Buckling Analysis of Woven Glass epoxy Laminated Composite Plate A Thesis Submitted In Partial Fulfillment of the Requirements for the degree of Master of Technology In Civil Engineering (Structural Engineering) By ARUN KUMAR R Roll No-207CE208 Department of Civil Engineering National Institute of Technology Rourkela Rourkela-769008, Orissa, India May, 2009 Buckling Analysis of Woven Glass epoxy Laminated Composite Plate A Thesis Submitted In Partial Fulfillment of the Requirements for the degree of Master of Technology In Civil Engineering (Structural Engineering) By ARUN KUMAR R Roll No-207CE208 Under The Guidance of Prof. S. K. Sahu and Prof. A. V. Asha Department of Civil Engineering National Institute of Technology Rourkela Rourkela-769008, Orissa, India May, 2009 NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA – 769008, ORISSA INDIA CERTIFICATE This is to certify that the thesis entitled, “BUCKLING ANALYSIS OF GLASS EPOXY LAMINATED COMPOSITE PLATES” s u b m i t t ed by Mr. Arun Kumar R in partial fulfillment of the requirement for the award of Master of Technology Degree in Civil Engineering with specialization in Structural Engineering at the National Institute of Technology, Rourkela (Deemed University) is an authentic work carried out by him under my supervision and guidance. To the best of my knowledge, the matter embodied in the thesis has not been submitted to any other University/ Institute for the award of any degree or diploma. Date: May 30, 2009 Prof. S. K. Sahu Place: Rourkela Prof. A. V. Asha Dept of Civil Engineering National Institute of Technology Rourkela – 769008 Acknowledgments I would like to express my gratitude to my guide, Dr. S K Sahu and Prof. A V Asha, for their encouragement, advice, mentoring and research support throughout my studies. Their technical and editorial advice was essential for the completion of this dissertation. Their ability to teach, depth of knowledge and ability to achieve perfection will always be my inspiration. My sincere thanks to Dr. S. K. Sarangi, Director and Prof M. Panda, Head of the Civil Engineering Department, National Institute of Technology Rourkela, for his advice and providing necessary facility for my work. I am very thankful to all the faculty members and staffs of civil engineering department who assisted me in my research, as well as in my post graduate studies. I would also like to thank Prof. B. B. Verma and other supporting staff in the Metallurgical & Materials engineering for their help. I also thank all my batch mates, who have directly or indirectly helped me in my project work and in the completion of this report. I also thank to Shuvranshu, Ravi, and all first year students for their friendly environment in civil computer laboratory. Finally, I am grateful to my parents K.G Radhakrishnan Nair and Suchetha. V for their love, support and guidance. They have always been supportive of my academic pursuit. Arun Kumar R CONTENTS ABSTRACT............................................................................................................................................ 2 LIST OF FIGURES ................................................................................................................................ 3 LIST OF TABLES .................................................................................................................................. 4 INTRODUCTION .................................................................................................................................. 6 Review of literature............................................................................................................................. 7 Aim and scope of study..................................................................................................................... 11 THEORETICAL FORMULATION .................................................................................................... 13 Theory of bending of thin plates ....................................................................................................... 13 Buckling of composite plate ............................................................................................................. 14 EXPERIMENTAL STUDY................................................................................................................. 23 Numerical Analysis........................................................................................................................... 32 RESULTS AND DISCUSSION ......................................................................................................... 35 CONCLUSION ..................................................................................................................................... 57 REFERENCES ..................................................................................................................................... 60 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 ABSTRACT There have been numerous studies on the composite laminated structures which find many applications in many engineering fields namely aerospace, biomedical, civil, marine and mechanical engineering because of their ease of handling, good mechanical properties and low fabrication cost. They also possess excellent damage tolerance and impact resistance. The mechanical behaviour of composite structures is of particular interest to engineers in modern technology. Buckling of plates is a well-established branch of research in composite structures stability. It has a wide range of applications in engineering science and technology. Buckling behaviour of laminated composite plates subjected to in-plane loads is an important consideration in the preliminary design of aircraft and launch vehicle components. The sizing of many structural subcomponents of these vehicles is often determined by stability constraints. Plates with circular holes and other openings are extensively used as structural members in aircraft design. The buckling behaviour of such plates has always received much attention by researchers. These holes can be access holes, holes for hardware to pass through, or in the case of fuselage, windows and doors. In some cases holes are used to reduce the weight of the structure. In aerospace and many other applications these structural components are also made up of composite material to further reduce the weight of the structure. The outstanding mechanical properties of composite structures, such as durability and corrosionresistance characteristics combined with low density, make it more attractive compared to conventional materials. In this study, the influence of cut-out shape, length/thickness ratio, and ply orientation and aspect ratio on the buckling of woven glass epoxy laminated composite plate is examined experimentally. Clamped –free -Clamped-free boundary condition is considered for all case. Experiments have been carried out on laminated composites with circular, square and rectangular cut-outs. The thickness of the plate was changed by increasing the number of layers. After the buckling experiments micro electroscopic scanning was performed for the failed specimens. Comparisons are made between the test results, by using two different approach. The results shows effect of various cut-out shapes, orientation of fiber, aspect ratio and length to thickness ratio on the buckling load. National Institute of Technology, Rourkela Page 2 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 LIST OF FIGURES Figure1.a :The thin plate notation ........................................................................................53 Figure 1.b: Laminated composite plate under in-plane compression . ..................................16 Figure 2.: Inplane forces and moments on laminae ............................................................... 