This book addresses the issue of designing the microstructure of fiber composite materials in order to obtain optimum perfor- mance.Besides the systematic treatment of conventional con- tinuous and discontinuous fiber composites,the book also presents the state-of-the-art of the development of textile structural com- posites as well as the nonlinear elastic finite deformation theory of flexible composites. The author's experience during twenty years of research and teaching on composite materials is reflected in the broad spectrum of topics covered,including laminated composites,statistical strength theories of continuous fiber composites,short fiber composites,hybrid composites,two-and three-dimensional textile structural composites and flexible composites.This book provides the first comprehensive analysis and modeling of the thermo- mechanical behavior of fiber composites with these distinct micro- structures.Overall,the inter-relationships among the processing, microstructures and properties of these materials are emphasized throughout the book. The book is intended as a text for graduate or advanced undergraduate students,but will also be an excellent reference for all materials scientists and engineers who are researching or working with these materials
This book addresses the issue of designing the microstructure of fiber composite materials in order to obtain optimum perfor- mance. Besides the systematic treatment of conventional con- tinuous and discontinuous fiber composites, the book also presents the state-of-the-art of the development of textile structural com- posites as well as the nonlinear elastic finite deformation theory of flexible composites. The author's experience during twenty years of research and teaching on composite materials is reflected in the broad spectrum of topics covered, including laminated composites, statistical strength theories of continuous fiber composites, short fiber composites, hybrid composites, two- and three-dimensional textile structural composites and flexible composites. This book provides the first comprehensive analysis and modeling of the thermo- mechanical behavior of fiber composites with these distinct micro- structures. Overall, the inter-relationships among the processing, microstructures and properties of these materials are emphasized throughout the book. The book is intended as a text for graduate or advanced undergraduate students, but will also be an excellent reference for all materials scientists and engineers who are researching or working with these materials
TSU-WEI CHOU Jerzy L.Nowinski Professor of Mechanical Engineering University of Delaware Microstructural design of fiber composites The righr of the Lainrsityo时Cambridge lu print anu yel The Uaivernly har prinred ad pubfished romtinousfy e1584. CAMBRIDGE UNIVERSITY PRESS Cambridge New York Port Chester Melbourne Sydney
TSU-WEI CHOU Jerzy L. Nowinski Professor of Mechanical Engineering University of Delaware Microstructural design of fiber composites The right of the University of Cambridge to print and sell »m granted by Henry VIII in 1534. and published continuousl since 1584. CAMBRIDGE UNIVERSITY PRESS Cambridge New York Port Chester Melbourne Sydney
Contents Preface xvii 1 Introduction 1 1.1 Evolution of engineering materials 1 1.2 Fiber composite materials 1 1.3 Why composites? 10 1.3.1 Economic aspect 10 1.3.2 Technological aspect 12 1.4 Trends and opportunities 17 1.5 Microstructure-performance relationships 19 1.5.1 Versatility in performance 20 1.5.2 Tailoring of performance 22 1.5.3 Intelligent composites 1.6 Concluding remarks 26 2 Thermoelastic behavior of laminated composites 29 2.1 Introduction 29 2.2 Elastic behavior of a composite lamina 30 2.2.1 Elastic constants 30 2.2.2 Constitutive relations 33 2.3 Elastic behavior of a composite laminate 39 2.3.1 Classical composite lamination theory 39 2.3.2 Geometrical arrangements of laminae 44 2.4 Thick laminates 46 2.4.1 Three-dimensional constitutive relations of a composite lamina 46 2.4.2 Constitutive relations of thick laminated composites 48 2.5 Thermal and hygroscopic behavior 54 2.5.1 Basic equations 55 2.5.1.1 Constitutive relations 55 2.5.1.2 Thermal and moisture diffusion equations 61 2.5.2 Hygroscopic behavior 62 2.5.2.1 Moisture concentration functions 62 2.5.2.2 Hygroscopic stress field 65
