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ScienceDirect Materials Today: Proceedings 4 (2017) 8645–8653
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ICAAMM-2016
Determination of Elastic Properties of Reverted Hexagonal Honeycomb Core: FEM Approach Rakesh.Potluria*, U. Koteswara Raob a*
b
P.G.Scholar,Dept. of Mechanical Engineering, PVPSIT, Kanuru, Vijayawada – 07, A.P, India. Associate. Prof, Dept. of Mechanical Engineering, PVPSIT, Kanuru, Vijayawada – 07, A.P, India.
Abstract Honeycomb structures are widely used in the applications such as satellites, aero planes, ships, bridges.... etc. due to their excellent mechanical properties. The prediction of the elastic constants for the honeycomb structures play a crucial role in the design of the structures using these materials. The experimental approach is the best way to determine the properties of the core but it is very expensive and time-consuming. Developments in the Finite Element theory has led the way to solve many realworld problems using computers by applying these methods. Therefore, FEM and analytical methods are the viable methods for the determination of the core properties in the honeycomb structures. In this paper, two different shapes of the honeycomb structures, hexagonal and reverted honeycombs were considered and the properties of the core were determined using finite element method. The main focus was given on finding out the out-of-plane properties because they are the most influential properties on the mechanical behavior of honeycomb sandwich structures. An MATLAB code was developed for analytical analysis of the honeycomb structure to study the variation of out of plane properties for both the types honeycomb structures with respect to the length of the honeycomb cell wall. © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the Committee Members of International Conference on Advancements in Aeromechanical Materials for Manufacturing (ICAAMM-2016). Keywords: Honeycomb Core; Sandwich Structures; FE Analysis; Ansys Workbench; Matlab;
* Corresponding author. Tel.: 9505266522. E-mail address:
[email protected] 2214-7853 © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the Committee Members of International Conference on Advancements in Aeromechanical Materials for Manufacturing (ICAAMM-2016).
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1. Introduction The sandwich structures are being used in many fields such as aerospace, naval, transportation and many more, due to their high bending strength & stiffness along with their low weight. A honeycomb sandwich structure contains a very light weight core which possesses high stiffness, sandwiched between two thin sheets which are known as face sheets. An adhesive layer joins the core to the face sheets. A honeycomb core consists an array of open cells, formed from very thin sheets of material, which are attached to each other. The general cell shapes consist of the hexagonal shape [Fig.1a]. The reverted honeycomb shape is shown in the [Fig.1b]. The complexity of the shape of sandwich structure makes it anisotropic even when the material with which it is made is isotropic. The experimental testing and finding the properties of the Honeycomb core is very difficult and expensive processes. Again the variability of core shape is also another issue to get an optimized core shape for a particular application. All of the reasons suggest that Finite Element Analysis of Honeycomb core is absolutely necessary in order to economically predict the properties of the core. Once we have homogenized the properties of the core, then we can add the sheet design and properties of adhesive layers to carry out further analysis of the sandwich structure, such as Impact behaviour, the dynamic behaviour of the sandwich structures. The basic reason is to save weight, however, smooth skins and excellent fatigue resistance are also the other reasons for using honeycomb structures. The combination of two face sheets and core gives a very efficient load bearing member. The face sheets are intended to carry tensile and compressive loads and the core is intended to carry transverse and shear loads. The major theoretical work for finding out the properties of the Honeycomb are given by Gibson and Ashby [3].
