, shear force, Q, and bending moment, M, in the

2btc sin a ðc cot a þ aÞ2

1

tc2 cos2 a c2

tc 1 1 þ 3 cos a ss : c

(7)

As shown in Fig. 5, bending effect of the truss members has little contribution to the compression modulus of the CLT. But the strength is greatly reduced by the bending effect, especially for CLT constructed by thick truss members. Considering the buckling strength of the strut, sbb,

Y. Hu et al. / Composites Science and Technology 125 (2016) 114e122

117

Fig. 4. Shear (a) test, (b) strength and (c) failure of the sandwich panel.

2 ðN cos a Q sin aÞ ba tc t2 1 c2 sin2 a εz : ¼ 2E sin2 a cos a a c

ta ¼

(10)

The equivalent compression shear failure strength of the lattice,

szs, is given by szs ¼

4ba tan a ðc cot a þ aÞ2

! c2 tc2 cos2 a tas ; c2 tc2 sin2 a

(11)

where tas denotes the shear strength of the adhesive layer. The ratio of the shear failure strength to the compression strength is given by

1 szs 2a 1 t2 tc tas 1 c2 sin2 a 1 þ 3 cos a ¼ : tc cos a szf c ss c

(12)

Fig. 5. Bending effects to the strength and stiffness of the CLT.

4.2. Compression failure map 2

sbb ¼

p2 tc2 sin a E; 3 c2

(8)

the equivalent compression buckling strength of the lattice, szb, is given by

szb

2p2 btc3 sin3 a tc2 tc 1 2 1 ¼ cos a 1 þ 3 cos a E: 3 c2 ðc cot a þ aÞ2 c c2 (9) Shear stress along the adhesive layer, ta, is given by

When szf ¼ szb, it requires

p2 tc2 sin2 a ss ¼ : 3 E c2

(13)

When szf ¼ szs, it requires

cos a

tc t2 tc 1 tas 1 c2 sin2 a 1 þ 3 cos a ¼2 : a c ss c

When szb ¼ szs, it requires

(14)

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p2 6

Y. Hu et al. / Composites Science and Technology 125 (2016) 114e122

tc2 c2

tc 1 a

tc2 2 sin c2

a

1 þ 3 cos a

tc c

1

sin2 a cos a ¼

tas : E (15)

Failure maps are derived through Eqs. (13)e(15), as shown in Fig. 6, where the inclination of the truss member varies from 15 , 45 , to 75 . When the truss member is ultra-thin, the LTSP fails at buckling. Increasing the member thickness and the adhesive length

being long enough, the LTSP fails at member fracture. When the adhesive length is not long enough, the LTSP fails at shear failure of the adhesion. Inclination of the truss member inﬂuences the failure mode. With larger inclination, to restrict the buckling the member should be thicker. With larger inclination, to restrict the shear failure, the adhesive length should be longer. As shown in Fig. 7, increasing adhesive shear strength, the adhesive length to avoid shear failure gets shorter.

4.3. Shear model Under horizontal displacement, dx, the displacement along the strut, dN, and that transverse to strut, dQ, are given by Ref. [18].

dN ¼ dx cos a; dQ ¼ dx sin a:

(16)

Internal forces in the corrugated truss members parallel to the shear force are given by

N ¼ EA

dx 12EI 6EI sin a cos a; Q ¼ 3 dx sin4 a; M ¼ 2 dx sin3 a; c c c (17)

Shear stress, txz1, is given by

Fig. 6. Compression failure maps for (a) a ¼ 15 , (b) 45 and (c) 75 .

Fig. 7. Compression failure maps, where a ¼ 45 , (a) E/ss ¼ 50 and (b) E/ss ¼ 100.