Contents Preface xvii 1 1.1 1.2 1.3 1.4 1.5 1.6 2 2.1 2.2 2.3 2.4 Introduction Evolution of engineering materials Fiber composite materials Why composites? 1.3.1 Economic aspect 1.3.2 Technological aspect Trends and opportunities Microstructure-performance relationships 1.5.1 Versatility in performance 1.5.2 Tailoring of performance 1.5.3 Intelligent composites Concluding remarks Thermoelastic behavior of laminated composites Introduction Elastic behavior of a composite lamina 2.2.1 Elastic constants 2.2.2 Constitutive relations Elastic behavior of a composite laminate 2.3.1 Classical composite lamination theory 2.3.2 Geometrical arrangements of laminae Thick laminates 1 1 1 10 10 12 17 19 20 22 24 26 29 29 30 30 33 39 39 44 46 2.4.1 Three-dimensional constitutive relations of a composite lamina 46 2.4.2 Constitutive relations of thick laminated composites 48 2.5 Thermal and hygroscopic behavior 54 2.5.1 Basic equations 55 2.5.1.1 Constitutive relations 55 2.5.1.2 Thermal and moisture diffusion equations 61 2.5.2 Hygroscopic behavior 62 2.5.2.1 Moisture concentration functions 62 2.5.2.2 Hygroscopic stress field 65
Contents 2.5.3 Transient interlaminar thermal stresses 67 2.5.3.1 Transient temperature field 67 2.5.3.2 Thermal stress field 68 2.5.4 Transient in-plane thermal stresses 73 2.5.4.1 Transient temperature field 74 2.5.4.2 Thermal stress field 77 Strength of continuous-fiber composites 80 3.1 Introduction 80 3.2 Rule-of-mixtures 81 3.3 Stress concentrations due to fiber breakages 85 3.3.1 Static case 3.3.1.1 Single filament failure 5 3.3.1.2 Multi-filament failure 3.3.2 Dynamic case 94 3.4 Statistical tensile strength theories 98 3.4.1 Preliminary 98 3.4.2 Strength of individual fibers 102 3.4.3 Strength of fiber bundles 104 3.4.4 Correlations between single fiber and fiber bundle strengths 106 3.4.4.1 Analysis 106 3.4.4.2 Single fiber strength distribution 108 3.4.5 Experimental measurements of Weibull shape parameter 109 3.4.5.1 Single fiber tests 110 3.4.5.2 Loose bundle tests 113 3.4.6 Strength of unidirectional fiber composites 115 3.4.6.1 Equal load sharing 115 3.4.6.2 Idealized local load sharing 118 3.4.6.3 Monte-Carlo simulation 132 3.4.7 Strength of cross-ply composites 134 3.4.7.1 Energy absorption during multiple fracture 134 3.4.7.2 Transverse cracking of cross-ply laminates 136 3.4.7.3 Statistical analysis 145 3.4.7.4 Transverse cracking and Monte-Carlo simulation 150 3.4.8 Delamination in laminates of multi-directional plies 157
Contents 2.5.3 Transient interlaminar thermal stresses 67 2.5.3.1 Transient temperature field 67 2.5.3.2 Thermal stress field 68 2.5.4 Transient in-plane thermal stresses 73 2.5.4.1 Transient temperature field 74 2.5.4.2 Thermal stress field 77 3 Strength of continuous-fiber composites 80 3.1 Introduction 80 3.2 Rule-of-mixtures 81 3.3 Stress concentrations due to fiber breakages 85 3.3.1 Static case 85 3.3.1.1 Single filament failure 85 3.3.1.2 Multi-filament failure 88 3.3.2 Dynamic case 94 3.4 Statistical tensile strength theories 98 3.4.1 Preliminary 98 3.4.2 Strength of individual fibers 102 3.4.3 Strength of fiber bundles 104 3.4.4 Correlations between single fiber and fiber bundle strengths 106 3.4.4.1 Analysis 106 3.4.4.2 Single fiber strength distribution 108 3.4.5 Experimental measurements of Weibull shape parameter 109 3.4.5.1 Single fiber tests 110 3.4.5.2 Loose bundle tests 113 3.4.6 Strength of unidirectional fiber composites 115 3.4.6.1 Equal load sharing 115 3.4.6.2 Idealized local load sharing 118 3.4.6.3 Monte-Carlo simulation 132 3.4.7 Strength of cross-ply composites 134 3.4.7.1 Energy absorption during multiple fracture 134 3.4.7.2 Transverse cracking of cross-ply laminates 136 3.4.7.3 Statistical analysis 145 3.4.7.4 Transverse cracking and Monte-Carlo simulation 150 3.4.8 Delamination in laminates of multi-directional plies 157
