LINEAR STATIC FINITE ELEMENT ANALYSIS OF COMPOSITE HAT-STIFFENED LAMINATED PLATES LEE BIING CHYUAN

Transcription

1 i LINEAR STATIC FINITE ELEMENT ANALYSIS OF COMPOSITE HAT-STIFFENED LAMINATED PLATES LEE BIING CHYUAN This Thesis is Submitted as a Partial Fulfillment of the Requirement for the Award of the Degree of Bachelor of Mechanical Engineering (Pure) Faculty of Mechanical Engineering Universiti Teknologi Malaysia MARCH, 5

2 ii I hereby declared that this thesis entitled Linear Static Finite Element Analysis of Composite Hat-Stiffened Laminated Plates is the result of my own work excepted as cited in references. Signature : Name of Author : LEE BIING CHYUAN Date : 1 March 5

3 iii This book is dedicated to my beloved parents, sisters and my dearest girl friend, thanks for their constant support and encouragement in everything.

4 iv ACKNOWLEDGEMENT The author would like to take this opportunity to express his gratitude to Dr. Nazri Kamsah, his respectful supervisor who has given his guidance, patience and invaluable advices in enabling the author to achieve the objective of this project. The author would also like to express appreciation to En. Shukur Abu Hassan who has unselfishly contributed his information, materials, and equipment in completing this project. Besides, the author would also like to thank all the staffs in PUSKOM for their kindness in helping him out by continuously contributing different ways of improvement and sharing their experience in handling different problems. Thank you very much.

5 v ABSTRACT Laminated composite plates are extensively used in the construction of aerospace, civil, marine, automotive and other high performance structures due to their high specific stiffness and strength, excellent fatigue resistance, long durability and many other superior properties compared to the conventional metallic materials. However, high modulus and strength characteristics of composites result in structures with very thin sections that are often prone to buckling. Stiffeners are required to increase the bending stiffness of such thin walled members. This project is carried out to investigate the behavior of the composite hat-stiffened laminated plates. The investigation is restricted to linear static analysis of composite stiffened panels. Unidirectional carbon fiber was used as reinforcement agent with epoxy resin as binder material. The plates were arranged symmetrically in geometry about the middle surface of the structure. The tensile and bending test had been carried out to study the stiffened panel. The mechanical properties and behavior of the stiffened panels were recorded. The numerical analysis has been done using finite element software and the results are compared with the experiment values. The experiment and numerical results show that the behavior of the composite laminated plates is depended on their fiber orientations and stiffeners give major effects in the bending stiffness of the composite plates. Keywords: Finite element; Stiffened plate; Hat stiffener; Composite

6 vi ABSTRAK Komposit laminat plat yang bersifat tinggi kekuatan, rintangan lesu yang tinggi, panjang hayat lesu dan banyak lagi sifat-sifat yang lebih maju bahan-bahan logam telah menjadikannya popular untuk pembinaan dalam bidang aerospace, civil, marin, automotif, dan struktur persembahan tinggi. Walau bagaimanapun, komposit yang bersifat modulus dan kekuatan tinggi menyebebkan struktur nipis seperti plat mudah untuk membengkok. Struktuk penguat diperlukan untuk meningkatkan kekuatan bengkokan struktur nipis ini. Projek ini akan menekankan analisis laminat plat komposit yang dikuatkan dengan stiffener berbentuk topi. Analisis ini dibataskan kepada linear statik analisis untuk plat komposit. Unidirectional karbon fiber digunakan sebagai bahan penguat dan epoxi sebagai pencantum. Plat adalah disusun secara simetri terhadap permukaan tengah struktur. Plat telah dikaji dengan ujian tegangan and bengkokan. Sifat-sifat mekanikal untuk plat itu telah direkodkan. Perisian unsur terhingga digunakan sebagai tambahan untuk mengkaji sifat-sifat plat ini dan keputusan dibandingkan dengan keputusan eksperimen. Keputusan eksperimen dan perisian menunjukkan bahawa sifatsifat stiffened plat bergantung kepada susunan arah fiber dalam plat dan stiffener memberi kesan utama kepada kekuatan bengkokan untuk plat komposit. Kata-kata kunci: Kaedah unsur terhingga; Stiffened plat; Stiffener berbentuk topi; komposit

7 vii TABLE OF CONTENTS CHAPTER TITLE PAGE TITLE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT TABLE OF CONTENTS LIST OF TABLE LIST OF FIGURE LIST OF SYMBOLS i ii iii iv v vii xii xiii xvi CHAPTER I INTRODUCTION 1.1 Introduction 1 1. Problem Statement 1.3 Objective Scope Methodology 4

8 viii CHAPTER II LITERATURE REVIEW ON COMPOSITE MATERIAL.1 Introduction Fibrous composites Laminated Composites Particulate Composites 14. Fiber Glass Fiber 17.. Carbon Fiber Aramid Fiber (Kevlar) Boron Fiber.3 Matrix.3.1 Polymer Matrix Composites (PMC) 1.3. Thermoplastic.3.3 Thermoset Polyester Epoxy 5 CHAPTER III THEORETICAL ANALYSIS OF COMPOSITE 3.1 Analysis of Lamina Stress-strain Relations For Plane Stress 9 In Specially Orthotropic Lamina 3.1. Stress-strain Relations For Plane Stress 31 In Generally Orthotropic Lamina 3. Theory of Plate Analysis of Laminate Classical Laminated Plate Theory Strains and Stress Variation in a 39 Laminate

9 ix Resultant Laminate Forces and 43 Moments Symmetric and Unsymmetrical 45 Laminates 3.4 Stiffened Plate Bending of Simply Supported 49 Rectangular Plates Governing Equations The Navier Solution 5 CHAPTER IV FINITE ELEMENT IMPLEMENTATION 4.1 Introduction Linear Static Analysis Finite Element Analysis Procedures Modeling for Unstiffened 57 Composite Laminated Plate 4.3. Modeling for Composite 61 Hat-Stiffened Laminated Plate CHAPTER V EXPERIMENTAL PROCEDURES 5.1 Composite Fabrication Hand Lay Up Method Vacuum Bagging Laminate Preparation Hand Lay Up Procedure Tensile Test Specimen Preparation Bending Test Specimen Preparation Tensile Test 75

10 x Experimental Determination of 76 Strength and Stiffness 5.5. Testing Apparatus Tensile Test Procedure Bending Test Testing Apparatus Bending Test Procedure 84 CHAPTER VI RESULT AND DISCUSSION 6.1 Tensile Test Result Discussion on Tensile Test Results Discussion on Graph Stress versus 9 Axial Strain Discussion on Graph Lateral Strain 9 versus Axial Strain 6. Bending Test Result Discussion on Unstiffened Composite 96 Laminated Plate 6.. Theoretical Analysis of Unstiffened 98 Composite Laminated Plate 6..3 Discussion on Composite Hat-Stiffened 99 Laminated Plate 6.3 FEA Simulation Result Discussion on Unstiffened Composite 13 Laminated Plate 6.3. Discussion on Hat-Stiffened Composite 14 Laminated Plate

11 xi CHAPTER VII CONCLUSION AND SUGGESTION 7.1 Conclusion Suggestion for Future Study 113 REFERENCES 115 APPENDIX A 117 APPENDIX B 15 APPENDIX C 131 APPENDIX D 136 APPENDIX E 14 APPENDIX F 15

12 xii LIST OF TABLE Table Title Page.1 Fiber and wire properties 1. Properties of fiber and conventional bulk materials 16.3 Typical glass fiber properties 17.4 Properties of carbon fiber 19.5 Typical properties of cast resin system Specimen Specification 7 5. Materials Specification Results of tensile test Summary of tensile test result Results of Load and Deflection for unstiffened composite plate Results of Load and Deflection for composite hat-stiffened 94 laminated plate 6.5 The analysis result of maximum deflection at 1 kg applied load Comparison of experiment results and FEA value for unstiffened 1 and stiffened plate

13 xiii LIST OF FIGURE Figure Title Page 1.1 Flow Chart of Methodology 6.1 Comparison of specific modulus between composite and metallics 8. Comparison of stress/strain relationship between composites and 9 metallics.3 Classes of Composite 1.4 Comparison between the conventional materials and composite 11 materials.5 Tensile stress-strain Curve for fiber, FRP and resin 3.1 Two principles typical of lamina 8 3. Specially orthotropic lamina Generally orthotropic lamina Plate subjected to pure bending (a) Direct stress on lamina of plate element. (b) Radii of curvature of 34 neutral surface. 3.6 Principle and structural coordinates, and lamination Geometry of deformation in the xz plane (a) In-plane forces on a flat laminate, (b) Moments on a flat laminate Geometry of an n-layered laminate Cross-sectional views of laminates A hat-stiffened plate Various types of stiffened panels 47

14 xiv 3.13 Schematic of T, J, blade, and Hat stiffener geometry Plate Geometry Finite element model FEA model Manual Lay-up process Vacuum Bag mould assembly A finished laminated composite plate Specimen Specification Tensile Test Specimen Materials and tool for hand lay-up process (a) Hat shaped stiffener, (b) Hat-stiffened plate Tensile Specimen Uniaxial loading in the 1-direction Uniaxial loading in the -direction Uniaxial loading at 45 to the 1-direction Instron 46 testing machine Specimens with strain gauge Location of the displacement transducers at the composite plate Hydraulic Press Machine Bending test rig Displacement transducer (LVDT) Plate specimen with strain gauge Failure mode of specimen with degree fiber orientation Failure mode of specimen with 9 degree fiber orientation Failure mode of specimen with 45 degree fiber orientation Failure mode of the unstiffened composite plate Failure of the Stiffened Plate Location of the strain gauges at the composite hat-stiffened plate Bent plate in half sinusoid wave with deformation scale of Displacement contour for hat-stiffened plate for bottom view Deformed shape of the hat-stiffened plate with deformation scale of 3 15

15 xv 6.1 Front view of deformed shape for the hat-stiffened plate with 16 deformation scale of Side view of the critical region for composite hat-stiffened plate Critical region of the hat-stiffened plate Displacement contour for hat-stiffened composite plate with 19 laminate property 6.14 Side view of the deformed hat-stiffened plate with laminate property 19

16 xvi LIST OF SYMBOLS A ij - Extensional stiffness a - Length of plate B ij - Coupling stiffness b - Width of plate D ij - Bending stiffness D - Flexural rigidity E i, E j - Young s modulus in i, j direction respectively e - Tab length G 1 - Shear modulus in 1- plane I - Moment of inertia k - Middle surface curvature L - Length between the tabs M i - Normal moment per unit of length M ij - Twisting moment per unit of length N i - Normal load per unit of length N ij - In-plane shear load per unit of length Q ij - Reduced stiffness Q ij - Transformed reduced stiffness Q mn - Load coefficient q - Transverse load

17 xvii r x, r y - Radii of curvature of the neutral surface in sections parallel to the xz and yz planes respectively v ij - Poisson s ratio for transverse strain in j-direction when subjected to a stress in the i-direction W - Width of the tensile test specimen w - Deflection in the z direction u, v, w - Displacement in the x-, y-, z-direction z k - Thickness of laminate γ - Shear strain τ - Shear stress ε i, ε j - Strain in I, j direction respectively θ - Angle of lamina σ - Stress component

18 CHAPTER I INTRODUCTION 1.1 Introduction Laminated composite have found usage in aerospace, automotive, marine, civil, and sport equipment applications. This popularity is due to excellent mechanical properties of composites as well as their amenability to tailoring of those properties. One of the most important structural configurations made of composite materials is known as a plate. By definition, a plate is a planar load-carrying component spanning two directions whose thickness is significantly less than its side lengths. Laminated plates are one of the simplest and most widespread practical applications of composite laminates. Laminated composite plates are extensively used in the construction of aerospace, civil, marine, automotive and other high performance structures due to their high specific stiffness and strength, excellent fatigue resistance, long durability and many other superior properties compared to the conventional metallic materials.

19 Laminated composite materials provide the designer with freedom to tailor the properties and response of the structure for given loads to obtain the maximum weight efficiency. However, high modulus and strength characteristics of composites result in structures with very thin sections that are often prone to buckling. Stiffeners are required to increase the bending stiffness of such thin walled members (plates, shells). Hence, the stiffened plates are widely used as structural components for aerospace, launch vehicles, and other industrial applications to obtain lightweight structures with high bending stiffness. Stiffened plates are also more tolerant to imperfections and resist catastrophic growth of cracks. The stiffening member also provides the benefit of added loadcarrying capability with a relatively small additional weight penalty. The present study focuses on the linear static behavior of composite hat-stiffened laminated plate. The finite element software will be used as an aid to study the linear static finite element analysis of laminated stiffened plates. 1. Problem Statement A composite plate is extensively used in aircraft structures, ships, bridges and other industrial applications and is loaded to varying conditions such as bending, buckling, vibration and so on. Therefore, optimization of the plate structural is needed to meet the working environment and gives the desired properties such high stiffness, strength. Normally stiffeners are used to increase the stiffness of the plate especially the bending stiffness.

20 3 1.3 Objective The objective of this project is: 1) Study the effects of hat-shaped stiffeners in the deformation of the composite laminated plates by experimentally and finite element simulation. ) Study the different shape of stiffener in strengthening the composite plate by finite element simulation. 1.4 Scope The scope of this project is: a) Literature study on composite materials, stiffener, laminate and plate structures. b) Fabrication of the composite plate which is arranged symmetrically in both geometry and material properties about the middle surface of the plates. c) Determine the mechanical properties and behavior of the composite laminated plate by carried out: a. Tensile test b. Bending test d) Linear static finite element analysis of the composite laminated plate. e) Comparison of the finite element simulation results with experiment value.

