1 Finite Element Analysis of Cut-Outs Advanced Materials Subjected to Compressive Buckling Load Hakim S. Sultan Aljibori W.P. Chong Engineering Department, College of Applied Sciences-SoharSultanate of Oman Email: [email protected] Mechanical Eng. Department, Faculty of Engineering, University of Malaya- Malaysia Abstract—A further study is carried out to continue the previous research, at which the work has been published in Journals of Materials and Design 31 (2010) 466-474 (available at Science Direct- Elsevier). Experiment work has been performed on the composite materials plates by using INSTRON machine. A simulation technique has been performed in this present research, but a new research element is added, that is finite element analysis was performed simultaneously. In present research, numerical study of the buckling response of compression-loaded quasi-static six layers woven cross-ply [0º/90º/0º]s laminated composite materials plates cutout is presented. The objective of this study is to obtain the buckling load with the effect of cutout sizes and cutout shapes numerically and compare that with experimental work. The experiment buckling loads are compared with the results obtained by ANSYS simulation program. Both experimental and numerical results are having a very good agreement. Results have shown that the size of cutout is getting larger; the buckling load of the plate is decreasing. Findings are also showing that the cutout area, cutout ratio (D/W), fiber weight, plate thickness and fiber type of the plate has a significant effect to the buckling load of the cross-ply laminated composite plates. Keywords: Composite materials, cutouts laminated plate, buckling load, compression, and cross-ply laminated. I. INTRODUCTION1 Rapid growth and huge demands from the transportation and manufacturing industries are making most of the products are fabricated by the advanced materials especially fiber reinforced composite materials, to meet the requirements of advanced design, cost saving, physical and chemical properties for the safety reasons. By now, our society faces the high-price oil and high-price raw materials crisis causing a high impact in the transportation industries, “This work was supported in part by the Mechanical Engineering Department University of Malaya”. Author Hakim S. Sultan Aljibori, Engineering Department, College of Applied Sciences-Sohar- Sultanate of Oman (e-mail: [email protected] Author W.P. Chong, Mechanical Eng. Dept, Faculty of Engineering, University of Malaya- Malaysia one practical solution is to reduce the structural weight but maintain or increase the payload efficiency at the same time [1]. It caused the use of composite materials are in widely and fast developing progress in some industries like aerospace, marine, automotive, biomedical, civil, military services and etc., due to their excellent mechanical properties such as high impact-strength (strength-to-weight ratio), high stiffness-to-weight ratio, high tear resistant, ease to handle and low fabrication cost [2-4]. Those industries have driven much of the development of our most sophisticated composite systems nowadays. Cut-outs are provided in structural components for ventilation, stability maneuverability and sometime to lighten the structure. For instance, aircraft components like wing, spar, fuselage and ribs, cutouts are necessary for accessing, inspection, electric and hydraulic lines, fuel lines as well as to reduce the overall weight of the aircraft. Cutouts are often found in composite structures [4]. During operation, these structural elements may experience compressive loads and thus lead to buckling. Hence, structural instability becomes a major concern in safe and reliable design of the composite materials. Woven fabric fiber is a way of weaving by interlacing the fiber thread of the weft and warp on a loom [5]. Many researchers have carried out the buckling behavior of laminated plates experimentally. Hakim et al., Ghannadpour et al. and P. Nemeth [5-9] investigated the buckling behavior of the laminated composite plates due to circular/elliptical cutouts under compression. Both studies have showed that the effects of