17 Figure3: Geometry of N layered laminate ..............................................................................19 Figure4: Instron testing machine ............................................................................................24 Figure5: Glass epoxy composite plate casting ....................................................................... 25 Figure 6: Plate with different cutout shapes........................................................................... 27 Figure 7: Test setup for clamped composite plate ...................................................................30 Figure 8: Scanning electron microscope .................................................................................31 Figure 9: Microscopic image of failed sample .......................................................................31 Figure 10: Applayed boundary condition and load.............................................................32 Figure 11: Buckled shape of aluminium plate ......................................................................36 Figure12-37: Load v/s displacement graph for composite plates ................................... 37-50 Figure 38: Buckled load v/s length to thickness ratio graph ...............................................52 Figure 39: Buckling load v/s aspect ratio graph .................................................................. 53 National Institute of Technology, Rourkela Page 3 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 LIST OF TABLES Table 1 : Plate tested in the present study. 28 Table 2 : Buckling Results of Aluminium Plate 35 Table 3 : Effect of Length to Thickness Ratio (L/t) 51 Table 4 : Effect of aspect ratio (a/b ratio) 53 Table 5 : Effect of Orientation 54 Table 6 : Effect of cut out shape 55 National Institute of Technology, Rourkela Page 4 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 CHAPTER-1 INTRODUCTION National Institute of Technology, Rourkela Page 5 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 INTRODUCTION In many engineering structures such as columns, beams, or plates, their failure develops not only from excessive stresses but also from buckling. Only rectangular thin plates are considered in the present study. When a flat plate is subjected to low in-plane compressive loads, it remains flat and is in equilibrium condition. As the magnitude of the in-plane compressive load increases, however, the equilibrium configuration of the plate is eventually changed to a non-flat configuration and the plate becomes unstable. The magnitude of the compressive load at which the plate becomes unstable is called the “critical buckling load.” A composite material consist of two or more materials and offers a significant weight saving in structures in view of its high strength to weight and high stiffness to weight ratios. Further, in a fibrous composite, the mechanical properties can be varied as required by suitably orienting the fibres. In such material the fibres are the main load bearing members, and the matrix, which has low modulus and high elongation, provides the necessary flexibility and also keeps the fibres in position and protect them from the environment. Development of new applications and new composites is accelerating due to the requirement of materials with unusual combination of properties that cannot be met by conventional monolithic materials. Actually, composite materials are capable of covering this requirement in all means because of their heterogeneous nature. Properties of composite arise as a function of its constituent materials, their distribution and the interaction among them and as a result an unusual combination of material properties can be obtained . Laminated composites are gaining wider use in mechanical and aerospace applications due to their high specific stiffness and high specific strength. Fiberreinforced composites are used extensively in the form of relatively thin plate, and consequently the load carrying capability of composite plate against buckling has been intensively considered by researchers under various loading and boundary conditions. Due to the excellent stiffness and weight characteristics, composites have been receiving more attention from engineers, scientists, and designers. During operation the composite laminate plates are commonly subjected to compression loads that may cause buckling if overloaded. Hence their buckling behaviours are important factors in safe and reliable design of these structures. National Institute of Technology, Rourkela Page 6 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 In view of difficulty of theoretical and numerical analysis for laminated structure behaviours, experimental methods have become important in solving the buckling problem of laminated composite plates. This symmetrically and laminated composite work deals with buckling analysis of plates under clamped -free –clamped- free boundary condition. The effects on buckling load by cut out size, length/thickness ratio, ply orientation, and length/breadth ratio are investigated. Review of literature Fiber-reinforced composites are used extensively in the form of relatively thin plate, and consequently the load carrying capability of composite plate against buckling has been intensively considered by researchers under various loading and boundary conditions. Thus far, there have been numerous studies on the fabric woven composite laminated structures which find widespread applications in many engineering fields namely aerospace, biomedical, civil, marine and mechanical engineering because of their ease of handling, good mechanical properties and low fabrication cost. They also possess excellent damage tolerance and impact resistance. The initial theoretical research into elastic flexural- torsional buckling was preceded by Euler’s (1759) treatise on column flexural buckling, which gave the first analytical method of predicting the reduced strengths of slender columns, and by Saint-Venant’s 1855 memoir on uniform torsion, which gave the first reliable description of the twisting response of members to torsion. However, it was not until 1899 that the first treatments were published of flexural-torsional buckling by Michell and Prandtl, who considered the lateral buckling of beams of narrow rectangular cross-section. Their work was extended by Timoshenko to include the effects of warping torsion in I-section beams. Most recently the invention of highspeed electronic computers exerted a considerable influence on the static and dynamic analysis of plates. Chen and Bert (1976) investigated optimal design of simply supported rectangular plates laminated to composite material and subjected to uniaxial compressive loading. Numerical results are presented for optimal-design plates laminated of glass/epoxy, boron/epoxy, and carbon/epoxy composite materials. National Institute of Technology, Rourkela Page 7 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Linear elastic buckling of plates that are subjected to in-plane forces is a problem of great practical importance that has been extensively researched over the past 60 years. Elastic instability of flat rectangular plates became an important research area when the design of the lightweight airframes was introduced. Fok (1984), has been applied the theory of thin plates to engineering structures. Some advantages of thin-walled structures are high strength coupled with the ease of manufacturing and the relative low weight. However, thin-walled structures have the characteristic of susceptibility of failure by instability or buckling. It is therefore important to the design engineer that accurate methods are available to determine the critical buckling strength. Laminated plates with strip-type delamination under pure bending were investigated analytically