21 4 1.5 Methodology The effects of stiffener will be determined through Bending Test and followed by structural analysis. Comparison will be made in term of ultimate load at failure and maximum deflection between the stiffened and unstiffened composite plates. The methodologies of the project are shown as follow: i) Identify Problem The objective of this project is to do the analysis of the composite hatstiffened laminated plate by using the experimental procedures. Analysis of the plate structure involves a lot of complex calculation and it takes plenty of time to do it. Therefore computer software will be used as an aid to study the linear static finite element analysis of laminated stiffened plates. ii) Literature Study After identify the objectives and scopes of this project, literature study will be carried out to gather all the information needed for this project. Literature study will focus on the topics such as follow: composite materials, plate theory, the effects of stiffener onto composite plates and finite element analysis. iii) Experiment Procedures Experiment is carried out to analysis the composite laminated plate. In this project, there are two type of experiment will be carried. The first experiment is tensile test which is to determine the mechanical properties of the

22 5 composite materials. The second experiment is bending test which is to analysis the behavior of the composite stiffened and unstiffened plate. All the specimens are fabricated by using hand lay-up technique and the candidate materials are unidirectional carbon fiber was used as reinforcement agent with epoxy resin as binder material. iv) FE Simulation There is plenty of computer software that suit for the FE simulation such as COSMOS/M, MSC/NASTRAN, and ABAQUS. Software that is user friendly and provides the easy methodology in modeling and FE analysis will be chosen. The materials properties that needed in FE simulation will be obtained from tensile test. v) Data Collection The data from the test will be collected includes: ultimate applied load, displacement and local strains. vi) Results Comparison After the experimental analysis and FE simulation have been done, the comparison of the result will be done in the behavior of the composite laminated plate and hat-stiffened plate to study the effects of the stiffener in improving the strength of the composite plate.

23 6 Identify Problem Objective and Scope Literature Study Composite, Plate Theory, Finite Element Analysis Experimentation FE Simulation Specimen Preparation Tensile Specimen & Plate Tensile Test To get material properties, E 1, E, v 1, v 1, and G 1. FEM Modeling for Laminated Plate Bending Test for Laminated Plate Finite Element Analysis (FEA) Results Comparison End Figure 1.1: Flow Chart of Methodology

24 CHAPTER II LITERATURE REVIEW ON COMPOSITE MATERIALS.1 Introduction Historically, modern composite get its start in the aerospace community when a need for improved material performance was voiced. A composite in its most basic definition are those that consist two or more materials on a macroscopic scale to produce desirable properties for a given application. It is only when the constituent phases have significantly different physical properties and thus the composite properties are different from the constituent properties that we have come to recognize these materials as composite. Composite materials can offer significant advantages over common metallics and plastics. Figure.1 shows the comparison of specific modulus between composite and conventional metallics.

25 8 Among the advantages of composite over metallics are: 1. High strength-to-weight ratio (a carbon lamina is 4 to 6 times greater than that of steel or aluminum).. High stiffness-to weight ratio (a carbon lamina is 3 to 5 times greater than that of steel or aluminum). 3. High fatigue endurance limit. 4. Low corrosion. 5. Excellent damping characteristics. 6. Versatile can be tailored to meet the performance needs. The most significant advantages over a plastic are: 1. Much greater strength. Much greater stiffness 3. Much lighter weight Figure.1: Comparison of specific modulus between composite and metallics[1]

26 9 One of the fundamental differences between a composite and a metal is the stress/strain relationship, as shown Figure.. Composites in general show a brittle catastrophic failure, whereas metallics generally show a yield prior to failure. Figure.: Comparison of stress/strain relationship between composites and metallics [1] In practice, most composites consist of a bulk material called matrix and a reinforcement materials called fiber, added primarily to increase the strength and stiffness of the matrix. Fibre-reinforced composite materials are the most commonly used modern composite materials that consist of high strength and high modulus fibers in a matrix material. Fibers could be carbon, fiberglass, Kevlar, polyester, nylon, ceramics, and boron. The matrix material is typically an epoxy, thermoplastic, polyester, vinyl ester, ceramics, or even metallics. In these composite, fibers are the principal load-carrying members, while the matrix materials keeps the fibers together, acts as a load-transfer medium between the fibers, and protects the fibers from being exposed to the environment. The matrix is considerably lower density, stiffness, and strength than the fibers. However, the combination of fibers and matrix can have very high strength and stiffness yet still have low density.

27 1 The fibers and matrix materials used in composites are either metallic or nonmetallic. The common metals fibre materials in use are aluminum, copper, iron, nickel, steel, and titanium while the organic fiber materials in use are glass, carbon, boron, and graphite materials []. Composite materials are commonly formed in three different types as shown in Figure.3: 1) Fibrous composites ) Laminated composites 3) Particulate composites Figure.4 shows the comparison between the conventional materials and composite materials. a) Fibrous b) Particulate c) Laminated Composite Composite Composite Figure.3: Classes of Composite []

28 11 Figure.4: Comparison between the conventional materials and composite materials [3].1.1 Fibrous composites A fibrous composite is the composite that consist fiber in a matrix. The stiffness and strength of the fibrous composite comes from the fibers that are stiffer and stronger than the same materials in bulk form. Whisker is the shorter fibers that exhibit better strength and stiffness properties than long fibers. Long fibers are used in straight form or woven form. A fiber is characterized geometrically not only by its very high length-todiameter ratio but by its near crystal-sized diameter. Strengths and stiffness of a few selected fibers materials are shown in Table.1. The strength-to density and stiffness-todensity ratios are usually used as indicators of the effectiveness of a fiber [4]. The long dimension reinforcement prevents the growth of the incipient cracks normal to the reinforcement that might lead to failure. Therefore fibers are effective in improve the fracture resistance of the matrix.

29 1 Table.1: Fiber and wire properties (Source: Adapted from Dietz. By permission of the American Society for Testing and Materials, 1965.) [4] Fiber or wire Density,ρ lb/in 3 (kn/ m 3 ) Tensile strength, S 1 3 lb/in (GN/ m ) S/ρ 1 5 in (km) Tensile stiffness, E 1 6 lb/in (GN/ m ) E/ρ 1 7 in (Mm) Aluminum.97 (6.3) 9 (.6) 9 (4) 1.6 (73) 11 (.8) Titanium.17 (46.1) 8 (1.9) 16 (41) 16.7 (115) 1 (.5) Steel.8 (76.6) 6 (4.1) 1 (54) 3 (7) 11 (.7) E-glass.9 (5) 5 (3.4) 54 (136) 1.5 (7) 11 (.9) S-glass.9 (4.4) 7 (4.8) 78 (197) 1.5 (86) 14 (3.5) Carbon.51 (13.8) 5 (1.7) 49 (13) 7 (19) 53 (14) Beryllium.67 (18.) 5 (1.7) 37 (93) 44 (3) 66 (16) Boron.93 (5.) 5 (3.4) 54 (137) 6 (4) 65 (16) Graphite.51 (13.8) 5 (1.7) 49 (13) 37 (5) 7 (18) Whisker has essentially the same near crystal-sized diameter as fiber, but is very short and stubby. Thus, a whisker is more perfect than a fiber and exhibits even higher properties. Whiskers are obtained by crystallization on a very small scale resulting in a nearly perfect alignment of crystal.

30 13.1. Laminated Composites Laminated composites consist of layers of various materials. There must be at least two different materials are bonded in laminated composites. Lamination is used to combine the best aspects of the constituent layers in order to achieve a more useful material. Each layer of the composite usually very thin and hence cannot be directly used. The layers can be formed in various orientations to form a multiplayer composite used for engineering applications [4]. The example of the laminated composites is bimetals, clad metals, laminated glass, plastic-based laminates, and laminates fibrous composites. Bimetal is the laminate that combines two different metals with significantly different coefficients of thermal expansion. Under change in temperature, bimetals warp or deflect a predictable amount and are well suited for use in temperature measuring devices. The cladding or sheathing of one metal with another is done to obtain the best properties of both. This is the concept of protection of one layer of material by another. Laminated fibrous composites are a hybrid class of composites involving both fibrous composites and lamination techniques. The common name of this composite is laminated fiber-reinforced composites. The layers of fiber-reinforced materials are built up with the fiber directions of each layer typically oriented in different directions to give different strengths and stiffness in the various directions. Therefore, the strengths and stiffness of the laminates fiber-reinforced composites can be tailored to the specific design requirements of the structural element being built.

31 Particulate Composites Particulate Composites consist of particles of one or more materials suspended in a matrix of another material [4]. Particle can be defined as a non-fibrous and generally has no long dimension with the exception of platelets. The particles can be either metallic or nonmetallic as can the matrix. Thus, there exist four possible combinations of it as: metallic in nonmetallic, nonmetallic in metallic, nonmetallic in nonmetallic, metallic in metallic. Metal matrix composites are an example of nonmetallic in metallic composites. Particulate composites are differ from the fiber types composite in the distribution of the additive constituent is usually random rather than controlled. Thus, particulate composites are usually considered as isotropic. The dimensions of the reinforcement determine its capability of contributing its properties to the composites. Particles are not very effective in improving the fracture resistance of the composite. Particles also share the load but as much smaller extent than those fibers in fibrous composite that lies parallel to the direction of load. Particles are effective in improving the stiffness but do not offer much strengthening to the composites. Particles are commonly used just simply to reduce the cost of the composites.. Fiber Fibers are the dominant constituents of most composite system. The function of the fibre is to produce high strength and stiffness at lowest weight in a combination with

32 15 matrix. One of the main objectives of any design should be able to place the fibers in positions and orientation so that they are able to contribute efficiently to load-carrying capability. The amount of fibre usually expressed in term of the volume fraction of fibre, V f or weight fraction, W f. Properties of some common types of fibres as well as some conventional materials is given in Table.. The functional requirements of fibers in a fiber/matrix composite are that they should have: 1) A high modulus of elasticity to give stiffness to the composite. ) A high ultimate strength. 3) A low variation of strength between individual fibers. 4) Stability during handling. 5) A uniform diameter.

33 16 Table.: Properties of fiber and conventional bulk materials (*Virgin strength values. Actual strength values prior to incorporation into composite are approximately.1 GPa) Material Fibers Tensile Modulus (E) (GPa) Tensile Strength (σ u ) (GPa) Density (ρ) (g/ cm 3 ) Specific modulus (E/ρ) Specific Strength (σ u /ρ) E-glass S-glass Graphite (high modulus) Graphite (high tensile strength) Boron Silica Tungsten Beryllium Kevlar 49 (aramid polymer) Conventional Materials Steel Aluminum alloys Glass Tungsten Beryllium

34 17..1 Glass Fiber Glass fibers account around 9% of the reinforcement used in structural reinforced plastic application. The most common glass fibers are silica based (~5 6% SiO ) with addition oxides of calcium, boron, sodium, aluminium and iron. The mechanical properties are not strongly dependent on composition, but chemical behavior, which reflected in terms of durability and strength retention in corrosion environment, is influenced by the details of the chemistry. Table.3 gives typical property values for different glass types. Table.3: Typical glass fiber properties [3] Glass type SG Thermal espansivity ( C -1 ) Tensile modulus (MPa) Undamaged Strength (GPa) Strand from roving A-glass E-glass AR-glass S/R-glass E-glass has low alkali content and is the commonest glass in the market and is used in the construction industry. It is employed widely, especially with polyester and epoxy resins. It has good strength, stiffness, electrical, weathering properties, and a reasonable Modulus Young. A-glass has high alkali content and was formerly used in the aircraft industry but is now gradually going out of production. C-glass (C for corrosion) has a higher resistance to chemical corrosion than E-glass but is more expensive and has lower strength properties. S-glass is produced for extra high strength and high modulus applications in aerospace and space research. These glass strands for

35 18 thermosetting resins may be used in a number of different forms such as chopped strands, chopped strand mat (CSM), continuous random mat (CRM), woven fabric with varying architectures, and milled glass fiber powder... Carbon Fiber Carbon fibers are very thin fibers and are typified by a combination of low density, high strength and high stiffness. They have diameters between 6 and 1 µm. Carbon fibers consist of 99.9% of chemically pure carbon. Carbon fibers are the predominant high strength; high modulus reinforcement used in the fabrication of high performance resin- matrix composites. There are two general sources for the commercial production o carbon fibers: synthetic fibers, similar to those used for making textiles, and pitch, which is obtained by the destructive distillation of coal. The textile fiber polyacrylonitrile (general known as PAN) is a synthetic fibre. The high-strength bonds between carbon atoms in the layer plane results in an extremely high modulus, while the weak van der waals-type bond between the neighboring layers results in a lower modulus in that direction. Compare with fiberglass, advanced composites are superior in lightweight and high stiffness but has similar strength. The properties of the three well-known carbon fibers are given in Table.4.

36 19 Table.4: Properties of carbon fiber [5] Property, units Pitch Rayon PAN Tensile strength, MPa Tensile Modulus, GPa Specific gravity Elongation, % Coefficient of thermal expansion Axial (1-6 / C) -1.6 to to.5 Transverse (1-6 / C) Fiber diameter, µm Aramid Fiber ( Kevlar) The aramid fiber forming polymer, that is, the aromatic polyamides. Aramid fibers are available in two forms: low and high modulus. The main advantage of aramid is the very low density (lower than glass and carbon), giving high values of specific strength and stiffness combined with excellent toughness.

37 ..4 Boron Fiber Boron fibers were among the first fiber specially developed for advanced composites. They have a density similar to glass but a tensile modulus six times greater. Because of their large size and stiffness boron filaments cannot be woven into cloths or handled like other fibers, so they are usually processed in parallel arrays of single thickness sheets or tapes..3 Matrix Matrix can be taken in the form of almost any material. There are three main materials that used as matrix in composite. That is metal matrix, polymer matrix, and ceramic matrix. However, those that have attracted most interest are those based on polymeric systems. The matrix should fulfill certain function. These are: 1) To bind the fibers together and protect their surface from damage during service life to the composite. ) To transfer stresses to the fibers efficiently by adhesion and/ or friction. 3) To disperse the fibers and separate them. 4) To be chemically and thermally compatible with fibers.

