Available online at www.sciencedirect.com

Materials

www.elsevier.com/locate/matdes

Materials and Design 29 (2008) 709–713

& Design

Short Communication

A study on composite honeycomb sandwich panel structure

Meifeng He, Wenbin Hu *

State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200030, PR China

Received 23 May 2006; accepted 2 March 2007Available online 19 March 2007

Abstract

Honeycomb sandwich structure combines high flexural rigidity and bending strength with low weight. Sandwich construction plays anincreasing role in industry, and sandwich structural designing is an available method for sandwich structures. However, the absence ofthe design variable is the principal problem of composite sandwich construction. In this paper, the structure and mechanical properties ofhoneycomb sandwich panels are introduced. The weight ratio range of honeycomb core that is deduced on the basis of optimum mechan-ical properties offer a principle foundation for designing the structure of honeycomb sandwich panels. The satisfying weight condition ofthe honeycomb core weight is 50–66.7% of the weight of the whole honeycomb sandwich panels by theoretical analysis. Based on thatconclusion, the honeycomb sandwich panels were designed and the results were verified by further experiments. Agreement between thetheoretical values of the sample and experimental results is good.� 2007 Elsevier Ltd. All rights reserved.

1. Introduction

Honeycomb sandwich materials are being used widely inweight sensitive and damping structures where high flex-ural rigidity is required, in many fields especially in theautomobile industry [1–3]. Honeycomb core sandwichpanel is formed by adhering two high-rigidity thin-facesheets with a low-density honeycomb core possessing lessstrength and stiffness. By varying the core and the thicknessand material of the face sheet, it is possible to obtain var-ious properties and desired performance, particularly highstrength-to-weight ratio [4]. Several types of core shapesand core material have been applied to the constructionof sandwich structures [5,6]. In this paper, the honeycombcore that consists of very thin mild-steel panel in the formof regular hexagonal cells perpendicular to the facings wasapplied. Whereas its honeycomb core must be stiff enoughto prevent one face panel of the honeycomb sandwichpanel from sliding over the other, when a honeycomb sand-wich panel subjected to flexural loading. Such rigidities arecalled the transverse shear stiffness of the honeycomb core.

0261-3069/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.matdes.2007.03.003

* Corresponding author. Tel.: +86 21 6293 3585; fax: +86 21 6282 2012.E-mail address: hmf752@sjtu.edu.cn (W. Hu).

When the core depth is much larger than the thickness ofthe face panels (most honeycomb sandwich panels belongto this category), the transverse shear stiffness of the sand-wich plate is almost entirely contributed by its core. Forsimplicity and efficiency, the cellular honeycomb core isidealized as a homogeneous material and its equivalentmechanical properties are used in analysis and design.Therefore, the knowledge of the equivalent transverseshear stiffness of honeycomb is very important for the anal-ysis and design of sandwich plates [7].

Even if the concept of sandwich construction is not verynew, it has primarily been adopted for non-strength part ofstructures in the last decade. This is because there are avariety of problem areas to be overcome when the sand-wich construction is applied to design of dynamicallyloaded structures. To enhance the attractiveness of sand-wich construction, it is thus essential to better understandthe local strength characteristics of individual sandwichpanel members. To optimize further the structural design,the present trend is to apply the principle of flexural rigidityand bending stiffness of sandwich plates. The weight ratiorange of honeycomb core that is deduced on the basis ofoptimum mechanical properties offer a principle founda-tion for designing the structure of honeycomb sandwich

Nomenclature

r1, r2 yield stress of two facing materialt1, t2 thickness of two facing skins (assuming that

both skins are of same each other)E1, E2 elastic (Young’s) modulus of two facing mate-

rialEf elastic (Young’s) modulus of facing materiale1, e2 strain of two facing skinsb breadth of the sandwich panelh height of sandwich panel including facing skinshf thickness of facing skinshc height of honeycomb core

Z distance from facing skin to centroidal axisIeq equivalent sectional inertia momentD flexural rigidityM flexural torquermax maximum tensile strength of facing skinDmax maximum flexural rigidityMmax maximum flexural torquey half height of sandwich panel including two fac-

ing skinsqf density of facing materialqc density of honeycomb core material

710 M. He, W. Hu / Materials and Design 29 (2008) 709–713

panels. Noteworthy, the experimental data agree satisfac-torily with the theoretical predictions. The useful resultsare extended to give a available design tool for sandwichpanels manufacturers.