Y. Hu et al. / Composites Science and Technology 125 (2016) 114e122

txz1

4 ¼ ðN cos a þ Q sin aÞ Au btc sin a tc2 2 4 cos a þ sin a Eεxz ; ¼ c2 ðc cot a þ aÞ2

txzf ¼

(18)

where the shear strain is deﬁned as εxz ¼ dx/c. Corrugated truss members orthogonal to the shear force behave as laminate and the component shear force, txz2, is given by

txz2 ¼

1 btc Gεxz ; cot a ðc cot a þ aÞ2

btc sin a ðc cot a þ aÞ2

1 t2 G þ cos2 a þ c2 sin4 a E εxz ; cos a c

(20)

Exz ¼

btc sin a ðc cot a þ aÞ2

1 t2 G þ cos2 a þ c2 sin4 a E : cos a c

(21)

In shearing the contribution to the stiffness from plate-like members orthogonal to the shear force is much more important and depends on the inclination, as shown in Fig. 8. Over 45 , contribution of orthogonal plate-like members is greater. But this effect is irrelevant to the thickness of the truss member. Obviously, members orthogonal to the shear force are much stiffer and stronger in shearing. Shear failure will be ﬁrstly induced by the members parallel to the shear force. Stress of the strut parallel to the shear force, sb, is given by

tc : sb ¼ Eεxz sin a cos a þ 3sin2 a c

1 G tc2 2 4 þ cos a þ sin a c2 ðc cot a þ aÞ2 cos a E 1 tc sbb : cos a þ 3sin2 a c btc

txzb ¼

(22)

Shear strength of the lattice induced by member fracture, txzf, is given by

(23)

(24)

As shown in Fig. 8, when truss members control the shear failure, contribution of orthogonal plate-like members is greater when the inclination is over 45 . In fact, the shear failure is usually dominated by the shear strength of the adhesive layer, tas, so that the shear strength, txzs, is given by

txzs ¼

Equivalent shear modulus of the lattice, Exz, is given by

Shear strength of the lattice induced by member buckling, txzb, is given by

(19)

where G is the shear modulus of the composite laminate. The equivalent shear stress is given by the summation of Eqs. (18) and (19) as

txz ¼

1 G tc2 2 4 þ cos a þ sin a c2 ðc cot a þ aÞ2 cos a E 1 tc ss ; cos a þ 3sin2 a c btc

119

ab ðc cot a þ aÞ2

tas :

(25)

According to Eq. (25), when the adhesive layer controls the shear failure, the strength is independent of the thickness of the truss member. Using this failure mode, the equivalent shear strength of the adhesive layer is 14 MPa. 5. Structural failures 5.1. Column failure For CLTSP, the interfacial property dominates its behavior in edgewise compression. The column length (H) varies from 80 mm to 240 mm, as shown in Fig. 9. The width (B) is 120 mm. The failure turns from end-crushing of the 80 mm column to facesheet debonding of the 240 mm column. Their peak loads (P) have little difference, varying from 70.6 kN to 64.6 kN. It is concluded that the corrugation design lets the debonding strength close to the skin compression failure strength (sfs), 294 MPa, calculated by

sfs ¼ P

. 2Btf ;

(26)

where tf is the skin thickness. This viewpoint is also testiﬁed by the failure of the 120 mm column, whose initial compression failure load is 82.64 kN, close to its ﬁnal brittle debonding failure load, 77.3 kN. 5.2. Flexural failure Flexural behaviors of the CLTSPs were also checked through three-point bending experiments, as shown in Fig. 9. The span (L) varies from 80 mm to 240 mm. The width is 120 mm. The peak load varies from 6.92 kN to 6.44 kN, almost independent of the span. Interfacial debonding failure controls the ﬂexural behavior. The peak load, P, can be simply evaluated by

P ¼ ts Bc:

Fig. 8. Shear contribution of plate-like members orthogonal to the shear force.