38 1.3.1 Polymer Matrix Composites (PMC) These are the most common and will the main area of discussion in here. Also known as FRP - Fiber Reinforced Polymers (or Plastics), these materials use a polymerbased resin as the matrix, and a variety of fibers such as glass, carbon and aramid as the reinforcement. Polymers used as matrix can be divided into two main groups: thermoplastics and thermosets. Since Polymer Matrix Composites combine a resin system and reinforcing fibers, the properties of the resulting composite material will combine something of the properties of the resin on its own with that of the fibers on their own. Figure.5 shows the tensile stress-strain curve for fiber, FRP composite, and resin. Overall, the properties of the composite are determined by: 1) The properties of the fiber ) The properties of the resin 3) The ratio of fiber to resin in the composite (Fiber Volume Fraction) 4) The geometry and orientation of the fibers in the composite

39 Figure.5: Tensile stress-strain Curve for fiber, FRP and resin [6].3. Thermoplastic Thermoplastics polymers consist of linear molecules, which are not interconnected. This means they have no chemical linkage between the chains so they do not undergo irreversible cross-linking reactions, but instead melt and flow on application of heat and pressure. The chemical valency bond along the chain is extremely strong, but the forces of attraction between the adjacent chains are weak. Because of their unconnected chain structure, thermoplastics may be repeatedly softened and hardened by heating and cooling respectively; with each repeated cycle, however, the materials tend to become more brittle. Example of thermoplastics is nylon, polyehtheretherketone (PEEK), polybutylene terephthalate, polycarbonate, polyethylene, and polysulphone.

40 3 Some of the advantages of the thermoplastic are: : 1) Indefinite shelf life. ) Good toughness. 3) High impact strength and fracture resistance. 4) Higher strains to failure. 5) Processing is concerned with physical transformations only. However, most of the thermoplastic resins can be eliminated because of inadequate mechanical performance at high temperatures..3.3 Thermoset Thermoset polymer is formed by a chemical reaction. In the first stage, a substance consisting of a series of long chain polymerized molecules, similar to those present in thermoplastics. In the second stage of the process, the chains become crosslinked; this reaction can take place either at room temperature or under the application of heat and pressure. The resultant materials will not flow and cannot be softened by heating. The example of the thermosets is epoxy, melamine, phenolic, polyester, polymide, ureas. The polymer matrix that will be used in preparation of the laminated plate in this project comes from this group of polymer.

41 4 Some of the advantages of the thermoset are: 1) Low viscosity level. Hence, is efficiently fluid to allow processing without further modification, while others need application of heat or the use of diluents to lower the viscosity level. ) Less creeps and stress relaxation then thermoplastics Polyester Polyesters are the most commonly used of polymeric resin materials. The major advantage of this resin is the ability for cure at room temperature. This allows large and complex structures to be fabricated where an oven cure would not be practical. They consist of a relatively low molecular weight unsaturated polyester dissolved in styrene. Styrene cures the resin by polymerization and forms cross-links across unsaturated sites in the polyester. The curing reaction is strongly exothermic. This will generate heat that can damage the final laminate. Styrene based unsaturated polyester resins have not been found of interest for carbon fiber laminated applications. The popularity of the polyester cause a family of resin has been developed to offer specific properties. A variety of products is possible with respect to the backbone chemistry, which allows the physical, thermal and chemical properties of the cured products to be influenced. Polyester resins are considered as a potential alternative because it can be demonstrated that differences in the chemical nature as compared to epoxies do not necessarily result in different composite properties.

42 Epoxy Epoxy resins are often used for the advanced structural applications. These resins are the primary matrix materials used in carbon fiber composites. There are generally two parts systems consisting of an epoxy resin and a hardener, which is either an amine or anhydride. Epoxy resins can be modified in various ways to give a broad spectrum of properties after cure and to meet a diverse range of processing condition. The higher performance epoxies require the application of heat during a controlled curing cycle to achieve the best properties. Table.5 shows the typical properties of cast resin systems. There are many resin curing agent combinations and the many different curing conditions that may be employed for proper cure. Hence, this allows the modification of the following properties: 1) Heat resistance (glass transition of the resin) ) Moisture absorption and performance in ht wet environment 3) Fracture toughness and impact resistance

43 6 Table.5: Typical properties of cast resin system [7] Property Polyester Epoxy Specific gravity Impact strength (J/m) Density (Mgm -3 ) Poisson ratio Thermal conductivity (W/m/ C) Tensile strength (MPa) Compression strength (MPa) Flexural strength (MPa) Tensile modulus (GPa)

44 CHAPTER III THEORETICAL ANALYSIS OF COMPOSITE 3.1 Analysis of Lamina A lamina or ply is a flat (sometimes curved as in a shell) arrangement of unidirectional or woven fibers in a matrix. It represents a fundamental building block for composite laminates. Lamina is made of two or more constituent materials that cannot be detected. The two typical lamina are shown in Figure 3.1 along with their principal materials axes which are parallel and perpendicular to the fiber direction. Unidirectional fiber-reinforced laminas exhibit the highest strength and modulus in the direction of the fibers, but they have very low strength and modulus in the transverse direction to the fibers. Discontinuous fiber-reinforced composite have lower strength and modulus than continuous fiber-reinforced composite.

45 8 Unidirectional Fibers Woven Fibers Figure 3.1: Two principles typical of lamina [4] Lamina is the basic building block in a laminated fiber-reinforced composite. Thus, the knowledge about the mechanical behavior of a lamina is essential to the understanding of laminated fiber-reinforced structures. In formulating the constitutive equations of a lamina we assume that [4]: 1) A lamina is a continuum, i.e., no gaps or empty spaces exist. ) A lamina behaves as a linear elastic material. The first assumption amounts to considering the macromechanical behavior of a lamina. If the fiber-matrix debonding and fiber breakage, for example, are to be included in the formulation of the constitutive equations of a lamina. The second assumption implies that the generalized Hooke s law is valid. It should be noted that the two assumptions could be removed if we were to develop micromechanical constitutive models for inelastic (e.g., plastic, viscoelastic, etc.) behavior of a lamina.

46 Stress-strain Relations for Plane Stress in Specially Orthotropic Lamina If the material has a texture like wood or unidirectionally reinforced fiber composites.the modulus E1 in the fiber direction will typically be larger than those in the transverse directions (E and E3). When E1 E E3, the material is said to be orthotropic. A unidirectional fiber-reinforced lamina is treated as an orthotropic material whose material symmetry planes are parallel and transverse to the fiber direction. The material coordinate axes x is taken to be parallel to the fiber, while the y- axes transverse to the fiber direction in the plane of the lamina as shown in Figure 3.. Figure 3.: Specially orthotropic lamina The stress-strain relations for specially orthotropic material by taking account the normal and shear stress and deformations are given as below: σ 1 Q = σ Q τ Q Q 1 ε1 ε Q 66 γ 1 (3.1)

47 3 Where theq, is the reduced stiffness, are ij Q 11 E1 = 1 v v 1 1 Q Q 1 v1e v1e1 = = 1 v v 1 v v 1 E = 1 v v (3.) Q 66 = G 1 The 5 th elastic constant v ij is a function of the others v ij v ji = i, j = 1,,.6 (3.3) E i E j where, E i, E j - Young s modulus in i, j direction respectively G 1 - Shear modulus in 1- plane v ij - Poisson s ratio for transverse strain in j-direction when subjected to a stress in the i-direction v ij ε j = (3.4) ε i

48 Stress-strain Relations For Plane Stress In Generally Orthotropic Lamina As mentioned previously, laminas are often constructed in such a manner that the principal material directions do not coincide with the natural direction of the body. This is not to be interpreted as that the material is itself is not longer orthotropic. We are just looking at an orthotropic material in a coordinate system that oriented at some finite angle to the principle material coordinate system as shown in Figure 3.3. This lamina is called generally orthotropic lamina. Figure 3.3: Generally orthotropic lamina The transformation equations for expressing stress-strain relationship in an x-y coordinate system σ x σ y = τ xy [ Q ] ε x ε y γ xy σ x Q σ y = Q τ xy Q Q Q Q 1 6 Q Q Q ε x ε y γ xy (3.5)

49 3 In which Q 11 = Q 11 4 cos θ + ( Q 1 + Q 66 )sin θ cos θ + Q sin 4 θ Q 1 = ( Q 11 + Q 4Q 66 )sin θ cos θ + Q (sin θ + cos θ ) Q Q 16 = Q 11 = ( Q 11 4 sin θ + ( Q Q 1 Q Q 66 )sin θ cos θ + Q 3 )sinθ cos θ + ( Q 1 Q cos + Q 4 66 θ 3 )sin θ cosθ (3.6) Q 6 = ( Q 11 Q 1 Q 66 3 )sin θ cosθ + ( Q 1 Q + Q 66 3 )sinθ cos θ Q 66 = ( Q 11 + Q Q 1 Q 66 )sin θ cos θ + Q (sin θ + cos θ ) The bar over the Q ij matrix denotes that we are dealing with the transformed reduced stiffness instead of the reduced stiffness, Q. ij 3. Theory of Plate The evaluation of the fundamental equations of orthogonal-stiffened plates is based on the following assumptions, which are accepted in the classical theory of elasticity of thin plates [8]. a) The linear elements perpendicular to the middle plane of the plate before bending remain straight and normal to the deflection surface of the plate after bending.

50 33 b) The materials of elements follow the Hook s law, where the materials are elastic, continuum, homogeneous, and different elastic characteristic in both x- and y-direction. c) The displacements of the points of the middle plane, in normal direction to this plane, are small in comparison to the thickness of the plate. d) The normal stress transverse to the plane of the plate can be disregarded. We consider a thin plate subjected to pure bending moments of intensity M x and M y per unit length uniformly distributed along its edges. We take the xy-plane to coincide with the middle plane of the plate before deflection and the x and y-axes along the edges of the plate as shown in Figure 3.4. The z-axes are taken positive downward. Figure 3.4: Plate subjected to pure bending [8] These moments are consider positive when they produce compression in the upper surface of the plate and tension in the lower as shown in Figure 3.5. The thickness of plate, h is considered small in comparison with other dimension. Let us consider an element cut out of the plate by two pairs of planes parallel to the xz and yz planes as shown in Figure 3.5(a). Assuming that during bending, the lateral sides of the element remain plane and rotate about the neutral axes nn to remain

51 34 normal to the deflected middle surface of the plate. Thus, the middle plane of the plate does not undergo any extension during bending and is therefore a neutral plane. (a) (b) Figure 3.5: (a) Direct stress on lamina of plate element. (b) Radii of curvature of neutral surface. [8] Let r x and r y denote the radii of curvature of the neutral surface in sections parallel to the xz and yz planes respectively as shown in Figure 3.5(b). The strain ε x and ε y in the x and y direction of an element lamina abcd at a distance z from the neutral surface are given by, z z ε x = ε y = (3.7) r r x y where r x, r y - Radii of curvature of the neutral surface in sections parallel to the xz and yz planes respectively as shown in Figure 3.5(b)

52 35 z - Distance from the neutral surface. ε x, ε y - Strain in the x and y direction. The strain ε x and ε y in term of the normal stresses σ x and σ y acting on the element are given by, ) ( 1 ) ( 1 x y y y x x v E v E σ σ ε σ σ ε = = (3.8) Substituting equation (3.7) into equation (3.8), the corresponding stresses in the lamina abcd are + = + = x y y y x x r v r v Ez r v r v Ez σ σ (3.9) These stresses are proportional to the distance z of the lamina abcd from the neutral surface and depend on the magnitude of the curvatures of the bent plate. The normal stresses distributed over the lateral sides of the element must be equal to the external moments M x and M y. Thus, we obtain the equations, = = / / / / h h y y h h x x z x z x M z y z y M δ δ σ δ δ δ σ δ (3.1)

53 36 Substituting equation (3.1) for σ x and σ y, we obtain, z r v r v E z M z r v r v E z M x y h h y y x h h x δ δ + = + = / / / / (3.11) If ) 1(1 1 3 / / v E h z v E z D h h = = δ Then, + = + = + = + = 1 1 x w v y w D r v r D M y w v x w D r v r D M x y y y x x (3.1) D is the flexural rigidity of the pate and w denotes the deflection of any point on the plate in the z direction.

54 Analysis of Laminate A laminate is a collection of stacked lamina with various orientations of principle materials directions in the lamina. The major purpose of lamination is to tailor the directional dependence of strength and stiffness to match the loading environment of the structural element. Once lamination is complete the stack of lamina are now referred to as a laminate as shown in Figure 3.6. The laminate takes on a combination of properties based upon the lamina orientation, fiber type, resin or matrix materials type, and the ratio of fiber-to-matrix content. Depending upon the angles at which the plies are stacked, an infinite number of physical and material properties can be produced for a given fiber and matrix materials. The mismatch of material properties between layers can cause shear stresses produced between the layers, especially at the edges of a laminate. This may cause delamination in the laminate structure. Besides, during the laminates manufacturing, materials defects such as interlaminar voids, delamination, incorrect orientation, damaged fibers, and variation in thickness may be introduced. Therefore, analysis and design procedures should account for any defects.

55 38 Figure 3.6: Principle and structural coordinates, and lamination [1] Classical Laminated Plate Theory Classical laminate plate theory is an extension of the theory for bending of homogeneous plates, but with an allowance for in-plane tractions in addition to bending moments, and for the varying stiffness of each ply in the analysis. In general cases, the determination of the tractions and moments at a given location will require a solution of the general equations for equilibrium and displacement compatibility of plates. This theory is treated in a number of standard texts, and will not be discussed here [4]. In the classical laminated plate theory (CLPT) it is assumed that the Kirchhoff hypothesis holds []: 1) Straight lines perpendicular to the middle surface (i.e., transverse normal) before deformation remain straight after deformation. ) The transverse normal do not experience elongation (i.e., they are inextensible).