Fig. 1. Calculated sectional area and equivalent sectional area.

2. The mechanical properties of honeycomb sandwich panels

Honeycomb sandwich structure possesses high flexuralrigidity and bending strength with low weight. Flexuralrigidity and bending strength are very important mechani-cal properties of honeycomb sandwich panels. The under-lying assumptions of the theory presented in the deducingprocedure are as follows [8]:

(1) The faceplates are very thin compared with the totalthickness of the sandwich.

(2) The shear stress over the depth of the core is consid-ered constant. This assumption may be made if thecore is too weak to provide a significant contributionto the flexural rigidity of the sandwich.

(3) The honeycomb construction is anisotropy.(4) The rotary inertia of the face plates about their own

centroidal axes is negligible.(5) The sandwich has equal thickness face plates (sym-

metric sandwich) and both face plates are of the samematerial with identical properties.

2.1. Flexural rigidity

Honeycomb core was used to apart one face sheet fromanother in honeycomb sandwich structure. Because of thisspecial structure the sectional inertia moment of honey-comb sandwich panel was increased and induced an obvi-ous increase of the flexural rigidity of panels [9,10]. Theflexural rigidity of panels is one of the most importantparameters in structural design. The calculated sectionalarea, as shown in Fig. 1, are assumed that the sectionalarea of two facing sheets are both effective.

According to the mechanical equilibrium condition, theequality can be obtained as follow:

r1t1 ¼ r2t2: ð1ÞThen,

r1

r2

¼ t1

t2

: ð2Þ

The Eq. (3) can be achieved by applying Hooke’s law.

e1 ¼r1

E1

; e2 ¼r2

E2

; ð3Þ

so,

e1

e2

¼ r1

E1

� E2

r2

¼ t2

t1

� E2

E1

: ð4Þ

The distance from facing skin to centroidal axis Z ofsandwich plate has been noted. There also have severalequalities.

e2

Z¼ e1

hþhc

2� Z

; Z ¼e2

hþhc

2

� �e1 þ e2

¼hþhc

2e1

e2þ 1

: ð5Þ

When Eq. (4) is used in Eq. (5), so that Eq. (5) reduces to

Z ¼E1t1

hþhc

2

� �E2t2 þ E1t1

: ð6Þ

M. He, W. Hu / Materials and Design 29 (2008) 709–713 711

As shown in Fig. 1.The equivalent sectional inertia mo-ment Ieq is given by

Ieq ¼ t1

hþ hc

2� Z

� �2

þ E2

E1

t2Z2 þ t31

12þ 1

12

E2

E1

t32

¼ t1

hþ hc

2

� �2

� hþ hc

2

� �Z � Z2

" #þ E2

E1

t2Z2

þ 1

12t31 þ

E2

E1

t32

� �: ð7Þ

When Eq. (6) is used in Eq. (7), so that Eq. (7) reduces to

Ieq ¼hþ hc

2

� �2 E2t2t1

E1t1 þ E2t2

� �þ 1

12t31 þ

E2

E1

t32

� �: ð8Þ

The flexural rigidity D of the sandwich panels is alsogiven by

D ¼ Ef Ieq: ð9ÞAssuming that both faces are of the same each other, the

facing material and the facing thickness are same. So wecan obtain E1 = E2 = Ef and t1 = t2 = hf. In many practicalsandwiches application, hf/hc lies in the range from 0.02 to0.1. The limiting conditions of t1 = t2� hc and h � hf � hc

always exist. When above several conditions are satisfied inthese cases, so that Eq. (9) reduces to

D ¼ E1Ieq ¼hþ hc

2

� �2 Ef hfð Þ2

2Ef hf

¼ 1

2Efhf

hþ h� 2hf

2

� �2

¼ 1

2Efhfðh� hfÞ2

� 1

2Efhf h

2c : ð10Þ

The expression of the flexural rigidity D of honeycombsandwich panels is

D ¼ 1

2Efhf h

2c : ð11Þ

2.2. Bending strength

The honeycomb sandwich structure does not get shearfracture when one face sheet is tensioned and the other iscompressed, which is the optimal flexural failure of thesandwich panels. This makes the honeycomb sandwichstructure can get better performed under the same mechan-ical condition. The fracture of the face sheet is the optimalflexural failure.