and experimentally by Yeh and Fang (1997). In the analysis, a two dimensional nonlinear finite element code based on updated lagrangian formulation was developed to analyze the bending behaviour of the laminated plates and the local buckling phenomenon of the sub laminates in the delaminated region. The formulation includes large displacements and large rotations needed to describe the local buckling phenomenon of the delaminated region. Radu and Chattopadhyay (2000) used a refined higher order shear deformation theory to investigate the dynamic instability associated with composite plates with delamination that are subject to dynamic compressive loads. Both transverse shear and rotary inertia effects are taken into account. The theory is capable of modelling the independent displacement field above and below the delamination. All stress free boundary conditions at free surfaces as well as delamination interfaces are satisfied by this theory. The procedure is implemented using the finite element method. Hwang and Mao (2001) conducted the non-linear buckling and post-buckling analyses to predict the delamination buckling load and delamination growth load. In order to predict the delamination growth load, the total strain-energy release rate criterion, criterion of strainenergy release rate component, and inter laminar-stress criterion are used. Experimental results are also provided to compare with the prediction. A procedure for determining the buckling load of the aluminium rectangular plate is presented by Supasak and Singhatanadgid(2002) .Buckling load of aluminum rectangular plates are determined using four different techniques, i.e. (1) a plot of applied load vs. outNational Institute of Technology, Rourkela Page 8 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 of-plane displacement, (2) a plot of applied load vs. end shortening, (3) a plot of applied load vs. average in-plane strain, and(4)the Southwell plot. In this study, buckling loads determined from different experiment methods were compared with the theoretical buckling loads. A dynamic analysis model is proposed by Wen-pei and Lin Cheng (2003) to acquire buckling load of plate. We used the dynamic measured data from selected test points and by modal analysis got the modal parameters-mode shape and frequency; and then, derived a flexible matrix with the above model parameters. Force analysis was used to get the flexible matrix of equivalent force and the characteristic equation for determining the buckling load of the member. . Wang and Lu (2003) was carried out an investigation to understand the buckling behaviour of local delamination near the surface of fiber reinforced laminated plates under mechanical and thermal loads. The shape of the delaminated region considered is rectangular and triangular. The displacement expression is composed of items with the effect of tensionshear coupling and the effect of bend-torsion coupling. The critical strains of laminated plates with various shaped local delamination and different stacking patterns are obtained by making use of the energy principle. Shukla and Kreuzer (2005) proposed a formulation based on the first-order shear deformation theory and von-Karman-type nonlinearity to estimates the critical/buckling loads of laminated composite rectangular plates under in-plane uniaxial and biaxial loadings. Different combinations of simply supported, clamped and free boundary conditions are considered. The effects of plate aspect ratio, lamination scheme, number of layers and material properties on the critical loads are studied. Pannok and Singhatanadgid (2006) studies the buckling behaviour of rectangular and skew thin composite plates with various boundary conditions using the Ritz method along with the proposed out-of-plane displacement functions. The boundary conditions considered in this study are combinations of simple support, clamped support and free edge. The out-ofplane displacement functions in form of trigonometric and hyperbolic functions are determined from the Kantorovich method. National Institute of Technology, Rourkela Page 9 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Buket Okutan Baba (2007) studied the influence of boundary conditions on the buckling load for rectangular plates. Boundary conditions consisting of clamped, pinned, and their combinations are considered. Numerical and experimental studies are conducted to investigate the effect of boundary conditions, length/thickness ratio, and ply orientation on the buckling behaviour of E-glass/epoxy composite plates under in-plane compression load. Buckling analysis of the laminated composites is performed by using finite element analysis software ANSYS. Tests have been carried out on laminated composites with circular and semicircular cut-outs under various boundary conditions. Comparisons are made between the test results and predictions based on finite element analysis. Pein and Zahari (2007) studied the structural behaviour of woven fabric composites subject to compressive load which is lacking. The main objective of this study is to carry out the experiment analysis for the 800gm woven glass-epoxy composite laminated plates with and without holes subjected to quasi-static compressive load. The ultimate load and the structural and material behaviour of the composite laminated plates under compression have also been studied. Finally, a parametric study is performed to investigate the effect of varying the fibre orientations and different central hole sizes onto the strength of the laminates. A progressive failure analysis algorithm has been developed by . Zahari and Azmee (2008) and implemented as a user subroutine in a finite element code (ABAQUS) in order to model the non-linear material behaviour and to capture the complete compressive response of woven composite plates made of glass-epoxy material. Tsai-Hill failure theory has been employed in the progressive failure methodology to detect failure of the woven composite laminates. Murat Yazici (2008) studied the influence of square cut-out upon the buckling stability of multilayered, steel woven fiber-reinforced polypropylene thermoplastic matrix composite plates are studied by using numerical and experimental methods. The laminated plates under uniform pressure are formed by stacking three composite layers bonded symmetrically. The FE and experimental results are presented for various fiber orientation angles and plate boundary conditions. National Institute of Technology, Rourkela Page 10 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Aim and scope of study Thus far, there have been numerous studies on the composite laminated structures which find widespread applications in many engineering fields namely aerospace, biomedical, civil, marine and mechanical engineering because of their ease of handling, good mechanical properties and low fabrication cost. They also possess excellent damage tolerance and impact resistance. From the literature, it is evident that most of the studies are based on the numerical approach. Less attention has been paid on the buckling of composite plates. Due to the practical requirements, cutouts are often required in structural components due to functional requirements, to produce lighter and more efficient structures. Most stability studies of composite plates with cutout have focused on square plates under simply supported conditions to minimize the mathematical complexities. From the literature review it was found that most of the studies were focused on unidirectional fibre. Industry driven woven fibers are being increasingly used in many industries. Hence we have to give more importance on its structural behaviour. It also indicate that the interaction among stacking sequence, cutout shape and length/thickness ratio on the buckling behaviour of woven fiber laminated