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Composite Materials Design and Applications 3rd Edition Gay
Composite Materials Design and Applications 3rd Edition Gay Digital Instant Download Author(s): Gay, Daniel ISBN(s): 9781466584877, 1466584874 Edition: 3 File Details: PDF, 19.84 MB Year: 2014 Language: english
K19063 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 2 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK an informa business www.taylorandfrancisgroup.com COMPOSITE MATERIALS COMPOSITE MATERIALS COMPOSITE MATERIALS T H I R D E D I T I O N THIRD EDITION T H I R D E D I T I O N Design and Applications Design and Applications Design and Applications Daniel Gay Gay K19063 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 2 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK an informa business www.taylorandfrancisgroup.com Composite materials Composite materials Composite materials T h i r d E d i T i o n Third EdiTion T h i r d E d i T i o n design and Applications design and Applications design and Applications daniel Gay Gay “This book covers the topics related to the mechanics of composite ma- terials in a very simple way. ... it is addressed to graduate and under- graduate students as well as to practical engineers who want to en- hance their knowledge and learn the guidelines of the use of composite materials. ... This book is...a good classroom material...[and] a good reference.” —Dr. Pierre Rahme, University of Notre Dame, Indiana, USA Considered to have contributed greatly to the pre-sizing of composite structures, Composite Materials: Design and Applications is a popular reference book for designers of heavily loaded composite parts. Fully updated to mirror the exponential growth and development of compos- ites, this English-language Third Edition: • Contains all-new coverage of nanocomposites and biocomposites • reflects the latest manufacturing processes and applications in the aerospace, automotive, naval, wind turbine, and sporting goods industries • Provides a design method to define composite multilayered plates under loading, along with all numerical information needed for implementation • Proposes original study of composite beams of any section shapes and thick-laminated composite plates, leading to technical formula- tions that are not found in the literature • Features numerous examples of the pre-sizing of composite parts, processed from industrial cases and reworked to highlight key in- formation • includes test cases for the validation of computer software using finite elements Consisting of three main parts, plus a fourth on applications, Composite Materials: Design and Applications, Third Edition features a technical level that rises in difficulty as the text progresses, yet each part still can be explored independently. While the heart of the book, devoted to the methodical pre-design of structural parts, retains its original character, the contents have been significantly rewritten, restructured, and expand- ed to better illustrate the types of challenges encountered in modern engineering practice. Materials Science/Mechanical Engineering “This book covers the topics related to the mechanics of composite ma- terials in a very simple way. ... It is addressed to graduate and un- dergraduate students as well as to practical engineers who want to enhance their knowledge and learn the guidelines of the use of compos- ite materials. ... This book is...good classroom material...[and] a good reference.” —Dr. Pierre Rahme, University of Notre Dame, Indiana, USA Considered to have contributed greatly to the pre-sizing of composite structures, Composite Materials: Design and Applications is a popular reference book for designers of heavily loaded composite parts. Fully updated to mirror the exponential growth and development of compos- ites, this English-language Third Edition: • Contains all-new coverage of nanocomposites and biocomposites • Reflects the latest manufacturing processes and applications in the aerospace, automotive, naval, wind turbine, and sporting goods industries • Provides a design method to define composite multilayered plates under loading, along with all numerical information needed for implementation • Proposes original study of composite beams of any section shapes and thick-laminated composite plates, leading to technical formula- tions that are not found in the literature • Features numerous examples of the pre-sizing of composite parts, processed from industrial cases and reworked to highlight key in- formation • Includes test cases for the validation of computer software using finite elements Consisting of three main parts, plus a fourth on applications, Composite Materials: Design and Applications, Third Edition features a technical level that rises in difficulty as the text progresses, yet each part still can be explored independently. While the heart of the book, devoted to the methodical pre-design of structural parts, retains its original character, the contents have been significantly rewritten, restructured, and expand- ed to better illustrate the types of challenges encountered in modern engineering practice. Materials Science/Mechanical Engineering ISBN: 978-1-4665-8487-7 9 781466 584877 90000
Composite materials T h i r d E d i T i o n design and Applications
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Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business Composite materials T h i r d E d i T i o n design and Applications daniel Gay
CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20140611 International Standard Book Number-13: 978-1-4665-8488-4 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
