3680 words - 15 pages

Effect of cell shape of honeycomb structure on the toughness and bending

strength of the overall structure

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(i) Abstract

Using a strong structure to construct an object is crucial to prevent it from rupturing due to

external forces such as bending. Honeycomb structures are widely used in constructing

bridges and airplanes due to its well-known rigidity. However, there’s a lack of research on

the effects of shapes on the overall strength of the honeycomb structure as most research

focus on the materials used in manufacturing them. In contrast, our research objective is to

investigate which common shape, namely circle, triangle, trapezium, square and hexagon

could provide the best toughness and bending strength for the honeycomb structure. The five

shapes of honeycomb structure were created using vanguard sheets and were tested by

loading a number of weights onto the centre until it collapsed. Meanwhile, static loading

method was used to provide even weight distribution throughout the honeycomb structure.

The average length of deflection of the honeycomb structure when handling different loads

were measured and graphs were plotted. The gradient and the area bounded by the graphs

were analyzed to determine the shape’s effectiveness on the honeycomb structures. The

experiment results revealed that hexagon gave the best toughness and bending strength to the

honeycomb structure mainly because of tessellation and three other factors. Due to

limitations, other tests regarding real life applications of the honeycomb structure were

unable to be carried out. Further research can be done regarding shock loading and etcetera,

which are more related to real life situations. Our research could contribute to the

manufacturing industry in picking the best shape, in producing honeycomb structures for

further usage.

(ii) Table of Contents

1.0 Introduction ............................................................. 4 – 5

2.0 Methods and Materials ........................................... 6 – 7

2.1 Apparatus and Materials .......................................... 6

2.2 Construction of Honeycomb Structures ................... 6

2.3 Methodology ............................................................ 7

3.0 Results and Discussions ........................................ 8 – 14

4.0 Conclusion and Recommendations .................... 15 – 16

5.0 References ........................................................... 17 – 18

6.0 Appendix ............................................................ 19 – 24

6.1 Appendix A ............................................................ 19

6.2 Appendix B ............................................................. 20

6.3 Appendix C ............................................................. 21

6.4 Appendix D .................................................... 22 – 24

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1.0 Introduction

Honeycomb structure attained its name due to its resemblance to the bee hives (Blitzer,

1997). It commonly refers to a structure which consists of a core made up of a series of

orderly-arranged hollow cells and two facing sheets covering the surfaces of the cell pattern

(Figure 1).

Figure 1: Composite Honeycomb Sandwich

(Extracted from: Bitzer. T, 1997. Honeycomb Technology, (p. 36))

The earliest record of honeycomb structure usage dates back all the way to as early as the

19th century, whereby it was used in the construction of railroad bridge located in Wales

(Bitzer, 1997).

During World War I and II, honeycomb structure became popular in the aviation industry

(“Honeycomb Structure Fails”, para. 6). It was first implemented into the design of aircraft

wing panel in 1919 and later proved to be one of the best sandwich structures as it has high

strength-to-weight ratio which is essential to the aviation industry (Yu & Cleghorn, 2005;

Gaetano G. Galletti, 2007). The scientific research in the late 20th century discovered several

other unique physical properties of honeycomb such as its transverse compressive properties

(Thotakuri, 2004) which later led honeycomb structure to gain its recognition in other

industries such as the sports industry, the information and technology industry and furniture

industry (IKEA, 2004; Busch 2004).

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The important parts of a honeycomb structure are the facing sheets of the structure and the

series of hollow cells, which help to withstand the longitudinal stress and carry the

transversal stress respectively. The individual cells as well as the facing sheets are bonded

together by the use of strong chemical adhesives (Galletti, Vinquist & Es-said, O.S, 2007).

This results in a highly rigid structure with relatively light weight. As shown in Figure 2,

structure 3 (honeycomb structure) is 37 times stiffer and 7 times stronger in bending strength

than structure 1 (non-honeycomb structure). Nonetheless, structure 3 is 9% heavier than

structure 1.

Figure 2: Rigidity Test

(Extracted from Bitzer. T, 1997, HoneycombTechnology, p 5)

In addition, it has been studied that when the honeycomb structure material is kept constant,

the variation of the cell’s geometries such as its angle, width and thickness affects the energy-

absorption property of the honeycomb structure (Veltin, 2009). There were many tests and

research conducted on regular hexagon honeycomb structure’s physical properties, but there

were limited research on the other common shapes such as triangle and square.