composites are needed to investigate in more detail. The aim of performing this research is to extend the knowledge of the structural behaviour of woven fabric composites subject to compressive load which is lacking. The main objective of this study is to carry out the experiment analysis for the woven glassepoxy composite laminated plates with and without holes subjected to static compressive load. National Institute of Technology, Rourkela Page 11 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Chapter-2 THEORETICAL FORMULATION National Institute of Technology, Rourkela Page 12 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 THEORETICAL FORMULATION The buckling of a plate involves two planes, namely, xz,yz and two boundary conditions on each edge of the plate. The basic difference between plate and column lies in the buckling characteristics. The column, once it buckles, cannot resist any additional axial load. Thus, the critical load of the column is also its failure load. On the other hand, a plate, since it is invariably supported at the edges, continues to resist the additional axial load even after the primary buckling load is reached and does not fail even when the load reaches a value 10-15 times the buckling load. Theory of bending of thin plates The theory for thin plates is similar to the theory for beams. In pure bending of beams, "the stress distribution is obtained by assuming that cross-sections of the bar remain plane during bending and rotate only with respect to their neutral axes so as to be always normal to the deflection curve." For a thin plate, bending in two perpendicular directions occur. A rectangular plate element is shown below: ( fig.1.a) Thin plate notation National Institute of Technology, Rourkela Page 13 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 The basic assumptions of elastic plate bending are: 1. Perfectly flat plate and of uniform thickness. 2. The thickness of the plate is small compared with other dimensions. For plate bending, the thickness, t, is less than or equal to ¼ of the smallest width of the plate. For plate buckling equations, the thickness, t, should be 1/10 of the smallest width of the plate. 3. Deflections are small, i.e., smaller or equal to 1/2 of the thickness. 4. The middle plane of the plate does not elongate during bending and remains a neutral surface. 5. The lateral sides of the differential element, in the above figure, remain plane during bending and rotate only to be normal to the deflection surface. Therefore, the stresses and strains are proportional to their distance from the neutral surface. 6. The bending and twisting of the plate element resist the applied loads. The effect of shearing forces is neglected. Buckling of composite plate Composite materials consist of two or more materials which together produce desirable properties that cannot be achieved with any of the constituents alone. Fiberreinforced composite materials, for example , contain high strength and high modulus fibers are the principal load carrying members, and the matrix material keeps the fibers together, act as a load-transfer medium between fibers from being exposed to the environment. The lay up sequence of unidirectionally reinforced “plies" as indicated in Fig.1. Each ply is typically a thin (approximately 0.2 mm) sheet of collimated fibers impregnated with an uncured epoxy or other thermosetting polymer matrix material. The orientation of each ply is arbitrary, and the layup sequence is tailored to achieve the properties desired of the laminate. Fiber reinforced composite materials for structural applications are made in the form of a thin layer, called lamina. A lamina is a macro unit of material whose material properties are determined through appropriate laboratory tests. Structural elements such as bars, beams and plates are then formed by stacking the layers to achieve desired National Institute of Technology, Rourkela Page 14 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 strength and stiffness. Fiber orientation in each lamina and stacking sequence of the layers can be choosen to achieve desired strength and stiffness . Governing equation A laminated plate is made by using a lamina as the building block. Its stiffness is obtained from the properties of the constituent laminae. To do this, we should know the orientations of the principle material directions of the laminae with respect to the laminate axis. Therefore , a knowledge of stress and strain through the laminate thickness is necessary. We shall make the following assumptions regarding the behaviour of a laminate: 1. It is made up of perfectly bonded laminae. 2. The bonds are infinitesimally thin and no lamina can slip relative to the other. This implies that the displacements are continuous across the lamina boundaries. As a result, the laminate behave like a lamina with special properties. 3.After buckling, a line originally straight and perpendicular to the middle surface of the laminate remains straight and perpendicular to the middle surface. 4. The strain perpendicular to the middle surface of the laminate is ignored. National Institute of Technology, Rourkela Page 15 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 (Fig.1.b) Laminated composite plate under in-plane compression. Classical Laminate Theory, has been used to derive the governing buckling equations for a plate subjected to in plane load. To derive the governing equations we have considered first the equilibrium of force and then the equilibrium of moment in a way as discussed below: The equilibrium equations in terms of the forces (Fig. 2.a) are x N xy 0 x y N xy N y 0 x y .............(1) Where Nx; Ny; and Nxy are the internal forces in normal and tangential direction. Again, the equilibrium equation in terms of the moments (Fig. 2.b) is 2 M xy 2 M y 2M x 2w 2w 2w 2 N N 2 N 0,...........................(2) x y xy xy xy x 2 y 2 x 2 y 2 National Institute of Technology, Rourkela Page 16 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 where, Nx ;Ny; Nxy are the forces applied at the edges. (fig 2.a) Inplane forces on laminate (fig.2.b) Moments on a laminate The resultant forces Nx; Ny and Nxy and moments Mx; My and Mxy acting on a laminate are obtained by integration of the stress in each layer or lamina through the laminate thickness. Knowing the stress in terms of the displacement, we can obtain the stress resultants Nx; Ny; Nxy; Mx ; My ; and Mxy. National Institute of Technology, Rourkela Page 17 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 The stress resultants are defned as t 2 N x x dz t 2 t 2 N y y dz t 2 t 2 t 2 N xy xy dz t 2 t 2 t 2 M y y zdz M xy xy zdz. ........(3) M x x zdz, t 2 t 2 t 2 Where x , y and xy are normal and shear stress. Actually, Nx ;Ny and Nxy are the force per unit length of the cross section of the laminate as shown in Fig.2.a. Similarly, Mx ;My; and Mxy are the moment per unit length as shown in Fig .2.b. Thus, the forces and moments for an N-layer laminate can be defined as N x h2 x x N zr N y y dz y dz, r 1 z r 1 N h xy 2 xy xy .........(4) M x h2 x x N zr M y y zdz y zdz, r 1 z r 1 M h xy 2 xy xy ...........(5) r r r r t where, z r and z r 1 are as defined in Fig. 3. Note that z 0 Substituting for x , y and xy 2 in equations (2) and (3) and integrating over the thickness of each layer and adding the results so obtained for N layers, we can write the stress resultants as National Institute of Technology, Rourkela Page 18 Buckling Analysis of Glass epoxy Laminated Composite Plate N x A11 N y A12 N A xy 16 A12 A22 A26 A16 x0 B11 A26 y0 B12 A66 xy0 B16 B12 B22 B26 M x B11 M y B12 M B xy 16 B12 B22 B26 B16 x0 D11 B26 y0 D12 B66 xy0 D16 D12 D22 D26 2009 B16 k x B26 k y , B66 k xy D16 k x D26 k y , D66 k xy ..........(6) and(7) Where Aij Qij r ( Z r Z r 1 ), N r 1 Bij 1 N Qij (Z r2 Z r21 ), 2 r 1 r Dij 1 Qij Z r3 Z r31 . 