v Contents Preface.................................................................................................................................xix Acknowledgments...............................................................................................................xxi Author.............................................................................................................................. xxiii Section I  PRINCIPLES OF CONSTRUCTION 1 Composite Materials: Interest and Physical Properties. ................................................3 1.1 What Is a Composite Material?................................................................................ 3 1.1.1 Broad Definition......................................................................................... 3 1.1.2 Main Features. ............................................................................................. 4 1.2 Fibers and Matrices.................................................................................................. 4 1.2.1 Fibers........................................................................................................... 4 1.2.1.1 Definition.................................................................................... 4 1.2.1.2 Principal Fiber Materials............................................................. 5 1.2.1.3 Relative Importance of Different Fibers in Applications.............. 6 1.2.2 Materials for Matrices. ................................................................................. 7 1.3 What Can Be Made Using Composite Materials?.................................................... 7 1.4 A Typical Example of Interest. .................................................................................. 9 1.5 Some Examples of Classical Design Replaced by Composite Solutions. ...................10 1.6 Main Physical Properties.........................................................................................10 2 Manufacturing Processes............................................................................................17 2.1 Molding Processes...................................................................................................17 2.1.1 Contact Molding........................................................................................17 2.1.2 Compression Molding................................................................................18 2.1.3 Vacuum Molding. .......................................................................................18 2.1.4 Resin Injection Molding.............................................................................19 2.1.5 Injection Molding with Prepreg................................................................. 20 2.1.6 Foam Injection Molding. ........................................................................... 20 2.1.7 Molding of Hollow Axisymmetric Components........................................ 20 2.2 Other Forming Processes. ....................................................................................... 22 2.2.1 Sheet Forming........................................................................................... 22 2.2.2 Profile Forming......................................................................................... 23 2.2.3 Forming by Stamping................................................................................ 23
vi ◾ Contents 2.2.4 Preforming by Three-Dimensional Assembly............................................. 24 2.2.4.1 Example: Carbon/Carbon......................................................... 24 2.2.4.2 Example: Silicon/Silicon............................................................ 24 2.2.5 Automated Tape Laying and Fiber Placement. ........................................... 24 2.2.5.1 Necessity of Automation. ........................................................... 24 2.2.5.2 Example. .................................................................................... 24 2.2.5.3 Example. .....................................................................................25 2.2.5.4 Example: Robots and Software for AFP—Automatic Fiber Placement Coriolis Composites (FRA)..............................25 2.3 Practical Considerations on Manufacturing Processes............................................ 26 2.3.1 Acronyms.................................................................................................. 26 2.3.2 Cost Comparison...................................................................................... 27 3 Ply Properties..............................................................................................................29 3.1 Isotropy and Anisotropy......................................................................................... 29 3.1.1 Isotropic Materials......................................................................................31 3.1.2 Anisotropic Material.................................................................................. 32 3.2 Characteristics of the Reinforcement–Matrix Mixture............................................33 3.2.1 Fiber Mass Fraction................................................................................... 34 3.2.2 Fiber Volume Fraction............................................................................... 34 3.2.3 Mass Density of a Ply.................................................................................35 3.2.4 Ply Thickness..............................................................................................35 3.3 Unidirectional Ply.................................................................................................. 36 3.3.1 Elastic Modulus......................................................................................... 36 3.3.2 Ultimate Strength of a Ply......................................................................... 38 3.3.3 Examples................................................................................................... 39 3.3.4 Examples of High-Performance Unidirectional Plies..................................41 3.4 Woven Ply...............................................................................................................41 3.4.1 Forms of Woven Fabrics.............................................................................41 3.4.2 Elastic Modulus of Fabric Layer................................................................ 42 3.4.3 Examples of Balanced Fabric/Epoxy.......................................................... 43 3.5 Mats and Reinforced Matrices. ................................................................................45 3.5.1 Mats...........................................................................................................45 3.5.2 Example: A Summary of Glass/Epoxy Layers.............................................45 3.5.3 Microspherical Fillers.................................................................................45 3.5.4 Other Classical Reinforcements. ................................................................ 