As variations in geometries of the cell play an important role in the honeycomb structure,

there lies a research gap of how other regular shaped cells will perform as compared to the

conventional hexagon cells. We aim to bridge the research gap by investigating the resulting

toughness and bending strength of a honeycomb structure when different shape cells are used

as the core of the structure. In our experiment, we will specifically test on the five common

shapes, namely, hexagon, circle, square, triangle, and trapezium.

1 2 3

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2.0 Methods and Materials

Overview: To determine the cell shape that gives the highest bending strength and toughness

as the core of a honeycomb structure through the investigation of the rate of deflection and

the heaviest load that each honeycomb structure can withstand.

2.1 Apparatus and Materials

Apparatus

Ruler

Weights of 20 Newton (N) and 50N

Penknives

Scissors

Scientific Calculator

Mechanical Pencil

Materials

Vanguard Sheets

Super Glue

2.2 Construction of Honeycomb Structures

1. 5 different cell shapes namely: circle, triangle, square, trapezium and hexagon were

chosen to be the core of the honeycomb structure. Each honeycomb structure

consisted of 23 core cells, which were of the same shape.

2. The thickness of each cell was kept constant at 2 centimeter (cm) and the cross

sectional area was fixed at approximately 16cm

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.

3. The vanguard sheets were first cut into strips of 2cm.

4. The square-shaped cells were the first to be made. The 2cm-thick strips were bent

according to the dimensions of the square. (Refer to Appendix B)

5. The bent strips were then sealed with super glue and the square-shaped cells were

formed.

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6. Once 23 square-shaped cells were formed, they were then glued together with a

formation of alternating rows of 5 cells and 4 cells (5-4-5-4-5). (Refer to Appendix C)

7. Two flat vanguard sheets were glued to the top and bottom of the cells formation

respectively. This is to create a sandwich composite structure.

8. Steps 4 to 7 were repeated to construct the remaining 4 cell shapes of the honeycomb

structure.

2.3 Methodology

1. The square honeycomb structure was the first to be experimented. It was placed on

two supports at the side. (Refer to appendix B)

2. A total weight of 70N (made up of a 20N weight and a 50N weight) was placed on top

of the honeycomb structure at the start of the experiment. The weights were placed at

the center of the structure by using the static loading method in order for the weights

to be evenly distributed among the cells.

3. The distance between the ground and the upper surface of the honeycomb structure

was measured. Readings were first taken from the front (L3) and back (L4) with the

help of a meter ruler. The average of the two readings was then calculated using the

formula (L3+L4)/2. The same step was repeated to calculate the average distance

between the ground and the lower surface of the honeycomb structure using the same

formula and the results were recorded. (Refer to Appendix B for experiment setup)

4. 20N weights were then added one by one onto the honeycomb structure and step 3

was repeated. A period of 10s was given in between loading intervals to ensure that

the honeycomb structure did not fail for that particular loading.

5. Step 4 was repeated until the square honeycomb structure collapsed.

6. Steps 1 to 5 were then repeated for the remaining 4 shapes of honeycomb structures.

7. The results for each cell shape were obtained, recorded and tabulated. (Refer to

appendix D)

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3.0 Results and Discussion

This section will discuss on the maximum weight, which the 5 different honeycomb

structures can withstand before collapsing and their rate of deflection. The results obtained

were analyzed and interpreted to compare the toughness and bending strength of the 5

different honeycomb structures. In this experiment, toughness is defined as the total weight a

structure can withstand before collapsing while bending strength is defined as a structure's

ability to resist deflection under load.

Figure 3 shows a graph of the average deflection versus the load on the honeycomb structure.

As toughness is defined to be the area under the graph of load versus deflection, we can use

Figure 3 to determine the toughness of each structure by calculating the area bounded by each

individual graph and the y-axis. Table 1 shows the area bounded by the y-axis

and each cell shape’s line graph.

Figure 3: Deflection of each cell shape under different loads.

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Table 1: Area bounded by the y-axis and each cell shape’s line graph.

From table 1, hexagon honeycomb structure has an area of 1180 (N mm), which is 58.3%

larger than that of the next best structure, which is the square honeycomb structure. This

suggests that hexagon structure is much tougher than the other structures. On the other hand,

circle honeycomb structure is the weakest in terms of toughness as it has the smallest area of

only 335 (N mm).

