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| موضوع: كتاب Introduction to Composite Materials Design السبت 03 أكتوبر 2020, 1:01 am | |
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أخوانى فى الله أحضرت لكم كتاب Introduction to Composite Materials Design Ever J. Barbero Second Edition
و المحتوى كما يلي :
Contents Acknowledgment xv Preface xvii List of Figures xxv List of Tables xxxi List of Symbols xxxiii List of Examples xli 1 Introduction 1 1.1 Basic Concepts 1 1.2 The Design Process 5 1.3 Composites Design Methods . 8 1.4 Design for Reliability . 9 1.4.1 Stochastic Representation 11 1.4.2 Reliability-based Design . 12 1.4.3 Load and Resistance Factor Design . 15 1.4.4 Determination of Resistance Factors 16 1.4.5 Determination of Load Factors . 17 1.4.6 Limit States Design . 18 1.5 Fracture Mechanics 18 Exercises 21 2 Materials 27 2.1 Fiber Reinforcements . 28 2.2 Fiber Types 29 2.2.1 Glass Fibers 29 2.2.2 Silica and Quartz Fibers . 30 2.2.3 Carbon Fibers 31 2.2.4 Carbon Nanotubes 33 2.2.5 Organic Fibers 35 2.2.6 Boron Fibers . 36 viiviii Introduction to Composite Materials Design 2.2.7 Ceramic Fibers 36 2.2.8 Basalt Fibers . 36 2.2.9 Metallic Fibers 37 2.3 Fiber–Matrix Compatibility . 37 2.4 Fiber Forms 38 2.4.1 Continuous and Discontinuous Fibers . 38 2.4.2 1D Textiles: Strand, Tow, End, Yarn, and Roving 40 2.4.3 2D Textiles: Fabrics . 42 2.5 Matrix Materials . 45 2.6 Thermoset Matrices . 48 2.6.1 Polyester Resins . 49 2.6.2 Vinyl Ester Resins 51 2.6.3 Epoxy Resins . 51 2.6.4 Phenolic Resins 52 2.7 Thermoplastic Matrices . 53 2.8 Creep, Temperature, and Moisture . 54 2.9 Corrosion Resistance . 57 2.10 Flammability . 58 Exercises 59 3 Manufacturing Processes 71 3.1 Hand Lay-up . 72 3.2 Prepreg Lay-up 74 3.3 Bag Molding . 75 3.4 Autoclave Processing . 76 3.5 Compression Molding 78 3.6 Resin Transfer Molding . 79 3.7 Vacuum Assisted Resin Transfer Molding . 81 3.8 Pultrusion . 83 3.9 Filament Winding 86 Exercises 88 4 Micromechanics 91 4.1 Basic Concepts 92 4.1.1 Volume and Mass Fractions . 92 4.1.2 Representative Volume Element . 94 4.1.3 Heterogeneous Material . 95 4.1.4 Anisotropic Material . 95 4.1.5 Orthotropic Material . 96 4.1.6 Transversely Isotropic Material . 97 4.1.7 Isotropic Material 97 4.2 Stiffness 97 4.2.1 Longitudinal Modulus 98 4.2.2 Transverse Modulus . 100 4.2.3 In-plane Poisson’s Ratio . 102Table of Contents ix 4.2.4 In-plane Shear Modulus . 103 4.2.5 Intralaminar Shear Modulus . 106 4.2.6 Restrictions on the Elastic Constants 106 4.2.7 Stress Partitioning Parameter 107 4.2.8 Periodic Microstructure . 109 4.3 Moisture and Thermal Expansion 112 4.3.1 Thermal Expansion . 113 4.3.2 Moisture Expansion . 114 4.3.3 Transport Properties . 115 4.4 Strength 116 4.4.1 Longitudinal Tensile Strength 117 4.4.2 Longitudinal Compressive Strength . 120 4.4.3 Fiber Microbuckling . 121 4.4.4 Transverse Tensile Strength . 128 4.4.5 Mode I Fracture Toughness . 129 4.4.6 Transverse Compressive Strength 131 4.4.7 Mohr-Coulomb 131 4.4.8 In-plane Shear Strength . 136 4.4.9 Mode II Fracture Toughness . 138 4.4.10 Intralaminar Shear Strength . 139 Exercises 140 5 Ply Mechanics 143 5.1 Coordinate Systems . 143 5.2 Stress and Strain . 143 5.2.1 Stress . 144 5.2.2 Strain . 147 5.3 Stress–Strain Equations . 149 5.4 Off-axis Stiffness . 153 5.4.1 Coordinate Transformations . 154 5.4.2 Stress and Strain Transformations . 155 5.4.3 Stiffness and Compliance Transformations . 159 5.4.4 Specially Orthotropic Lamina 162 Exercises 164 6 Macromechanics 167 6.1 Plate Stiffness and Compliance . 168 6.1.1 Assumptions . 168 6.1.2 Strains . 170 6.1.3 Stress Resultants . 173 6.1.4 Plate Stiffness and Compliance . 174 6.2 Computation of Stresses . 