48 3.6 Multidimensional Fabrics....................................................................................... 49 3.6.1 Example: A Four-Dimensional Architecture of Carbon Reinforcement..... 49 3.6.2 Example: Three-Dimensional Carbon/Carbon Components..................... 50 3.7 Metal Matrix Composites....................................................................................... 50 3.7.1 Some Examples. ......................................................................................... 50 3.7.2 Unidirectional Fibers/Aluminum Matrix. ...................................................52 3.8 Biocomposite Materials...........................................................................................53 3.8.1 Natural Plant Fibers...................................................................................53 3.8.1.1 Natural Fibers. ............................................................................53 3.8.1.2 Pros............................................................................................53
Contents ◾ vii 3.8.1.3 Cons...........................................................................................53 3.8.1.4 Examples................................................................................... 54 3.8.2 Natural Vegetable Fiber–Reinforced Composites...................................... 54 3.8.2.1 Mechanical Properties............................................................... 54 3.8.2.2 Biodegradable Matrices............................................................. 54 3.8.3 Manufacturing Processes........................................................................... 56 3.8.3.1 With Thermosetting Resins....................................................... 56 3.8.3.2 With Thermoplastic Resins.........................................................57 3.9 Nanocomposite Materials........................................................................................57 3.9.1 Nanoreinforcement. ....................................................................................57 3.9.1.1 Nanoreinforcement Shapes.........................................................57 3.9.1.2 Properties of Nanoreinforcements. ............................................. 58 3.9.2 Nanocomposite Material............................................................................61 3.9.3 Mechanical Applications........................................................................... 62 3.9.3.1 Improvement in Mechanical Properties..................................... 62 3.9.3.2 Further Examples of Nonmechanical Applications.................... 64 3.9.4 Manufacturing of Nanocomposite Materials............................................. 64 3.10 Tests....................................................................................................................... 66 4 Sandwich Structures. ...................................................................................................69 4.1 What Is a Sandwich Structure?. .............................................................................. 69 4.1.1 Their Properties Are Surprising. ................................................................. 69 4.1.2 Constituent Materials................................................................................ 70 4.2 Simplified Flexure. .................................................................................................. 71 4.2.1 Stress......................................................................................................... 71 4.2.2 Displacements........................................................................................... 72 4.2.2.1 Contributions of bending moment M and of shear force T .... 72 4.2.2.2 Example: A Cantilever Sandwich Structure............................... 73 4.3 Some Special Features of Sandwich Structures........................................................74 4.3.1 Comparison of Mass for the Same Flexural Rigidity 〈EI〉..........................74 4.3.2 Deterioration by Buckling of Sandwich Structures.....................................74 4.3.2.1 Global Buckling........................................................................ 75 4.3.2.2 Local Buckling of the Skins....................................................... 75 4.3.3 Other Types of Damage.............................................................................76 4.4 Manufacturing and Design Problems......................................................................76 4.4.1 Example of Core Material: Honeycomb.....................................................76 4.4.2 Shaping Processes...................................................................................... 77 4.4.2.1 Machining................................................................................. 77 4.4.2.2 Deformation.............................................................................. 77 4.4.2.3 Some Other Considerations. ...................................................... 77 4.4.3 Inserts and Attachment Fittings................................................................ 78 4.4.4 Repair of Laminated Facings..................................................................... 79 4.5 Nondestructive Inspection. ..................................................................................... 80 4.5.1 Main Nondestructive Inspection Methods................................................ 80 4.5.2 Acoustic Emission Testing..........................................................................81
