# SANDWICH COMPOSITE BEAMS for STRUCTURAL APPLICATIONS

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2 March 24-08, 2014, Santiago, Chile Let f = f(x) be the transverse load acting on a beam. Let us consider a rectangular beam with cross-section ( b, h) where x is the axial direction, y is along the width direction and z along the height direction. The length of the beam is L.The transverse load will produce internally normal and shear stresses ( σ ; ). Let δ w be a virtual xx τ xz transversal displacement along z coordinate direction, and δψ be the virtual section rotation. The external wor produced by the acting load on a virtual transversal displacement is given by L δ Vext = fδwdx (2) 0 When the beam undergoes a virtual transversal displacement and virtual rotation, the internal stresses produce a virtual strain energy given by: δ where int L = 0 A σ σ : δε dadx; σ = ; τ ε ε = γ U (3) δε xx and xz δγ are the normal and shear strains associated with the virtual displacement and rotations. Integration is taen over all the section, and will depend on the composite section model, 1 or 2. If it assumed that the core region is in plane strain conditions, while the sin is always in plane stress conditions, then in the first case, whereas for the second. Matrices and are the constitutive matrices for elastic behavior. Integrating the virtual strain energy expression through the sandwich beam thicness, layer by layer, the virtual strain energy becomes: 5 δ U = δε CεdAdx (4) int = 1 L A Upon introduction of discretization into finite elements, vector of strains may be written in terms of the vector of lateral displacements by means of an interpolation matrix, so that for each layer: T K = B C BdAdx (5) L A is the layer stiffness matrix. As the sin layers are made of an anisotropic material, rotation matrix results to the main axes directions. This matrix is set equal to the identity matrix for the core material. is used to refer Introduction of the above results into the expression of the principle of virtual wor, Eq. (1) leads to: (6) Being the vector of applied loading. Details are available in Reddy, J. (1993), Reddy, J. (2004). 3. RESULS AND DISCUSSION 3.1 Flat position failure mode Composite materials mechanical behavior is dependent on several factors, i.e, fiber and matrix bonding, plies stacing sequence, plies thicnesses and orientations, angular directions with respect to layup reference directions, etc. The fem model was constructed using the mechanical properties shown in Tab. 1. The bi-axial fiber sins were modeled by plies with ply angles (±45) 2, sequenced by the core material. The core material occupied the middle of the beam. The model can be described by [(±45) 2 /0] s. Different number of plies and orientations were verified, however the [(±45/0] s was the simplest to show good agreement with reported results.

3 Fem models were created using Abaqus software for sandwich composite beams. Sin layers were placed in horizontal position (flat) as well as in vertical one (edge position). Figure 1 is a schematic representation of the four point bending test of the laminated sandwich composite using the 100 N universal testing machine.. P/2 P/2 0.4L 0.2L 0.4L L Horizontal sin layers model. Vertical sin layers model. Figure 1. Schematic representation of a four- point bending test. Manalo et al. (2009) presented the load and midspan deflection experimental results for the beams of rectangular cross-sections tested in the flat and edge positions. Figure 2. Vertical displacements of composite sandwich. The midspan deflection of horizontal beam (Fig. 1: horizontal sin layers) tested in the flat position increased linearly until a load around 4550 N was reached. The corresponding reported midspan deflection was 24 mm. An Abaqus 3D deformable solid model was used to represent the rectangular beam subjected to the four-point bending test. The beam dimensions were 50x20 mm. Model 1 had sin layers placed horizontally on the top and bottom of the beam. The total thicness of the sin layers were 1.92 mm. Figure 2 shows results of the vertical displacement distribution (U2) for the composite solid model of the laminates sandwich beam [(±45) 2 /0] s. The displacements are in meters. The fem maximum vertical displacement result for a four-point bending test simulation was 21.8 mm.

4 March 24-08, 2014, Santiago, Chile Figure 3. Principal stress distribution on composite sandwich core layer. Flat position Figure 4. Principal stresses distribution on composite sandwich bottom sin layer. Flat position. Stresses in the core layer are represented in Fig. 3. Figure 4 shows stresses for the bottom sin layer. The stress distribution for the top layer is shown in Fig. 5. The stresses are in SI units (N/m 2 ). Experimental observations report that some tension cracs were observed at the bottom part of the core material. The fem maximum principal stresses in the core materials are at 13.4 MPa (Fig. 3), thus very close to the maximum tensile stresses for the core material (14 MPa). The fem results (Fig. 3) could explain the observed tension cracs at the bottom of the core material. However, it was observed also that core cracs did not cause the final failure. The failure was due to compressive sin stresses followed by delamination between the core and sin materials. There were no shear stresses properties on the report in order to verify the claim by the simulation.