180 6.3 Common Laminate Types 181 6.3.1 Laminate Description 182 6.3.2 Symmetric Laminates 182x Introduction to Composite Materials Design 6.3.3 Antisymmetric Laminate 184 6.3.4 Balanced Laminate 184 6.3.5 Quasi-isotropic Laminates . 184 6.3.6 Cross-ply Laminate . 189 6.3.7 Angle-ply Laminate . 190 6.3.8 Specially Orthotropic Laminate 190 6.4 Laminate Moduli . 192 6.5 Design Using Carpet Plots 194 6.5.1 Stiffness Controlled Design . 196 6.5.2 Design for Bending 201 6.6 Hygrothermal Stresses 204 Exercises 213 7 Strength 217 7.1 Lamina Failure Criteria . 220 7.1.1 Strength Ratio 220 7.1.2 Maximum Stress Criterion 221 7.1.3 Maximum Strain Criterion . 223 7.1.4 Interacting Failure Criterion . 226 7.1.5 Hygrothermal Failure 232 7.2 Laminate First Ply Failure 233 7.2.1 In-Situ Strength . 237 7.3 Laminate Strength 243 7.3.1 Ply Discount . 243 7.3.2 Truncated-Maximum-Strain Criterion . 246 7.4 Strength Design Using Carpet Plots 252 7.5 Stress Concentrations 258 7.5.1 Notched Plate Under In-plane Load 260 Exercises 265 8 Damage 267 8.1 Continuum Damage Mechanics . 267 8.2 Longitudinal Tensile Damage 269 8.3 Longitudinal Compressive Damage . 273 8.4 Transverse Tension and In-plane Shear . 277 8.4.1 Limitations 279 8.4.2 Approximations 280 8.4.3 Displacement Field 280 8.4.4 Strain Field 281 8.4.5 Laminate Reduced Stiffness . 282 8.4.6 Lamina Reduced Stiffness 282 8.4.7 Fracture Energy . 283 8.4.8 Solution Algorithm 285 8.4.9 Lamina Iterations 285 8.4.10 Laminate Iterations . 285Table of Contents xi Exercises 286 9 Fabric-reinforced Composites 289 9.1 Weave Pattern Description . 289 9.2 Analysis 293 9.3 Tow Properties 297 9.4 Element Stiffness and Constitutive Relationship 301 9.4.1 Bending-Restrained Model . 302 9.4.2 Bending-Allowed Model . 303 9.5 Laminate Properties . 305 9.5.1 Elastic Constants . 305 9.5.2 Thermal and Moisture Expansion Coefficients . 306 9.6 Failure Analysis 308 9.6.1 Stress Analysis 308 9.6.2 Damage Initiation, Evolution, and Fracture 310 9.6.3 Cross-ply Approximation 314 9.7 Woven Fabrics with Gap . 316 9.8 Twill and Satin 318 9.8.1 Twill Weave with n g > 2, ns = 1, ni = 1 318 9.8.2 Twill Weave with ns = 1 . 321 9.8.3 Satin Weave with ni = 1 . 323 9.8.4 Twill and Satin Thermo-elastic Properties . 325 9.9 Randomly Oriented Reinforcement . 326 9.9.1 Elastic Moduli 326 9.9.2 Strength 328 Exercises 329 10 Beams 339 10.1 Preliminary Design 340 10.1.1 Design for Deflections 341 10.1.2 Design for Strength . 343 10.1.3 Design for Buckling . 345 10.1.4 Column Behavior . 346 10.2 Thin-Walled Beams . 348 10.2.1 Wall Constitutive Equations . 352 10.2.2 Neutral Axis of Bending and Torsion 354 10.2.3 Axial Stiffness 356 10.2.4 Mechanical Center of Gravity 357 10.2.5 Bending Stiffness . 358 10.2.6 Torsional Stiffness 364 10.2.7 Shear of Open Sections . 367 10.2.8 Shear of Single-Cell Closed Section . 376 10.2.9 Beam Deformations . 377 10.2.10 Segment Deformations and Stresses 378 10.2.11 Restrained Warping of Open Sections . 382xii Introduction to Composite Materials Design Exercises 383 11 Plates and Stiffened Panels 385 11.1 Plate Bending . 386 11.2 Plate Buckling 387 11.2.1 All Edges Simply Supported . 388 11.2.2 All Sides Clamped 391 11.2.3 One Free Edge 392 11.2.4 Biaxial Loading 392 11.2.5 Fixed Unloaded Edges 393 11.3 Stiffened Panels 393 11.3.1 Stiffened Panels under Bending Loads . 394 11.3.2 Stiffened Panel under In-plane Loads 399 Exercises 406 12 Shells 409 12.1 Shells of Revolution . 411 12.1.1 Symmetric Loading 412 12.2 Cylindrical Shells with General Loading 421 Exercises 427 13 Strengthening of Reinforced Concrete 429 13.1 Strengthening Design . 431 13.2 Materials . 433 13.2.1 Concrete . 434 13.2.2 Steel Reinforcement . 434 13.2.3 FRP 435 13.3 Flexural Strengthening of RC Beams 435 13.3.1 Unstrengthened Behavior 436 13.3.2 Strengthened Behavior 436 13.3.3 Analysis . 