viii ◾ Contents 5 Conception: Design and Drawing...............................................................................85 5.1 Drawing a Composite Part......................................................................................85 5.1.1 Specific Properties......................................................................................85 5.1.2 Guide Values of Presizing.......................................................................... 86 5.1.2.1 Material Characteristics............................................................. 86 5.1.2.2 Design Factors........................................................................... 88 5.2 Laminate................................................................................................................ 88 5.2.1 Unidirectional Layers and Fabrics............................................................. 88 5.2.1.1 Unidirectional Layer. ................................................................. 88 5.2.1.2 Fabrics....................................................................................... 89 5.2.2 Correct Ply Orientation............................................................................. 89 5.2.3 Laminate Drawing Code........................................................................... 90 5.2.3.1 Standard Orientations............................................................... 90 5.2.3.2 Laminate Middle Plane............................................................. 90 5.2.3.3 Description of the Stacking Order............................................. 93 5.2.3.4 Midplane Symmetry.................................................................. 93 5.2.3.5 Specific Case of Balanced Fabrics.............................................. 94 5.2.3.6 Technical Minimum. ................................................................. 95 5.2.4 Arrangement of Plies................................................................................. 96 5.2.4.1 Proportion and Number of Plies................................................ 96 5.2.4.2 Example of Pictorial Representation.......................................... 97 5.2.4.3 Case of Sandwich Structure....................................................... 97 5.3 Failure of Laminates............................................................................................... 98 5.3.1 Damages. ................................................................................................... 98 5.3.1.1 Types of Failure......................................................................... 98 5.3.1.2 Note: Classical Maximum Stress Criterion Shows Its Limits...........................................................................99 5.3.2 Most Frequently Used Criterion: Tsai–Hill Failure Criterion.................. 100 5.3.2.1 Tsai–Hill Number.................................................................... 100 5.3.2.2 Notes........................................................................................101 5.3.2.3 How to Determine the Stress Components σℓ, σt, and τℓt in Each Ply...............................................................................101 5.4 Presizing of the Laminate......................................................................................102 5.4.1 Modulus of Elasticity—Deformation of a Laminate. ................................102 5.4.1.1 Varying Proportions of Plies.....................................................102 5.4.1.2 Example of Using Tables..........................................................103 5.4.2 Case of Simple Loading............................................................................103 5.4.3 Complex Loading Case: Approximative Proportions According to Orientations.........................................................................................109 5.4.3.1 When the Normal and Tangential (Shear) Loads Are Applied Simultaneously............................................................109 5.4.3.2 Example. ...................................................................................114 5.4.3.3 Note.........................................................................................117 5.4.4 Complex Loading Case: Optimum Composition of a Laminate. ..............119 5.4.4.1 Optimum Laminate.................................................................119 5.4.4.2 Example. .................................................................................. 122
Contents ◾ ix 5.4.4.3 Example. ...................................................................................125 5.4.4.4 Notes....................................................................................... 126 5.4.5 Notes for Practical Use Concerning Laminates....................................... 127 5.4.5.1 Specific Aspects for the Design of Laminates. .......................... 127 5.4.5.2 Delaminations......................................................................... 128 5.4.5.3 Why Is Fatigue Resistance So Good?. .......................................129 5.4.5.4 Laminated Tubes......................................................................133 6 Conception: Fastening and Joining...........................................................................135 6.1 Riveting and Bolting.............................................................................................135 6.1.1 Local Loss of Strength..............................................................................135 6.1.1.1 Knock-Down Factor.................................................................135 6.1.1.2 Causes of Hole Degradation.................................................... 136 6.1.2 Main Failure Modes in Bolted Joints of Composite Materials..................138 6.1.3 Sizing of the Joint.....................................................................................138 6.1.3.1 Recommended Values. ..............................................................138 6.1.3.2 Evaluation of Magnified Stress Values......................................140 6.1.4 Riveting....................................................................................................140 6.1.5 Bolting. .....................................................................................................141 6.1.5.1 Example of Bolted Joint............................................................141 6.1.5.2 Tightening of the bolt..............................................................143 6.2 Bonding. ................................................................................................................143 6.2.1 Adhesives Used.........................................................................................143 6.2.2 Geometry of the Bonded Joints................................................................145 6.2.3 Sizing of the Bonding Surface Area..........................................................146 6.2.3.1 Strength of adhesive. ................................................................146 6.2.3.2 Design......................................................................................147 6.2.3.3 Stress in Bonded