56 39 3) The transverse normal rotate such that they remain perpendicular to the middle surface after deformation. The first two assumptions imply that the transverse displacement is independent of the transverse (thickness) coordinate and the transverse normal strain ε z is zero. The third assumption implies the zero shear strains, γ xz =, γ yz = Strains and Stress Variation in a Laminate Knowledge of the variation of stress and strain through the thickness is essential to definite the extensional and bending stiffness of a laminate. When definition the stiffness of the laminate, the laminate is presumed to consist of perfectly bonded lamina. Moreover, the bonds are presumed to be infinitesimimally thin as well as nonshear-deformable. That is, the displacements are continuous across lamina boundaries so that no lamina can slip relative to another. Therefore, the laminate acts as a single layer with very special properties, but nevertheless acts as a single layer of material. The implications of the Kirchhoff or the Kirchhoff-Love hypothesis on the laminate displacement u, v, and w in the x, y, and z- direction are derived by the used of the laminate cross section in the xz plane as shown in Figure 3.7.

57 4 Figure 3.7: Geometry of deformation in the xz plane [4] The displacement in the x-direction of point B from the undeformed to the deformed middle surface is u. The line ABCD remains straight under deformation of the laminate, uc = u z c β (3.13) Where β is the slope of the laminate middle surface in the x-direction. w β = (3.14) x Then, the displacement, u, at any point z through the laminate thickness is w u = u z (3.15) x Similarly, the displacement, in the y-direction is w v = v z (3.16) y

58 41 By virtue of the Kirchhoff-Love hypothesis where ε z = γ xz = γ yz =, the laminate strains have been reduced to ε x, ε y, and γ xy. For small strains (linear elasticity), the remaining strains are defined in terms of displacement as x u x = ε y v y = ε (3.17) x v y u xy + = γ Thus, for the derived displacement u and v in Equation (3.15) and (3.16), the strains are x w z x u x = ε y w z y v y = ε (3.18). y x w z x v y u xy + = γ or + = xy y x xy y x xy y x k k k z γ ε ε γ ε ε (3.19) Where the middle surface strains are + = x v y u y v x u xy y x γ ε ε (3.)

59 4 and the middle surface curvatures are = y x w y w x w k k k xy y x (3.1) The stress-strain relations for the k th layer of a multiplayer laminate can be written as { } [ ] {} k k k Q ε σ = (3.) Thus, the stresses in the k th layer can be expressed in terms of the laminate middle surface strains and curvatures as + = xy y x xy y x k k xy y x k k k z Q Q Q Q Q Q Q Q Q γ ε ε τ σ σ (3.3) Value ij Q is different for each layer of the laminate.

60 Resultant Laminate Forces and Moments The resultant forces and moments acting on a laminate are obtained by integration of the stresses in each lamina through the laminate thickness as given below. = = = / / 1 1 t t N k k xy y x z z k xy y x xy y x dz dz N N N k k τ σ σ τ σ σ (3.4) and = = = / / 1 1 t t N k k xy y x z z k xy y x xy y x z dz z dz M M M k k τ σ σ τ σ σ (3.5) N x is a force per unit length (width) of the cross section of the laminate as shown in Figure 3.8(a). Similarly M x is a moment per unit length as shown in Figure 3.8(b). z k and z k-1 are defined in Figure 3.9, noted that z = -t/. (a) (b) Figure 3.8: (a) In-plane forces on a flat laminate, (b) Moments on a flat laminate [4]

61 44 Figure 3.9: Geometry of an n-layered laminate [4] When the lamina stress-strain relations, equation (3.3), are substituted into equations (3.4) and (3.5), we get + = = k k k k z z z z xy y x xy y x N K k xy y x zdz k k k dz Q Q Q Q Q Q Q Q Q N N N γ ε ε (3.6) + = = k k k k z z z z xy y x xy y x N K k xy y x dz z k k k zdz Q Q Q Q Q Q Q Q Q M M M γ ε ε (3.7) However, x ε, y ε, xy γ, x k, y k and xy k are not function of z but are the middle surface values so can removed from under the summation signs. Thus equations (3.6) and (3.7) can be rewritten as + = xy y x xy y x xy y x k k k B B B B B B B B B A A A A A A A A A N N N γ ε ε (3.8)

62 45 M M M x y xy B = B B B B B 1 6 B B B ε x ε y γ xy + D D D D D D 1 6 D D D k k k x y xy (3.9) Where A B D ij ij ij = = = N ( Qij ) ( zk zk ) k 1 k = N ( Qij ) ( zk zk 1 ) k = 1 k N 3 3 ( Qij ) ( zk zk 1 ) k = 1 k (3.3) A ij are called extensional stiffness, bending stiffness. B ij are called coupling stiffness, and D ij are called Symmetric and Unsymmetrical Laminates The laminate that is symmetric in geometry and materials properties about the middle surface called symmetric laminate as shown in Figure 3.1(a). For unsymmetrical laminate there are not symmetric about the middle surface as shown in Figure 3.1(b). Because of the symmetric, all the coupling stiffness, that is shown to be zero. While for the unsymmetrical laminate, B is not zero. ij B ij can be A general laminate has layer of different orientations θ where -9 θ 9. The laminate [/45/9/9/45/] and [-45/9/9/-45] are the examples of symmetric laminates. The laminate [/9//9//9], [-3/6/-3/3/-3/45] are the example of the

63 46 unsymmetrical laminate. The numbers in the bracket denote the orientation of the lamina from the references axes as shown in Figure 3.3. The elimination of coupling between bending and extension has two important practical ramifications. First, the laminates are much easier to analyze than the laminates with coupling. Second, the laminates do not tendency to twist from the inevitable thermally induced contractions that occur during cooling following the curing process. Symmetric laminates are commonly used unless special cases need an unsymmetrical laminates. Many physical applications of laminated composites require nonsymmetrical laminates to achieve design. (a) Symmetric (b) Unsymmetrical Figure 3.1: Cross-sectional views of laminates [6] 3.4 Stiffened Plate Stiffened plates have been used for many years especially in the fields of bridges, ships, aircraft and towers. With the advancement of fiber-reinforced composite materials, current engineering application such as high-speed aircraft designs use these same stiffened panel concepts incorporating the newer materials. These newer materials provide more design variables to optimize and improve the chances of

64 47 minimizing structural weight. By taking advantage of the beneficial tailoring capability of the material, the panel face sheets and core sheet become orthotropic by them, further complicating stiffness, thermal expansion, and thermal bending formulations. Stiffeners are used when it is required to stiffen essentially flat load-bearing panels. These stiffeners can be any geometry shape, but often top hat sections are used as shown in Figure These sections can be varied in strength and stiffness by using different configurations. Ideally the top hats will be bonded to the load-bearing plate rather than bolted, to enable the maximum stiffness of the overall unit to be achieved. Figure 3.1 illustrates the typical stiffened panels. Figure 3.11: A hat-stiffened plate [6] Figure 3.1: Various types of stiffened panels [6]

65 48 Stiffeners are commonly used to increase the bending stiffness of thin-walled members (plates and shells). The stiffeners add an extra dimension of complexity to the model compared to unstiffened plates. They can carry more service load than unstiffened plates for a given unit weight. Stiffened panels are quite efficient for lightly loaded areas and applications of high temperature gradients. These qualities make them desirable for use as hot structure on high-speed vehicles where weight reduction is a paramount objective. Figure 3.13 represents the schematic of the typical stiffener geometry. Stiffener can be divided into two main groups. First is the closed section stiffener such as hat-shaped stiffener and the second is the open section such as I, T and J-shaped stiffeners. Figure 3.13: Schematic of T, J, blade, and Hat stiffener geometry [6]

66 Bending of Simply Supported Rectangular Plates Governing Equations Let us consider the general class of laminated rectangular plates that are simply supported along edges x =, x = a, y =, y = b and subjected to an external transverse load q (x,y) as shown in Figure 3.14, in the absence of thermal effects and in plane forces. Figure 3.14: Plate Geometry [9] The general equation of motion governing bending deflection w for a unidirectional laminated plate can be expressed by the following equation, w w w D 11 + ( D1 + D66 ) + D = q (3.31) 4 4 x x y y To obtain the solution for the deflection equation (3.31) must be solved subject to the simply supported boundary conditions on all edges of the rectangular plate. At x = and x = a w = M x = At y = and y = b w = M y = (3.3)

67 5 Where the bending moments are related to the transverse deflection by the following equations, M x = D 11 w + D x 1 w y M y = D 1 w + D x w y (3.33) M xy = D 66 w x y 3.5. The Navier Solution In Navier method, the displacement w is expanded in a double trigonometric (Fourier) series in terms of unknown parameters. The choice of the trigonometric functions in the series is restricted to those which satisfy the boundary conditions of the problem. The load q(x, y) is also expanded in a double trigonometric series. Substitution of the displacement and load expansions into the governing equation should result in an invertible set of algebraic equations among the parameters of the displacement expansions. The boundary conditions in equation (3.3) are satisfied by the following form of the transverse deflection, where n= 1 m= 1 w( x, y) = W sinαx sin βy (3.34) mn mπ nπ α = and β = a b

68 51 W mn are coefficients to be determined such that the governing equation (3.31) is satisfied everywhere in the domain of the plate. The load can also be expanded in the series form as, n= 1 m= 1 q( x, y) = Q sinαx sin βy (3.35) mn where Q mn 4 b = ab a mπx nπy q( x, y) sin sin dxdy a b (3.36) Substitute the equations (3.34), (3.35) and (3.36) into equation (3.31), yields n= 1 m= { W [ D α + ( D + D ) α β + D β ] + Q } sinαx sin βy = mn mn (3.37) The equation must hold for every point (x,y) of the domain < x < a and < y < b, the expression inside the curl brackets should be zero for every m and n. This yields where 4 Q mn W mn = (3.38) d mn [ D m s + ( D + D ) m n s D n ] d mn = π (3.39) b where s = b/a

69 5 Then the equation (3.34) becomes Qmn w( x, y) = sinαx sin βy (3.4) d n= 1 m= 1 mn The load coefficients Q mn are different for various types of loading. In particular, for uniformly distributed load q (x, y) =, a constant, on the surface of the plate, we have 16q = for m, n odd. (3.41) π mn Q mn For a point load Q located at (x, y ), the load coefficients are given by q (x, y) = Q. Q mn = 4 q mπxo nπy o sin sin m, n = 1,, 3, (3.4) ab a b

70 CHAPTER IV FINITE ELEMENT IMPLEMENTATION 4.1 Introduction The finite element method (FEM) is a powerful computational technique for the solution of differential and integral equations that arise in various fields of engineering and applied science. Typical problems areas of interest in engineering and mathematical physics that are solvable by use of the finite element method include structural analysis, fluid flow, mass transport, and electromagnet potential [9]. The basic idea of the finite element method is to view a given domain as an assemblage of simple geometric shapes, called finite element, for which it is possible to systematically generate the approximation functions needed in the solution of differential equations by any of the variation and weighted-residual methods. The ability to represent domains with irregular geometries by a collection of finite element makes the method a valuable practical tool for the solution of boundary, initial, and eigenvalue problem arising in various fields of engineering.

71 54 The model that produced by this method represents the ideal condition of the problem. It is because in modeling the problem, we have to consider all the factors that will influence the analysis result. For instance, in calculating the stresses in a composite laminated plate under bending condition, the results are affected by the properties of the composite materials and the angle of lamination. If there is any changing of these factors, we need to calculate the results from the basic as mentioned in chapter III. The finite element method is applied in analysis the continuum structure. This structure consist the individual elements that connected with nodes as shown in Figure 4.1. In this modeling, we can obtain the deflections, stresses, strain and many other related information which depends on the analysis that we done. Figure 4.1: Finite element model The finite element method (FEM) can be divided into three categories depending on the nature of the problem to be solved. The first category is equilibrium problems or time-independent problem. The majority of applications of the FEM are included in this category. The solution of equilibrium problems in the solid mechanics area, displacement distribution and stress distribution can be solved by this method.

72 55 The eigenvalue problems of solid and fluids mechanics are fall into the second category. These are steady-state problems whose solution often requires the determination of natural frequencies and mode shapes of vibration of solids and fluids. Another class of eigenvalue problems includes in the stability of structures and the stability of laminar flows. The third category is the multitude of time-dependent or propagation problems of continuum mechanics. This category is composed of the problems that result when the time dimension is added to the problems of the first and second category. As indicated previously, the finite element method has been applied to numerous problems, both structural and nonstructural. This method has a number of advantages that have made it very popular. The abilities are given below [1], 1) Model irregularly shaped bodies quite easily. ) Handle general load conditions without difficulty. 3) Model bodies composed of several different materials because the element equations are evaluated individually. 4) Handle unlimited numbers and kinds of boundary conditions. 5) Vary the size of the elements to make it possible to use small element where necessary. 6) Alter the finite element model relatively easily and cheaply. 7) Include dynamic effects. 8) Handle nonlinear behavior existing with large deformations and nonlinear materials.

73 56 4. Linear Static Analysis The linear static analysis represents most of the basic analysis. Linear means that the computed response displacement or stress, for example is linearly related to the applied force. Whereas, static means that the forces do not vary with time or, that the time variation is insignificant and can therefore be safely ignored [6]. In this part, we presume that the structures are in equilibrium. When the applied loads are shifted, the structure will return into the undeformed shape. In some cases, the structures undergo to deform without any additional load. In this condition, the structure becomes instable and subjected to buckle. The static analysis equation is: [K]{u} = {f} where [K] is the system stiffness matrix (based on the geometry and properties), f is the vector of applied forces (which we specify), and u is the vector of displacements that need to compute. Once the displacements are computed, it will be used to compute element forces, stresses, reaction forces, and strains. The applied forces may be used independently or combined with each other. The loads can also be applied in multiple loading subcases, in which each subcase represents a particular loading or boundary condition. Multiple loading subcases provide a means of solution efficiency, whereby the solution time for subsequent subcases is a small fraction of the solution time for the first, for a particular boundary condition.

