Numerical Modeling and Experimental Investigation of the Failure Modes of the Cellular Foam Sandwich Structures

Transcription

1 Journal of Metals, Materials and Minerals, Vol.18 No.2 pp , 2008 Numerial Modeling and Experimental Investigation of the Failure Modes of the Cellular Foam Sandwih Strutures Jörg FELDHUSEN 1, Sirihai TORSAKUL 2 *, Alexander BREZING 1 and Sivakumara KRISHNAMOORTHY 1 1 RWTH Aahen University of Tehnology, Aahen, Germany 2 Rajamangala University of Tehnology Thanyaburi, Patumthani Abstat Reeived Nov. 17, 2008 Aepted Feb. 11, 2009 The use of sandwih materials an lead to eonomial advantages in many appliations by means of weight redution. In spite of its large demand, its distribution in the field of mehanial engineering is onstrained due to unsolved problems in the onnetion tehnology and unertainties in the mehanis of suh strutures. Hene, in this field, there exists a demand for the support of engineers who failitate the design of sandwih strutures. This paper desribes the methods, utilizing strategies for 3D-modeling and the simulation of sandwih strutures by using the ommerial FEM-System ALGOR and its interfae with a CAD-system. The four-point bending test was performed in order to determine the load-defletion behaviour of a sandwih plate under stati loading onditions. In the experimental part of this work, the simulated loading ase was tested repetitively on a servo-hydrauli mahine. The linear elasti behaviour and the different failure of sandwih plate onditions were investigated. The results obtained in the assoiation with the FEM riteria, were ompared to the analytial and experimental results. The analytial data reflets that the omputed ompressive stress values failitate a good working agreement with the analytial results. The value of the shear stresses from the simulation was approximately 0.26 MPa, while aording to the empirial formulas by Zenkert, the alulated shear stress aounts to be 0.29 MPa. The results from experiment show that the ore shear failure takes plae in the region predited by FEM omputations. Key words : Sandwih material, Modelling and simulation, FEM-Software, Four-point bending, Shear stress Introdution A sandwih material is a omposite material. A Sandwih struture usually onsists of two thin, stiff, strong sheets of omposite material separated by a relatively soft ore material. (1,2) Faes and ore are then bonded together to form an effiient load arrying assembly. Lightweight sandwih onstrutions are used to inrease the speifi stiffness, whih formulate the strengthening of strutures for funtional and eonomial reasons. (3) The fae arries tensile and ompressive stresses, whereas the ore arries transverse fores as well as shear stresses. (4) The priniple of sandwih onstrution is well established in the fields of shipbuilding and aerospae tehnology. Nowadays, sandwih panels an be found in many other tehnologial fields suh as in high-speed ferries, high-speed passenger trains, marine industry, building industry or automotive appliations. Espeially in the naval industry, there is a strong trend to use sandwih shells in the onstrution of ship hulls. Other innovative examples inlude ivil engineering strutures, suh as highway bridge deks. (5,6) An effetive understanding of the sandwih mehanis is neessary for effetive design. Designers of sandwih panels must ensure that all potential failure modes are well onsidered in their analysis. The Finite Element Method (FEM) is a ommon and most effetive tool for strutural analysis of sandwih onstrution. In the frame work of this paper, modelling, simulation and experimental verifiation of PURfoam ore with steel faes for stati loading onditions are onsidered. The faes and ore materials were assumed to be linear-elasti and Phone (+49) , (+49) * storsakul@yahoo.om Phone , Fax