Contents 3.4.8.1 Free-edge delamination 160 3.4.8.2 General delamination problems 165 3.4.9 Enhancement of composite strength through fiber prestressing 166 4 Short-fiber composites 169 4.1 Introduction 169 4.2 Load transfer 169 4.2.1 A single short fiber 170 4.2.2 Fiber-fiber interactions 171 4.3 Elastic properties 176 4.3.1 Unidirectionally aligned short-fiber composites 177 4.3.1.1 Shear-lag analysis 177 4.3.1.2 Self-consistent method 177 4.3.1.3 Bound approach 178 4.3.1.4 Halpin-Tsai equation 181 4.3.2 Partially aligned short-fiber composites 182 4.3.3 Random short-fiber composites 187 4.4 Physical properties 194 4.4.1 Thermal conductivity 194 4.4.2 Thermoelastic constants 198 4.5 Viscoelastic properties 200 4.6 Strength 201 4.6.1 Unidirectionally aligned short-fiber composites 202 4.6.1.1 Fiber length considerations 203 4.6.1.2 Probabilistic strength theory 205 4.6.2 Partially oriented short-fiber composites 216 4.6.3 Random short-fiber composites 224 4.7 Fracture behavior 227 5 Hybrid composites 231 5.1 Introduction 231 5.2 Stress concentrations 233 5.2.1 Static case 233 5.2.2 Dynamic case 243 5.3 Tensile stress-strain behavior 247 5.3.1 Elastic behavior 249 5.3.2 First cracking strain 251 5.3.3 Differential Poisson's effect 254 5.3.4 Differential thermal expansion 256
Contents X1 3.4.8.1 Free-edge delamination 160 3.4.8.2 General delamination problems 165 3.4.9 Enhancement of composite strength through fiber prestressing 166 4 Short-fiber composites 169 4.1 Introduction 169 4.2 Load transfer 169 4.2.1 A single short fiber 170 4.2.2 Fiber-fiber interactions 171 4.3 Elastic properties 176 4.3.1 Unidirectionally aligned short-fiber composites 177 4.3.1.1 Shear-lag analysis 177 4.3.1.2 Self-consistent method 177 4.3.1.3 Bound approach 178 4.3.1.4 Halpin-Tsai equation 181 4.3.2 Partially aligned short-fiber composites 182 4.3.3 Random short-fiber composites 187 4.4 Physical properties 194 4.4.1 Thermal conductivity 194 4.4.2 Thermoelastic constants 198 4.5 Viscoelastic properties 200 4.6 Strength 201 4.6.1 Unidirectionally aligned short-fiber composites 202 4.6.1.1 Fiber length considerations 203 4.6.1.2 Probabilistic strength theory 205 4.6.2 Partially oriented short-fiber composites 216 4.6.3 Random short-fiber composites 224 4.7 Fracture behavior 227 5 Hybrid composites 231 5.1 Introduction 231 5.2 Stress concentrations 233 5.2.1 Static case 233 5.2.2 Dynamic case 243 5.3 Tensile stress-strain behavior 247 5.3.1 Elastic behavior 249 5.3.2 First cracking strain 251 5.3.3 Differential Poisson's effect 254 5.3.4 Differential thermal expansion 256
xi试 Contents 5.4 Strength theories 256 5.4.1 Rule-of-mixtures 257 5.4.2 Probabilistic initial failure strength 257 5.4.3 Probabilistic ultimate failure strength 262 5.5 Softening strips 273 5.6 Mechanical properties 275 5.7 Property optimization analysis 279 5.7.1 Constitutive relations 279 5.7.2 Graphical illustration of performance optimization 282 6 Two-dimensional textile structural composites 285 6.1 Introduction 285 6.2 Textile preforms 287 6.2.1 Wovens 288 6.2.2 Knits 292 6.2.3 Braids 294 6.3 Methodology of analysis 300 6.4 Mosaic model 302 6.5 Crimp(fiber undulation)model 308 6.6 Bridging model and experimental confirmation 314 6.7 Analysis of the knee behavior and summary of stiffness and strength modeling 319 6.8 In-plane thermal expansion and thermal bending coefficients 327 6.9 Hybrid fabric composites:mosaic model 335 6.9.1 Definitions and idealizations 336 6.9.2 Bounds of stiffness and compliance constants 340 6.9.2.1 Iso-strain 341 6.9.2.2 Iso-stress 343 6.9.3 One-dimensional approximation 344 6.9.4 Numerical results 345 6.10 Hybrid fabric composites:crimp and bridging models 348 6.10.1 Crimp model 349 6.10.2 Bridging model 352 6.10.3 Numerical results and summary of thermoelas- tic properties 354 6.11 Triaxial woven fabric composites 356 6.11.1 Geometrical characteristics 356 6.11.2 Analysis of thermoelastic behavior 358 6.11.3 Biaxial non-orthogonal woven fabric composites 365