According to the theory of mechanics of materials, theequality can be obtained as follow:

rmax ¼Mmax

I eq

y; rmax ¼EfMmax

Ef Ieq

y ¼ Ef Mmax

Dy: ð12Þ

Then,

Mmax ¼rmaxD

Efy: ð13Þ

The limiting condition of y ¼ hfþhc

2� hc

2always exists

because the thickness of facing skin is very thin. Whenabove condition is satisfied in this case, so that Eq. (13)reduces to

Mmax ¼rmax

12Ef hfbh2

c

Efhc

2

¼ rmaxhf hcb: ð14Þ

3. Deducing the weight range of honeycomb core on the basis

of optimum mechanical properties

3.1. Deducing from the flexural rigidity

From Eq. (11) we have already gotten the expression ofthe flexural rigidity D of honeycomb sandwich panels.

D ¼ 1

2Efhfh

2c :

The mass area ratio W of the honeycomb sandwichpanels is associated with the density of facing material qf

and the density of honeycomb core material qc, as givenby

W ¼ 2qfhf þ qchc; ð15Þ

where for convenience we write

x ¼ qchc=W ; ð16Þ

where x is the weight ratio of honeycomb core, then we canobtain the follow equality from Eqs. (15) and (16)

hf ¼W2qf

ð1� xÞ: ð17Þ

Eqs. (16) and (17) provide two homogeneous equalitiesfor the unknowns hf and hc in Eq. (11), the flexural rigidityD can then be determined

D ¼ Ef

2

Wqc

��������2 W

2qf

��������x2ð1� xÞ: ð18Þ

When the flexural rigidity D and the weight ratio of honey-comb core x satisfy the condition of dD

dx ¼ 0, the maximumflexural rigidity Dmax will exist.

The weight ratio of honeycomb core x is now deter-mined by the above limiting condition

dDdx¼ 2x� 3x2 ¼ 0: ð19Þ

The solutions of Eq. (19) are

x ¼ 0 or x ¼ 2=3: ð20Þ

x = 0 does not satisfy the practical application and onlyx = 2/3 is the useful root.

According to the definition of x, when the weight ofhoneycomb core is 2/3 of the weight of the whole honey-comb sandwich panels, the maximum flexural rigidity canbe obtained. In other words, the weight of honeycomb coreis two times of the weight of face sheets.

Fig. 2. Schematic diagram of 3-point bending test.

Table 1Contrastive values of honeycomb sandwich sample

Weight(g)

Bending strength(MPa)

Flexural rigidity(N m)

Testing value 253.02 327.0 462.7Theoretical

value255.53 370 518.4

712 M. He, W. Hu / Materials and Design 29 (2008) 709–713

3.2. Deducing from the bending strength

From Eq. (14) we have already obtained the expressionof the flexural torque M of honeycomb sandwich panels.

M ¼rmax

12Ef hfbh2

c

Efhc

2

¼ rmaxhfhcb:

Similarly, the above expression also includes theunknowns hf and hc which are shown in Eqs. (16) and(17), the flexural torque M can be derived as follow:

M ¼ rmaxbWqc

�������� W

2qf

�������� xð1� xÞ½ �: ð21Þ

In like manner, when flexural torque M and the weightratio of honeycomb core x satisfy the condition of dM

dx ¼ 0,the maximum flexural torque Mmax will exist.

Where for convenience we write

dMdx¼ rmaxb

Wqc

�������� W

2qf

��������ð1� 2xÞ ¼ 0: ð22Þ

The solution of Eq. (22) is

x ¼ 1

2:

According to the above root of Eq. (22), when theweight of honeycomb core is the same as the weight offace sheets, the maximum bending strength can beobtained. By above theoretical analysis, the weight ratioof honeycomb core xwould meet a condition of 0.5 6x 6 0.667, so that the optimum mechanical propertiescan be obtained.

4. Experiments

Based on the range of the weight ratio of honeycombcore x, the honeycomb sandwich panels were designedand the results were verified by further experiments.