cutout size, shape, plate aspect ratio, fiber orientations and stacking sequences, and boundary conditions have a significant effect on the buckling behavior of the plates. Züleyha Aslan & Sahin M. [10] examined the effects of delaminations size on the critical buckling load and compressive failure load of E-glass/epoxy composite laminates with multiple large delaminations experimentally and numerically. They discovered that the longest and nearsurface delamination size influences the buckling load and compressive failure load of composite laminates. Compressive buckling analysis on metal-matrix composite (MMC) plates with central square holes was performed by Fig. 1: The determination of the buckling load [14] L. Ko [11]. Study showed that by increasing the hole sizes, compressive buckling strengths of the perforated MMC plates could be considerably increased under certain boundary conditions and aspect ratios. M. F. Altan & M. E. Kartal [12] also investigated the changes of buckling coefficients of symmetrically laminated reinforced concrete plates with central rectangular hole under biaxial static compression loadings. x [0º/90º/0º] s l e II. PROCEDURE AND BUCKLING LOAD OF LAMINATED t COMPOSITE PLATES In the work of Laurin et al. [13], it has been derived that the mathematic model of buckling of laminated composite plate. The buckling load of a thin composite cross-ply laminated plate with a ratio R = l/w, simply supported and subjected to a compressive loading is presented. The buckling load per unit length is given by N xcr 2 A 2 2 4 m A11 2 R A12 2 A66 222 R l m 2 (1) d d Plate thickness (t) in mm: E-glass (600 g) = 3.230 E-glass (400 g) = 2.320 Carbon (400 g) = 1.625 Kevlar-29 (200 g) = 2.200 Six layers w Where l is the plate length, w is the plate width, m is the buckling mode, A is the bending stiffness of the laminate given by the following relation: A 3 h 1 3 k 1 hk3 Q k (2) Fig. 2 Geometry of laminated composite material plate k Where the subscript k indicates the kth layer from the top of laminate, hk and hk+1 are respectively the distance from the mid-plan to the bottom and the top of the kth layer and Qk is the stiffness expressed in the laminate axis of the kth layer. The first-buckling mode is the one that leads to the buckling load and thus depends on the ratio A11/A22. Laminate composite plates constituted by plies of the sane orientation but with different stacking sequences could exhibit different A11/A22 ratios (and thus different buckling loads). Buckling load is the compressive load which is just sufficient to bend the plate slightly, the plate will remain straight after the load is releasing. For the determination of buckling load graphically, the last point on the curve where just left from the straight line and the value of this point on the y-axis is called as the buckling load as illustrated in Figure 1. III. DETERMINATION OF THE MECHANICAL PROPERTIES OF LAMINATED COMPOSITE PLATE The mechanical properties of laminated composite plates are obtained under quasi-static loading conditions according ASTM standards. Average mechanical properties of the laminated composite materials obtained from the experiment results are listed in Table 1. In this table, Ex, Ey and Ez are Young’s modules corresponding to x, y and z planes; Gxy, Gyz and Gxz are the shear modules corresponding to x-y, y-z and x-z planes, respectively; and Prxy, Pryz and Prxz are the corresponding Poisson’s ratios. 1. TABLE1 MECHANICAL PROPERTIES OF LAMINATED COMPOSITE Ex Ey Ez Prxy=Pryz=Prxz Gxy=Gyz=Gxz Fiber (GPa) (GPa) (GPa) (GPa) type E-glass (400 gram) Carbon (400 gram) Kevlar29 (200 gram) 72.40 7.10 7.10 0.22 2.40 224.00 14.00 14.00 0.20 14.00 61.00 4.20 4.20 0.35 2.90 IV. NUMERICAL BUCKLING ANALYSIS In the present study, buckling analysis is carried out for the laminated composite plates with and without central circular/square cutouts. These plates are analyzed by using 3 ANSYS package. The buckling load is determined by solving for eigen-values and the corresponding eigenvectors represents the buckled mode shape. Figure 3 shows the boundary conditions and typical finite element mesh as same as experimental conditions. As the element