Civil Engineering Dimension, Vol. 19, No. 1, Marh 017, 9-5 ISSN 1410-950 print / ISSN 1979-570X online DOI: 10.9744/CED.19.1.9-5 Experimental and Theoretial Defletions of Hybrid Composite Sandwih Panel under Four-point Bending Load Fajrin, J. 1*, Zhuge, Y., Wang, H., and Bullen, F. Abstrat: This paper presents a omparison of theoretial and experimental defletion of a hybrid sandwih panel under four-point bending load. The paper initially presents few basi uations developed under three-point load, followed by development of model under four-point bending load and a omparative analysis between theoretial and experimental results. It was found that the proposed model for prediting the defletion of hybrid sandwih panels provided fair agreement with the experimental values. Most of the sandwih panels showed theoretial defletion values higher than the experimental values, whih is desirable in the design. It was also notied that the introdution of intermediate layer does not ontribute muh to redue the defletion of sandwih panel as the main ontributor for the total defletion was the shear deformation of the ore that mostly determined by the geometri of the samples and the thikness of the ore. Keywords: Defletion; four-point bending; hybrid sandwih panel; theoretial model. Introdution A onept of hybrid sandwih struture with intermediate layer has been introdued by Mamalis et al. [1] whih signifiantly enhaned the load arrying apaity of the original sandwih panel. An experimental investigation with different wood based materials for the intermediate layer in smallsale samples was onduted by Fajrin et al. [] and the results onfirmed the laim of the previous study [1]. A further investigation with statistial design of experiment approah has also onfirmed the signifiant impovement ahieved by the introdution of the intermediate layer []. It was found that intermediate layer made of jute fiber omposite and medium density fiber improved the strutural performane of the hybrid sandwih panel. The basi theoretial onept of hybrid sandwih panel with intermediate layer that established under three-point bending load sheme has been disussed throughly as reported by Fajrin [4]. 1 Department of Civil Engineering, Faulty of Engineering, University of Mataram, Mataram 8115, Nusa Tenggara Barat, INDONESIA Centre of Exellene in Engineered Fibre Composites (CEEFC), University of Southern Queensland (USQ), Toowoomba, QLD 450, AUSTRALIA *Corresponding author; e-mail: jauhar.fajrin@unram.a.id Note: Disussion is expeted before June, 1 st 017, and will be published in the Civil Engineering Dimension, volume 19, number, September 017. Reeived 07 Otober 016; revised 06 January 017; aepted 4 February 017. The established model showed the potential of the onept to improve the flexural rigidity and stiffness of the sandwih panel. The hybrid sandwih panel ontaining intermediate layer with intermediate properties between the skins and ore, generates a higher stiffness by only a slight inrease in weight ontributed by intermediate layer. More reently, the behaviour of the new developed panel under in-plane shear loading has been reported [5], whih speifially foused on statistial analysis of the results. In the real appliation, however, it is also important to evaluate the performane of a struture under a pure bending load sheme (four-point bending load). This paper disusses the development of theoretial model of hybrid sandwih panel with intermediate layer under four-point bending load. The omparison of theoretial and experimental defletion were provided. This paper presents few basi uations developed under three-point load, followed by the development of model under four-point load and a omparative analysis between theoretial and experimental results. Basi Conept of the New Developed Hybrid Composite Sandwih Panel The researh work fouses on introduing a new layer in between the skin and the ore of a standard sandwih panel struture to form a hybrid struture. A natural fiber omposites (NFC) laminate is plaed as an intermediate layer in between aluminum skin and expanded polystyrene (EPS) ore to produe a hybrid omposite sandwih panel as shown in Figure 1(b). Hene, this new struture is a ombination of two omponents; a panel with aluminum skins and EPS ore as an integrated sandwih struture and 9