Based on observation from Figure 3, the graph for hexagon honeycomb structure is placed

below the remaining 4 line graphs whereas the circle honeycomb structure is above the

others. In order to identify our findings regarding their bending strength, we proceed to

further analysis of calculating the gradient of each graph by making use of their best-fit-lines.

Figure 4 to Figure 8 show the best-fit-line of each individual graph whereby the gentler the

gradient, the lower the rate of deflection, and thus the higher the bending strength of the

honeycomb structure.

Cell Shape Area (Newton millimeter [N mm])

Circle 335

Square 745

Trapezium 570

Triangle 560

Hexagon 1180

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Figure 4: Best-fit-line for circle honeycomb structure.

Figure 5: Best-fit-line for square honeycomb structure.

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Figure 6: Best-fit-line for trapezium honeycomb structure.

Figure 7: Best-fit-line for triangle honeycomb structure.

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Figure 8: Best-fit-line for hexagon honeycomb structure.

By comparison, hexagon honeycomb structure has the highest bending strength as its line

graph has the gentlest slope, with a gradient of 0.0292mm/N. On the other hand, circle

structure’s line graph has the steepest slope, with a gradient of 0.0525mm/N, which is almost

twice as steep as that of hexagon structure. This suggests that circle honeycomb structure has

a bending strength, which is almost two times weaker than that of hexagon structure.

From the results obtained, it is observed that there is a relationship between toughness and

bending strength. Honeycomb structures with high bending strength tend to have high

toughness as well. Hence, observations for both physical properties shall be explained at the

same time.

The reason that hexagon honeycomb structure is the toughest and has the highest bending

strength is that its cells could be placed side by side repeatedly without any additional space.

This property of hexagon is known as tessellation (Jon Stefansson, 1999). It is the tessellation

of hexagon cells that provides the structure with outstanding capabilities to absorb energy

(McGill, 2010). When bending occurs, the cells receive maximum support from neighboring

cells that are not in line with the line of bending. Thus, hexagon honeycomb structure is able

to withstand more weight with the least deflection. On the contrary, circle honeycomb

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structure does not have tessellation causing it to be the weakest in terms of both toughness

and bending strength.

The interlocking system of cells also plays a part in determining the toughness and bending

strength of the honeycomb structure. As seen from the arrangement of cells, hexagon and

circle structures have stronger interlocking system as compared to the remaining 3 structures

because there are no obvious divisive lines found between the rows of cells in the structure.

With a weaker interlocking system, stresses are not effectively distributed throughout the

structure, resulting in certain areas to be subjected to higher stress loads (Jaafar, Thanoon,

Najm, Abdulkadir, & Ali, 2006). Hence, hexagon and circle honeycomb structures are

stronger in terms of toughness and bending strength. However, according to the results

obtained, circle honeycomb structure is the weakest. This is possibly due to the fact that the

property of tessellation has a greater impact on the toughness and bending strength of the

honeycomb structure.

Another feature that is worth noting is the symmetry of the arrangements of cells. In our

experiment, we made use of 23 cells for all of the structures, arranging them in rows of four

and five. The only shape of which its cells cannot be arranged symmetrically is triangle. With

reference to the photos taken, it can be seen that the rows of four triangle cells are protruding

out of the structure when they are glued side by side with the rows of five triangle cells. As

pressure is defined as force per unit area (Stanbrough, 2008), this non-symmetrical

arrangement of triangle cells gave rise to a larger pressure and thus weaker support at one

side of the structure. Due to this, several cells reach their toughness limit earlier than the

others, thus weakening the overall structure. This explains why triangle honeycomb structure

is relatively weaker than the other structures.

Other than that, the number of symmetry axes in a cell shape may affect the toughness and

bending strength of the honeycomb structures. A higher number of symmetry axes suggest

that the structure has a higher bending strength and toughness because it has a higher number

bending orientations. Hexagon, having six symmetry axes, which is relatively higher than the

other shapes, contributes to its honeycomb structure having a high bending strength and

toughness.

The four factors that result in a structure having high bending strength and toughness are

tessellation, high degree of interlocking system, high number of symmetry axes in each cell

and a symmetrical arrangement of cells. Therefore, hexagon honeycomb structure is the

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strongest among all the structures tested in this experiment as it possesses all of the properties

mentioned above.