437 13.3.4 Strong Strengthening Configuration (SSC) . 439 13.3.5 Weak Strengthening Configuration (WSC) . 441 13.3.6 Balanced Strengthening Configuration (BSC) . 443 13.3.7 Serviceability Limit States . 445 13.3.8 Summary Design Procedure: Bending . 451 13.4 Shear Strengthening . 456 13.4.1 Summary Design Procedure: Shear . 460 13.5 Beam-column . 463 13.5.1 Column: Pure Axial Compression . 465 13.5.2 Summary Design Procedure: Column . 468 13.5.3 Beam-column: Combined Axial Compression and Bending 471 13.5.4 Summary Verification Procedure: Beam-column . 477 Exercises 487Table of Contents xiii Appendix A Gauss Distribution 489 Appendix B Weibull Distribution 491 Appendix C Conversion of Units 495 Bibliography 497 Index 50 List of Symbols overline ( ) Transformed, usually to laminate coordinates widetilde ( ) f Undamaged (virgin), or effective quantity ( ) c Average α Load factor. Also, fiber misalignment ασ Standard deviation of fiber misalignment α0 Angle of the fracture plane α1, α2 Longitudinal and transverse coefficient of thermal expansion (CTE) αA, αT Axial and transverse CTE of fibers [α] Membrane compliance of a laminate α, β, γ Thickness ratio used with carpet plots [α] In-plane compliance of a laminate [β] Bending-extension compliance of a laminate [δ] Bending compliance of a laminate θk Orientation of lamina k in a laminate β1, β2 Longitudinal and transverse coefficient of moisture expansion δb, δs Bending and shear deflections of a beam ϵ1t Ultimate longitudinal tensile strain ϵ2t Ultimate transverse tensile strain ϵ1c Ultimate longitudinal compressive strain ϵ2c Ultimate transverse compressive strain ϵfu Ultimate fiber strain (tensile) ϵmu Ultimate matrix strain (tensile) ϵ Strain tensor εij Strain components in tensor notation ϵα Strain components in contracted notation ϵe α Elastic strain ϵ pα Plastic strain ϵ0 x, ϵ0 y, γxy 0 Strain components at the midsurface of a shell eϵ Effective strain in contracted notation (ϵ6 = γ6) εe Effective strain in tensor notation (ϵ6 = γ6/2) γ6u Ultimate shear strain γxy 0 In-plane shear strain κ0 x, κ0 y, κ0 xy Curvatures of the midsurface of a shell xxxiiixxxiv Introduction to Composite Materials Design λ Lame constant. Also, crack density µ Mean value of a distribution η Eigenvalues ηL, ηT Coefficients of influence, longitudinal, transverse η2, η4, η6 Stress partitioning parameters ηi = Ei/E Modular ratio in the transformed section method ϕ Resistance factor. Also, angle of internal friction ϕ(z) Standard PDF ϕx, ϕy Rotations of the normal to the midsurface of a shell ϖ Standard deviation ρ Density ρf, ρm, ρc Density of fiber, matrix, and composite ψ Load combination factor σ Stress tensor σ0 Weibull scale parameter σij Stress components in tensor notation σα Stress components in contracted notation σe Effective stress τL, τT Longitudinal and transverse shear stress ν Poisson’s ratio ν12 In-plane Poisson’s ratio ν23, ν13 Intralaminar Poisson’s ratios ν xy Laminate Poisson ratio x-y νA Axial Poisson’s ratio of fibers Γ Gamma function Λ0 22, Λ0 44 Dvorak parameters Ω = √I-D Integrity tensor 2a0 Representative crack size g Damage activation function df Degradation factor kf Fiber stress concentration factor m Weibull shape parameter n1, n2, n3 Components of the vector normal to a surface p(z) Probability density function (PDF) r1(φ), r2(φ) Radii of curvature of a shell tk Thickness of lamina k in a laminate t1, t2, t3 Projection components of a vector on the coordinate axes 1, 2, 3 tt = 4a0 Transition thickness u, v, w Components of the displacement along the directions x, y, z u0, v0, w0 Components of the displacement at the midsurface of a shell w Fabric weight per unit area z Standard variable [A] Membrane