3 r 1 r n ..........(8) fig (3) Geometry of an N-layered laminate Here, Aij are the extensional stiffness, Bij the coupling stiffness, and Dij the flexural stiffness. For antisymmetric angle-ply and cross-ply laminates stress resultants are simplified in the following sections: National Institute of Technology, Rourkela Page 19 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 In the case of angle-ply laminates where the fibre orientation ᶱ alternates from lamina to lamina as +ᶿ/-ᶿ/+ᶿ/-ᶿ, the force and moment resultants are N x A11 N y A12 N 0 xy A12 A22 0 0 x0 B11 0 y0 B12 A66 xy0 B16 M x B11 M y B12 M B xy 16 B12 B22 B26 B16 x0 D11 B26 y0 D12 B66 xy0 D16 B16 k x B26 k y , B66 k xy B12 B22 B26 D12 D22 D26 D16 k x D26 k y , D66 k xy .......(9) and (10) Such a laminate is called an anti-symmetric angle-ply laminate. In this type of laminate, if each lamina has the same thickness, it is then called a regular anti-symmetric angle-ply laminate. For such a laminate, equations (6) and (7) reduce to N x A11 N y A12 N 0 xy A12 A22 0 0 x0 0 0 y0 0 A66 xy0 B16 Mx 0 M y 0 M B xy 16 0 0 B26 B16 x0 D11 B26 y0 D12 0 xy0 0 0 0 B26 D12 D22 0 B16 k x B26 k y , 0 k xy 0 k x 0 k y , D66 k xy ...........(11) and (12) Let the laminae are oriented alternatively at 00 and 900. A laminate of this type is termed as a cross-ply laminate. Such a laminate can, again, be either symmetric cross-ply or antisymmetric cross-ply. Substituting for Nx;Ny;Nxy;Mx;My;Mxy from equations (9) and (10), after substituting for x0 , y0 and xy0 kx; ky; kxy in equations (1) and (2), we get the governing equations as National Institute of Technology, Rourkela Page 20 Buckling Analysis of Glass epoxy Laminated Composite Plate A11 2u 0 2v0 2u 0 2u 0 2v0 2u 0 3w 3w ( A A ) A ( 2 ) A A B 3 B 12 66 16 26 66 11 16 xy xy x 2 x 2 y 2 y 2 x 3 x 2 y ( B12 2 B66 ) A16 3w 3w B 0 26 xy 2 y 3 2u 0 2u 0 2u 0 2v 0 2v 0 2v 0 3w ( A A ) A A 2 A A B 12 66 26 66 26 22 16 xy xy x 2 y 2 x 2 y 2 x 3 ( B12 2 B66 ) D11 2009 3w 3w 3w 3 B B 0 26 22 x 2 y xy 2 y 3 4w 4w 4w 4w 4w 3u 0 4 D ( 2 D 4 D ) 4 D D B 16 12 66 26 22 11 x 4 x 3 y x 2 y 2 xy 3 y 4 x 3 3B16 3u 0 3u 0 3u 0 3v 0 3v 0 ( B 2 B ) B B ( B 2 B ) 12 66 26 16 12 66 x 2 y xy 2 y 3 x 3 xy 2 ( B12 2 B66 ) 3v 0 3v 0 2w 2w 2w B N N 2 N 22 x y xy xy xy 2 y 3 x 2 y 2 For a general laminate, all the above three equations, have to be solved simultaneously as they are coupled. National Institute of Technology, Rourkela Page 21 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Chapter-3 Experimental Study National Institute of Technology, Rourkela Page 22 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 EXPERIMENTAL STUDY In view of difficulty of theoretical and numerical analysis for laminated structure behaviours, experimental methods have become important in solving the buckling problem of laminated composite plates. The experimental and numerical analysis done on aluminium plate showed an appreciable match in the results. Taking the above proof for the correctness of the experimental procedure. Here the same experimental procedure was followed for a composite plate. To understand the effect of cut out shape, length/thickness ratio, ply orientation, and length/breadth ratio on the compressive behaviour of woven glass epoxy laminated composite plates compression test was performed. The specimen was clamped at two side and kept free at other two sides The specimens were loaded in axial compression by using a tensile testing machine of 100 tonne load capacity. The buckling load is determined from the load –displacement curve. In this study both out of plane displacement and end shortening of the plate was plotted against the applied load. Buckling load is determined from the intersection point of two tangent drawn from the pre buckling and post buckling regions. In this study buckling load of composite plate determined by using the above two method and compared with each other. Buckling Experiment of aluminium plate In this study buckling load of aluminium plates determined numerically and experimentally. Two different plate length were used: 300mm and 200mm. The width and thickness of the plates are 200mm and 1.7mm respectively. The Youngs modulus value was 70000N/mm2 and poissons ratio was taken as 0.3. Test procedure The specimen were loaded in axial compression using a Instron tensile testing machine of 100 KN capacity. The specimen was clamped at two ends and kept free at the other two ends. A dial gauge was mounted at the centre of the specimen to observe the lateral National Institute of Technology, Rourkela Page 23 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 deflection. All specimen were loaded slowly until buckling. The experimental set up is shown below. Clamped boundary conditions were simulated along the top and bottom edges, restraining 40mm length .For axial loading, the test specimens were placed between the two extremely stiff machine heads, of which the lower one was fixed during the test, whereas the upper head was moved downwards by servo hydraulic cylinder. All plates were loaded at constant cross-head speed of 1mm/min. The test set up is shown below. fig.(4.a) Instron testing machine Fig. (4.b) National Institute of Technology, Rourkela Page 24 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 As the load was increased the dial gauge needle started moving, and at the onset of buckling there was a sudden large movement of the needle. The load corresponding to this point will be the buckling load of the specimen. The load v/s displacement curve and load v/s end shortening curve was plotted. The displacement is plotted on the x -axis and load was plotted on the y- axis. The load, which is the initial part of the curve deviated linearity, is taken as the critical buckling load. That point is determined from the intersection of two tangent drawn from the pre-buckling and post-buckling regions. Composite Specimen Preparation and Manufacturing To meet the wide range of needs which may be required in fabricating composites, the industry has evolved oven a dozen separate manufacturing processes as well as a number of hybrid processes. Each of these processes offers advantages and specific benefits which may apply to the fabricating of composites. Hand lay-up and spray-up are two basic moulding processes. The hand lay-up process is the oldest, simplest, and most labour intense fabrication method. The process is most common in FRP marine construction. In hand lay-up method liquid resin is placed along with reinforcement (woven glass fiber) against finished surface of an open mould. Chemical reactions in the resin harden the material to a strong, light weight product. The resin serves as the matrix for the reinforcing glass fibers, much as concrete acts as the matrix for steel reinforcing rods. The percentage of fiber and matrix was 50:50 in weight. (Fig.5.a) Glass fiber National Institute of Technology, Rourkela (fig. 5.b) Plate casting Page 25 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Contact moulding in an open mould by hand lay-up was used to combine plies of WR in the prescribed sequence. A flat plywood rigid platform was selected. A plastic sheet was kept on the plywood platform and a thin film of polyvinyl alcohol was applied as a releasing agent by use of spray gun. Laminating starts with the application of a gel coat (epoxy and hardener) deposited on the mould by brush, whose main purpose was to provide a smooth external surface and to protect the fibers from direct exposure to the environment. Ply was cut from roll of woven roving. Layers of reinforcement were placed on the mould at top of the gel coat and gel coat was applied again by brush. Any air which may be entrapped was removed using serrated steel rollers. The process of hand lay-up was the continuation of the above process before the gel coat had fully