5 The stresses in the bottom sin layer (Fig. 4) are about 12% below the maximum tensile stress for the sin materials (Tab. 1.). The maximum stresses happen in the region between the loads. However, we cannot reach a conclusion without first observing the scenario of the top sin layer. The stresses in the top sin layers are compressive stresses. The maximum compressive stresses of the central region are at MPa (Fig 5.). These stresses are 1% below the maximum compressive stress of the sin material which is 211 MPa (Tab. 1). It should explain the reason why the specimen failed due to compressive failure of composite sins. Figure 5. Principal stresses distribution on composite sandwich top sin layer. Flat position Edge position failure mode Laminated sandwich composite rectangular beams placed on the vertical position, edge position, are also setched in Fig. 1. The sin layers are placed in vertical position at the vertical sides of the rectangle. An abaqus 3D deformable composite solid model was constructed. The solid beam model had dimension 20x50 mm. Model 2 assumes four vertical sin layers at each side of the core layer, with a total 1.92 mm for the sin thicness [(±45) 2 /0] s. The experimental investigation mentions the edgewise rectangular beam bending test results. Load and deflection increased linearly until 5000 N during the experiment. Cracs were observed appearing in the core material leading to slope reduction of load against deflection curve, ie, different mechanical properties. Next, the loading increased until 5500 N and the deflections reached 8 mm. However, the deflections progressed even further without an increase in the applied load. The failure occurred with an approximate 14 mm deflection. The Figure 6 shows the vertical beam displacement under a 5500 N load obtained by the fem model simulation. The displacements in the pure bending region are mm. (0.4L)[4(0.4L) 2 3L 2 ] The maximum displacement formula w max = P corresponding to the four bending test 24EI 3 3 H t s H t c settings turns w max = 9.06 mm, with EI = Es + Ec being H=beam height, t= beam thicness, E= Young s module; s= sin material and c=core material. The results are in good agreement with the fem model simulation ones.

6 March 24-08, 2014, Santiago, Chile Figure 5. Vertical displacements of composite sandwich. Edge Position. The stresses in the vertical core material are represented in Fig. 6. Figure 7 shows the stresses in the leftmost sin layer. It can be observed that the maximum stress level (Fig. 6) in core material (+14.5 MPa) is higher than the maximum tensile core stress level (Tab. 1). Figure 6. Principal stresses on composite sandwich core layer. Edge Position This stress level explains the appearance of tensile cracs in core material. However, the load- deflection experimental curve shows an increase in the amount of deflection without any increase of the applied load. Certainly, the mechanical properties available (Tab. 1) would not the material behavior changes. Figure 7 shows the principal stresses reached in the leftmost sin layer material. The sin tensile and compressive stresses are approximately 30% below the maximum stress levels (Tab. 1). Based on the core stress level, expect outcome would be a failure of the core material. The experimental observation mentions that the core tensile cracs did not progress due to the presence of vertical sin layers. The constant load-deflection plateau represents a stress

7 redistribution leading to progressive compressive and tensile sin failure. Additional mechanical properties are needed to simulate the non-linear behavior. We can conclude that the fem models predict close enough the experimental observations. However, the models would need more mechanical properties to characterize the delamination and other experimental measures. 4. REFERENCES Figure 7. Principal stresses on composite sandwich leftmost sin layer. Edge Position Manalo, A.C., Aravinthan, T., Karunasena, W, Flexural Behaviour of Laminated Fibre Composite Sandwich Beams. The Second Official International Conference of International Institute for FRP in Construction for Asia- Pacific Region. APFIS, South Korea, December, 2009 Van Erp, G, Rogers, D A highly sustainable fiber composite building panel Proceeding of the International Worshop on Fibre Composites in Civil Infrastructure Past, Present and Future. December 2008, University of Southern Queensland, Toowomba, Queensland, Australia. Islam, M.M., Aravinthan, T., Van Erp, G., Behaviour of Innovative Fibre Composite Sandwich Panels under Point Load. The Second Official International Conference of International Institute for FRP in Construction for Asia- Pacific Region. APFIS, South Korea, December, 2009 Reddy, J An introduction to the finite element method.. McGraw-Hill, Inc. Reddy, J Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press. Gibson, R Principle of Composite Materials Mechanics. CRC Press 5. RESPONSIBILITY NOTICE The author(s) is (are) the only responsible for the printed material included in this paper.

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