Areas.............................................................148 6.2.3.4 Example of single-lap adhesive joint......................................150 6.2.4 Case of Bonded Joint with Cylindrical Geometry. ....................................150 6.2.4.1 Bonded Circular Flange. ...........................................................150 6.2.4.2 Tubes Fitted and Bonded into One Another.............................150 6.2.5 Examples of Bonding. ...............................................................................150 6.2.5.1 Laminates.................................................................................150 6.3 Inserts. ...................................................................................................................152 6.3.1 Case of Sandwich Parts. ............................................................................152 6.3.2 Case of Parts under Uniaxial Loads..........................................................154 7 Composite Materials and Aerospace Construction...................................................155 7.1 Aircraft..................................................................................................................155 7.1.1 Composite Components in Aircraft. .........................................................155 7.1.2 Allocation of Composites Depending on Their Nature.............................156 7.1.2.1 Glass/Epoxy, Kevlar/Epoxy......................................................156 7.1.2.2 Carbon/Epoxy..........................................................................157 7.1.2.3 Boron/Epoxy............................................................................157 7.1.2.4 Honeycombs. ............................................................................157 7.1.3 Few Comments........................................................................................158
x ◾ Contents 7.1.4 Specific Aspects of Structural Strength.....................................................158 7.1.5 Large Transport Aircraft. ..........................................................................159 7.1.5.1 Example. ...................................................................................159 7.1.5.2 How to Determine the Benefits................................................159 7.1.5.3 Example: Civil Transport Aircraft A380-800, Airbus (EUR) ...................................................................... 161 7.1.5.4 Example: Civil Transport Aircraft B 787-800, Boeing (USA). ....................................................................161 7.1.5.5 Example: Civil Transport Aircraft A350-900, Airbus (EUR)................................................................... 163 7.1.6 Regional Aircraft and Business Jets..........................................................165 7.1.6.1 Example: Regional Aircraft ATR 72-600, EADS (EUR), Alenia (ITA) ............................................................................165 7.1.6.2 Example: Business Aircraft Falcon, Dassault Aviation (FRA). ......165 7.1.6.3 Example: Cargo Aircraft WK2 and Suborbital Space Plane SST2, Scaled Composites (USA)–Virgin Group (UK).............166 7.1.7 Light Aircraft...........................................................................................168 7.1.7.1 Trends......................................................................................168 7.1.7.2 Aircraft with Tractor Propeller.................................................168 7.1.7.3 Aircraft with Pusher Propeller..................................................169 7.1.7.4 Modern Glider Planes. ..............................................................170 7.1.8 Fighter Aircraft.........................................................................................170 7.1.9 Architecture and Manufacture of Composite Aircraft Parts.....................171 7.1.9.1 Sandwich Design......................................................................171 7.1.9.2 Rib-Stiffened Panels.................................................................173 7.1.10 Braking Systems.......................................................................................178 7.2 Helicopters............................................................................................................179 7.2.1 Situation...................................................................................................179 7.2.2 Composite Areas. ......................................................................................180 7.2.2.1 Example: Helicopter EC 145 T2, Airbus-Helicopter (EUR).....180 7.2.2.2 Example: Helicopter X4, Thales–Safran (FRA), Airbus-Helicopter (EUR)���������������������������������������������������������180 7.2.3 Blades.......................................................................................................181 7.2.3.1 Design of a Main Rotor Blade..................................................181 7.2.3.2 Advantages...............................................................................181 7.2.3.3 Consequences...........................................................................181 7.2.4 Rotor Hub................................................................................................183 7.2.4.1 Example: Rotor Hub Starflex, Eurocopter (FRA–GER)...........183 7.2.4.2 Example: Rotor Hub Spheriflex, Eurocopter (FRA–GER).......184 7.2.5 Other Working Composite Parts..............................................................184 7.3 Airplane Propellers................................................................................................186 7.3.1 Propellers for Conventional Aerodynamics...............................................186 7.3.1.1 Example: Propeller Blade, Hamilton Sundstrand (USA)– Ratier Figeac (FRA)�����������������������������������������������������������������186 7.3.1.2 Example: Airplane with Tilt Rotors, V-22 Osprey Bell Boeing (USA) and Dowty Propellers (UK)�����������������������������187 7.3.2 High-Speed Propellers..............................................................................188