Fajrin, J. et al../ Experimental and Theoretial Defletions of Hybrid Composite / CED, Vol. 19, No. 1, Marh 017, pp. 9 5 intermediate layer laminates made of NFC that resulting in a hybrid struture. When a monolithi panel manufatured as a homogeneous material is subjeted to a loading sheme, the typial stress distribution is a straight diagonal line from the top to the bottom surfae as shown by the dotted-line in Figure 1. The stress distribution, however, will have a onsiderable transformation at the top and bottom interfae between the skin and ore layers for sandwih struture, as shown in Figure 1(a). Many authors have identified the stress disontinuity as a prime ontributor for failure in sandwih panel. The idea of introduing an intermediate layer, whih has intermediate properties between the skins and ore, is to redue the problem, as depited in Figure 1(b). This onept an be best explained using the Hooke s laws whih relate indued stress to the material s modulus of elastiity. When intermediate layers with elasti modulus between those of the skin and ore are inserted, the abrupt step between the high and low stresses within the skins and ore an be redued. This onfiguration, of two layers of skins and intermediate layers and the ore in between, theoretially generates a higher flexural strength for the sandwih panel. Davies [6] highlighted that in sandwih onstrution, the yield stress of skin material is of less onern beause the load arrying apaity of the struture is typially determined by wrinkling of the fae in ompression or by the shear failure of the ore. It is thus beomes ruial to provide more lateral support for the fae by introduing another layer between those of the faes and ore. The urrent ommon approah to address the issue is either inreases the faes thikness or improves the quality of the ore. Both approahes however may have signifiant impat on the overall ost. The prie of skin material is normally expensive, while the prie of the ore is muh less than that of the skins, but an inreased thikness of the ore an also result in higher overall ost. Figure 1. Typial Stress Distribution in Sandwih Panel: (a) Conventional Sandwih Panel and (b) Hybrid Sandwih Panel with Intermediate Layer Development of Theoretial Frameworks for Defletion under Four-Point Bending Load In a homogeneous material, the defletion due to shear is often negleted. For a sandwih panel, however, the ore material is usually not rigid in shear and thus the defletion is not negligible in most ases [7]. The defletion, δ, of a homogeneous beam under three-point bending load is given by: FL 48EI (1) In whih F is the applied load and L is the span length, while EI is the flexural rigidity whih is the produt of the modulus of elastiity (E) and the seond moment of area (I). In the ase of sandwih panel, this uation an be modified as [8]: FL () 48(EI) The ontribution of the ore shear to the defletion of sandwih struture that is ommonly negleted in ordinary beam analysis an be obtained as per Equation [8]. FL () 4(AG) Where A is the area and G is the shear modulus of the ore material. The total defletion at the enter point of sandwih beam an be obtained by Equation 4: FL FL (4) 48(EI) 4(AG) For the flexural properties of sandwih struture under four-point bending load, ASTM C 9-00 [9] stated that the total defletion is a sum of defletion due to bending and shear as shown in Equation 5, where D (N-mm ) is the stiffness, U (N) is the panel shear rigidity, P (N) is the applied load and L (mm) is the span length. 11PL PL 768D 8U (5) The above uation is derived from a flexural test under four-point bending load at quarter point loading span, as shown in Figure (a). Under a fourpoint bending load with third point loading sheme in whih the two point loads applied at an ual distane (L/) of the span length, as depited in Figure (b), Roylane [10] reommended the following uation: 0