2 112 FELDHUSEN, J. et al. isotropi material. A simulation model based on the finite element method is onsidered to simulate a four point bending test. The failure modes of sandwih plates are arried out using the ommerial finite element ode ALGOR V18. The FE-Models refer to the analysis performed using solid elements and plate elements. The four-point bending test is then performed in order to verify the failure modes behaviour of a sandwih plate under stati loading. The sandwih theory presented by Allen and Zenkert, (1,7) is used to ompute the behaviour of sandwih plate. The aim of this work is to analyse the mehanial behaviour of sandwih plate by using FEM, in order to predit failure modes of suh strutures for design appliations. The obtained results onur exellent with the experiments and the analytial omputations. FE-Modelling Sandwih materials are modelled here by assembling standard finite elements to form the omponents of the sandwih, the faes and the ore. The oplanar nodes of the faes and ore share ommon displaement. The modelling of adhesive between fae and ore is not onsidered here beause the thikness of the adhesive is too thin ompared to sandwih dimensions. Some ommerial FEM-softwares provide speial elements to model sandwih materials. These speial features are not onsidered here. The sandwih material dimensions are taken in aordane with DIN (8) (200x1440x60 mm 3.). The model here was reated using Pro/ENGINEER TM (Figure 1). This geometry information was transferred to the FEM-Software, using the standard Initial Graphis Exhange Speifiation format file (IGES). Materials and Experimental Proedures Materials Paramaters The behaviour of ellular materials theory was given by Gibson and Ashby. (7) Here, formulae for the predition of almost any mehanial parameter were empirially derived from experimental results (Formula 1). Sine foams are available in a wide range of densities, the first design problem is to hoose the right density. If proper material data tables are not available, the following formula ould be employed to determine the unknown parameters for design alulations. E k l m n = CE ρ, G = CG ρ, σ = Cσ ρ τ = C ρ, and τ The following table shows the material properties of the onsidered sandwih material. Table 1. Material parameters for the sandwih material Fae material (Steel) Core material (PUR) E [MPa] G [MPa] ν ρ [kg/m 3 ] 206,000 75, , , (1) Figure 1. Model of the Sandwih by ALGOR (9) The sandwih model onsists of solid element (BRICK) and plate element (PLATE). The solid element is used for ore material and the plate element is used for fae materials. The nodal displaement of brik element and plate element are shared at the same position. After meshing, the fae material and ore material share ommon nodes. Contat pair should be defined between the fae sheet and the ore. The type of ontat, "Bonded" was used for this model. The two surfaes were found to be in perfet ontat throughout the analysis. It was found that when a node on one surfae deflets, the node on the adjoining surfae will deflet the same amount in the same diretion.

3 Numerial Modeling and Experimental Investigation of the Failure Modes of the Cellular Foam Sandwih Strutures 113 Experimental Setup The quasi-stati tests were performed to get relevant load and displaement levels for the four-point bending tests. Speimens within onfiguration were tested at room temperature, 22 C, in a servo-hydrauli testing mahine. Speifiation of the Dimension The four-point bending test was aomplished following the DIN for sandwih materials (Figure 2). The dimensions of sandwih plate are presented in Table 2. h L B = 5h Ef d Ef L = 24h L S = 10h F L A = 20h E,G b tf tf h+ d = 2 Figure 2. Geometry of the four-point bending test, aording to DIN h Y Z X Figure 3. Sandwih plates Step and Test Equipment The sandwih plate speimens were tested with 3 kn Hydrauli press ontrolled by DYNA- MESS TM ontroller. The ontroller has been set up for a load rate of kn/s. Eah speimen has been plaed in the test apparatus as shown in Figure 4. The ylindrial loading and support rollers, made of steel and having a diameter of 60 mm, are plaed suh that the effetive beam span (displaement between support rollers) is 1,200 mm, and the loading span (distane between loading rollers) is 600 mm. A linear varying displaement transduer (LVDT) is plaed at the midspan of the sandwih plate and is onneted to the ontroller to reord displaements. Table 2. The dimensions of four-point bending test Parameters h L L A L B L S b t f D Dimension [mm] 60 1,440 1, Sandwih Plate The sandwih materials have been fabriated from steel faings and PUR foam ore. The material properties of this sandwih material are provided in Table 1. The steel faings are bonded to the PUR ore with an epoxy adhesive. The dimensions of the sandwih plates are fabriated as indiated in the standard DIN (Figure 3). Figure 4. Experiment Test Setup Experimental Proedure In this apparatus the upper (loading) rollers are moved downward against the sandwih speimen. The speimen is loaded at the rate of kn/s until failure. The displaement of the midspan of the sandwih plate is monitored during