Contents ◾ xi 7.4 Aircraft Reaction Engine.......................................................................................190 7.4.1 Employed Materials..................................................................................190 7.4.2 Refractory Composites.............................................................................191 7.4.2.1 Specific Features.......................................................................191 7.4.2.2 Fibers........................................................................................191 7.4.2.3 Matrices. ...................................................................................192 7.4.2.4 Applications. .............................................................................192 7.4.2.5 Example: Jet Engine Leap®, CFM International, General Electric (USA)–SNECMA (FRA) �����������������������������193 7.5 Space Applications.................................................................................................194 7.5.1 Satellites...................................................................................................194 7.5.2 Propellant Tanks and Pressure Vessels......................................................195 7.5.3 Nozzles.....................................................................................................196 7.5.4 Other Composite Components for Space Application..............................198 7.5.4.1 For Engines..............................................................................198 7.5.4.2 For Thermal Protection. ............................................................198 7.5.4.3 For Energy Storage.................................................................. 200 8 Composite Materials for Various Applications..........................................................203 8.1 Comparative Importance of Composites in Applications. ..................................... 203 8.1.1 Relative Importance in terms of Mass and Market Value........................ 204 8.1.2 Mass of Composites Implemented According to the Geographical Area............................................................................. 205 8.1.3 Average Prices.......................................................................................... 205 8.2 Composite Materials and Automotive Industry.................................................... 206 8.2.1 Introduction............................................................................................ 206 8.2.1.1 Example: Golf Model, Volkswagen (GER).............................. 206 8.2.1.2 Relative Weight Importance of Materials................................ 207 8.2.2 Composite Parts...................................................................................... 208 8.2.2.1 Brief Reminder........................................................................ 208 8.2.2.2 Current Functional Design. ..................................................... 208 8.2.2.3 Notable Composite Components. .............................................210 8.2.2.4 Notes........................................................................................212 8.2.2.5 Use of Natural Fibers. ...............................................................213 8.2.3 Research and Development......................................................................214 8.2.3.1 Structure..................................................................................215 8.2.3.2 Mechanical Parts......................................................................215 8.2.4 Motor Racing...........................................................................................216 8.3 Wind Turbines......................................................................................................217 8.3.1 Components.............................................................................................217 8.3.2 Manufacturing Processes..........................................................................218 8.4 Composites and Shipbuilding. ...............................................................................219 8.4.1 Competition.............................................................................................219 8.4.1.1 Example: Ocean-Going Maxi-Trimaran.................................. 220 8.4.1.2 Example: Single Scull.............................................................. 222 8.4.1.3 Example: Surfboard. ................................................................ 223 8.4.2 Vessels..................................................................................................... 223
xii ◾ Contents 8.5 Sports and Leisure................................................................................................ 223 8.5.1 Skis.......................................................................................................... 223 8.5.1.1 Equipment of a Skier............................................................... 223 8.5.1.2 Main Components of a Ski...................................................... 224 8.5.2 Bicycles.................................................................................................... 225 8.5.2.1 Machine.................................................................................. 226 8.5.2.2 Other Specific Equipments...................................................... 226 8.5.3 Tennis Rackets........................................................................................ 226 8.6 Diverse Applications............................................................................................. 226 8.6.1 Pressure Gas Bottle.................................................................................. 226 8.6.2 Bogie Frame............................................................................................ 227 8.6.3 Tubes for Offshore Installations. .............................................................. 227 8.6.4 Biomechanical Applications. .................................................................... 228 8.6.5 Cable Car................................................................................................ 229 Section II  Mechanical Behavior of Laminated Materials    9 Anisotropic Elastic Medium......................................................................................233 9.1 Some Reminders. ...................................................................................................233 9.1.1 Continuum Mechanics.............................................................................233 9.1.2 Number of Distinct φijkℓ Terms............................................................... 