74 Finite Element Analysis Procedures The FEA modeling is divided into two sections, namely; Modeling for normal composite laminated plate and modeling for composite hat-stiffened laminated plate Modeling for Unstiffened Composite Laminated Plate In this modeling, a 5 mm square plate will be created. The plate is made of carbon fiber with average thickness.14 mm and the mechanical properties of the carbon fiber are given in Appendix A. The model is simply supported around the outer edge and a 1g gravity load is applied normal to the plate. The plate is modeled with flat plate elements. Nodal displacements and element stresses are computed. 5 mm 5 mm Figure 4.: FEA model This model uses SI units: millimeters (mm) for length, Newton (N) for force, and second (sec) for time. Below describe the procedure to create the geometry, finite element mesh, load and constraints.

75 58 1) Modeling the geometry of the plate Start to create the plate by following this step of common, Geometry/Curve- Line/Rectangle. From the appearance window, enter the first corner of rectangle and normally we enter all zero for the first corner. Then enter the diagonally opposite corner of the rectangle. In this model, the diagonally opposite corner is 5 for X and Y while Z equal to. Then click OK. Resize and center the display of the rectangle by pressing Ctrl+A. ) Creating the applied force area To create the applied force area on the center of the rectangle chooses Geometry/ Curve-Circle/Center. Enter the location at the center of circle with X and Y equal to 15 and Z equal to. Click OK. Then enter the radius of the circle equal to.5. Click OK and Cancel. 3) Cresting the Boundary Surface We may use the Geometry Boundary Surface command to create a boundary. A series of lines and curves with coincident endpoints are selected. Holes can be added by picking existing curves inside the boundary curves that form closed holes. Boundaries are created from any number of continuous curves. These curves must be either joined at the ends or have coincident points and be fully enclosed. They cannot just intersect. Boundaries can contain holes, as long as the area of the hole is completely contained within the boundary and they do not overlap. MSC/N4W will automatically determine which curves if any represent holes in the boundary. Because of the arbitrary geometric nature of boundaries, many models may require you to be more careful in the mesh generation process to obtain a good mesh.

76 59 4) Defining the material properties After creating the surface, the characteristics of the materials should be defined by using command Material under the submenu Model. MSC/N4W supports seven types of materials - Isotropic, D Orthotropic, 3D Orthotropic, D Anisotropic, 3D Anisotropic, Hyperelastic (Mooney-Rivlin/Polynomial form), and Other Types. From the appearance window, click the material type button and select D orthotropic. In general the D material types should only be used by plane (and axisymmetric) elements and the 3D formulations should only be used by solid elements. For some analysis programs however, the 3D formulations are used to add transverse properties to plate elements. Then enter the properties of the material. For bending test, the material properties that needed are modulus Young shear modulus Young, and Poisson s ratio. 5) Defining the Element Properties Select the submenu property from the menu model. Click on the Elem/Property type button and under the volume element, check the Laminate common. Model/ Property/(Element/property type)/ Laminate. Then click OK. Properties of this type are different than those for any other type of element. We must specify a material ID, thickness and orientation angle for each layer or ply in the laminate. In general, we must list all plys in the laminate. If the laminate is symmetric, the Symmetric Layers option can be set with only enter one half of the layers. MSC/N4W supports up to 9 plys on a property, but only 18 at a time can be displayed in the dialog box. By pressing Next or Prev, the dialog box will scroll to show the other plys that make up the property that we are defining. 6) Meshing the model Mesh the model by following this step of common. Mesh/Mesh Control/Size along curves. This command defines the number and spacing of elements along selected curves. When setting the mesh size using this method, it overrides all

77 6 point and default sizes. After selecting the curves, we will see the Mesh Size along Curve dialog box. Choose a "Number of Elements" and then every curve that we selected will be meshed with that number of elements. After defining the mesh size along the curves, mesh the model by using the following command Mesh/Geometry/Surface. Select all the surfaces and then click OK to mesh the model. 7) Defining constraint on model After the FEA model bas been mesh, we need to put the constraint on the model as given in his common Model/ Constraint/ Set. The constraints must be created in sets and we can create nodal constraints, geometry based constraints or constraint equations. In this modeling, we use geometry based constraints that allow us to select points, curves or surfaces to constrain before or after nodes are on them. Geometry based constraints have three options, fixed, pinned or no rotations. The model is simply supported around the outer edge, therefore we use pinned command around the curves at the outer edge of the model. Simply select the curves through the standard entity selection box, and then select the type of constraint. Nodes attached to that curve will then be constrained upon translation or expansion. 8) Defining load on model Similarly to the constraint, we need to set the load first. Model/ Load/ Set. We can make a new load set or activates an existing set. Enter an ID which does not appear in the list of available sets. Then enter a title and press OK. Then we put the load on the model. Model/Load/On Surface. Select the surface where the load applied. In this problem,the load will be applied on the surface at center of the model.

78 61 9) Analysis the FEA model After the previous have been done, we can now start to analyze our FEA model. There is several type of analysis that we can do with this software. It depends on what type of output that we need. In this problem, the linear static analysis will be done to obtain the stress distribution and the displacement. After the model has been analyzed, we can obtain the analysis output in the form that we need by using this command, View/Select. We can choose the deformed style and contour for the verities output Modeling for Composite Hat-Stiffened Laminated Plate Similarly to the normal laminated plate, a 5 mm square plate will be created. The plate is made of carbon fiber with average thickness.14 mm and the mechanical properties of the carbon fiber are given in Appendix A. The only different is in this modeling, the plate is stiffened by a hat-shaped stiffener. 1) Modeling of the FEA model In order to the complexity of the structure, the stiffened plate model is not suitable to be drawn by using the device in MSC/N4W. The more appropriate way to prepare the FEA model is using engineering technical drawing software such as Autocad, Solidwork, etc. In this project, the SOLIDWORK software is used to draw the FEA model. This model uses SI units: millimeter (mm.) for length, Newton (N) for force, and seconds (sec) for time. Note that MSC/N4W assumes a consistent set of units, so you need to be consistent and not mix units. The detail drawing of the FEA model is enclosed at Appendix B. After finish the drawing, save the drawing in ACIS format (*sat).

79 6 ) Importing the FEA model into FEM software Start to import the FEA model by choosing the submenu import from file. File/Import/Geometry. A window will come out and then choose the directory where you want to import the model. After choosing model from the directory, a window will appear. Under the Entity Options change the geometry scale factor to 1. Then click OK. This is important because if we not change to scale 1, the size of the model that we import is not coinciding with our actual model size. For instance, if the actual height of the model is 1 mm and we use scale factor 39.37, the height of model that we imported into the FEA software will become 3937 mm which is times bigger than our actual model size. 3) Defining the material properties As mentioned before, the characteristics of the materials are defined by using command Material under the submenu Model. Choose the D orthotropic material and a window will appear. Key-in the modulus Young, Shear modulus, and Poisson s ratio into the window to define the material properties of the model. 4) Define the element properties Because of the improperly analysis results obtained from the laminate property, therefore the hat-stiffened plate model will be model by using solid property. Select the submenu property from the menu model. Click on the Elem/Property type button and under the volume element, check the solid common. Model/ Property/(Element/property type)/ Solid. Then click OK. 5) Meshing the model Mesh the model by following this step of common. Mesh/Geometry/ Solids. A window will come out and then under the basic curve sizing, change the Max

80 63 Element size to 1. Then click OK. Another window will appear, under the property column, select the element property title that put in at step 4. Then click OK to mesh the model. The model is mesh by using the tetrahedral element. The following procedures in modeling the FEA model are same as the unstiffened composite laminated plate from step 7 to step 9. The procedures listed above are general steps in solving FEA structural problem. The additional steps are depending on the type of the model and analysis that need to carry out.

81 CHAPTER V EXPERIMENTAL PROCEDURES 5.1 Composite Fabrication There are various techniques for the fibre-reinforced composite fabrication and these may be considered into two main group [3]: a) Open mould process in which during the mould operating, the material is in contact with the mould on one surface only. b) Closed mould technique in which the composite is shaped between the male and female moulds Both the open and closed mould process can be divided into three categories: manual, semi-manual, and automatic. The manual techniques include the hand lay-up and pressure bag. The semi-manual techniques cover the cold press, hot press and the resin-injection method. The automatic techniques include pultrusion, filament winding and injection moulding.

82 65 The driving factors behind manufacturing considerations for composite materials are primarily cost effectiveness, the minimization of scrap, the control of assembly operation and the sourcing of standard parts. Furthermore, products of nominally the same form, but manufactured different routes, could have markedly different properties. This not only affects the stiffness and strength, but also other attributes such as surface finish, chemical resistivity and internal damping, as well as electrical and thermal properties. This chapter will just discus the two commonly used method in fabricate the laminated composite, which are hand lay-up and vacuum bagging method Hand Lay-up Method The hand lay-up technique is one of the oldest, simplest and most commonly used methods for manufacture of composite, or fiber-reinforced, products. This technique is best used where production volume is low and other forms of production would prove too expensive. In this technique only one mould is used and this may be either male or female. This is the process wherein the application of resin and reinforcement is done by hand onto a suitable mold surface. The resulting laminate is allowed to cure in place without further treatment [6].

83 66 The typical process of the Hand lay-up is listed below: 1) Mold Preparation - A mold of the part to be made is created and a release film is applied to the molds surface. ) Gel Coating - This consists of a specially formulated resin layer that will become the outer surface of the laminate when it is complete. This layer is only necessary when a good surface appearance is required. 3) Hand Lay-Up - Fiberglass is applied in the form of chopped strand mat, cloth or woven roving. Premeasured resin and catalyst (hardener) are then thoroughly mixed together. To ensure complete air removal and consolidation of the excess resin, serrated rollers are used to press the material evenly against the mold. As shown in Figure ) Finishing - The composite is allowed to completely harden and any machining or assembly can be performed. Some advantages of the Hand lay-up process are: 1) Large and complex items can be produced. ) Relatively little equipment investment is needed. 3) The start-up lead-time and cost are minimal. 4) Tooling costs are low. 5) Semiskilled workers are easily trained. 6) Design flexibility. 7) Molded-in inserts and structural changes are possible. 8) Higher fiber contents and longer fibres than with spray lay-up.

84 67 Some disadvantages of the Hand lay-up process are: 1) A labor-intensive process. ) A low volume process. 3) Longer curing times, since room temperature catalysts are usually used. 4) Part quality is very dependant upon operator skill. 5) Product uniformity is difficult among parts. 6) Only one good (molded) surface is obtained. 7) Waste produced is high. 8) Health and safety considerations of resins. The lower molecular weights of hand lay- up resins generally mean that they have the potential to be more harmful than higher molecular weight products. The lower viscosity of the resins also means that they have an increased tendency to penetrate clothing etc. Figure 5.1: Manual Lay-up process [6]

85 Vacuum Bagging This is basically an extension of the hand lay-up process described above where pressure is applied to the laminate once laid-up in order to improve its consolidation. This is achieved by sealing a plastic film over the wet laid-up laminate and onto the tool. The air under the bag is extracted by a vacuum pump and thus up to one atmosphere of pressure can be applied to the laminate to consolidate it [6]. Some advantages of the vacuum bagging process are: 1) Higher fiber content laminates can usually be achieved than with standard wet lay- up techniques. ) Lower void contents are achieved than with wet lay-up. 3) Better fibre wet-out due to pressure and resin flow throughout structural fibres, with excess into bagging materials. 4) Health and safety: The vacuum bag reduces the amount of volatiles emitted during cure. Some disadvantages of the vacuum bagging process are: 1) The extra process adds cost both in labor and in disposable bagging materials. ) A higher level of skill is required by the operators. 3) Mixing and control of resin content still largely determined by operator skill.

86 69 Figure 5.: Vacuum Bag mould assembly [6] 5. Laminate Preparation The first step in preparation of the laminate is to choose the types of fibre and matrix that will be used to fabricate a laminate. As mentioned in the previous chapter, there are several types of fibre and matrix in the market, so in this project the materials that will be used are the carbon fibre and epoxy as the resin. Second step is to design the lamina orientation in the laminate. In this project, the lamination that used in tensile test specimens are [///], [9/9/9/9], [45/45/45/45], whereas for laminate plate is [/9/9/]. All the laminates that will be produced are four layers laminate and symmetric to the middle surface of the laminate. Thus, there is no coupling between bending and extension. The fabrication method that will be used in this project is hand lay-up method. The mechanical properties that produced by this method are not good because the difficulty in removing the entrapped air.

87 Hand Lay-up Procedure The procedures that used in the fabrication of composite plate are as follow: 1) Water is used to clean up the surface of glass plate in order to avoid any foreign particles or dusts remain on the surface. The cleanliness of the glass surface will affect the quality of the finish product. ) A plastic sheet is placed on the glass surface. Silicon sealant is used to bond the plastic to the glass plate. 3) The surface of the plastic sheet is cleaned using tissue paper before the first layer of carbon fiber placed on it. 4) The mixture of the resin and hardener which according to the weight ratio mentioned before is spread and flatten on the surface of the glass table by using a brush. 5) A layer of fibre is placed on the resin. A roller is used to wet the fibre evenly with the resin and to remove the entrapped air. 6) Repeat the procedures (4) and (5) until the desired layer or thickness of laminate. 7) Anther plastic sheet is placed on the surface pf the laminated composite produced. Again silicon sealant is used to bond between the two plastic sheet to avoid any leakage occur. 8) The laminated composite is then cured at the room temperature at least 4 hours to ensure that it is dry enough for further processes. 9) A finished laminated composite plate is obtained and shown in figure 5.3.