Fajrin, J. et al../ Experimental and Theoretial Defletions of Hybrid Composite / CED, Vol. 19, No. 1, Marh 017, pp. 9 5 P(L a) L (x) (x a) x (L a) ) x 6LEI L a Pa L (x (L a)) x (L a ) x (6) 6LEI a Figure. Deformation due to Core Shear under Fourpoint Loading Sheme [4, 8]. Hene, the total defletion under four-point bending load is a linear superposition of the defletion due to bending and shear, whih gives: PL PL (1) 196(EI) 6(AG) The above uation onfirms the uation derived by Manalo et al. [11] for sandwih panel beam in flatwise position: PL PL (1) 196D 6AG Figure. Two Alternatives for Applying Load in Fourpoint Bending Load Sheme as Desribed in ASTM C 9-00 [9]. (a) Quarter Point Loading Sheme, and (b) Third Point Loading Sheme. For the third load sheme, ual load distane was applied, with a = L/ and x = L/. Inluding these two values in the above uation results in: PL 196EI (7) For sandwih panel, this uation an be modified as PL (8) 196(EI) As mentioned earlier, the ontribution of shear defletion should be onsidered in sandwih panel espeially when a low density ore is employed. The deformation under four-point bending load is shown in Figure. The defletion of the loading point due to this deformation mode is given by the following uations [4,8]: L / Q G bd (9) Q(L / ) (10) G bd Sine in third point bending load, Q = P/, then PL (11) 6(AG) In whih D is the uivalent flexural rigidity. Determining shear modulus of ore material (G) experimentally is tehnially diffiult. Somayaji [1] suggested the following relationship as a onvenient proedure to establish suh value: E G (14) (1 v) For onventional sandwih panel, (EI) is defined by Equation 15 [7,8]. (EI) bt btd b E f E f E (15) 6 1 Where t is the thikness of the fae, b is the panel width, d is the distane between the midplanes of the upper and bottom faes and is the ore thikness. Ef and E are the elasti modulus of the skins and ore respetively. While for hybrid sandwih panels with intermediate layer, it is alulated based on Equation 16 as proposed by Fajrin [4]. (EI) bt bt d bt bt d f f 1 i i bt E f Ei E (16) 6 6 1 Where d1 and d are the distane between the midplanes of the upper and bottom faes and intermediate layer respetively. The thiknesses of materials; fae, intermediate layer and ore are denoted as tf, ti and t respetively. Ef, Ei and E are 1
Fajrin, J. et al../ Experimental and Theoretial Defletions of Hybrid Composite / CED, Vol. 19, No. 1, Marh 017, pp. 9 5 the modulus elastiity of onstituent materials; fae, intermediate layer and ore respetively. Sample Preparations and Experimental Program In order to verify the developed model, two stages of experimental work with medium and large sale samples were onduted subsuently. For medium sale; two groups of hybrid sandwih panels with jute fibre omposites (JFC) and hemp fibre omposites (HFC) intermediate layer were ompared to a group of samples without intermediate layer as the ontrol (CTR). The thikness of the intermediate layer was maintained at mm. Eah group of samples was repliated 5 times so that a total of 15 samples were tested in medium sale. The length of span was 450 mm and the samples were ut into the size of 550 x 50 x mm for length, width and thikness, respetively. An aluminium sheet was ut into the ruired size for the skins, with the thikness of 0.5 mm for all samples. While expanded polystyrene (EPS) was employed for the ore with a thikness of 1 mm for CTR speimens and 15 mm for hybrid sandwih panels (JFC and HFC). All medium sale samples were maintained to have a onstant overall thikness of mm. A similar arrangement was also used for the large sale experiment; three speimens groups whih inlude two groups of hybrid sandwih panels and a group of onventional sandwih panels as the ontrol. The large sale samples were shaped in the size