4 114 FELDHUSEN, J. et al. the test using the LVDT desribed above. This displaement represents the defletion of sandwih plate in the vertial diretion. The applied load and the elapsed time were reorded by a plotter integrated with DYNA-MESS ontroller and by a digital data aquisition system. This digital data is used for the analytial assessment. Core shear In order to eliminate the fae sheet wrinkling mode, the fae sheet of the sandwih plate was reinfored by gluing sheet metals with a thikness of 1.5 mm symmetrially at the load transmission areas as shown in Figure 7. Result and Disussion Faesheet Wrinkling The wrinkling failure mode of the sandwih plate ours at about 3,000 N. The failure ours spontaneously at the weakest region of the sandwih plate under ompressive loading Figure 5. This failure formulates an unstable bukling of the faesheet under the longitudinal ompressive load in ombination with a ompressive failure with the ore. This ombined mode therefore eliminates the ourrene of failure at other support loads, where the faesheet will only arry tensile stress in a longitudinal diretion. Figure 5. Faesheet wrinkling Figure 7. Core shear failure by 5.5 kn As expeted, a faesheet wrinkling does not our. Instead, the sandwih speimen fails learly at a higher load of about 5.5 KN approximately. The mode of failure is shear ore failure, as seen in Figure 7. his failure ours, if the shear stress in the ore is higher than the shear strength of the ore material. Finally, it was examined whether this material failure an be predited by the FEM simulation. The highest shear stresses our between the support rollers as predited by theory, whih an be seen in Figure 8. The ompressive strength of the ore material is alulated as 0.56 MPa based on ZENK97. (7) Simulation shows that the maximum ompressive stress in the failure region during the load of 3000N is about 0.42 MPa Figure 6. Figure 8. Shear stress distribution in ore Figure 6. Compressive stress distribution in ore The omparison of the shear stress between the simulation and the theoretial alulations during the load ase of 5.5 KN was arried out.

5 Numerial Modeling and Experimental Investigation of the Failure Modes of the Cellular Foam Sandwih Strutures 115 The maximum shear stresses from the simulation an be approximated to 0.26 MPa, whereas the alulations using the empirial formulas based on ZENK97 (7), aounts to 0.29 MPa. The results show that the agreement between theory and experiment were very good. = 2τ xz 2 x 0.24 tan 2ϕ = = σ σ z ϕ = 42 x τ Figure 9. Analysis of the shear stress angle The shear stress angle an be determined by Mohr s Cile theory. Therefore, the angle of the ore shear was 42 degree, whih was good agreement with experimental result, as seen in Figure 9. Conlusions This paper gives a guideline to model the sandwih material and to predit the failure modes. The omparison of the omputation results are performed, whose results are validated by experiments. The analytial models of failure are useful for sandwih failure modes, the results of the simulation agree very well with sandwih theory. The failure modes of sandwih plate were investigated in order to ompare with the FEM results. The experimental results show that the deformations of the sandwih plate in elasti region agrees very well with the FEM results. Aknowledgements This researh has been supported by Chair and Institute for Engineering Design (IKT), Aahen University of Tehnology, Germany. Furthermore, speial thanks to the Hybrid Struture team and workshop team of IKT for their kind ooperation. Referenes 1. Allen, H.G Analysis and Design of Strutural Sandwih Panels. London : Pergamon Press Ltd. 2. Bull, P Damage Tolerane and Residual Strength of Composite Sandwih Strutures. Stokkholm : KTH Aeronautial and Vehile Engineering. 3. Pflung, J., Vagrimde, B. and Verpoest, I Material effiieny and ost effetiveness of Sandwih Materials. Leuven, Belgium : Katholieke University. 4. Burman, M Fatigue Crak Initiation and Propagation in Sandwih Strutures. Stokholm : Division of Lightweight Strutures, Royal Institute of Tehnology. 5. Hohe, J. and Libresu, L Core and Fae- Sheet-Sheet Anisotropy in Deformation and Bukling of Sandwih Panels. AIAA J. 42: Starliger, A Development of Effiient Finite Shell Elements for Analysis of Sandwih Strutures under Large Instabilities. Düsseldorf : VDI-Verlag GmbH. 7. Zenkert, D The Handbook of Sandwih Constrution. West Midlands : Engineering Materials Advisory Servie, Ltd. 8. DIN Prüfung von Kernverbunden: Biegeversuh. Deutshe Institut für Normung e.v. 9. Torsakul, S Modellierung und Simulation eines Verbunds von Sandwihplatten zur Entwiklung einer mehanishen Verbindungstehnik. A thesis submitted to the faulty of mehanial engineering of the RWTH Aahen University of Tehnology in partial fulfilment of the requirement for dotoral degree.