hardened. Again, a plastic sheet was covered the top of plate by applying polyvinyl alcohol inside the sheet as releasing agent. Then, a heavy flat metal rigid platform was kept top of the plate for compressing purpose. The plates were left for a minimum of 48 hours before being transported and cut to exact shape for testing. The following constituent materials were used for fabricating the plate: 1. E-glass woven roving as reinforcement 2. Epoxy as resin 3. Hardener as catalyst 4. Polyvinyl alcohol as a releasing agent After 48 hours curing the specimen were cut in to desired sizes ,with and without cutout shown in fig. Circular, square, and rectangular cutout of same area(9.62cm2)were made for the experiments. The specifications of plate tested in the present study shown in the table-1 and the plate with various cut out shape was shown in fig.6. The mechanical properties of the composite plates were determined by Instron tensile testing machine of 100KN load capacity. A specimens whose fiber direction coincide with the loading direction was used to obtain the modulus of elasticity along the fiber direction. The specimen were loaded step-bystep up to rupture by the test machine. Strains in the fiber ( 1 ) and transverse directions ( ( 2 ) were measured,by using these strains E values are determined. National Institute of Technology, Rourkela Page 26 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 The mechanical properties of the tested specimen obtained as E11=7.7Gpa, E22=7.7Gpa, 12 0.12 and G12 = 2.81Gpa. circular Rectangular square Rectangular ( Fig.6) The plate with different cutout shape tested in the present study National Institute of Technology, Rourkela Page 27 Buckling Analysis of Glass epoxy Laminated Composite Plate Plate no: Plate1 Plate2 Plate3 Plate4 Plate5 Plate6 Plate7 Plate8 Plate9 Plate10 Stacking sequence Length(mm) Thickness (mm) 2009 Width(mm) [0]4 130 1.5 120 [0]4 130 1.32 120 [0]4 130 1.33 120 [0]6 130 2.25 120 [0]6 130 2.23 120 [0]6 130 2.21 120 [0]8 130 2.96 120 [0]8 130 3.37 120 [0]8 130 3.31 120 [0]8 175 3.31 120 [0]8 175 3.2 120 [0]8 175 3.15 120 [0]8 200 3.2 120 [0]8 200 3.1 120 [30/-30]8 130 3.31 120 [30/-30]8 130 3.28 120 [30/-30]8 130 3.25 120 [45/-45]8 130 3.24 120 [45/-45]8 130 3.24 120 [0]8 60 3.3 120 [0]8 60 3.28 120 [0]10 130 3.65 120 [0]10 130 3.65 120 [0]12 130 3.85 120 [0]12 130 3.83 120 Table 1 : Plate tested in the present study. National Institute of Technology, Rourkela Page 28 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Buckling Experiments for composite plates The specimen were loaded in axial compression using a uniaxial tensile testing machine of 100 tonne capacity. It is shown in fig.8.a. The specimen was clamped at two ends and kept free at the other two ends. A dial gauge was mounted at the centre of the specimen to observe the lateral deflection. All specimens were loaded slowly up to failure. Clamped boundary conditions were simulated along the top and bottom edges, restraining 40mm length .For axial loading, the test specimens were placed between the two extremely stiff machine heads, of which the lower one was fixed during the test, whereas the upper head was moved downwards by servo hydraulic cylinder. The shape of the plate after buckling was shown in fig.8.b. All laminated plates were loaded at constant cross-head speed of 200Kn/min. Finally the microscopic scanning was performed for the failed samples by using the JEOL-JSM-6480LV Scanning Electron Microscopic device shown in fig.9. The image of failed specimen obtained after scanning was shown in fig.10. As the load was increased the dial gauge needle started moving, and at the onset of buckling there was a sudden large movement of the needle. The load corresponding to this point will be the buckling load of the specimen. The load v/s displacement curve and load v/s end shortening curve was plotted. The displacement is plotted on the x -axis and load was plotted on the y- axis. The load, which is the initial part of the curve deviated linearity,is taken as the critical buckling load. That point is determined from the intersection of two tangent drawn from the pre-buckling and post-buckling regions. National Institute of Technology, Rourkela Page 29 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 (fig.7) . Test set up for both side clamped boundary condition (Fig 7.a)Before Buckling National Institute of Technology, Rourkela ( fig.7.b) After Buckling Page 30 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Scanning Electron Microscope (fig.8) Microscopoic image of the failure ( fig.9) National Institute of Technology, Rourkela Page 31 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Numerical Analysis ANSYS was used to carry out the finite element analysis in the work. ANSYS is used to analyse the critical buckling load aluminium plates of different sizes. The dimension of the specimen were 300*200* 1.7mm and 200*200*1.7mm in length, width and thickness .Eigen value buckling analysis in ANSYS has four steps: 1.Build the model : It includes defining element type, real constants, material properties and modelling. In this study shell ,Elastic 8node 93 selected as the element type. 2.Solution(Static Analysis): It includes applying boundary conditions, applying loads and solving the static analysis. The applied boundary condition and load is shown below. Fig.10 National Institute of Technology, Rourkela Page 32 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 3. Eigen buckling analysis: Eigenvalue buckling analysis predicts the theoretical buckling strength of an ideal linear elastic structure. 4. Postprocessor: This steps includes listing buckling loads and viewing buckled shapes. We can plot the deformed and undeformed shape of the plate. National Institute of Technology, Rourkela Page 33 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 CHAPTER- 4 RESULTs AND DISCUSSION National Institute of Technology, Rourkela Page 34 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 RESULTS AND DISCUSSION The buckling load for clamped- free aluminium plate determined. The results were both experimental analysis and finite element analysis. The agreement between the two method was generally good. The critical buckling loads obtained experimentally and by ANSYS is shown in the table2 . plate Length Width Thickness Experimental ANSYS No. mm mm mm Buckling Buckling load(N/mm) load(N/mm) Plate-1 300 200 1.7 11.75 13.44 Plate-2 200 200 1.7 24.25 30.55 Table 2 : Buckling Results of Aluminium Plate It was observed that the buckling load of plate-1 obtained from experimental and numerical analysis are identical and less than that of plate-2.The experimental buckling loads for both specimens are less than the ANSYS results. The deformed and undeformed shape of the aluminium plate was shown in the fig.12. National Institute of Technology, Rourkela Page 35 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Fig.11 It is observed that all the laminated plates buckled globally until complete failure occurred as expected. Experimental buckling loads were identified from the load-displacement plots, and load- end shortening graph. Following graphs shows the load versus end-shortening curves and load versus out of plane displacement for the tested panels with and without central holes, different angle orientations, different aspect ratio and different length/thickness ratio. It is interesting to note that all the tested panels behave in a similar fashion where, their behaviour is almost linear initially before reaching the peak loads. Beyond those peak points of the load-displacement curves, majority of the laminates experienced large displacements before failure. From the electron microscopic scanning it was found that, the bonding between the matrix and glass laminate was breaked during the failure. The glass fiber was came out from the plate. National Institute of Technology, Rourkela Page 36 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 The load v/s out-of-plane displacement (4layer,130*120*1.32mm, [0/0/0/0]4 ) and load v/s end shortening for Plate-1 are shown in fig.12 & 13 respectively. From the graph we can find that the displacement of the plate started at a load of 14KN, after which the plate was deflecting outward with an increase in the load. The thickness of the plate is very small. Hence the plate shows a large deflection for small increment in the load. The critical buckling load obtained from both the graphs was almost equal. (Fig.12) Load versus out of plane displacement graph (Fig.13) Load versus end shortening graph National Institute of Technology, Rourkela Page 37 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 The load v/s out of plane displacement graph for Plate-2 (6 layer, 130*120*2.23mm.