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4.0 Conclusion and Recommendations

In conclusion, this experiment was done with the aim of determining the cell shape that gives

the highest bending strength and toughness to the honeycomb structure. The objective was

achieved by investigating the deflection of each honeycomb structure when it was subjected

to increasing loads.

From the results obtained, it was found that hexagon honeycomb structure has the gentlest

gradient from its linear line graph as compared to the other 4 structures (trapezium, square,

triangle and circle). This shows that it has the strongest bending strength among the other

structures. On the other hand, hexagon honeycomb structure also has the largest area bounded

by the line graph and the y-axis, which proves that it is the toughest. The more significant

factors affecting the bending strength and toughness of the honeycomb structure are the

tessellation property and the degree of interlocking between cells. As a result, we can

conclude that hexagon is the best shape to be used as the core of the honeycomb structure.

Limitations were observed in the experiment which may lead to inaccurate results. When the

experiment was conducted, crackling sound was heard from the honeycomb structures before

failure occurred. Further investigations found that the crackling sounds were due to failure of

the bonding sections between cells. Hence, the structure might fail partly due to glue failure.

Since super glue is the strongest bonding agent available that can be applied onto the

vanguard sheet, a more suitable material that can withstand stronger bonding agents such as

solder should be used. This is to provide a more accurate result by minimizing the degree of

bonding failure.

In addition, due to apparatus limitation, there were only 20N weight plates available to be

used on the honeycomb structures. Hence, the exact weight at which each honeycomb

structure failed could not be determined precisely. This could undermine the actual results. It

is recommended that a greater variety of weight plates such as 1N weight plates to be used.

This will improve the accuracy of the results obtained.

Further studies on how the toughness and bending strength of the honeycomb structure is

affected by shock loading instead of static loading can be conducted. In real life situations,

most structures are subjected to both static and shock loading. In this experiment, the

honeycomb structure only experienced static loading as the weights were placed gently on the

structure. We suggest that the weights to be dropped onto the honeycomb structure from a

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determined height so that it would experience shock loading.

Furthermore, cost is an important factor for manufacturers and industry players to maximize

their profits. Further studies can be done to determine the cost of manufacturing the five

different cell shape honeycomb structures. This enables them to find out which structure

provides the highest strength-to-cost ratio.

The findings from this research conclude that hexagon honeycomb structure is the strongest

in terms of toughness and bending strength. Manufacturers will be able to use these findings

to enhance the structural design of their products. This will enable them to build better quality

products which can withstand higher external forces.

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5.0 References

Barboutis, I., & Vassiliou, V. (2004). Strength properties of lightweight paper honeycomb

panels for the furniture. Retrieved from http://users.auth.gr/jbarb/Publications/lightweight

honeycomb furniture.pdf

Bitzer, T. (1997). Honeycomb technology. (1 ed., p. 235). Great Britain: Combridge

University Press. Retrieved from

http://books.google.com.sg/books?id=oBNSdDN84hIC&printsec=frontcover&source=gbs_g

e_summary_r&cad=0

Galletti, G. G., Vinquist, C., & Es-said, O. S. (2007). Theoretical design and analysis of a

honeycomb panel sandwich structure loaded in pure bending. Retrieved from

http://www.sciencedirect.com.ezlibproxy1.ntu.edu.sg/science/article/pii/S1350630707000842

Hohe, J., & Becker, W. (2000). A mechanical model for two-dimensional cellular sandwich

cores with general geometry. Retrieved from

http://www.sciencedirect.com/science/article/pii/S0927025600001452

Honeycomb structures fail. (n.d.). Retrieved from

http://www.ukessays.com/essays/engineering/honeycomb-structures-fail.php

Jaafar, M. S., Thanoon, W. A., Najm, A. M. S., Abdulkadir, M. R., & Ali, A. A. A. (2006).

Strength correlation between individual block, prism and basic wall panel for load bearing

interlocking mortarless hollow block masonry. Construction and Building Materials, 20(7),