The mild-steel sheets Q235 were used as the honeycombcore and face sheets materials in the present study. Thesample, 130mm · 100 mm · 4.2 mm, was composed oftwo face sheets, 130 mm · 100 mm · 0.6 mm, and a honey-comb core, 130 mm · 100 mm · 3 mm. The cell shape ofhoneycomb core is regular hexagon. The length of side ofregular hexagon is 5 mm. The wall thickness of core is2.65 mm. The core thickness is 3 mm. The weight of honey-comb core is 133.85 g and whole honeycomb sandwichpanels are 255.53 g. For x ¼ 133:85 g

255:53 g¼ 0:524, the designed

sample was in the range of x. A suitable assistant bondingcoating was prepared between face sheets and honeycombcore. The sample had been performed a heat treatment at830 �C for 10 min, and then cooled down until room tem-perature in the furnace. To avoid oxidation of sample, pureargon gas (purity 99.995%) was flowed through the furnaceduring the heat treatment. Then the sample was taken outto the air.

After the processing, the 3-point bending test was per-formed to obtain the flexural rigidity and bending

strength of the honeycomb sandwich beam with a dimen-sion of 130 mm · 15 mm · 4.2 mm that had been sub-jected to the 3-point loading. The sample was tested by3-point bending using Shimadzu UTM machine, as shownin Fig. 2 (Schematic diagram of 3-point bending test),applying loading through a roller of diameter d of10 mm in accordance with the ASTM standard C393-62.The crosshead speed 0.05 mm/s is kept constant, so thatthe maximum load occurs between 3 and 6 min after thestart of the test. During the bending test, a foil sheet ofthickness 0.2 mm was placed in between the sample andthe indentation roller to prevent failure due to localindentation.

By 3-point bending test, the experimental results of theflexural rigidity and the bending strength were obtained.The theoretical values of the flexural rigidity and bendingstrength can be calculated using Eqs. (11) and (14). Thecontrastive values are shown in Table 1. The theoreticalvalues of the model agree well with the experimentalresults.

5. Conclusion

According to the theoretical analysis, we have a goodunderstanding of the effects on designing the sandwichstructure. To achieve the maximum flexural rigidity andbending strength, the satisfying weight condition of thehoneycomb core weight is 50–66.7% of the weight of thewhole honeycomb sandwich panels. To verify the conclu-sion experimentally, the flexural rigidity and the bendingstrength of honeycomb sandwich sample are measured.The measured flexural rigidity and bending strength arein relatively good agreement with the calculated values.By comparing our experimental results with the results cal-culated theoretically, we conclude that the weight conditionof the honeycomb sandwich core is appropriate. That canhelp the researchers to design the honeycomb sandwichstructure.

M. He, W. Hu / Materials and Design 29 (2008) 709–713 713

Acknowledgments

The authors are grateful for the university Science andTechnology Beijing.

References

[1] Yu SD, Cleghorn WL. Free flexural vibration analysis of symmetrichoneycomb panels. J Sound Vib 2005;284:189–204.

[2] Wang B, Yang M. Damping of honeycomb sandwich beams. J MaterProcess Technol 2000;105:67–72.

[3] Kim Hyeung-Yun, Hwang Woonbong. Effect of debonding onnatural frequencies and frequency response functions of honeycombsandwich beams. Compos Struct 2002;55:51–62.

[4] Petras A, Sutcliffe MPF. Failure mode maps for honeycomb sandwichpanels. Compos Struct 1999;44:237–52.

[5] Renji K, Nair PS, Narayanan S. Modal density of compositehoneycomb sandwich panels. J Sound Vib 1996;195(5):687–99.

[6] Paik Jeom Kee, Thayamballi Anil K, Kim Gyu Sung. The strengthcharacteristics of aluminum honeycomb sandwich panels. Thin WallStruct 1999;35:205–31.

[7] Cunningham PR, White RG, Aglietti GS. The effects of variousdesign parameters on the free vibration of doubly curved compositesandwich panels. J Sound Vib 2000;230:617–48.

[8] Cunningham PR, White RG. A new measurement technique for theestimation of core shear strain in closed sandwich structures. ComposStruct 2001;51:319–34.

[9] Khatua TP, Cheng YK. Bending and vibration of multiplayersandwich beams and plates. Int J Numer Meth Eng 1973;6:11–24.

[10] Yu L, Yang S, Gibson RF, Chen WH. Modal parameter evaluationof degraded adhesively bonded composite beams. Compos Struct1988;43:79–91.