xii Contents 5.4 Strength theories 256 5.4.1 Rule-of-mixtures 257 5.4.2 Probabilistic initial failure strength 257 5.4.3 Probabilistic ultimate failure strength 262 5.5 Softening strips 273 5.6 Mechanical properties 275 5.7 Property optimization analysis 279 5.7.1 Constitutive relations 279 5.7.2 Graphical illustration of performance optimization 282 6 Two-dimensional textile structural composites 285 6.1 Introduction 285 6.2 Textile preforms 287 6.2.1 Wovens 288 6.2.2 Knits 292 6.2.3 Braids 294 6.3 Methodology of analysis 300 6.4 Mosaic model 302 6.5 Crimp (fiber undulation) model 308 6.6 Bridging model and experimental confirmation 314 6.7 Analysis of the knee behavior and summary of stiffness and strength modeling 319 6.8 In-plane thermal expansion and thermal bending coefficients 327 6.9 Hybrid fabric composites: mosaic model 335 6.9.1 Definitions and idealizations 336 6.9.2 Bounds of stiffness and compliance constants 340 6.9.2.1 Iso-strain 341 6.9.2.2 Iso-stress 343 6.9.3 One-dimensional approximation 344 6.9.4 Numerical results 345 6.10 Hybrid fabric composites: crimp and bridging models 348 6.10.1 Crimp model 349 6.10.2 Bridging model 352 6.10.3 Numerical results and summary of thermoelastic properties 354 6.11 Triaxial woven fabric composites 356 6.11.1 Geometrical characteristics 356 6.11.2 Analysis of thermoelastic behavior 358 6.11.3 Biaxial non-orthogonal woven fabric composites 365
Contents xiii 6.12 Nonlinear stress-strain behavior 366 6.13 Mechanical properties 368 6.13.1 Friction and wear behavior 368 6.13.2 Notched strength 371 7 Three-dimensional textile structural composites 374 7.1 Introduction 374 7.2 Processing of textile preforms 376 7.2.1 Braiding 377 7.2.1.1 2-step braiding 377 7.2.1.2 4-step braiding 379 7.2.1.3 Solid braiding 382 7.2.2 Weaving 382 7.2.2.1 Angle-interlock multi-layer weaving 383 7.2.2.2 Orthogonal weaving 387 7.2.3 Stitching 387 7.2.4 Knitting 389 7.3 Processing windows for 2-step braids 389 7.3.1 Packing of fibers and yarn cross-sections 390 7.3.2 Unit cell of the preform 395 7.3.3 Criterion for yarn jamming 398 7.4 Yarn packing in 4-step braids 402 7.4.1 Unit cell of the preform 402 7.4.2 Criterion for yarn jamming 403 7.5 Analysis of thermoelastic behavior of composites 405 7.5.1 Elastic strain-energy approach 406 7.5.2 Fiber inclination model 407 7.5.3 Macro-cell approach 414 7.5.3.1 Geometric relations 414 7.5.3.2 Elastic constants 416 7.6 Structure-performance maps of composites 419 7.7 Mechanical properties of composites 428 7.7.1 Tensile and compressive behavior 428 7.7.2 Shear behavior 431 7.7.3 Fracture behavior 432 7.7.3.1 In-plane fracture 432 7.7.3.2 Interlaminar fracture 435 7.7.4 Impact 440 8 Flexible composites 443 8.1 Introduction 443 8.2 Cord/rubber composites 445
Contents xiii 6.12 Nonlinear stress-strain behavior 366 6.13 Mechanical properties 368 6.13.1 Friction and wear behavior 368 6.13.2 Notched strength 371 7 Three-dimensional textile structural composites 374 7.1 Introduction 374 7.2 Processing of textile preforms 376 7.2.1 Braiding 377 7.2.1.1 2-step braiding 377 7.2.1.2 4-step braiding 379 7.2.1.3 Solid braiding 382 7.2.2 Weaving 382 7.2.2.1 Angle-interlock multi-layer weaving 383 7.2.2.2 Orthogonal weaving 387 7.2.3 Stitching 387 7.2.4 Knitting 389 7.3 Processing windows for 2-step braids 389 7.3.1 Packing of fibers and yarn cross-sections 390 7.3.2 Unit cell of the preform 395 7.3.3 Criterion for yarn jamming 398 7.4 Yarn packing in 4-step braids 402 7.4.1 Unit cell of the preform 402 7.4.2 Criterion for yarn jamming 403 7.5 Analysis of thermoelastic behavior of composites 405 7.5.1 Elastic strain-energy approach 406 7.5.2 Fiber inclination model 407 7.5.3 Macro-cell approach 414 7.5.3.1 Geometric relations 414 7.5.3.2 Elastic constants 416 7.6 Structure-performance maps of composites 419 7.7 Mechanical properties of composites 428 7.7.1 Tensile and compressive behavior 428 7.7.2 Shear behavior 431 7.7.3 Fracture behavior 432 7.7.3.1 In-plane fracture 432 7.7.3.2 Interlaminar fracture 435 7.7.4 Impact 440 8 Flexible composites 443 8.1 Introduction 443 8.2 Cord/rubber composites 445
