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Determination of Mechanical Properties of Aluminum Honeycomb Structures Using Finite Element Analysis

Embry-Riddle Aerospace Engineering| Benjamin Tincher, Dr. David Sypeck

ERAUDetermination of Mechanical Properties of Aluminum Honeycomb Structures Using Finite Element Analysis

Table of Contents1. Introduction2. Backgrounda. Honeycomb Structuresb. Material Property Characterizationc. Finite Element Analysis3. Experiment4. Results and Discussion5. Conclusions6. Future Work7. References8. Acknowledgements

1. IntroductionCommonly found in aerospace applications, honeycomb panels are known for exceptional strength to weight properties. Honeycomb structures are relatively cheap and simple to mass produce [1]. When designing honeycomb type structures, it is very beneficial to predict the material properties of a designed structure even before a sample is made. Finite Element Analysis (FEA) allows for this type of prediction for many structural applications. Current theories have been presented to predict material properties based on the geometry of the honeycomb. These theories have been proven relatively accurate, but FEA offers much more than the limiting material properties. Not only can FEA confirm and possibly increase accuracy of the predicted values from theory calculations, but also it can give visualizations of deformation and stress distributions within the structure. The aim of this work is to conduct FEA on common commercially available aluminum honeycomb structures as a proof of concept. Having theoretical values for material properties of the honeycomb, the analysis methods can be confirmed or disqualified. Having proved methods for FEA of known honeycomb structures, the same methods can then be applied to novel honeycomb designs.2. Backgrounda. Honeycomb StructuresCellular solids are those which contain portions of empty space and portions of solid material. The empty space can be either closed or open to the atmosphere and form cells within the volume. Many cellular solids can be found in nature such as foams, sponges, and woods. Honeycomb structures are a specific type of cellular solid in which thin solid walls forming prismatic cells are nested together to fill a single plane [2]. As with many structural designs, honeycombs borrow their shape and name from nature; specifically the hexagonal honeycomb of bees as shown in Figure 1. Hexagonal shapes are often found in nature, like carbon structures, due to their high special efficiency, and it is not surprising that nature produces hexagonal honeycombs.

Figure 1: Natural bee honeycomb structure [3].One of the earliest recorded examples of manmade cellular solids was in 1638 when cellular structure caught the attention of Galileo when reporting that "Art, and nature even more, makes use of these in thousands of operations in which robustness is increased without adding weight, as is seen in the bones of birds and in many stalks that are light and very resistant to bending and breaking in his observations [4]. In 1665, Robert Hook noted the structure of cork was not unlike that of bee honeycombs [5], and even Darwin, in 1859, noted on the efficiency of bee honeycomb structures [6]. The first honeycomb patent was registered in 1904 for manufacturing paper honeycomb structures [7]. Other processes for man-made structures were developed continued in the early 1900s involving sheet metal corrugation, expansion, and molding. These three processes are still utilized today.The most widely used method of production is the expansion method. In this method, adhesive is preferentially applied to sheeting of material as the sheets are stacked on top of each other. After cure, the sheets are gently pulled apart forming open cells where the adhesive is absent. Figure 2 shows a schematic representation of the expansion method.

Figure 2: Expansion process for honeycomb production [8]. For processing higher density honeycomb from thicker materials corrugation is the most common method of production. Sheets of metal are first corrugated to specified geometry. Then, adhesive is applied to the most external faces and the corrugated sheets are stacked so that they are aligned to form hexagonal cells. Figure 3 shows the corrugation production process. It should be noted that both the expansion and corrugated methods of production produce structures having double wall thickness where adhesive is applied which increases both weight and strength.

Figure 3: Corrugation process for honeycomb production [8].The advantages of honeycomb structures are high specific material properties, where specific properties are defined as characteristic values divided by a reference value (solid material properties, weight, mass, density, etc.). When honeycombs are sandwiched between facing panels, the resulting composite exhibits excellent specific strength and stiffness in bending as well as axial buckling resistance. For this reason, sandwich panel design is commonly used in aerospace and automotive industries where weight saving is crucial. Much like an I-beam, the facing plates resist most of the in-plane normal stresses, tension and compression; whereas, the honeycomb core resists shear stresses as shown in Figure 4 and 5 [9].

Figure 4: Honeycomb sandwich panel compared to I-beam [10].

Figure 5: Stress Distribution within sandwich construction [10].As seen in Figure 6, the stiffness and flexural strength of panels are intensely maximized with only a minimal increase in weight by incorporation of honeycomb sandwich design. Not only for structural use, but honeycombs are also attractive materials due to their large surface areas. For this reason, they have also found use in applications such as catalytic converters, where they form the skeleton of emission filters, or heat exchangers. Or, due to unique buckling behavior, honeycombs have also been used for energy-absorbing applications such as the crushable cartridges found on the landing struts of the Apollo 11 module [11]. Depending on the application, honeycombs are made from many different materials extending from nano-scale carbon structures [12] to recycled paper for structural and many other applications. But, the most traditional structural materials used are aluminum or polymer matrix composites.

Figure 6: Comparison of sandwich design properties as a function of core thickness [10].Along with selection of material and production process, geometry is also an important consideration when designing a honeycomb structure for specific applications. The geometry of the structure can be used to tailor the structural properties of the honeycomb. Common honeycomb geometry notation is given in Figure 7 [10].

123Figure 7: Common geometrical variables for honeycomb structures [10].The value of the cell size is one of the most important parameters as it is directly related to the final density of the honeycomb. It is obvious that larger cell sizes produce lower densities for a given wall thickness which could be maximized for the highest specific strengths. But, if the cell size is too large, dimpling of the facing skins could occur within the cell area in sandwich construction. Specific cell geometry notation is demonstrated in Figure 8.

Figure 8: Cell geometry.A regular hexagonal honeycomb is one that a uniform web length, l, and angles, , of 30. Further characterization of honeycomb structures includes calculation of the nominal density. For regular double walled hexagonal honeycombs the density is calculated per Equation 1(1)

where * is the honeycomb density and s is the base material density. This relative density is an important factor and is commonly used to predict many material properties of the honeycomb structure.b. Material Property CharacterizationConsider Figure 9 below depicting the application of force to the faces of a simple cube.

Figure 9: Normal (left) and shear (right) stresses.When characterizing mechanical properties of materials, it is important to be able to predict deformation of a material in response to a defined stress. In general, two types of stresses can be applied to a material, normal and shear. Normal stress is caused by a force that acts normal, or perpendicular, to a particular face. Equation 2 represents the calculation of normal stress(2)

where F represents the applied force and A represents the area over which the force is applied. Shear stress is caused by a force that is applied parallel to a particular face. Equation 3 shows the calculation of shear stress(3)

22

Deformation occurs when a stress is applied to a material. Deformation is typically measured using strain; for which, normal and shear strain exist in response to normal and shear stress respectively. Equations 4 and 5 show calculation of normal strain, , and shear strain, , respectively and are defined by the parameters in Figure 10 below.

(4)

(5)

Figure 10: Shear (left) and normal (right) strain.Most materials hold a direction relationship between stress and strain up to a limiting stress value. This portion of stress and strain is known as elastic deformation. Within elastic deformation, the direct relationship is defined by a linear constant, specifically Youngs modulus, E, for normal stress/strain and shear modulus, G, for shear stress/strain. The equations governing elastic stress and strain are shown in Equations 6 and 7.

(6)

(7)

Elastic modulus values are used to compare the stiffness of different materials and structures. The higher the modulus, the stiffer the structure; or more simply, less deformation is experienced under loading. The properties of a particular honeycomb are often listed as the ratio of the honeycomb property to that of the base solid material