(27)

Accordingly, the shear strength varies from 4.8 MPa to 4.47 MPa, a little greater than the shear strength derived from the shear experiments. If the facesheet controls the bending failure, the peak load can be simply evaluated by

120

Y. Hu et al. / Composites Science and Technology 125 (2016) 114e122

Fig. 9. Deformation curves when length or span being (a) 80 mm, (b) 120 mm, (c) 160 mm, (d) 200 mm and (e) 240 mm and (f) peak load variation.

Y. Hu et al. / Composites Science and Technology 125 (2016) 114e122

P ¼ 4sfs Btf c=L:

121

(28)

According to the compression strength of the skin, 294 MPa, the critical span (Lcr) for panels failing at facesheet compression failure is given by

Lcr ¼ 4sfs tf =ts :

(29)

The critical span is 245 mm when ts ¼ 4.8 MPa and 336 mm when ts ¼ 3.5 MPa. Longer than this value, the CLTSP will fail at facesheet compression failure. The shear failure mode in the experiments is consistent with the simpliﬁed analysis. 6. Discussions 6.1. Predictions From Eq. (11), the compression strength controlled by the interface shear failure is

. szs ¼ 4tas ba ðc þ aÞ2 :

(30)

From Eq. (25), tas ¼ 14 MPa. The compression strength controlled by the interface shear failure is 14.0 MPa, very close to the tested strength, 13.6 MPa. In the experiments, the ratio of szs to szf is 1.48. According to Eq. (12), the predicted value is 1.40 for tas ¼ 13.6 MPa and ss ¼ 294 MPa. All these predictions demonstrate that the models proposed in Section 4 are reasonable. 6.2. Advantages of corrugation design Node area decides the anti-shear ability of the LTSP. Usually, this area for each truss member, An, is given by

An ¼ Am =sin a;

(31)

where Am is the cross section area of the truss member. Adopting corrugation design,

An ¼ Am a=ð2tc Þ:

(32)

The adhesive area is greatly enlarged, as shown in Fig. 10, where the node area reaches 100 mm2, much greater than usual lattice structures. Correspondingly, the shear strength of CLT is much larger compared with usual lattice structures [4,16]. Some lattice structures adopt woven method [1e3,19] or buried node technique [17] and their shear strength will be greatly enhanced. Meanwhile, behaviors of their skins will be greatly reduced induced by these initial damages. For usual sandwich panels, it is not a good choice for engineers to enhance the shear resistance of the sandwich panel in the way of damaging the skin. Moreover when the skin is ultrathin, the woven method and the buried node technique cannot be adopted to construct lattice truss sandwich panels. Compared with other lattice truss structures [4,16,17,19,20], the CLT has greater relative density and its compressive strength is also stronger, as shown in Fig. 10. 7. Conclusions In this research, a novel corrugated lattice truss sandwich panel reinforced by carbon ﬁbers was designed and fabricated through mould pressing method. The fabrication method proposed in this research makes the structure have advantages compared with previous lattice truss composites: (a) Co-curing guarantees the adhesive strength; (b) Mould pressing improves the volume fraction of the carbon ﬁber in the lattice structure and guarantees the

Fig. 10. (a) Shear and (b) compression strengths of typical lattice truss composite structures.

strut strength; (c) Corrugation design enlarges the node area and improves the shear strength. This technique has also been used to make lattice-core sandwich cylinder [21]. Through the experiments, it is concluded that: In compression, strut fracture and strut buckling would be the potential failure modes. But shear failure at the adhesive layer induced by the horizontal component of the strut force cannot be neglected when the truss member is strong enough. In this research the shear-controlled strength in compression is over 13 MPa. In shearing, truss member failure and adhesion failure are the potential failure modes. Usually the CFRP truss member is strong enough, so that the adhesive failure is dominant for the lattice-core sandwich panel. Adopting corrugated topology, the lattice truss panel has much greater shear strength due to greatly enlarged node area. In this research, the shear strength is over 3.3 MPa.

Acknowledgments Supports from National Natural Science Foundation of China (11372095) and State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-0215G01) are gratefully acknowledged.

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