[0/0]6) is shown in fig.14. The critical buckling load was determined from the intersection of tangents drawn from the pre-buckled region and post buckled region. The load v/s end shortening graph obtained from the test is shown in fig.15.The buckling load obtained from both graphs was almost equal. (Fig.14) Load-out of plane displacement (Fig.15) Load- end shortening National Institute of Technology, Rourkela Page 38 Buckling Analysis of Glass epoxy Laminated Composite Plate The load v/s out of plane displacement graph for 2009 Plate-3 (8 layer ,130*120*3.31mm [0/0/0/0]8 ) is shown in fig.16. The displacement started at 15KN load and the buckling occurred between 20 and 25KN. The load v/s end shortening graph is shown in fig. 17. The buckling load obtained from the load v/s end shortening plot was slightly different from load v/s out of plane displacement. (Fig.16) Load v/s out of plane displacement (fig.17) Load v/s end shortening National Institute of Technology, Rourkela Page 39 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 In Plate-4(8 layer, 175*120*3.31mm, [0/0]8 ), the aspect ratio was changed by varying the length. The plot of load v/s out of plane displacement and load v/s end shortening is shown in fig. 18 & 19 respectively. (fig.18) Load v/s out of plane displacement (fig.19) Load-end shortening National Institute of Technology, Rourkela Page 40 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 In Plate-5( 8layer, 200*120*3.2mm, [0/0/0/0]4 ),the length was again increased to study the effect of aspect ratio on buckling load. The load v/s out of plane displacement and load v/s end shortening plotted for plate 5 is shown in fig.20 & 21 respectively. (Fig.20) Load –out of plane displacement (fig.21) Load v/s end shortening National Institute of Technology, Rourkela Page 41 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 In Plate-6 ( 8 layer,130*120*3.31 mm, [30/-30/30/-30]8 ) , the fiber orientation was changed from 00 to 300 .The buckling load was determined from fig.22 & fig.23 . It was found to be less compared to buckling load of plate with 00 orientation. (Fig.22) Load v/s out of plane displacement (fig.23) Load v/s end shortening National Institute of Technology, Rourkela Page 42 Buckling Analysis of Glass epoxy Laminated Composite Plate In 2009 Plate:-7( 8layer, 130*120*3.24mm, [45/-45/45/-45]8 ) the orientation was again changed to 450. The corresponding variation in load displacement graph is shown below. (fig.23) Load-out of plane displacement (fig.24) Load-end shortening National Institute of Technology, Rourkela Page 43 Buckling Analysis of Glass epoxy Laminated Composite Plate In 2009 Plate-8 (10 layer, 130*120*3.5mm, [0/0/0/0]10 ) the number of layers was increased to 10. Hence the thickness of the plate increased. The load v/s out of plane displacement and load v/s end shortening is shown below. The buckling load obtained from both graphs was nearly equal. Load-out of plane displacement graph Load v/s end shortening graph National Institute of Technology, Rourkela Page 44 Buckling Analysis of Glass epoxy Laminated Composite Plate In 2009 Plate-9 ( 12 layer ,130*120* 3.8mm, [0/0/0/0]12 ) the thickness was again increased by increasing the number of layers. Here 12 layers are used. The plots for load v/s out of plane displacement and load v/s end shortening is shown in fig.27 and 28 respectively. (Fig.27) Load- out of plane displacement (fig.28) Load –end shortening graph National Institute of Technology, Rourkela Page 45 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 For Plate-10 ( 8 layer,60*120*3.1mm, [0/0/0/0]8 ), it was difficult to fit the dial gauge with the plate due to its short length. Hence only load v/s end shortening was plotted and is shown in fig.29 . ( Fig.29) Load-end shortening National Institute of Technology, Rourkela Page 46 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Plate with circular cut out In plate-11 (12 layer,130* 120*3.75mm, [0/0/0/0]12) a circular cutout was made at the centre. It results in decrease in the buckling load. The load v/s out of plane displacement and load v/s end shortening is shown in the fig.30 and 31respectively. (Fig.30) Load v/s out of plane displacement (fig.31) Load v/s end shortening National Institute of Technology, Rourkela Page 47 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Here the load v/s displacement graph for plate with square cut out is given. The buckling determined from load v/s out of plane displacement and load v/s end shortening for Plate-12 (12 layer,130*120*3.65mm, [0/0/0/0]12 ) was almost equal . (Fig.32) Load v/s out of plane displacement (Fig.33) Load v/s end shortening National Institute of Technology, Rourkela Page 48 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 The load v/s out of plane displacement and load v/s end shortening graph for plate 13 with rectangular cut out is shown in the following figure. It was observed that buckling load for this plate less as compared to the plate with circular cutout. (fig.34) Load v/s out of plane displacement (fig.35) Load v/s end shortening National Institute of Technology, Rourkela Page 49 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Plate-14 (12 layer,130*120*3.68mm , [0/0/0/0]12 ) having the rectangular cutout in the transverse direction was subjected to compressive loading. The load v/s out of plane displacement and load v/s end shortening was plotted and is shown in fig.36 and 37 respectively. It was observed that the plate 14 gives less buckling load as compared to other plates with cutout. (Fig.36) Load v/s out of plane displacement (Fig.37) Load v/s end shortening National Institute of Technology, Rourkela Page 50 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Effect of Length to Thickness Ratio (L/t) Plates with different thickness are used extensively due to design requirements. Thus, the buckling response of plates with its length to thickness ratio must be fully understood in the structural design. In this study the thickness of the plate was increased by increasing number of layers. The experimental results shows that the variation in buckling load is very sensitive to the thickness of the plate. The variation in buckling load with change in the thickness of the plate is shown in fig.38. From the graph in it is observed that the buckling load decreases with increase in length to thickness ratio. Sl. Length Width Thickness Buckling Buckling no mm mm mm Load(KN) Load(KN) Graph1 Graph2 1 130 120 1.5 15.3 15.5 2 130 120 1.32 15.2 15.5 3 130 120 1.33 15.1 15 4 130 120 2.25 17.65 17.8 5 130 120 2.23 17.3 17 6 130 120 3.29 20 19 7 130 120 3.37 22.5 23 8 130 120 3.31 22 22.5 9 130 120 3.62 26.5 26 10 130 120 3.65 27 26.5 11 130 120 3.85 33.5 34.5 12 130 120 3.85 34 36 Table 3: Effect of Length to Thickness Ratio (L/t) National Institute of Technology, Rourkela Page 51 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 (Fig.38) Buckling load v/s length to thickness