492-498. Retrieved from

http://www.sciencedirect.com/science/article/pii/S0950061805000759

McGill. (2010). Multi-scale mechanics and design optimization lab. Retrieved from

http://mdog.mcgill.ca/research.html

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Stanbrough, J. L. (2009, November 21). Physics at bhs. Retrieved from

http://www.batesville.k12.in.us/physics/default.html

Stefensson, J. (n.d.). What is hexagonal. Retrieved from

http://www.ehow.com/about_6360694_hexagonal_.html

Thotakuri, M. (2004). Transverse compressive properties of honeycomb core under oblique

loading. Retrieved from

http://soar.wichita.edu/dspace/bitstream/handle/10057/1558/t07114.pdf?sequence=1

Veltin, B. A. (2009). Effect of geometric parameters on the in-plane crushing behavior of

honeycombs and honeycombs with facesheets. Retrieved from

http://www.engr.psu.edu/rcoe/theses/Atli-Veltin_Bilim.pdf

Xu, X. F., Qiao, P., & Davalos, J. F. (2001). Transverse shear stiffness of composite

honeycomb core. Retrieved from http://cee-faculty.ce.wsu.edu/Faculty/Qiao/j-data/22-

2001.pdf

Yu, S. D., & Cleghorn, W. L. (2005). Free flexural vibration analysis of symmetric

honeycomb panels. Retrieved from

http://www.sciencedirect.com/science/article/pii/S0022460X04005784

Zhu, H. X., & Chen, C. Y. (2007). Combined effects of relative density and material

distribution on the mechanical properties of metallic honeycombs. Retrieved from

http://www.sciencedirect.com/science/article/pii/S0167663611000329

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6.0 Appendix

6.1 Appendix A (Apparatus & Materials)

Apparatus

Ruler Weights Scientific Calculator

Mechanical Pencil Scissors Penknives

Materials

Vanguard Sheets Super Glue

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6.2 Appendix B (Dimensions of Cell Shapes and Experiment Set Up)

Shapes Area(cm

2

) Perimeter(cm) Dimensions(cm)

Circle 16.0 14.20 14.2

Square 16.0 16.00 4+4+4+4

Triangle 16.0 18.30 6.1+6.1+6.1

Trapezium 16.0 16.20 4.1+4.1+3+5

Hexagon 16.0 15.00 2.5+2.5+2.5+2.5+2.5+2.5

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6.3 Appendix C (5-4-5-4-5 Formation)

Hexagon Square Trapezium

Triangle Circle

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6.4 Appendix D (Tabulation of Result)

Trapezium

L1 = 174mm L2 = 174mm L3 =191mm L4 = 193mm

Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290

L1’ (mm) 173 173 172 171 171 169 169 F

L2’ (mm) 173 172 171 170 169 169 168 F

L3’ (mm) 190 190 189 189 188 187 186 F

L4’ (mm) 192 191 191 190 189 189 188 F

Average

deflection,

δave (mm)

1 1.5 2.25 3 3.75 4.25 5.25

Circle

L1 = 174mm L2 = 174mm L3 =194mm L4 = 194mm

Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290

L1’ (mm) 172 171 171 169 F

L2’ (mm) 173 172 171 170 F

L3’ (mm) 192 191 189 189 F

L4’ (mm) 192 191 191 188 F

Average

deflection,

δave (mm)

1.75 2.75 3.5 5

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Square

L1 = 177mm L2 = 173mm L3 =196mm L4 = 192mm

Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290

L1’ (mm) 175 174 173 173 172 172 171 169 F

L2’ (mm) 172 172 172 171 171 170 169 168 F

L3’ (mm) 194 193 193 193 192 192 191 190 F

L4’ (mm) 192 192 192 191 190 189 189 187 F

Average

deflection,

δave (mm)

1.25 1.75 2 2.5 3.25 3.75 4.5 6

Triangle

L1 = 174mm L2 = 173mm L3 =195mm L4 = 194mm

Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290

L1’ (mm) 173 172 172 171 170 169 F

L2’ (mm) 172 172 171 171 170 168 F

L3’ (mm) 194 193 193 191 190 189 F

L4’ (mm) 193 193 192 192 191 189 F

Average

deflection,

δave (mm)

1 1.5 2 2.75 3.75 5.25

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Hexagon

L1 = 174mm L2 = 174mm L3 =194mm L4 = 195mm

Weight(N) 70 90 110 130 150 170 190 210 230 250 270 290

L1’ (mm) 174 173 173 172 172 171 171 170 169 168 167 F

L2’ (mm) 174 173 172 172 172 171 170 170 170 170 168 F

L3’ (mm) 193 193 193 192 192 192 191 190 189 188 187 F

L4’ (mm) 194 194 193 193 193 192 192 191 190 189 188 F

Average

deflection,

δave (mm)

0.5 1 1.5 2 2 2.75 3.25 4 4.75 5.5 6.75

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