of 1150x100x5 mm with the span length of 900 mm. Jute fiber omposites (JFC) and medium density fiber (MDF) were used for the intermediate layer of large sale samples with the thikness of 5 mm. Similarly, the ore of sandwih panel was an EPS foam with a thikness of 50 mm for CTR samples and 40 mm for hybrid panels (JFC and MDF). Aluminium sheet with a thikness of 1 mm was employed as the fae of all samples in large sale experiment. A total of 15 samples that omprises of 5 samples for eah group were tested in the large sale experiment. The flexural testing was arried out using a 100 kn servo-hydrauli mahine with a loading rate of 5 mm/min. The longitudinal strains were measured using strain gauges attahed at the middle top and bottom surfae of samples. A system 5000 data logger reorded all the applied load, defletion and strains. The testing proess were started by setting the loading pins to nearly touh the top surfae of the speimen and terminated after a visible ollapse mehanism was enountered. The testing was also terminated when the speimen undergoing large displaement without any inrease in load. The atual set up of flexural testing is presented in Figure 4. Figure 4. The Atual Set-up of Testing under Four-point Bending Load. (a) Testing Set-up for Medium Sale Samples, and (b) Testing Set-up for Large Sale Samples. Results and Disussion The theoretial values of defletion were estimated as per Equation 1 with the orresponding uivalent bending stiffness, (EI), for onventional and hybrid sandwih panels. The bending stiffness of onventional sandwih panel is alulated as per Equation 15, while for hybrid sandwih panels, it is alulated based on Equation 16. The results are presented in Table 1 and Table. In order to simplify the analysis, only two samples were seleted for eah group to be disussed throughly. For the same reason, the analysis was only foused to ompare the defletion of sandwih panels under two partiular loads (P), whih is 50 N and 100 N. Medium Sale Samples Table 1 presents the theoretial defletion (theo) and experimental defletion (exp) values of medium sale sandwih panels in the linear elasti region. As mentioned earlier, two partiular loads (P) have been hosen in the elasti region of the load-defletion urve, whih are 50 N and 100 N for the omparison purposes. In general, the experimental values were in reasonable agreement with the theoretial values. The differenes range from.9% to 5.4%. Most of the sandwih panels showed experimental values lower than the theoretial values, whih aording to Teles et al. [1] an be onsidered as highly desirable in the design. It an also be seen that for the seleted samples in CTR group (CTR-1 and CTR-), the differene between theoretial and experimental values ranges from 17.1% to 5.4%. While the seleted samples in JFC group (JFC- and JFC-5), the theoretial framework tended to underestimate the experimental defletion values. The theoretial estimation were approximately 4%-.1% lower than the experimental values. Meanwhile, the theoretial defletion values for sandwih panel in HFC group
Fajrin, J. et al../ Experimental and Theoretial Defletions of Hybrid Composite / CED, Vol. 19, No. 1, Marh 017, pp. 9 5 Table 1. Theoretial and Experimental Defletion Values of Medium Sale Sandwih Panels Samples Geometri b P % CTR JFC HFC 1 5 1 5 51.57.80 4789906 50 0.17 1.18 1.5 1.0 1.5 5.4 51.57.80 4789906 100 0.4.7.71.0 1.5 5.4 51.0.0 45111811 50 0.18 1. 1.41 1. 1.17 17.1 51.0.0 45111811 100 0.6.45.81. 1.. 50.0 15.0 50915545 50 0.16 1.85.01.1 0.96-4.5 50.0 15.0 50915545 100 0..69 4.01 6.0 0.67 -.1 50,00 15.05 5070971 50 0.16 1.86.0.1 0.96-4.0 50,00 15.05 5070971 100 0..71 4.0 6.0 0.67 -.8 50.50 16.55 54661658 50 0.15 1.67 1.8 1.9 0.96-4. 50.50 16.55 54661658 100 0.0.4.64.5 1.04.9 5.50 17.0 601680685 50 0.1 1.55 1.68 1.4 1.0 0.1 5.50 17. 