ratio. Effect of aspect ratio (a/b ratio) In this study, the laminated plates are evaluated at four different aspect ratios. The tested plate and their corresponding buckling load was shown in table-4.The buckling load decreases continuously with increasing aspect ratio but the rate of decrease is not uniform. In this study aspect ratio was changed from 0.5 to 1.67.It is observed that buckling load was maximum for aspect ratio 0.5 and minimum for aspect ratio 1.67. When the aspect ratio changed from 0.5 to 1, the variation in buckling load is almost 24%. There are loss of 21% of buckling load between aspect ratios 1 and 1.5. The aspect ratio and buckling load was plotted along x and y axis as shown in fig.39. From that graph, it is observed that the rate of decrease in buckling load is decreasing with increase in aspect ratio. Sl. Length Width Thickness Buckling Buckling no mm mm mm Load(KN) load(KN) Graph1 Graph2 1 130 120 3.29 20 19.8 2 130 120 3.37 22.5 23 3 130 120 3.31 22 23.5 National Institute of Technology, Rourkela Page 52 Buckling Analysis of Glass epoxy Laminated Composite Plate 4 175 120 3.31 18.2 18.7 5 175 120 3.2 17.9 18.4 6 175 120 3.15 18.9 19 7 200 120 3.2 17 18 8 200 120 3.1 17.5 18.2 9 60 120 3.29 27 10 60 120 3.2 26 2009 Table 4 : Effect of aspect ratio (a/b ratio) (fig.39) Buckling load v/s aspect ratio graph. Effect of fibre orientation In this study the buckling load of composite plates with different fiber orientation was determined. The result is shown in the Table-5 . The result shows that the buckling load is decreasing with increase in fiber orientation angle. The maximum buckling load was occurred at [0]8. When the orientation of the fiber changed from 00 to 300 , the corresponding change in buckling load was almost 20% . Reduction of 30% in buckling load is observed as the ply orientation angle increases from 0 0 to 450. The variation of buckling load with fiber orientation shown in fig.40. National Institute of Technology, Rourkela Page 53 Buckling Analysis of Glass epoxy Laminated Composite Plate Sl. orientation Length Width Thickness no. (mm) (mm) (mm) 2009 Buckling Buckling load(kn) load(kn) from From graph1 graph 2 1 0 130 120 2.96 22.5 22 2 0 130 120 3.3 22 23.5 3 0 130 120 3.37 23 23.5 4 30 130 120 3.31 21.05 20.5 5 30 130 120 3.28 20.5 20 6 30 130 120 3.25 20.0 20.5 7 45 130 120 3.18 16.3 16 8 45 130 120 3.24 17.2 17.5 Table 5 : Effect of Orientation (Fig.40) Buckling load v/s fiber orientation National Institute of Technology, Rourkela Page 54 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Effect of cut out shape Plates with different types of cut outs are used extensively due to design requirements. Thus, the buckling response of plates with cut out must be fully understood in the structural design. In this section, the effects of circular, square and rectangular shapes with same areas are taken in to account. The experiments indicate that the variation of the buckling loads is very sensitive to the presence of cut out. It can be seen that buckling load generally decreases with presence of cutout. We can observe that the buckling load for plate without cutout are about 25% and 30% higher than that of [0]12 with circular and square cutout. The plate with rectangular cutout gives the minimum buckling load. Sl. No. Of Cutout Length Breadth Thickness Buckling Buckling no layers shape (mm) (mm) (mm) Load(kn) load(kn) Graph1 Graph2 1 12 without 130 120 3.7 34.5 36 2 12 Circular 130 120 3.78 24.5 25.75 3 12 Square 130 120 3.81 23.75 24.5 4 12 Rectangular1 130 120 3.65 22 22.5 5 12 Rectangular2 130 120 3.7 23 23.8 Table 6 : Effect of cut out shape National Institute of Technology, Rourkela Page 55 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Chapter-5 CONCLUSION National Institute of Technology, Rourkela Page 56 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 CONCLUSION This study considers the buckling response of laminated rectangular plates with clamped-free boundary conditions. The laminated composite plates have varying L/T ratio, aspect ratio, cut out shape and ply orientation. From the present analytical and experimental study, the following conclusions can be made. 1. It was noted that different length to thickness ratio affected the critical buckling load. The buckling load decreases as the L/t ratio increases. The rate of decrease of buckling load is not uniform with the rate of increase of L/t ratio. 2. As the aspect ratio increases, the critical buckling load of the plate decreases. When the aspect ratio changed from 0.5 to 1, the variation in buckling load is almost 24%. The rate of change of buckling load with the aspect ratio is almost uniform. 3. It was seen that the different fiber orientation angles affected the critical buckling load. When the fiber angle increases, the buckling load decreases. The plate with [0] 8 layup has the highest buckling load and the plate with [45]8 layup has the lowest buckling load. 4. The reduction of the buckling load due to the presence of a cutout is found to be significant. It is noted that the presence of cutout lowers the buckling load and it varies with the cutout shape. The plate with circular cutout yielded the greatest critical buckling load. National Institute of Technology, Rourkela Page 57 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Future scope of the work In the present study the buckling load of the laminated plate was determined. The effect of cutout shape, length to thickness ratio, aspect ratio and fiber orientation on buckling load was studied. The future scope of the present investigation can be expressed as follows, (a) Buckling analysis of delaminted industry driven woven composite plates with and without cutouts. (b) Buckling analysis of laminated woven fiber composite plates with delamination by numerical approach for different boundary conditions. (c). Dynamic stability of woven fiber laminated and delaminated composite plates. National Institute of Technology, Rourkela Page 58 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 Chapter-6 REFERENCES National Institute of Technology, Rourkela Page 59 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 REFERENCES 1. A K Sreevastva, R.K Singh. Effect of aspect ratio on buckling of composite plates-. Journal of Composites Science and Technology 59 (1999) 439-445 2. Buket Okutan Baba and Aysun Baltaci. Buckling characteristics of symmetrically and anti-symmetrically laminated composite plates with central cutout,- Applayed Composite Materials – 14(2007):265–276 3. C.W. Pein and R. Zahari. Experimental investigation of the damage behaviour of woven fabric glass/epoxy laminated plates with circular cut-outs subjected to compressive force,International Journal of Engineering and Technology, (2007)Vol. 4, No. 2, pp.260-265 4. 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Design of composite-material plates for maximum uniaxial compressive buckling load - Proc. Okla. Acad. Sci. (1976)56: 104-107. 26. Wen-pei, Cheng, Ming-hsiang and Cheer-germ, Analysis modeling for plate buckling load of vibration test, Journal of Zhejiang University science 2005 6A(2):132-140. 27. Wu Zhen and Chen Wanji, Buckling analysis of angle-ply composite and sandwich plates by combination of geometric stiffness matrix, Journal of Comput. Mech. (2007) 39: 839–848. 28. X. Wang and G. Lu . Local buckling of composite laminar plates with various delaminated shapes – Journal of Thin-Walled Structures 41 (2003) 493–506. National Institute of Technology, Rourkela Page 62 Buckling Analysis of Glass epoxy Laminated Composite Plate 2009 29. Yeliz Pekbey. A Numerical and Experimental Investigation of Critical Buckling Load of Rectangular Laminated Composite Plates with Strip Delamination -. Journal of Reinforced Plastics and Composites; (2006)25; 685. 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