type, SHELL Layered 99 element with six degree of freedom is selected, and structural elastic with orthotropic material is chosen. Real constant was defined by entering the values of number of layers, fiber angle orientations and ply’s thickness. The sketch of real constant model is shown in Figure 4. Mechanical properties are shown in the Table 1. To simulate clamped loaded edges, the displacement UX, UY, UZ and the rotations ROTX, ROTY, ROTZ of all nodes at edges are set equal to zero. To mesh the shell model, free and mapped meshing with “concatenating” operation is used. Better meshing skill is important to yield better and accurate results. The meshing of the test specimens are illustrated in Figure 5 by the ANSYS program. To apply loading on the top of the shell model, a unit pressure is applied along the upper nodes. As to perform eigen-buckling, pre-bucking system is switched on and extraction mode is operated before proceeding to final result. Finally, the buckling load of the first buckling mode is always as our favorite result, normally. Pressure UX, UZ, ROTX, ROTY, ROTZ = 0 Free edge Free edge UX, UY, UZ, ROTX, ROTY, ROTZ =0 Fig. 3 Boundary, loading and meshing conditions of laminated composite 0º 90º 0º Ply 6 0º Ply 5 90º Ply 4 0º Ply 3 Ply thickne ss Ply 2 Ply 1 Fig.4: Number of plies, fiber orientations and thickness of composite Fig. 5: The meshing of test specimens (a) fine plate, (b) plate with central circular cutout, and (c) plate with central square cutout V. RESULTS AND DISCUSSION In this present work, the buckling load results are obtained experimentally and numerically for cross-ply [0º/90º/0º]s laminated composite plates with and without central circular/square cutouts, of which including the E-glass fiber 400 gram types, carbon fiber 400 gram types and Kevlar-29 fiber 200 gram types; except the E-glass fiber 600 gram types which is performed experimentally only. The experimental results produced the load-displacement curve of each of the specimens, while the numerical results are obtained from the nodal solution graphics simulated by ANSYS program. The experimental and numerical buckling loads for all the test specimens are summarized in Table 2. It is seen from this table, the agreement between the experiment and finite element prediction is showing good. For E-glass fiber 400 gram type plates, the differences are in between 0.03 – 2.47 %; for carbon fiber 400 gram type plates, the differences are found in the range 0.52 – 2.70 %. The differences for the Kevlar-29 200 gram type plates are slightly higher, dropped at 1.47 – 8.24 %, although these are acceptable. Also, it is observed that the buckling load is greatly depending on its cutout size (preferable in term of cutout ratio, d/w). As cutout ratio increases, the buckling load is decreasing. It is also found that the buckling load of the plate with central circular cutout is higher than the plate with central square cutout. In additional, for the same cutout size’s plate, the carbon fiber plate always has the highest buckling load, following by the E-glass fiber plate and Kevlar-29 fiber plates. The buckling load of the plate is affected by their fiber weight and thickness as well. Figures 6–8, from (a) – (c) show the nodal solution graphics for the cross-ply laminated composite plates, with and without central circular/square cutouts, respectively. All the results of the specimens is tabulate in Table 2 2. TABLE 2 SUMMARY OF THE EXPERIMENTAL AND NUMERICAL BUCKLING LOAD OF LAMINATED COMPOSITE PLATE Experime NumeriCut-ntal cal Differn Plate Cutout out buckling Buckli-ces type size ratio load ng load (%) (kN) (kN) Without 0 1.15260 cutout ECircular d = 0.40 1.05771 glass 16 mm fiber Circular d = (600 0.65 0.98738 26 mm gram) Circular d = 0.90 0.81208 36 mm Without 0 0.41074 0.41052 0.05 cutout Circular d = 0.40 0.38389 0.39102 1.82 16 mm Circular d = 0.65 0.36483 0.35604 2.47 26 mm ECircular d = 0.90 0.30101 0.29784 1.06 glass 36 mm fiber Square (400 (16×16) 0.40 0.36566 0.36576 0.03 gram) mm Square (26×26) 0.65 0.34423 0.34860 1.25 mm Square (36×36) 0.90 0.27114 0.26994 0.44 mm Without 0 0.46187 0.45948 0.52 cutout Circular d = 0.40 0.43523 0.42504 