Fig.1a: General Hexagonal Honeycomb
Fig.1b: Reverted Hexagonal Honeycomb
Meraghni et.al [4] used CLT theory to determine out-of-plane elastic constituents of honeycomb and tubular cores using finite element analysis. Saito et.al [5] performed a parametric study to determine the elastic properties of the aluminium core sandwich beams. Ilke Aydincak et.al [6] considered different FEM model alternatives and performed analysis to come up with the reliable finite element model of the sandwich panel. Kelsey et.al [7] have theoretically evaluated the out-of-plane shear moduli of a hollow hexagonal honeycomb core, using the energy method. Anita Catapano et.al [8] have performed the optimal design at honeycomb and also performed the sensitivity analysis on the influence of geometric parameters of the unit cell on the effective elastic properties. A review of the sandwich structures, their applications, analysis can be found [1-3] Xu et.al [9] studied the thickness effect for evaluation of effective elastic coefficients for a honeycomb core structures. V.N. Burlayenko et.al [10] studied about the structural benefits of foam filled honeycomb structures using FEM approach. First a finite element analysis of hallow honeycomb using shell modelling and solid modelling was used for modelling the foam core. There was a substantial improvement in the properties of the honeycomb core filled with foam core. Zheng Chen et.al. [11] Tried to understand the influence of the thicknesses of Kraft paper honeycomb core and medium density fibreboard skins on the stiffness of the sandwich panel. S. Belouettar et. al. [12] studied the static and fatigue behaviours of honeycomb sandwich composites, made of aramid fibres and aluminium cores, are investigated through four-point bending tests. Chun Lu et. al. [13] mechanical performance of the Composite Honeycomb Sandwich was characterized using finite element analysis (FEA) and three-point bending Test.
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Nomenclature FEM Ct Tc h l v Ec u RVE
- Finite Element Method - Cell core height - Cell foil thickness - Length of the inclined wall - Length of the straight wall - Volume of core geometry - Effective elastic strain - Applied displacement - Representative Volume Element
2. Problem Modelling 2.1. Problem Objective The objective of the present work is to find out the out-of-plane properties of the hexagonal honeycomb structure using a FEM. The FEM model and the results are validated with available literature [3]. Then using the same FEM model we try to predict the out-of-plane properties of the reverted hexagonal structure. Also the finite element analysis is extended to determine the variation in out-of-plane properties with change in the cell wall length dimension ‘l’ as shown in Fig.2 & Fig.3 for both the shapes. A total of two types of materials are used to check the results and to make a comparison between the two honeycomb shapes.
Co re He ig ht
Co re He ig ht Fig.2: RVE of Hexagonal Honeycomb
Fig.3: Reverted Hexagonal Honeycomb
2.2 Materials Two types of aerospace grade aluminium alloy materials namely aluminium 5052 and aluminium 5086H112 were used to simulate both the Hexagonal as well as Reverted-Hexagonal shapes. The material properties considered here were shown in Table.1 The data was taken from the datasheets obtained from the Hexcel Composites and Mat Web materials website. Table 1: Elastic Properties of Materials used for Analysis.
Material
E (GPa)
ν
ρ (Kg/m3)
Aluminum5052 Aluminum5086H112
70 71
0.33 0.33
2680 2660
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2.3 Geometry and Finite Element Model Fig. 1a and Fig. 1b shows the geometry of the hexagonal honeycomb core and the reverted honeycomb core. Fig.2 and Fig. 3 shows an RVE of the hexagonal honeycomb and that of reverted hexagonal structure which are used for the determination of elastic properties using finite element analysis. The advantage of Symmetry and periodicity of the RVE was considered to reduce the size of the FE model and Fig.4 and Fig.5 shows the FE models of both the core structures. The following dimensions are used for the cores: l = 1.899 mm, h = 1.899 mm, Ct = 2.5 mm, Tc = 0.0254 mm. A shell mesh was adopted for this purpose. The sensitivity of the material parameters was analyzed and the mesh settings were chosen according to the convergence studies. Shell 181 element was used to mesh the geometry. It is a 4 node element with 6 DOF at each node suitable for analyzing moderately thick shells.
Fig.4: FEM model of Hexagonal Honeycomb.
Fig.5: FEM model of the Reverted Honeycomb.
2.4 Loads & Boundary Conditions Three different load cases are taken, for finding out the three-different out-of-plane elastic constants, Ez, Gxz and Gyz. To find Ez, Compression loading conditions were imposed and to find Gxz, Gyz Shear loading conditions were imposed. Different boundary conditions are applied at different edge sets. The edge sets are shown in Fig.6 and Fig.7. The applied boundary conditions are shown in Table 2.
Fig.6: Edge Sets for Hexagonal Honeycomb.