Xiv Contents 8.2.1 Rubber and cord properties 446 8.2.2 Unidirectional composites 447 8.2.3 Laminated composites 449 8.2.4 Cord loads in tires 453 8.3 Coated fabrics 456 8.4 Nonlinear elastic behavior-incremental analysis 459 8.4.1 Geometry of wavy fibers 460 8.4.2 Axial tensile behavior 462 8.4.2.1 Iso-phase model 462 8.4.2.2 Random-phase model 465 8.4.2.3 Nonlinear tensile stress-strain behavior 467 8.4.3 Transverse tensile behavior 471 8.4.3.1 Iso-phase model 471 8.4.3.2 Random-phase model 472 9 Nonlinear elastic finite deformation of flexible composites 474 9.1 Introduction 474 9.2 Background 478 9.2.1 Tensor notation 478 9.2.2 Lagrangian and Eulerian descriptions 480 9.3 Constitutive relations based on the Lagrangian description 485 9.3.1 Finite deformation of a composite lamina 485 9.3.2 Constitutive equations for a composite lamina 487 9.3.2.1 Strain-energy function 487 9.3.2.2 General constitutive equations for a unidirectional lamina 488 9.3.2.3 Pure homogeneous deformation 490 9.3.2.4 Simple shear 492 9.3.2.5 Simple shear superposed on simple extension 495 9.3.3 Constitutive equations of flexible composite laminates 499 9.3.3.1 Constitutive equations 499 9.3.3.2 Homogeneous deformation 500 9.3.3.3 Simple extension of a symmetric composite laminate 502 9.3.4 Determination of elastic constants 505 9.3.4.1 Tensile properties 505 9.3.4.2 Shear properties 506
xiv Contents 8.2.1 Rubber and cord properties 446 8.2.2 Unidirectional composites 447 8.2.3 Laminated composites 449 8.2.4 Cord loads in tires 453 8.3 Coated fabrics 456 8.4 Nonlinear elastic behavior - incremental analysis 459 8.4.1 Geometry of wavy fibers 460 8.4.2 Axial tensile behavior 462 8.4.2.1 Iso-phase model 462 8.4.2.2 Random-phase model 465 8.4.2.3 Nonlinear tensile stress-strain behavior 467 8.4.3 Transverse tensile behavior 471 8.4.3.1 Iso-phase model 471 8.4.3.2 Random-phase model 472 9 Nonlinear elastic finite deformation of flexible composites 474 9.1 Introduction 474 9.2 Background 478 9.2.1 Tensor notation 478 9.2.2 Lagrangian and Eulerian descriptions 480 9.3 Constitutive relations based on the Lagrangian description 485 9.3.1 Finite deformation of a composite lamina 485 9.3.2 Constitutive equations for a composite lamina 487 9.3.2.1 Strain-energy function 487 9.3.2.2 General constitutive equations for a unidirectional lamina 488 9.3.2.3 Pure homogeneous deformation 490 9.3.2.4 Simple shear 492 9.3.2.5 Simple shear superposed on simple extension 495 9.3.3 Constitutive equations of flexible composite laminates 499 9.3.3.1 Constitutive equations 499 9.3.3.2 Homogeneous deformation 500 9.3.3.3 Simple extension of a symmetric composite laminate 502 9.3.4 Determination of elastic constants 505 9.3.4.1 Tensile properties 505 9.3.4.2 Shear properties 506
Contents XV 9.4 Constitutive relations based on the Eulerian description 508 9.4.1 Stress-energy function 509 9.4.2 General constitutive equations 511 9.4.3 Pure homogeneous deformation 514 9.4.4 Simple shear superposed on simple extension 515 9.4.5 Determination of elastic compliance constants 517 9.5 Elastic behavior of flexible composites reinforced with wavy fibers 519 9.5.1 Introduction 519 9.5.2 Longitudinal elastic behavior based on the Lagrangian approach 520 9.5.3 Longitudinal elastic behavior based on the Eulerian approach 522 References 526 Author index 556 Subject index 563
Contents xv 9.4 Constitutive relations based on the Eulerian description 508 9.4.1 Stress-energy function 509 9.4.2 General constitutive equations 511 9.4.3 Pure homogeneous deformation 514 9.4.4 Simple shear superposed on simple extension 515 9.4.5 Determination of elastic compliance constants 517 9.5 Elastic behavior of flexible composites reinforced with wavy fibers 519 9.5.1 Introduction 519 9.5.2 Longitudinal elastic behavior based on the Lagrangian approach 520 9.5.3 Longitudinal elastic behavior based on the Eulerian approach 522 References 526 Author index 556 Subject index 563