601680685 100 0.7.09.6.0 1.1 1.1 (HFC-1 and HFC-5) were higher than the experimental values, exept for speimen HFC-1 under 50 N load. The differene within the HFC group ranges from.9% to 0.1%. Table 1 also shows the geometris of samples; width (b) and ore thikness (t). The uivalent bending stiffness, (EI), of both onventional and hybrid sandwih panels is also presented within the table, as well as the defletion due to bending (b) and the defletion due to shear (s). It is learly shown that the hybrid sandwih panels provide reasonably higher uivalent bending stiffness. The result is ertainly not surprising sine the hybrid sandwih panels embedded an intermediate layer whih was onsidered when estimating the uivalent bending stiffness. Theoretially, when bending stiffness inreased the defletion should be dereased. However, it is not always the ase in sandwih panels as shown in Table 1. Under the same load, the defletion of hybrid sandwih panel even higher than those of onventional sandwih panels. For example, the sandwih panels with JFC and HFC intermediate layer have the theoretial defletion values of.0 mm (JFC-5) and 1.8 mm (HFC-1), respetively. While onventional sandwih panel without intermediate layer (CTR) has a theoretial defletion value of 1.5 mm (CTR-1). The reason for this an be learly obtained by heking the ontribution of bending and shear deformation of the ore to the overall defletion. As seen in Table 1, bending only ontributes around 8% to 1% to the total defletion. For instane, the defletion due to bending for speimen CTR- under 100 N load was 0.6 mm, whih was only 1.81% of the overall defletion of.81 mm. On the other hand, shear deformation ontributes 87.19% to the total defletion (.45 mm). Overall, the shear deformation of the ore, whih has very low shear modulus (G =.69 MPa), was the main ontributor for the overall theoretial defletion, approximately 87% to 9%. The result onfirms the finding reported by Sharaf et al. [14] whih stated that the shear deformation is the signifiant ontributor for the overall defletion of sandwih panels with soft ore. More speifially, they reported that the ontribution of shear deformation to the overall defletion is about 75% for sandwih panel with soft ore and approximately 50% for hard ore [14]. It seems that for defletion due to shear deformation of the ore, as per Equation 11, the ontribution of samples geometri, the width and the thikness of the ore, is ruial. As seen in Table 1, the thiknesses of CTR samples ore (t) were substantially higher than those of hybrid sandwih panel with JFC and HFC intermediate layer that resulting in smaller defletion. The thiknesses of the ore for CTR group in medium sale samples showed in the table were around.-.8 mm. While the ore thiknesses of hybrid sandwih panels were measured around 15. to 17. mm. Large Sale Samples The theoretial and experimental defletion values of the larger sale sandwih panels were presented in Table. Similar to the values for medium sale samples, there is reasonably agreement between the theoretial and experimental findings that range from.7% to 6% within the elasti region of loaddefletion urves. For the large samples, it was observed that the experimental values were mostly lower than the theoretial values. The theoretial defletion values for sandwih panels with JFC intermediate layer are, however, lower than the experimental values. For the ontrol group, the differene was approximately 8.9% to 6%. Within JFC group, the values differ by 6.% to 5.% while for MDF group the differene ranges from % to 11.%. The ontribution of shear deformation of the ore to the total defletion of large sale samples is also signifiant whih ranges from 88% to 9% meaning that the