Fig.7: Edge Sets for Reverted Honeycomb.
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Table 2: Boundary Conditions used for Finite Element Analysis.
Edges Edge set 1 Edge set 2 Edge set 3 Edge set 4
Load Case 1(Gxz) ux uy uz u 0 0 Free 0 0 Free 0 Free 0 0 Free
Load case 2(Gyz) ux uy uz 0 u 0 Free Free 0 0 Free Free 0 0 Free
ux 0 0 0 0
Load Case 3(Ez) uy 0 0 0 0
uz -u Free Free 0
2.5 Analytical Analysis A MATLAB code was developed in order to compute the results for different geometries of the Honeycomb structure using the theoretical relations that were developed by the Gibson & Ashby [3]. The geometry and Material properties are the parameters that are to be given as input to the program and it calculates and gives out the different values of elastic constants. And other such results which were used to compare with the FEM results as shown in Fig.8 & Fig.9. 3. Results and observations: The effective out-of-plane properties of the Honeycomb structures can be obtained from the formula
E.C
2 strain.Energy s eq2 vol
(1)
Where the strain energy is calculated from the ANSYS Analysis. ε is the equivalent strain and Vol is the Volume of the Geometry which can be given by
V Ct tc (h 2l )
(2)
Where b = height of core and t = thickness of honeycomb foil. l1 = length of inclined face and l2 = length of straight face. The ε is given by formula
ε=
(3)
Where h = Core height u = applied displacement. A comparison was made between the results that are calculated using ANSYS workbench to that of the results calculated from MATLAB. The comparison of results shows that a very less change or deviations in the results that are obtained from the FEM approach and the analytical approach. Table 3: Effective Out-Plane Elastic properties of Hexagonal Honeycomb.
Constants (MPa) Ez Gxz Gyz
G&A (Matlab) 1120.15 215.39 215.39
Al5052 (FEM) 1125.7633 236.5184 190.96715
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Fig.8: Comparison of FEM & Matlab results for HC
Fig.9: Comparison of FEM & Matlab results for RHC
Table 4: Effective Out-Plane Elastic properties of Reverted Hexagonal Honeycomb.
Constants (MPa)
G&A (Matlab)
Al5052 (FEM)
Ez Gxz Gyz
1493.4 215.3949 195.52
1435.3586 228.95976 199.37111
The above table.3 and table.4 show the comparison between the results of finite element analysis to that of analytical approach for the material 1. The results calculated from the material 2 using the finite element analysis and analytical approaches are shown in the form of graphs in Fig.10 and Fig.11. The Finite Element Models of the Honeycomb structure showing the strain energy (SE) in the RVE of the cell structures analysed in ANSYS are shown in Fig.10 and Fig.11.
Fig.10: SE Model for Hexagonal Honeycomb.
Fig.11: SE Model for Reverted Honeycomb.
A parametric study was performed using ANSYS to see the effect of change in the length of the Honeycomb straight wall on the out-of-plane properties of the Honeycomb structure. This is mainly considered because if the length of the cell increases the manufacturing and assembly of the honeycomb structure will become easier, if we take the present manufacturing process of the Hexagonal honeycomb. The variation of the Ez, Gxz &Gyz along with the change in the length of the Honeycomb cell for a regular Hexagonal Shape is shown in Fig.12, Fig.13 and Fig.14.
Rakesh Potluri et. al. / Materials Today: Proceedings 4 (2017) 8645–8653
Fig.12: Variation of Ez w.r.t Length for Hexagonal Honeycomb.
Fig.13: Variation of Gxz w.r.t Length for Hexagonal Honeycomb.
Fig.14: Variation of Gyz w.r.t length for Hexagonal Honeycomb.
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From the above graphs we can observe that the magnitudes of Ez, Gxz and Gyz decreases with the increase in length ‘l’. This may be due to the fact that with increase in the cell wall length. The number of cells of the core decreases in the Honeycomb structure which may lead to the decrease in the strength of the structure. With the increase in the length of the cell wall the stiffness of the core decreases and this change in the stiffness behaviour of core is one of the reasons to observe such type of change in the effective elastic out-of-plane properties of a regular hexagonal-structure.