234 9.2 Orthotropic Material............................................................................................ 236 9.3 Transversely Isotropic Material............................................................................. 236 10 Elastic Constants of Unidirectional Composites. ......................................................239 10.1 Longitudinal Modulus Eℓ..................................................................................... 239 10.2 Poisson Coefficient................................................................................................241 10.3 Transverse Modulus Et......................................................................................... 242 10.4 Shear Modulus Gℓt............................................................................................. 244 10.5 Thermoelastic Properties. .......................................................................................245 10.5.1 Isotropic Material: Recall.........................................................................245 10.5.2 Case of Unidirectional Composite........................................................... 246 10.5.2.1 Coefficient of Thermal Expansion along the Direction ℓ......... 246 10.5.2.2 Coefficient of Thermal Expansion along the Transverse Direction t................................................................................247 10.5.3 Thermomechanical Behavior of a Unidirectional Layer........................... 248 11 Elastic Constants of a Ply in Any Direction..............................................................249 11.1 Flexibility Coefficients...........................................................................................249 11.2 Stiffness Coefficients. .............................................................................................255 11.3 Case of Thermomechanical Loading. .....................................................................257 11.3.1 Flexibility Coefficients..............................................................................257 11.3.2 Stiffness Coefficients. ................................................................................259 12 Mechanical Behavior of Thin Laminated Plates.......................................................263 12.1 Laminate with Midplane Symmetry..................................................................... 263 12.1.1 Membrane Behavior................................................................................ 263 12.1.1.1 Loadings.................................................................................. 263 12.1.1.2 Displacement Field.................................................................. 264
Contents ◾ xiii 12.1.2 Apparent Elastic Moduli of the Laminate. ................................................267 12.1.3 Consequence: Practical Determination of a Laminate Subject to Membrane Loading..............................................................................267 12.1.3.1 Givens of the Problem..............................................................267 12.1.3.2 Principle of Calculation........................................................... 268 12.1.3.3 Calculation Procedure............................................................. 269 12.1.4 Flexure Behavior...................................................................................... 272 12.1.4.1 Displacement Field.................................................................. 272 12.1.4.2 Loadings.................................................................................. 273 12.1.4.3 Notes........................................................................................275 12.1.5 Consequence: Practical Determination of a Laminate Subject to Flexure......278 12.1.6 Simplified Calculation for Bending......................................................... 278 12.1.6.1 Apparent Failure Strength in Bending..................................... 278 12.1.6.2 Apparent Flexure Modulus...................................................... 279 12.1.7 Thermomechanical Loading Case. ........................................................... 280 12.1.7.1 Membrane Behavior................................................................ 280 12.1.7.2 Behavior under Bending.......................................................... 283 12.2 Laminate without Midplane Symmetry................................................................ 283 12.2.1 Coupled Membrane–Flexure Behavior.................................................... 283 12.2.2 Case of Thermomechanical Loading. ....................................................... 285 Section III  Justifications, Composite Beams, and Thick Laminated Plates 13 Elastic Coefficients....................................................................................................289 13.1 Elastic Coefficients for an Orthotropic Material................................................... 289 13.1.1 Reminders............................................................................................... 289 13.1.2 Elastic Behavior Equation in Orthotropic Axes....................................... 290 13.2 Elastic Coefficients for a Transverse Isotropic Material......................................... 292 13.2.1 Elastic Behavior Equation. ....................................................................... 292 13.2.2 Rotation about an Orthotropic Transverse Axis...................................... 295 13.2.2.1 Problem................................................................................... 295 13.2.2.2 Technical Form....................................................................... 300 13.3 Case of a Ply......................................................................................................... 302 14 Damage in Composite Parts: Failure Criteria...........................................................303 14.1 Damage in Composite Parts................................................................................. 303 14.1.1 Industrial Emphasis of the Problem......................................................... 303 14.1.1.1 Causes of Damage................................................................... 303 14.1.1.2 Diversity of Composite Parts................................................... 304 14.1.2 Influence of Manufacturing Process........................................................ 304 14.1.2.1 Example: Injected Part with Short Fibers. ................................ 305 14.1.2.2 Example: Parts with Pronounced Curvatures.......................... 305 14.1.3 Typical Area and Singularities in a Same Part......................................... 305 14.1.4 Degradation Process within the Typical Area.......................................... 306 14.1.4.1 Example: Composite Short Fiber Plate.................................... 306 14.1.4.2 Example: Laminate Consisting of Unidirectional Plies............ 307