2.40 16 mm Circular d = 0.65 0.40524 0.39930 1.49 26 mm Circular d = Carbo 0.90 0.35037 0.34134 2.65 36 mm n fiber Square (400 (16×16) 0.40 0.42087 0.40980 2.70 gram) mm Square (26×26) 0.65 0.39215 0.38670 1.41 mm Square (36×36) 0.90 0.32165 0.31374 2.52 mm Without 0 0.34362 0.33684 2.01 cutout Circular d = 0.40 0.27785 0.28200 1.47 16 mm Circular d = 0.65 0.25000 0.26004 3.86 26 mm Keval Circular d = 0.90 0.20195 0.22008 8.24 r-29 36 mm fiber Square (200 (16×16) 0.40 0.25490 0.26688 4.49 gram) mm Square (26×26) 0.65 0.23943 0.25266 5.24 mm Square (36×36) 0.90 0.19718 0.20220 2.48 mm a b c Fig. 6: Nodal solutions for E-glass fiber (400 gram) plates. (a) plate without cutout; (b) plates with central circular cutout d = 36 mm; (C) plates with central square cutout sizes (36 × 36) mm. 5 VI. EFFECT OF CUTOUT SHAPE a Due to the design requirements and philosophy, different cutout shape may be used. Effect of cutout shape can be seen clearly that, for the same fiber type and same cutout size, the plate with central circular cutout has higher buckling load than the one with central square cutout, nearly about 1.02 – 1.11 times. This behavior is at least partially explained by noting that, the central cutout area which was subtracted from the plate is the main cause. With the same cutout diameter or width, the area of square is higher than the area of circle. Therefore, the more area is subtracted, the more losing of mass in the central of plate, it will experience a larger loss in central bending stiffness, tends to buckle at lower loading. VII. EFFECT OF CUTOUT SIZE b c Cutout size, normally preferable referring to cutout ratio, d/w, where d is the cutout width or diameter, and w is the plate width. Many researchers tend to use this term to investigate the relationship in between of the buckling load and cutout ratio. In this study, it is clear to show that the plate has no cutout or small cutout has higher strength than the plate has larger cutout. It is because a loss of mass (less material) in the center is a loss of the interfacial bond between the matrix and fibers. The interface is responsible for transmitting the loading from the matrix to fibers, which contribute the greater portion of composite strength. As a result, as cutout size is getting bigger means the bonding is getting loosing, it will reduce the strength of plate. Inherently, it associated with the central located cutout is a loss in bending stiffness in the central region of a plate that grows in important as the central cutout size increases. As the more losing in bending stiffness caused by the increasing of central cutout size will result in reduction of buckling strength. VIII. VALIDATION OF BUCKLING LOAD AND CUTOUT RATIO Fig.7 Nodal solutions for arbon fiber (400 gram) plates, (a) plate without cutout; (b) plates with central circular cutout (d = 36 mm); (c) plates with central square cutout sizes (36 × 36) mm Agreement between the experimental buckling loads and the finite element buckling load predictions is having a very good tolerance. Figures 9 and 10 present the comparisons of buckling load vs. cutout ratio between the experimental and numerical results for all the specimens. It is seen that the results obtained from numerical buckling analysis close to experimental buckling results. As mentioned before, the buckling load of the plate decreases while the cutout ratio is increasing. In the same Figures, the comparison also has been made between the present results with the numerical results investigated by Tercan M. & Aktaş M. [14]. Tercan M. & Aktaş M. had investigated the buckling behavior of 1 × 1 rib knitting laminated plates with cutouts, which the plates are made from five layers glass fabrics and CY225 epoxy resin, with length L = 80 mm and width w = 25 mm. Their experimental works including the boundary and loading conditions are similar with the present research, therefore heir numerical results based on the same experiment set up are validated to compare. It is observed that the laminated composite plates manufactured by Tercan M. & Aktaş M. higher buckling load than the plates in this present research at low cutout ratios, it dropped evidently