88 71 Figure 5.3: A finished laminated composite plate 5.3 Tensile Test Specimen Preparation The specimen size is prepared according to ASTM D-339 standard, which is a standard test method for tensile properties of polymer matrix composite materials. Figure 5.4: Specimen Specification

89 7 The details of the tensile test specimen are given in Table 5.1 and Table 5.. From the tables we can mention that the materials used is carbon fibre and epoxy as the resin. The unidirectional lamina is used in producing the specimen. The weight ratio of resin to the fibre is 5 to 5. This means that by referring to the weight of the produced laminate, 5 % of the weight is contributed by the fibre and 5 % by the resin. There is another weight ratio that commonly use is 6 to 4. This means 6% resin and 4 % fibre. Besides, we can also use volume ratio to determine the ratio of matrix to reinforcement in laminate. But weight ratio is common use because of the easy determination of the ratio compare with volume ratio. The aluminum tab is attached to the specimen by using epoxy adhesive. Before attaching the tab to the specimen, we need to do sand blasting process for the tab to roughen the smooth surface. This is because the coarse surfaces will give good holding compare with the smooth surface. This process has been done in the casting laboratory. Figure 5.5 shows the specimens that have been produced by using hand lay-up method. There are three specimens for each type of lamination. We need to get the average of the experimental data so that our results are more accurate and close to the exact data. Table 5.1: Specimen Specification Specimen Orientation W (mm) e (mm) L (mm) 1 [///] [9/9/9/9] [45/45/45/45]

90 73 Table 5.: Materials Specification Matrix Epoxy Fibre Carbon Number of layer 4 Type of lamina Unidirectional Tab Aluminum Ratio of matrix to reinforcement 5% -- Matrix 5% -- Unidirectional carbon Figure 5.5: Tensile Test Specimen 5.4 Bending Test Specimen Preparation There are two composite plate have been produced for the bending test, one is for the unstiffened plate and another one is for the stiffened. The materials that used for

91 74 the plate are also carbon fiber and epoxy. The weight ratio of resin to the fiber is 5 to 5. The orientation of the lamina for the composite is /9/9/. The materials and tool that used for the hand lay-up process are shown in figure 5.6. Roller Epoxy Hardener Carbon fiber lamina Figure 5.6: Materials and tool for hand lay-up process For the hat-stiffened plate, there is a stiffener mould has been made to produce the composite stiffener. Then the stiffener will be attached to the composite plate by using epoxy adhesive as shown in figure 5.7.

92 75 (a) (b) Figure 5.7: (a)hat shaped stiffener, (b) Hat-stiffened plate 5.5 Tensile Test Tensile test is commonly performed in order to determine the in-plane tensile properties for materials specifications, research and development, quality assurance, structural design and analysis. In this test, we may be obtained the ultimate tensile strength, ultimate tensile strain, tensile modulus, and Poisson s ratio and transition strain in the test direction. The tensile test that will be conducted in this project is based on American Society for Testing and Material tensile Test Method (ASTM D339). This method is used to determine the tensile properties for polymer matrix composite materials reinforced by high modulus fibres. The composite forms are limited to continuous fibre or discontinuous fibre-reinforced composites in which the lamina is balanced and symmetric with respect to the best direction.

93 76 A specimen having a constant rectangular cross section as shown in Figure 5.8 is mounted in the grips of a mechanical testing machine and monotonically loaded in tension while recording load. The ultimate strength of the material can be determined from the maximum load carried before failure. The displacement transducer is used to monitor the strain of the specimen then the stress-strain response of the material can be determined. Figure 5.8: Tensile Specimen where, e = tab length w = width of the specimen t = thickness of each layer L = length between the tab Experimental Determination of Strength and Stiffness When the tensile load is subjected to a tension load, it wills results extension in the direction of the applied load and contraction perpendicular to the load. The basic tenet of the experiments is that the stress-strain behavior of the materials is linear from zero loads to the ultimate or fracture load. There are three loading condition (longitudinal, transverse, and angle) of the tensile test will be performed to obtain the

94 77 properties of the lamina in the principle material directions. First, consider a uniaxial tension test in the 1-direction on a flat piece of a unidirectional reinforced lamina as shown in Figure 5.9. The tensile properties is calculated using the following equations, Figure 5.9: Uniaxial loading in the 1-direction P σ 1 = A σ 1 E1 = ε1 ε v1 = ε1 Pult X = A (5.1) where P, P ult Applied load and maximum load obtained in tensile test respectively σ 1 X Average stress in the 1-direction Axial or longitudinal strength (1-direction) ε,ε 1 Strain at the applied and transverse load respectively

95 78 v 1 Poisson s ratio E 1 A Young s modulus in the 1-direction Cross-sectional area of the specimen Second, consider a uniaxial tension test in the -direction on a flat piece of unidirectional reinforced lamina as in Figure 5.1. The tensile properties is calculated using the following equations, Figure 5.1: Uniaxial loading in the -direction σ E P = A σ = ε ε 1 v 1 = (5.) ε where σ Y E Pult Y = A Average stress in the -direction Transverse strength (-direction) Young s modulus in the -direction

96 79 At this point, the stiffness properties of the lamina should satisfy the reciprocal relations as following, v E 1 1 v E 1 = (5.3) If the equation (5.3) has not been satisfied, one of these possibilities exists: 1) The data were measured incorrectly. ) The calculations were performed incorrectly. 3) Linear elastic stress-strain relations cannot describe the material. Third, we consider a uniaxial tension test at 45 to the 1-direction on a flat piece of lamina as shown in Figure The shear modulus is calculated using the following equations, Figure 5.11: Uniaxial loading at 45 to the 1-direction E G x 1 P = A (5.4) ε x 1 = (5.5) v1 ( + ) E E E E x 1 1

97 8 where E x Young s modulus in the x-direction G 1 Shear modulus in the 1- plane ε x Strain at the applied load 5.5. Testing Apparatus Instron 46 testing machine is used to perform the tensile test as shown in Figure 5.1. This machine consists of computer system, control panel, crosshead, load frame panel, and load cell grip. The engineering constants that would be obtained are Poisson s ratio and Young s modulus. Figure 5.1: Instron 46 testing machine

98 Tensile Test Procedure The details of the specimen materials, lamination, and specification are mentioned earlier in section 5.4. Strain gauge is attached to the center point of the specimen as shown in Figure 5.13 to obtain the strain reading. Figure 5.13: Specimens with strain gauge The crosshead displacement rate is mm/minute. Below is the procedure to conduct the tensile test. 1) The specimen is fixed to the grip of the Instron testing machine and the specimen shall be in axial alignment with the direction in pull. ) Strain gauge is connected to the data logger and reset the initial value to zero before load is applied. 3) Select the required test software and enter the specimen details such as width, thickness and length at specimen menu. 4) Select the crosshead speed, maximum load, and other data. 5) Select the outputs that we want from the test. 6) Set the load balance to zero press the IEEE button to run the test. 7) All the data will be taken automatically and display on the monitor screen in graph. 8) Finally we can printer out the data and draw the graph using plotter.

99 8 The specimen will be loaded by pushing the specimen at a constant rate until the specimen fail. 5.6 Bending Test Bending test is performed in order to investigate the behavior of the simply supported unstiffened and stiffened composite laminated plate under a distributed load on a small area at the center of the plate. In this testing, the magnitude of the lateral load and the deflection of the plates at various will be collected as shown in Figure One of the displacement transducer is located at the center of the plate and is known as 1 st location. Another transducer is located at the coordinate and is known as nd location. nd location 1 st location Figure 5.14: Location of the displacement transducers at the composite plate

100 Testing Apparatus The hydraulic pressing machine is used to perform the bending test as shown in Figure This machine uses manual hydraulic system to operate and the maximum power that can be generated is 1 ton. This machine consists two main parts which are hydraulic arm and pressing pump. A test rig is fabricated to test the composite plate as sown in Figure This test rig is made by four pieces of L-bar and bars were jointed together by using arc welding technique. The detail drawing of the test rig is enclosed at Appendix B. This rig is used as the base to put the composite plate on the pressing machine as shown in Figure Besides, two displacement transducer (LVDT) will be used to measure the deflection of the plate as shown in Figure Hydraulic Press arm Bending test rig Hydraulic Pump Figure 5.15: Hydraulic Press Machine

101 84 Figure 5.16: Bending test rig Figure 5.17: Displacement transducer (LVDT) 5.6. Bending Test Procedure The details of the specimen materials, lamination, and specification are mentioned earlier in section 5.4. Strain gauge is attached to the center point of the specimen as shown in Figure 5.18 to obtain the strain reading. 1) Put the test rig on the pressing machine and lock the rig on the machine by using G-clamp.

102 85 ) Put the plate on the center of the test rig and a LVDT is placed at the center node in order to obtain the deflection on this node. 3) Connect the LVDT, strain gauge, and load cell to the data logger. 4) Set the initial value of the LVDT to zero. 5) Apply load on the plate by pressing the hydraulic pump. 6) Record down the deflection of the plate at every 5 kg increment of force and stop the test once the plate failed. Figure 5.18: Plate specimen with strain gauge

103 CHAPTER VI RESULT AND DISCUSSION 6.1 Tensile Test Result The tensile test is conducted based on the American Society for Testing and Materials Tensile Test Method (ASTM-339). In this project, the tensile test has been performed for three different type of laminate orientation composite as mentioned at chapter 5. The engineering constants have been measured in the tensile test and the full data and the graphs of Stress versus strain for different types of specimens are shown in APPENDIX C. In this analysis, we assumed that the composite laminate satisfy the linear elastic stress-strain relations from zero loads to the ultimate or fracture load. Table 6.1 and 6. show the summary results obtained during the tensile test.

104 87 Table 6.1: Results of tensile test Specimen [///] [9/9/9/9] [45/45/45/45] Thickness, t (mm) Specimen Specimen Specimen Average Modulus Young, E (GPa) Specimen Specimen Specimen Average Shear Modulus, G 1 (GPa) Specimen Specimen Specimen Average Table 6.: Summary of tensile test result Specimen Orientation [///] [9/9/9/9] [45/45/45/45] Maximum load (KN) Ultimate Stress, σ ult (MPa) Modulus Young, E 1 (GPa) Poisson Ratio,v Modulus Young, E (GPa) Poisson Ratio,v Modulus Young, E x (GPa) Shear Modulus, G 1 (GPa)

105 Discussion On Tensile Test Results By referring to Table 6., we can mention that the Young s modulus for the longitudinal direction (E 1 ) is GPa, the Young s modulus for the transverse direction (E ) is 7.97 GPa, the shear modulus (G 1 ) is GPa, and the Poisson s ratio for 1- plane is.853. In comparison, the average ultimate stress and maximum load for the specimen with degree fiber orientation is the highest among the tested samples. The maximum recorded applied load before failure is kn. This has been verified that the fiber gives the highest strength at the longitudinal direction and the failure of this specimen is shown in Figure 6.1. The figure 6.1 shows that the specimen failed by spreading out its fiber and obviously we can see the breakage of the fibers. Figure 6.1: Failure mode of specimen with degree fiber orientation The specimens with 9 degree fibers orientation represented the lowest strength among the tested specimens. The maximum applied load before failure is.88 kn. This is because the fibers give the lowest strength at the transverse direction of the fibers. For this type of orientation, only the resin is used to resist the tension caused by the tensile load. The failure mode of this specimen is shown in Figure 6.. From the figure, we can mention that the specimens failed at the transverse direction of the specimen which is also the fiber orientation.

106 89 Figure 6.: Failure mode of specimen with 9 degree fiber orientation The strength for the specimen with 45 degree fibers orientation is higher than the specimen with 9 degree fiber orientation but lower than the specimen with degree fibers orientation. The maximum applied load before failure is.5836 kn. The failure mode of this type of specimen is shown in Figure 6.3. From this figure, we can mention that the specimens failed at the fiber orientation. The modulus Young that obtained from these specimens is used to define the shear modulus of the material and the obtained value is GPa. Figure 6.3: Failure mode of specimen with 45 degree fiber orientation The mechanical properties listed in Table 6.1 will be used in modeling the FEA model in numerical analysis.

107 Discussion On Graph Stress Versus Axial Strain Based on the data obtained during tensile test, graph stress versus axial strain has been plotted as shown in Figure C1 to Figure C5 in Appendix C. Graphs are plotted with Stress versus strain for three types of lamination of specimens. By referring to the Figure C1, it represents the graph for the specimens with degree fibers orientation in which the tensile load applied at the longitudinal direction of the fibers. The graph plotted is similarly for the three samples which show a straight line from origin with a positive gradient. Therefore, we can conclude that the increment of the axial strain is proportional to the applied stress. When the applied stress increases, an axial strain will also increase accordingly. Thus, the materials have fulfilled the linear elastic stressstrain relations. The Young s modulus (E 1 ) of the materials can be obtained from the gradient of the graphs. Besides, the straight lines also represent that the fibers in general show a brittle catastrophic failure in which it doesn t experience plastic as metallic materials which generally show a yield prior to failure. The Figure C shows the graph for the specimen with 9 degree fibers orientation in which the tensile load applied at the transverse direction of the fibers. The graph plotted also similar for the three samples of specimen. From the plotted graph, it is evident that when the applied stress increases, an axial strain will also increase accordingly and represent a yield before the specimens show the plastic condition. When the plastic condition occurred, the axial strain increases without any additional loads. Therefore, the graph shows horizontal straight lines when the stress achieves until certain level of applied loads. The maximum stress that can be afforded by the specimen is less than 7 MPa. This value is great lesser than the specimen with degree fibers orientation which maximum stress is more than 85 MPa. The plastic condition represented is due to the resin of the laminated composite. As mentioned before, the strength is weak at the transverse direction of the fiber. Therefore, in this loading condition, most of the tensile loads are carried by the resin in the samples. The resin

108 91 used is polymer and polymer represents elastic and plastic characteristic when we apply load on it. Hence, we can conclude that this graph is actually representing the behavior of the resin. The Young s modulus (E ) of the materials can be obtained from the gradient of the graphs on linear condition. The Figure C3 shows the graph for the specimen with 45 degree fibers orientation in which the tensile load applied at the 45 degree direction of the fibers. The graph plotted also similar for the three samples of specimen. The graph represents the lines which are linear at the first and then slightly become non-linear when the applied stress reached up to 6 MPa and it is evident that when the applied stress increases, an axial strain will also increase accordingly and experience plastic condition before failure occurred. As explained in the previous paragraph, the plastic condition represented is due to the resin of the laminated composite. But for this type of orientation, the plastic condition is not as large as the plastic condition for the specimen with 9 degree fibers orientation. The maximum stress that can be afforded by the specimen is around 11 MPa which is greater than the specimen with 9 degree fibers orientation. This is because the contributions of the fibers in resisting the tensile load but is not as strong as the specimens with degree fibers orientation. The Young s modulus (E x ) on the loading direction can be obtained from the gradient of the graphs on linear condition then the shear modulus (G 1 ) in 1- plane is obtained by using equation (5.5).