Fig.15 Variation of Ez w.r.t length for Reverted Hexagonal Honeycomb
Fig.16. Variation of Gxz w.r.t Length for Reverted Honeycomb
Fig.17: Variation of Gyz w.r.t Length for Reverted Hexagonal Honeycomb.
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Fig.15, Fig.16, Fig. 17 shows the variation in different out of plane properties w.r.to variation in the cell wall length l for a reverted honeycomb structure. From the above graphs we can observe that as the length of the cell wall increases, the Ez value is decreasing and then again it is increasing in trend. Similar type of behaviour can be observed when the change in the cell wall length is drawn against the change in Gyz. But the Gxz goes on increasing with respect to the increase in the cell wall height. 4. Conclusion In the present work, three-dimensional finite element analysis was carried out for finding out the out-ofplane elastic properties of the Hexagonal Honeycomb and results were compared with theoretical formulations. Then this approach was extended to find the Equivalent out-of-plane elastic properties of a Reverted Honeycomb core structure. The influence of cell length on the out-of-plane elastic properties was investigated for both the cell shapes of the Honeycomb core. It was observed that the Elastic constants Ez, Gxz and Gyz decreases w.r.t the increase in the cell wall length l in case of the regular hexagonal honeycomb structure. For a reverted honeycomb structure, it was observed that the Ez, Gyz were decreasing with the increase in the cell wall length up to some extent and then they were increasing with the future increase in the cell wall length and however the Gxz behavior of the reverted honeycomb was observed to be similar to that of the Hexagonal honeycomb. The behaviour of the reverted Honeycomb structure that was observed through the FEM analysis has to be examined more deeply by different finite element models, experimental undertaking etc., to find out the exact reasoning of this type of behaviour. 5. References [1] Tom Blitzer, Honeycomb Technology: Materials, Design, Manufacturing, Applications and Testing, third ed., Chapman & Hall, 1997. [2] Vinson JR. The behavior of sandwich structures of isotropic and composite materials. Technomic Publishing Company; 1999. [3] Lorna j.Gibson. Michael F.Ashby, Cellular solids- structure & Properties, second ed., Cambridge University press, 1999. [4] F. Meraghni, F. Desrumaux, M.L. Benzeggagh, J. Composites: Part A 30 (1999) 767–779. [5] Saito, T., Parbery, R.D., Okuno, S. and Kawano, S. (1997), J. Sound and Vibration, 208(2): 271–287 [6] Ilke Aydincak, Altan Kayran, J. Sandwich Structures and Materials, 2009; 11: 385-408 [7] Kelsey S, Gellatly RA, Clark BW. J..Aircraft Eng 1958; 30(358):294–302. [8] Anita Catapano, Marco Montemurro, J. Composite Structures 118 (2014) 664–676. [9] Xu FX, Qiao P. Int J Solids Struct 2002; 39:2153–88. [10] Burlayenko VN, Sadowski T, J. Compos Struct 2010;92:2890–900. [11] Zheng Chen, Ning Yan, J. Composites: Part B 43 (2012) 2107–2114. [12] S. Belouettar, A. Abbadi, Z. Azari, R. Belouettar, P. Freres,J. Composite Structures 87 (2009) 265–273 [13] Chun Lu, Mingyue Zhao, Liu Jie, Jing Wang, Yu Gao, Xu Cui, Ping Chen, Procedia Engineering 99 ( 2015 ) 405 – 412 [14] Barbero E J, Finite element analysis of composite materials, second ed.. Taylor and Francis,Group; 2014. [15] Grediac M, Int J Solids Struct 1993; 30(13):1777–88. [16] Shi G, Tong P, Int J. Solids Struct 1995; 32(10):1383–93. [17] Becker W. J. Appl Mech 1998; 68:334–41. [18] Noor, A.K. and Burton, W.S, J. Appl. Mech. Rev., 49(3): 155–199. [19] Hexcel Composites. HexWeb honeycomb attributes and properties, Duxford, Cambridge, CB24QD, UK; 1999