below the present research’s buckling loads of carbon and E-glass plates at higher cutout ratios. It is due to the different materials in used in the research and their different properties influences, with the different plate manufacturing process and cutout shapes (The eccentricity of the plates are fixed at e/w = 0.4 and varying different cutout ratios by Tercan M. & Aktaş M. in their numerical simulations). The most important evidence and similarity between the comparisons is that all the plots are showing the same trend in the buckling load vs. cutout ratio curve, noting that the buckling load of the plate decreases while the cutout ratio is increasing. IX. CONCLUSION Buckling load ( kN ) Buckling load ( kN ) An experimental and finite element analysis study of the buckling behavior of the woven composite fiber/epoxy laminated plates, with and without central circular/square cutouts subjected to quasi-static compressive loading has been presented. Four different fiber types’ laminated composite plates are fabricated to test experimentally; they are E-glass fiber 600 gram & 400 gram, carbon fiber 400 gram and Kevlar-29 fiber 200 gram. Circular cutout sizes are fixed at d = 16 mm, 26 mm and 36 mm, and the square cutout sizes are fixed at (16×16) mm, (26×26) mm, and (36×36) mm. Eigenbuckling is introduced in this study to solve the buckling load by ANSYS simulation program. From the results and discussion, the effects of fiber weight, plate thickness, fiber type, cutout size and shape on the 0.60 buckling load of the laminated composite plates are welldiscussed. In addition, the following conclusions can be summarized as below: Tercan M. & Aktaş M.[4] 0.50 a) For all cases of symmetrical laminates, the cross-ply Carbon fiber 400 gram [0˚/90˚/0˚]s laminates, this type of ply configuration is 0.40 capable of absorbing large amount of energy before E-glass fiber 400 gram fracture. b) As the central cutout size increases, the cutout 0.30 ratio increases proportionally, the buckling load of Kevlar-29 fiber 200 gram laminated composite plate will be reduced. 0.20 c) A loss of mass in the centre of the laminated composite plate will lose the interfacial bonding of its matrix and Experimental Numerical 0.10 fibers. The strength of plate will reduce as the bonding is losing. Tercan M. & Aktaş M. (fixed at plate’s e/w ratio at 0.4) [4] d) More fiber weight gain more matrixes during 0.00 composition, resulting in the increasing of plate thickness. 0 0.2 0.4 0.6 0.8 1 Cutout ratio, d/w Thicker plate produces great stiffer strength to buckling at higher load. e) The reducing of central bending stiffness of the Fig. 9 Comparisons of buckling load vs. cutout ratio for composite plates with/without central circular laminated composite plate caused by the increasing of cutouts central cutout size yields a reduction in buckling resistance of the plate. f) In same fiber type and cutout size plates, the one with central circular cutout has higher buckling strength than the 0.60 one with central square cutout. g) Carbon fibers give the best mechanical properties than Tercan M. & Aktaş M.[4] 0.50 E-glass fibers and Kevlar-29 fibers. Having the highest buckling load, great modulus and strength in low weight. Carbon fiber 400 gram 0.40 h) The low compressive strength of Kevlar-29 is due to the anisotropic properties and low shear stiffness. Although E-glass fiber 400 gram 0.30 its compressive strength is low, it undergoes a huge Kevlar-29 fiber 200 gram displacement without heavy damage and crack before its 0.20 failure. This prove that Kevlar-29 is good capable in shearing. 0.10 Tercan M. & Aktaş M. (fixed at plate’s e/w ratio at 0.4)[4] ACKNOWLEDGMENT 0.00 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Cutout ratio, d/w Fig.10 Comparisons of load vs. cutout ratio for laminated composite plates with/without central square cutouts 1 The authors would like to thank the University of Malaya, (Malaysia) and college of Applied Sciences-Sohar (Sultanate of Oman) for the financial support for experimental work and Finite element analysis. 7 REFERENCES [1] R.M. O’Higgins, M.A. McCarthy, C.T. McCarthy. 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