109 Discussion On Graph Lateral Strain Versus Axial Strain Figure C4 shows the graph lateral strain versus axial strain for specimen with degree fibers orientation. This graph shows a straight line with positive gradient crossing the origin of the graph. This shows that it is linear relationship between the transverse strain and the longitudinal strain. From the results obtained, the axial strain is always positive and lateral strain is always negative. This is because when tensile load is applied at the longitudinal direction of the specimen, it will cause elongation in this direction and accompanied by contraction in the transverse direction. The Poisson s ratio (v 1 ) of the specimen is denoted by the gradient of the graph. Figure C5 shows the graph lateral strain versus axial strain for specimen with 9 degree fibers orientation. This graph shows a straight line with positive gradient crossing the origin of the graph. This shows that it is linear relationship between the transverse strain and the longitudinal strain. Similarly to the degree fibers orientation specimen, the axial strain is also always positive and lateral strain is always negative. This is because when tensile load is applied at the longitudinal direction of the specimen, it will cause elongation in this direction and accompanied by contraction in the transverse direction. The result also shows that an axial strain is always higher than the lateral strain for any load increment. The Poisson s ratio (v 1 ) of the specimen is denoted by the gradient of the graph.

110 93 6. Bending Test Result In this project, the bending test has been performed for the composite hatstiffened laminated plate and unstiffened plate. The behavior of plates has been measured in the bending test and the full data as well as the graphs load versus displacement for different types of plates are shown in APPENDIX D. Table 6.3 and Table 6.4 show the summary results obtained during the bending test. The plates are simply supported around the outer edge and load is applied normal to the plate until the failure occurred. Bending test is performed in order to investigate the behavior of the simply supported unstiffened and stiffened composite laminated plate under a distributed load on a small area at the center of the plate. Table 6.3: Results of Load and Deflection for unstiffened composite plate Load Displacement, (mm) (kg) Center Coordinate

111 94 Table 6.4: Results of Load and Deflection for composite hat-stiffened laminated plate Load Displacement, (mm) (kg) Center Coordinate The obtained results include the magnitude of the lateral load in kg and deflection in mm of the plates at various locations as shown in Figure The results of the bending test show that the composite hat-stiffened plate has the highest applied load, which is 4 kg compare with unstiffened composite plate which is 14 kg. The maximum deflection before failure occurred for unstiffened plate at the center and coordinate- are 14 and 9 mm respectively. While the maximum deflection before failure occurred for hat-stiffened plate at the center and coordinate- are 14 and 9 mm respectively. The reason that the maximum carry load of stiffened plate is higher than unstiffened plate is mainly because of the stiffener. Stiffener increased the stiffness and strength of the composite by increasing the moment of inertia of the plate structure. This can be clearly defined by using the equation of the deflection of the beam which is simply supported as shown below;

112 95 3 5WL w = (6.1) 384 EI where, w - Vertical deflection W - Applied load L - Distance between the supports E - Modulus Young I - Moment of inertia 3 The moment of inertia of the normal rectangular plate is defined by I = bd / 1. When the stiffener is attached to the plate, it will change the cross-section area of the normal plate and then increases the moment of inertia of the plate. The more stiffeners are added, the higher of moment inertia is increased. Therefore, it is evident that when we fixed all the variables in equation (6.1) except I and w, the deflection will be reduced if the value of I is increased. Hence, we can conclude that stiffened plate are quite efficient for lightly loaded areas and also can carry more service load than unstiffened plates for a given unit weight. Besides that, the strength and stiffness of the composite plate is also influenced by the orientation of fiber in the composite. In this project, the fiber orientation is same for the stiffened and unstiffened composite plate which is (/9) s.

113 Discussion on Unstiffened Composite Laminated Plate Figure D1 shows the graph applied load versus deflection for unstiffened composite laminated plate. The deflection is recorded through data logger and the full data of the bending test listed as in Appendix D. In this case, the deflections are measured at every 5 kg increment of the applied load up to failure. From the results, we can see that two lines like stairs are obtained. This is mainly because of the data logger used cannot measure the displacements which are smaller than 1mm. By referring the approximate line value in the graph, it shows a non-linear relationship between the deflection and the applied load and the lines show ogif pattern. This implies that in the early stage, less strength is required to create deflection. And slowly, more strength has to be applied to create the deflection in the later stage. In this testing, the plate was assumed to be deformed symmetrically to the center of the plate. Therefore, we just examined quarter of the composite plate is convenient and the displacement transducers are located at the position as shown in Figure The first location represents the center of the composite plate while the second location is 3.5 inches away from the center which is denoted by coordinate. From Figure D1, it is obviously that the deflection at the center is higher than the deflection at coordinate. This implies that the maximum deflection is occurred at the center of the entire plate. The failure mode of the plate is shown in Figure 6.4. The damage of the plate is very small compare to the entire area of the plate. As the plate is about to fail, some cracking sound emitted from the plate. It is assumed that the noise is caused by matrix cracking process. The matrix started to crack at the center of the plate at the lower surface and then the crack spread from the center to all direction around the center. After matrix cracking, delamination occurred and followed by fiber breakage.

114 97 Figure 6.4: Failure mode of the unstiffened composite plate Figure D shows the applied load versus strain for unstiffened composite plate. The results is obtained in, 9, (x- and y- direction) and 45 degree fiber direction at the center of the plate. This graph shows a non-linear relationship between the strain and applied load. The graph represents the lines which are linear at the first and then slightly become non-linear when the applied stress reached up to 6 kg and it is evident that when the applied stress increases, an axial strain will also increase accordingly and experience plastic condition before failure occurred. From the graph, it shows that the strain at 9 and 45 degree are always higher than the strain in degree for all the applied loads. The strain gauge in 9 degree direction gives the highest maximum strain value and follow by the strain gauge in 45 degree; strain gauge in degree direction gives the lowest maximum strain value. This implies that the plate deform much in 9 degree than degree direction.

115 Theoretical Analysis of Unstiffened Composite Laminated Plate The theory lamination results are based on the macromechanical behavior of lamina and laminate as mentioned earlier in Chapter III. The results and the steps calculation for the stiffness matrix for the laminate [ /9 /9 / ] is given in Appendix F. Besides that, the sample calculation of the maximum deflection for the unstiffened plate is also given in Appendix F and the comparison of the maximum deflection for experiment results and theoretical values in listed in Table F. From this table, we can mention that the maximum deflection at 1 kg applied load for theoretical value is mm which approximate to the experiment results which give 14 mm. Referring to Table 6.5, FEA analysis give the highest value of maximum deflection. The large difference may due to the material properties in FEA analysis is not exactly same as the specimen in experiment. Table 6.5: The analysis result of maximum deflection at 1 kg applied load Maximum Deflection at 1 kg, (mm) Experiment FEA Theory

116 Discussion on Composite Hat-Stiffened Laminated Plate Figure D3 shows the graph applied load versus deflection for hat-stiffened composite laminated plate. The full data of the bending test is listed in Appendix D. In this case, the deflections are measured at every 5 kg increment of the applied load up to failure. The graph plotted is similarly to the graph in Figure D1 in which also represents two lines like stairs. By referring to the approximate line value, the lines show that the deflection is increased proportional to the applied load. The graph also shows that the deflection at center is always higher than the deflection at coordinate-. Figure 6.5 represents the failure of the stiffened plate. From the figure, we can mention that the plate failed at the stiffener in which cracks were produced on the stiffener and fibers were pulled out from the matrix. This implies that the critical region of the structure is at the stiffener at the area near the edge between stiffener and plate. The local cracking at the failure edges shift the location of the maximum force further into the interior of the bonded length between stiffener and plate. Figure 6.5: Failure of the Stiffened Plate

117 1 Figure D4 shows the applied load versus strain for hat-stiffened composite plate. The result is obtained in and 9 (x- and y- direction) degree fiber direction at the location as shown in Figure 6.6 and the strains are representing the strain on the surface of the plate. This graph shows a non-linear relationship between the strain and applied load. At low applied load, the graph is linear and then slightly become non-linear when the applied stress reached up to 1 kg. From the graph in Figure D4, it shows that the strain at location and 4 are represented by line that is linear from origin. This implies that the strains behave linearly in the degree fiber orientation and the strain value in this direction is greatly lower than the strain value in 9 degree direction. The strain- is higher than the strain-4 and this means that the location is deformed much than location 4. The strains in 9 degree direction are representing by the strain value at location 1, 3 and 5. Refer to the graph, the in this direction increased very slowly at the early stage and the increment of the strain increased when the applied stress reached up to 1 kg. This is clearly shown in line stain-3 and strain-5. Strain-1 is lower with compare to strain-3 and strain-5. This is because location 1 is far from the center of the plate and it is less deformation with compare to location 3 and 5. Srain-3 is higher than strain-5 and this implies that location 3 deform much than location 5. Finally, it can be concluded that the strain in the direction of degree is lower than the strain in the direction of 9 degree.

118 11 Figure 6.6: Location of the strain gauges at the composite hat-stiffened plate 6.3 FEA Simulation Result The linear static FE simulation has been carried for the unstiffened composite laminated plate and composite hat-stiffened laminated plate. The full results of the FEA simulation are given in Appendix E. Linear static analysis use the linear theory of structure in which it based on the assumption to small displacements to calculate structural deformation. Distributed loads were applied on the round surface on the plate and it produced the bending condition with the upper layer in compression. Table 6.6 shows the comparison between the experiment results and finite element analysis for maximum deflection at 1 kg. From Table 6.6, it shows that the FEA value is higher than experiment value for unstiffened plate and gives % of deviation. However, for hat-stiffened plate, the FEA

119 1 value is lower than experiment value and gives 33% of deviation which is considered high if comparing to unstiffened plate. The difference of the deflection between the experimental and FEA simulation is caused by the following factors: 1) The mechanical properties used in the FEA simulation are not exactly same as the specimen in experiment. ) The thickness of the laminates produced is not uniform. 3) There is excessive or insufficient resin between the laminas. 4) Existence of voids caused by the air bubble entrapped between the laminas. 5) The bonding between the stiffener and plate is imperfect. Besides that, there are two more FEA analysis has been done for the squareshaped and T-shaped of stiffened plate. From the obtained results, it shows that the square-shaped stiffened plate give the smallest maximum deflection at 1 kg applied load and follow by hat-stiffened plate gives the second low maximum deflection and the T-shaped stiffened plate gives the biggest maximum deflection among the stiffened plate. This implies that the T-shaped stiffener is less efficiency in strengthening the stiffness of the composite plate. For the overall results, the maximum deflection of the stiffened plate is greatly less than the unstiffened plate. Table 6.6: Comparison of experiment results and FEA value for unstiffened and stiffened plate Maximum Deflection at 1 kg, (mm) Specimen Difference, Experimental FEA (%) Unstiffened Plate Hat-stiffened Plate Square shaped stiffened Plate T shaped-stiffened Plate

120 Discussion On Unstiffened Composite Laminated Plate FEA simulation has been done on the unstiffened composite plate and the result is listed in Table 6.6. Figure E1 in Appendix E represents the displacement contour of the unstiffened plate under 1 kg distributed load on the center of the plate. This figure shows that the plate represented a symmetrical deformed shape to the center and the regions with red color experience the highest deformations compare with the regions with other colors. Therefore, the center of the plate is the critical part for the whole structure and the maximum deflection occurs at the center of the plate and the displacement reduced from the center of the plate. The maximum displacement of the structure is mm at node 548. The outer edge of the plate gives the lowest deformation. The deformed shape of the plate is in a half sinusoid wave and is shown in Figure 6.7. Figure 6.7: Bent plate in half sinusoid wave with deformation scale of 5 The Von Mises stress contour for the unstiffened plate is shown in Figure E to E5 in Appendix E. These figures show the Von Misses stress contour of each layer of the laminate. The stress results show that the critical region of this structure at the center of the plate which is also the applied area of the structure. The maximum stress is 46.4

121 14 MPa, 63.1 MPa, 3.8 MPa and 5 MPa for layer 1,, 3 and 4 respectively. From the results, we can also know that the outer layer of the laminate is subjected to higher stress than the inner layer where the distributed stress in layer 1 and 4 are higher than the distributed stress in layer and 3. Therefore, the critical region of the structure is on the surface of the plate especially the area near the applied load Discussion On Hat-Stiffened Composite Laminated Plate The FEA results for hat-stiffened composite laminated plate are shown in Figure E6 and E7 in Appendix E. The analysis results show that the structure experiences to bend as unstiffened plate in which the hat-stiffened plate deformed symmetrically to the center of the plate. The center subjected to bend much than other part it is the location where the applied load located. The maximum displacement of the plate structure is.9997 mm at node Figure E 6 shows the displacement contour of the hatstiffened plate. This figure shows that the regions with red color experience the highest deformations compare with the regions with other colors. Figure 6.8 represents the displacement contour of hat-stiffened plate for bottom view and it shows that the maximum displacement is at the center of the stiffener which is same as unstiffened plate. Besides that, it also shows that the stiffener doesn t change much in the deformation pattern but it helps a lot in reducing the deformation and increasing the strength of the structure for a unit of load. Figure 6.9 and 6.1 show the deformed shape of the structure. The FEA results for square-shaped and T-shaped stiffened plate are shown in Figure E8 to E13 respectively in Appendix E.