Preface The science and technology of composite materials are based on a design concept which is fundamentally different from that of conventional structural materials.Metallic alloys,for instance, generally exhibit a uniform field of material properties;hence,they can be treated as homogeneous and isotropic.Fiber composites,on the other hand,show a high degree of spacial variation in their microstructures,resulting in non-uniform and anisotropic pro- perties.Furthermore,metallic materials can be shaped into desired geometries through secondary work (e.g.rolling,extrusion,etc.); the macroscopic configuration and the microscopic structure of a metallic component are related through the processing route it undergoes.With fiber composites,the co-relationship between microstructure and macroscopic configuration and their dependence on processing technique are even stronger.As a result,composites technology offers tremendous potential to design materials for specific end uses at various levels of scale. First,at the microscopic level,the internal structure of a component can be controlled through processing.A classical example is the molding of short-fiber composites,where fiber orientation,fiber length and fiber distribution may be controlled to yield the desired local properties.Other examples can be found in the filament winding of continuous fibers,hybridization of fibers, and textile structural forms based upon weaving,braiding,knitting, etc.In all these cases,the desired local stiffness,strength,toughness and other prespecified properties may be achieved by controlling the fiber type,orientation,and volume fraction throughout the structural component. Second,the external geometrical shape of a structural component can also be designed.Advances in the technology of filament winding enable the automated production of components with complex contours.It is now also feasible to fabricate three- dimensional fiber preforms using advanced textile technology.As the ability to fabricate larger and more integrated structural components of net shape is further enhanced,the need to handle and join a large number of small parts,as is currently done with metallic materials,diminishes
Preface The science and technology of composite materials are based on a design concept which is fundamentally different from that of conventional structural materials. Metallic alloys, for instance, generally exhibit a uniform field of material properties; hence, they can be treated as homogeneous and isotropic. Fiber composites, on the other hand, show a high degree of spacial variation in their microstructures, resulting in non-uniform and anisotropic properties. Furthermore, metallic materials can be shaped into desired geometries through secondary work (e.g. rolling, extrusion, etc.); the macroscopic configuration and the microscopic structure of a metallic component are related through the processing route it undergoes. With fiber composites, the co-relationship between microstructure and macroscopic configuration and their dependence on processing technique are even stronger. As a result, composites technology offers tremendous potential to design materials for specific end uses at various levels of scale. First, at the microscopic level, the internal structure of a component can be controlled through processing. A classical example is the molding of short-fiber composites, where fiber orientation, fiber length and fiber distribution may be controlled to yield the desired local properties. Other examples can be found in the filament winding of continuous fibers, hybridization of fibers, and textile structural forms based upon weaving, braiding, knitting, etc. In all these cases, the desired local stiffness, strength, toughness and other prespecified properties may be achieved by controlling the fiber type, orientation, and volume fraction throughout the structural component. Second, the external geometrical shape of a structural component can also be designed. Advances in the technology of filament winding enable the automated production of components with complex contours. It is now also feasible to fabricate threedimensional fiber preforms using advanced textile technology. As the ability to fabricate larger and more integrated structural components of net shape is further enhanced, the need to handle and join a large number of small parts, as is currently done with metallic materials, diminishes