stiffness of a laminate with components Aij ; i, j = 1, 2, 6 Bending-extension coupling stiffness of a laminate BijList of Symbols xxxv Cij 3D stiffness matrix CDF Cumulative distribution function (CDF) CF , Cσ Strength and load coefficient of variance (COV) CTE Coefficient of thermal expansion D Damage tensor [D] Bending stiffness of a laminate with components Dij ; i, j = 1, 2, 6 Ex, Ey, Gxy Laminate moduli E Young’s modulus E1, E2 Longitudinal and transverse moduli EA, ET Axial and transverse moduli of fibers F Resistance (material strength) F1t Longitudinal tensile strength F2t Transverse tensile strength F6 In-plane shear strength F1c Longitudinal compressive strength F2c Transverse compressive strength F4 Intralaminar shear strength Fft Apparent fiber tensile strength Fmt Apparent matrix tensile strength Fcsm−t Tensile strength of a random-reinforced lamina Fb x, Fyb, Fxy b Flexural strength G Shear modulus G12 In-plane shear modulus G23 Transverse shear modulus GA, GT Axial and transverse shear modulus of fibers GIc, GIIc Fracture toughness mode I and II [H] Transverse shear stiffness of a laminate Hij ; i, j = 4...5 HDT Heat distortion temperature I Moment of inertia of the cross-section of a beam IF Failure Index M Bending moment applied to a beam Mx, My, Mxy Bending moments per unit length at the midsurface of a shell MT x , MyT , Mxy T Thermal moments per unit length Nx, Ny, Nxy Membrane forces per unit length at the midsurface of a shell NT , ϵT Membrane thermal force and strain caused by thermal expansion NT x , NyT , Nxy T Thermal forces per unit length Q Reduced stiffness matrix in lamina coordinates x1, x2, x3 Q∗ Intralaminar reduced stiffness matrix Q Reduced stiffness matrix in laminate coordinates X, Y, Z Qe Undamaged reduced stiffness matrix in lamina coordinates Qe Undamaged reduced stiffness matrix in laminate coordinates QCSM Reduced stiffness of a random-reinforced lamina R Strength ratio, safety factor [R] Reuter matrixxxxvi Introduction to Composite Materials Design Re = 1 − CDF Reliability Sij 3D compliance matrix S∗ Intralaminar components of the compliance matrix S SF T Stress-free temperature [◦C] Tg Glass transition temperature T = T(θ) Stress transformation matrix from laminate to lamina coordinates T−1 = T(−θ) Stress transformation matrix from lamina to laminate coordinates Vx, Vy Transverse shear forces per unit length at the midsurface of a shell Vf, Vm Fiber and matrix volume fraction Vv Void content (volume fraction) Wf, Wm Fiber and matrix weight fraction Symbols Related to Fabric-reinforced Composites θf, θw Undulation angle of the fill and gap tows, respectively Θf, Θw Coordinate transformation matrix for fill and gap af, aw Width of the fill and gap tows, respectively gf, gw Width of the gap along the fill and gap directions, respectively hf, hw, hm Thickness of the fill and gap tows, and matrix region, respectively n g Harness ns Number of subcells between consecutive interlacings ni Number of subcells in the interlacing region zf(x), zw(y) Undulation of the fill and gap tows, respectively Afill, Awarp Cross-section area of fill and warp tows Ffa Apparent tensile strength of the fiber Fmta, Fmsa Apparent tensile and shear strength of the matrix Lfill, Lwarp Developed length of fill and warp tows Tf, Tw Stress transformation matrix for fill and gap V o f Overall fiber volume fraction in a fabric-reinforced composite Vmeso Volume fraction of composite tow in a fabric-reinforced composite V f f , Vfw Volume fraction of fiber in the fill and warp tows w Weight per unit area of fabric Symbols Related to Beams β Rate of twist ϕ Angle of twist λ2 Dimensionless buckling load ωs Sectorial area ω Principal sectorial area ηc, ζc Mechanical shear center Γs′′ Area enclosed by the contour eb, eq Position of the neutral surface of bending and torsion q Shear flowList of Symbols xxxvii s, r Coordinates along the contour and normal to it yc, zc Mechanical shear center zG, zρ, zM Geometric, mass, and mechanical center of gravity (EA) Axial stiffness (EIyG), (EIzG) Mechanical moment of inertia (EIyGzG) Mechanical product of inertia (EIη), (EIζ) Bending stiffness with respect to principal axis of bending (Eω) Mechanical sectorial static moment (EI!) Mechanical sectorial moment of inertia (GA) Shear stiffness (GJR) Torsional stiffness (EQ!ζ) Mechanical sectorial linear moment (EQζ(s)) Mechanical static moment K Coefficient of restraint Ni xs Shear flow in segment i Le Effective length of a column T Torque Z = I/c Section modulus Symbols Related to Strengthening of Reinforced Concrete α, αi Load factor, partial load factors αc, βc Stress-block parameters for confined section β1 Stress-block parameter for unconfined section εbi Initial strain at the soffit εc Strain level in the concrete εcu Ultimate axial strain of unconfined concrete εccu Ultimate axial compressive strain of confined concrete εf Strain level in FRP εfd FRP debonding strain εfu, εfe FRP allowable and effective tensile strain ε∗ fu FRP ultimate strain εs Strain level in the steel reinforcement ε y Steel yield strain κa FRP efficiency factor in determination of fcc ′ κb FRP efficiency factor in determination of εccu κv Bond reduction factor κ" FRP efficiency factor ϕF Factored capacity ϕ Strength reduction factor (resistance factor) ϕ(Pn, Mn) Factored (load, moment) capacity ϕecc Eccentricity factor ρf FRP reinforcement ratio ρg Longitudinal steel reinforcement ratioxxxviii Introduction to Composite Materials Design ψ Load combination factor ψf FRP strength reduction factor c Position of the neutral axis cb Position of the neutral axis, BSC bf Width of FRP laminae b, h Width and height of the beam d Depth of tensile steel dfv Depth of FRP shear strengthening fc;s Compressive stress in concrete at service condition fc′ Concrete compressive strength, unconfined fcc ′ Concrete compressive strength, confined ff;s Stress in the FRP at service condition fl Confining pressure ffu ∗ FRP tensile strength ffu, ffe FRP allowable and effective tensile strength fs;s Stress in the steel reinforcement at service condition fy Steel yield strength h, b Height and width of the cross-section n Number of plies of FRP nf, ns Number of FRP strips and steel bars in shear rc Radius of edges of a prismatic cross-section confined with FRP sf, ss FRP and steel spacing in shear tf Ply thickness of FRP wf Width of discontinuous shear FRP Ac Area of concrete in compression Ae Area of effectively confined concrete Af Area of FRP A g Gross area of the concrete section Afb Area of FRP, BSC Asi Area of i-th rebar As(A′ s) Tensile (compressive) steel reinforcement area Ast Sum of compressive and tensile steel reinforcement areas Asv FRP and steel shear area C Axial compressive force in the concrete CE Environmental exposure coefficient D Column diameter Ec Modulus of concrete Ef Modulus of FRP Es Modulus of steel (EI)cr Bending stiffness of the cracked section F Nominal capacity (strength) L Load (applied load, moment, or stress) Le Active bond length of FRP Mn Nominal moment capacityList of Symbols xxxix Mu Required moment capacity Pn Nominal axial compressive capacity (strength) Pu Required axial strength SDL Stress resultant of the dead load SLL Stress resultant of the live load Ts, Tf Tensile force in steel and FRP U Required capacity Vn Nominal shear capacity Vu Required shear capacity Vc, Vf, Vs Nominal shear strength of concrete (C), FRP (F), and steel stirrups (S)
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