122 15 Figure 6.8: Displacement contour for hat-stiffened plate for bottom view Figure 6.9: Deformed shape of the hat-stiffened plate with deformation scale of 3

123 16 Figure 6.1: Front view of deformed shape for the hat-stiffened plate with deformation scale of 3 Figure E7 shows the solid Von Mises stress contour of the hat-stiffened plate. Figure 6.11 shows the front view of the structure. From this figure, we can see that the critical region of the whole structure is located at the edge between the stiffener and the plate. The critical regions will experience the highest stress distribution. This is because these parts support most of the applied load on the structure. Whereas, other parts generally experience lower stress (blue and pink color) and they are not so critical. The maximum stress that experiences by this structure is MPa at node This result is same as experiment result in which the specimen is failed at the connection of the stiffener and plate as shown in Figure 6.5. From Figure 6.1, we can see that the maximum stress that on the upper surface of the stiffened plate is MPa at node 471 which is lower than the maximum stress on the connection between the stiffener and plate. Figure 6.11 clearly shows the stress distribution on the connection between the stiffener and plate. Similarly to the square-shaped and T shaped stiffened plate, the critical region of the structure is at the connection between the stiffener and plate.

124 17 Figure 6.11: Side view of the critical region for composite hat-stiffened plate Figure 6.1: Critical region of the hat-stiffened plate

125 18 In this analysis, the property used is solid which is different with the analysis of unstiffened plate in which the property used is laminate. This is because it cannot be meshed properly when using laminate property for stiffened plate. But the displacement result of the FEA analysis for laminate property and solid property is same. The only different for the analysis results is the distribution stress on the structure. For laminate property, we can obtain the distribution stress for each layer of the laminate. Whereas, for solid property; we can only get the stress distribution for the whole structure but the critical region obtained is same as the results obtained by using laminate property. Therefore, in order to the unavailability to mesh the stiffened plate, solid property is used to obtain the displacement analysis and the critical region analysis as well as the results are shown in Appendix E and has been explained in the previous paragraph. The FEA analysis for the hat-stiffened plate by using laminate property is shown in Figure This figure shows the displacement contour of the stiffened plate. It is obviously that the stiffened plate is deformed improperly as the results for solid property. The whole structure represents pink colour which implies that the displacement is approximate to zero. By referring to the contour bar at the side, it shows that this the structure has a maximum displacement which is mm but it doesn t shown in the figure. Besides, the maximum displacement is greatly larger than the experiment value which gives 3 mm displacement. Hence, it can be concluded that this structure is not be modeled properly. Figure 6.14 represents the side view of the deformed mode of the hatstiffened plate. From this figure, we can see that the plate is deformed through the stiffener. This implies that there is no connection between the stiffener and plate and stiffener doesn t give any support to the plate in defending the applied load. This problem is solved by defining the hat-stiffened composite plate as solid property and the results is discussed in the previous paragraphs.

126 19 Figure 6.13: Displacement contour for hat-stiffened composite plate with laminate property Figure 6.14: Side view of the deformed hat-stiffened plate with laminate property

127 CHAPTER VII CONCLUSION AND SUGGESTION 7.1 Conclusion The composite materials are increasingly important as an engineering material in diverse applications such as aerospace, automotive, marine, civil, sport equipment applications, and other industrial applications. A composite stiffened plate is a general form widely used in those applications. In a unidirectional composite the longitudinal properties are controlled by the fiber properties and give the highest strength, whereas the transverse properties are matrix dominated and give the lowest strength. However, high modulus and strength characteristics of composites result in structures with very thin sections that are often prone to buckling. Stiffeners are required to increase the bending stiffness of such thin walled members (plates, shells). The main objectives of this project are to study the effects of hat-shaped stiffeners in the deformation of the composite laminated plates by experimentally and finite element simulation and study the effects of stiffener s geometry in strengthening the composite plate by simulation. The finite element static analysis of composite

128 111 stiffened plate using FEA software is presented. The deformation of the unstiffened composite laminate pate and composite stiffened plate has been experimentally determined and compared with the value predicted using FEA simulation. It is observed that the deviation between the experimental and FEA values are small for unstiffened plate but is large for composite stiffened plate and the factors influenced the experimental value were discussed in the previous chapter. The tensile test results show that for composite material under tensile loading, there is a linear relationship between stress and strain as well as the transverse and longitudinal strains before yield has started. This is due to the axial strain is directly proportional to the applied load in the axial direction. Besides, the highest value of ultimate stress and modulus Young can be obtained by aligning the fiber parallel to the direction of the applied load. The bending test results show that the maximum deflection of the stiffened plate at the 1 kgf applied is smaller (3 mm) than the unstiffened plate (14 mm). The results also show that the stiffened plate can carry more service load (4 kg) than unstiffened plates (14 kg) for a given unit weight. Therefore, it can be concluded that stiffened panels are quite efficient for lightly loaded areas. From this testing, we also found that the failure of the unstiffened plate occurred at the area near the applied load which on the top surface of the plate. While for the hat-stiffened plate, the failure occurred at the area near the edge between stiffener and plate. The local cracking at the failure edges shift the location of the maximum force further into the interior of the bonded length between stiffener and plate. For the unstiffened plate, the FEA simulation result shows that the outer layer of the laminate is subjected to higher stress than the inner layer. The maximum displacement obtained for this model is 16.8 mm which is % higher than the

129 11 experimental value. For hat-stiffened plate, the maximum displacement obtained is.1 mm which is 33 % lower that the experiment value. By comparing the maximum deflection at 1kg applied load between the unstiffened and stiffened plate, it shows that the deflection value for unstiffened plate is greatly higher than the stiffened plate. Hence, it can be concluded that the stiffener is effective in increasing the strength and reducing the deformation of the composite plate. The linear static finite element analysis also have been done for the different shape of the stiffened plate and the comparison of results for few examples on static analysis of laminated stiffened plate gives an overview regarding the selection of stiffener sections in engineering designs. The FEA simulation show that different type of the stiffener will give different effects in strengthens the stiffness of the composite plate. The results show that the square-shaped stiffened plate is more efficient in strengthen the composite plate in which it give the smallest maximum deflection at 1 kg applied load and follow by hat-stiffened plate and the T-shaped stiffened plate gives the highest maximum deflection among the stiffened plate. Besides that, through this analysis, we also know that the critical region of the laminated stiffened plate is located at the edge between the stiffener and plate which is same as the experiment result. The theoretical analysis of the maximum deflection at 1 kg applied load for unstiffened plate is mm which is approximate to the experiment value which is 14 mm. This show that the Navier method is suitable in determining the displacement but this method take a long estimation time. Generally, this project has achieved it objectives based on the results from experiments and FEA simulation.

130 Suggestion for Future Study The objectives of this project are to investigate the deformation and stress in composite laminated plate and to study the effects of stiffener in increasing the bending stiffness of the composite laminated plate. Therefore, some suggestions were given in order to improve this project in the future. 1) In this project, the composite plate that stiffened by hat shaped stiffener was tested. This project can be extended by using the various shape of stiffener. Different shape of the stiffener will give different effect to the bending stiffness of the composite plate. ) Extend the analysis to other laminated plate with different lamina orientation for further observation of the lamina orientation in the stiffness properties. 3) In this project, the plate was tested with simply supported along all edges and subjected to a small area distributed load at the center of the plate. Therefore, this project can be improved further with different boundary condition and different type of apply loads such as clamped plate and distributed load on the surface of the plate. 4) The materials that used in this project were high strength carbon fiber and epoxy. Analysis with other materials such as glass/vinylester and aramid/epoxy can be used to study the effects of the material to the strength properties of the plate. 5) Various layers of lamina, width and length of the plate can be tested for the further investigation.

131 114 6) Improve the hand lay up method. This is because this method is easy to cause air bubble entrapped between the lamina and affect the accuracy of the results. 7) In this project, one sample of plate was tested for deformation and stresses investigation. The number of the testing plate should be increased in order to obtain the more accurate results.

132 115 REFERENCES 1) CompositePro for Windows TM, Reference Guide.pdf, Peak Composite Innovation, United States of America,. ) Reddy, J.N. and Miravete, A., Practical Analysis of Composite Laminates, CRC Press, United States of America, ) Eckold, Geoff, Design and Manufacture of Composite Structures, Woodhead Publishing Limited, England, ) Jones, Robert M., Mechanics of Composite Materials, Scripta Book Company, Washington, ) Fitzer, Erich, Carbon Fibers and Their Composites, Springer-Verlag, Germany, ) 7) L. Hollaway, Polymers and Polymer Composites in Construction, Thomas Telford Ltd, London, ) Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, Mcgraww-Hill International Book Company, New York, ) Reddy, J.N., Theory and Analysis of Composite Plates, Universiti Putra Malaysia, 1997.

133 116 1) Nazri Kamsah, Finite Element Method, University Technology Malaysia, 4 11) Calcote, Lee R., The Analysis of Laminated Composite Structures, Van Nostrand Reinhold Company, Canada, ) Troitsky, M.S., Stiffened Plates: Bending, Stability and Vibrations, Elsevier Scientific Publishing Company, New York, ) Whitney, James M., Structural Analysis of Laminated Anisotropic Plates, Technomic Publishing Company, United States of America, ) Rafaat M. Hussein, Composite Panels / Plate: Analysis and Design, Technomic Publishing Company, United States of America, ) Reddy, J.N., An Introduction to the Finite Element Method, McGraw-Hill, Inc., United State of America, ) Cook, R.D., Concepts and Application of Finite Element Analysis, John Wiley & Sons, Inc, Canada, ) John, L. Clarke, Structural Design of Polymer Composites, St. Edmunelsbury Press, London, 1996.

134 117 APPENDIX A AMERICAN SOCIETY FOR TESTING AND MATERIALS TEST METHOD (ASTM-339)

135 118

136 119

137 1

138 11

139 1

140 13

141 14

142 15 APPENDIX B TECHNICAL DRAWING OF TEST RIG, STIFFENER, STIFFENED PLATE

143 16

144 17

145 18

146 19

147 13

148 131 APPENDIX C RESULTS OF TENSILE TEST

149 13 Table C1: Specification of Specimen 1 UD (1) UD () UD (3) Number of layer Lamination [///] [///] [///] Thickness, t (mm) Width, W (mm) Cross sectional area, A (mm ) Table C: Specification of Specimen UD9 (1) UD9 () UD9 (3) Number of layer Lamination [9/9/9/9] [9/9/9/9] [9/9/9/9] Thickness, t (mm) Width, W (mm) Cross sectional area, A (mm ) Table C3: Specification of Specimen 3 UD45 (1) UD45 () UD45 (3) Number of layer Lamination [45/45/45/45] [45/45/45/45] [45/45/45/45] Thickness, t (mm) Width, W (mm) Cross sectional area, A (mm )

150 133 Stress VS Axial Strain 1 1 Stress, (MPa) Axial Strain, (1E-6) Sample1 Sample Sample3 Figure C1: Graph stress versus axial strain for specimen with degree fiber orientation Stress VS Axial Strain Stress, (MPa) Axial Strain (1E-6) Sample1 Sample Sample3 Figure C: Graph stress versus axial strain for specimen with 9 degree fiber orientation

151 134 Stress VS Axial Strain Stress, (MPa) Axial Strain, (1E-6) Sample1 Sample Sample3 Figure C3: Graph stress versus axial strain for specimen with 45 degree fiber orientation Lateral Strain VS Axial Strain Lateral Strain, (-u) Axial Strain, (u) Graph C4: Graph transverse strain versus longitudinal strain for specimen with degree fibers orientation

152 135 Lateral Strain VS Axial Strain Lateral Strain (-u) Axial Strain (u) Graph C5: Graph transverse strain versus longitudinal strain for specimen with 9 degree fiber orientation

153 136 APPENDIX D RESULTS OF BENDING TEST

154 137 Specimen : Unstiffened Composite Laminated Plate Number of layer : 4 Lamination : /9/9/ Table D1: Results of bending test for unstiffened composite laminated plate Load(kg) Displacement, (mm) (center) Displacement, (mm) (Coordinate ) Strain- (-µ) Strain-9 (-µ) Strain-45 (-µ)

155 138 Load VS Displacement Load, (kg) Displacement, (mm) DisplCenter Coordinatel- Poly. (DisplCenter) Poly. (Coordinatel-) Graph D1: Graph applied load versus displacement for unstiffened composite laminated plate Applied Load VS Strain 1 1 Applied Load, (kg) Strain, (-u) Degree 9 Degree 45 Degree Graph D: Graph strain versus applied load for unstiffened composite laminated plate

156 139 Specimen : Composite Hat-Stiffened Laminated Plate Number of layer : 4 Lamination : /9/9/ Table D: Results of bending test for hat-stiffened composite laminated plate Load(kg) Displacement (center), (mm) Displacement (), (mm) Strain -1 (-µ) Strain - (-µ) Strain -3 (-µ) Strain -4 (-µ) Strain -5 (-µ)

157 14 Load(kg) Displacement (center), (mm) Displacement (), (mm) Strain -1 (-µ) Strain - (-µ) Strain -3 (-µ) Strain -4 (-µ) Strain -5 (-µ)

158 141 Load VS Diaplacement 3 5 Load, (kg) Displacement, (mm) Center Coordinate Poly. (Center) Poly. (Coordinate ) Graph D3: Graph applied load versus displacement for composite hat-stiffened laminated plate Applied Load VS Strain 5 Applied Load, (kg) Strain, (-u) Strain-1 Strain- Strain-3 Strain-4 Strain-5 Graph D4: Graph strain versus applied load for composite hat-stiffened laminated plate

159 14 APPENDIX E FINITE ELEMENT METHOD ANALYSIS RESULTS

160 143 Figure E1: Displacement contour of unstiffened plate with simply supported around the outer edge Figure E: Lamina 1 Von Mises stress contour of the unstiffened plate

161 144 Figure E3: Lamina Von Mises stress contour of the unstiffened plate Figure E4: Lamina 3 Von Mises stress contour of the unstiffened plate

162 145 Figure E5: Lamina 4 Von Mises stress contour of the unstiffened plate Figure E6: Displacement contour of hat-stiffened plate with simply supported around the outer edge

163 146 Figure E7: Von Mises stress contour of the hat-stiffened plate Figure E8: Displacement contour of square shaped-stiffened plate with simply supported around the outer edge

164 147 Figure E9: Von Mises stress contour of square shaped-stiffened plate Figure E1: Critical region of square shaped-stiffened plate