Fajrin, J. et al../ Experimental and Theoretial Defletions of Hybrid Composite / CED, Vol. 19, No. 1, Marh 017, pp. 9 5 Table. Theoretial and Experimental Defletion Values of Large Sale Sandwih Panels Samples Geometri b P % CTR JFC MDF 4 4 5 101. 51.90 9666786849 50 0.07 0.5 0.60 0.55 1.09 8.9 101. 51.90 9666786849 100 0.1 1.06 1.0 0.95 1.6 6.0 99.5 51.17 94807464 50 0.07 0.55 0.6 0.55 1.1 1.5 99.5 51.17 94807464 100 0.14 1.10 1.4 1.1 1.1 1.5 100.7 40. 117045155 50 0.06 0.69 0.75 0.8 0.9-6.7 100.7 40. 117045155 100 0.11 1.8 1.49.0 0.75-5. 100. 40.17 1198051840 50 0.06 0.69 0.75 0.8 0.94-6. 100. 40.17 1198051840 100 0.11 1.9 1.50.0 0.75-4.9 99.6 9. 9908906154 50 0.07 0.71 0.78 0.7 1.11 11. 99.6 9. 9908906154 100 0.1 1.4 1.56 1.5 1.04.7 100.7 9.0 99675977 50 0.06 0.71 0.77 0.7 1.10 10.4 100.7 9.0 99675977 100 0.1 1.4 1.55 1.5 1.0.0 ontribution of bending was only about 8% to 1%. Overall, the defletion of hybrid sandwih panel was slightly larger than those of onventional sandwih panel although they have higher uivalent bending stiffness. Conlusions The experimental study of hybrid sandwih panels with intermediate layer has been arried out under four-point stati bending loads. Two main findings are outlined as follows. First, the proposed model for prediting the defletion of hybrid sandwih panels provided fairly agreement results with the experimental values. The differenes range from.9% to 5.4%. Most of the sandwih panels showed experimental values lower than the theoretial values that an be onsidered as highly desirable in the design. Seond, the introdution of intermediate layer does not ontribute muh to redue the defletion of sandwih panel as the main ontributor for the total defletion was the shear deformation of the ore that mostly determined by the geometri of the samples and the thikness of the ore. Aknowledgements The authors would like to aknowledge The Centre of Exellene in Engineered Fibre Composites (CEEFC), University of Southern Queensland (USQ) for providing aess to laboratory failities. Also, the authors would like to greatly appreiate the sponsorship from the Government of Indonesia through DGHE Projet and The University of Mataram, whih made this researh possible. Referenes 1. Mamalis, A.G., Spentzas, K.N., Pantelelis, N.G., Manolakos, D.E., and Ionnidis, M.B., A New Hybrid Conept for Sandwih Strutures, Composite Strutures, 8, 008, pp. 5-40.. Fajrin, J., Zhuge, Y., Bullen, F., and Wang, H., The Implementation of Statistial Inferene to Study the Bending Strength of Sustainable Hybrid Sandwih Panel, Advaned Material Researh, 50-5, 011, pp. 956-961.. Fajrin, J., Zhuge,Y., Bullen, F., and Wang, H., Signifiane Analysis of Flexural Behaviour of Hybrid Sandwih Panels, Open Journal of Civil Engineering,, 01, pp. 1-7. 4. Fajrin, J., Alternative Theoretial Frameworks for Hybrid Sandwih Panel with Intermediate Layer, Jurnal Rekayasa Sipil, 11(), 015, pp 1-11. 5. Fajrin, J., The Appliation of Statistial Design of Experiments to Study The In-Plane Shear Behaviour of Hybrid Composite Sandwih Panel, Civil Engineering Dimension, 18(1), 016, pp 5-0. 6. Davies, J.M., Lightweight Sandwih Constrution, Blakwell Siene, 001, London. 7. Zenkert, D., An Introdution to Sandwih Constrution, Solihull, EMAS, 1995. 8. Deshpande, V.S., The Design of Sandwih Panels with Foam Cores, Leturing Handout, Cambridge University, 00. 9. ASTM Standard C 9-00, Standard Test Method for Flexural Properties of Sandwih Constrution, ASTM International, 000, Philadelphia, Pa 1910. 10. Roylane, D., Beam Displaements, Department of Materials Siene and Engineering, Massahusetts Institute of Tehnology, 000, Cambridge, USA. 11. Manalo, A., Aravinthan, T., Karunasena, W., and Islam M.M., Flexural Behavior of Strutural Fiber Composite Sandwih Beams in Flatwise and Edgewise Positions, Composite Strutures, 9 (4), 010, pp. 984-995. 1. Somayaji, S., Civil Engineering Materials, Prentie Hall, 1995, Englewood, New Jersey, USA. 4
Fajrin, J. et al../ Experimental and Theoretial Defletions of Hybrid Composite / CED, Vol. 19, No. 1, Marh 017, pp. 9 5 1. Teles, R.F., Menezzi, C.H.S., Souza, F., and Souza M.R., Theoretial and Experimental Defletions of Glued Laminated Timber Beams Made from Tropial Hardwood, Wood Material Siene and Engineering, 01, pp. 1-6. 14. Sharaf, T., Shawkat, W., and Fam, A., Strutural Performane of Sandwih Wall Panels with Different Foam Core Densities in One-Way Bending, Journal of Composite Materials, 44 (19), 010, pp. 49-6. 5