xiv ◾ Contents 14.2 Form of a Failure Criterion....................................................................................310 14.2.1 Features of a Failure Criterion..................................................................310 14.2.1.1 Failure Criterion Is a Design Tool. ............................................310 14.2.1.2 Many Criteria...........................................................................310 14.2.2 General Form of a Failure Criterion.........................................................310 14.2.2.1 Development of a Criterion......................................................310 14.2.2.2 Case of an Orthotropic Material. ..............................................311 14.2.3 Linear Failure Criterion............................................................................312 14.2.3.1 Example: Plane State of Stress in an Orthotropic Material.......312 14.2.3.2 Example: Maximum Stress Failure Criterion............................313 14.2.3.3 Note: Maximum Eligible Strain Criterion................................313 14.2.4 Quadratic Failure Criterion......................................................................314 14.2.4.1 General Form...........................................................................314 14.2.4.2 Specific Case of Plane Stress.....................................................314 14.2.4.3 Note: Simplified Form for the Quadratic Criterion..................315 14.3 Tsai–Hill Failure Criterion....................................................................................316 14.3.1 Isotropic Material: The von Mises Criterion.............................................316 14.3.1.1 Material Is Elastic and Isotropic...............................................316 14.3.1.2 Notes........................................................................................318 14.3.2 Orthotropic Material: Tsai–Hill Criterion. .............................................. 320 14.3.2.1 Notes....................................................................................... 320 14.3.2.2 Case of a Transversely Isotropic Material..................................321 14.3.2.3 Case of Unidirectional Ply under In-Plane Loading................ 323 14.3.3 Evolution of Strength Properties of a Unidirectional Ply Depending on the Direction of Solicitation���������������������������������������������������������������324 14.3.3.1 Tensile and Compressive Strength............................................324 14.3.3.2 Shear Strength..........................................................................325 15 Bending of Composite Beams of Any Section Shape. ................................................327 15.1 Bending of Beams with Isotropic Phases and Plane of Symmetry......................... 328 15.1.1 Degrees of Freedom..................................................................................329 15.1.1.1 Equivalent Stiffnesses...............................................................329 15.1.1.2 Longitudinal Displacement......................................................329 15.1.1.3 Rotation of the Section.............................................................329 15.1.1.4 Elastic Center.......................................................................... 330 15.1.1.5 Transverse Displacement along y Direction............................. 330 15.1.1.6 Transverse Displacement along z Direction..............................331 15.1.2 Perfect Bonding between the Phases.........................................................332 15.1.2.1 Displacements..........................................................................332 15.1.2.2 Strains......................................................................................332 15.1.2.3 Stress........................................................................................333 15.1.3 Equilibrium Relationships........................................................................333 15.1.3.1 Longitudinal Equilibrium........................................................333 15.1.3.2 Transverse Equilibrium........................................................... 334 15.1.3.3 Moment Equilibrium...............................................................335
Contents ◾ xv 15.1.4 Constitutive Equations............................................................................ 336 15.1.5 Technical Formulation.............................................................................337 15.1.5.1 Assumptions.............................................................................337 15.1.5.2 Expression of Normal Stress.....................................................337 15.1.5.3 Expression of Shear Stress.........................................................338 15.1.5.4 Shear Coefficient for the Section. ............................................. 340 15.1.6 Energy Interpretation.............................................................................. 342 15.1.6.1 Energy Due to Normal Stress σxx. ............................................ 342 15.1.6.2 Energy Due to Shear Stress τ. .................................................. 343 15.1.7 Extension to the Dynamic Case.............................................................. 344 15.2 Case of Beams of Any Cross Section (Asymmetric).............................................. 346 15.2.1 Technical Formulation............................................................................ 347 15.2.2 Notes........................................................................................................351 16 Torsion of Composite Beams of Any Section Shape..................................................353 16.1 Uniform Torsion. ...................................................................................................353 16.1.1 Torsional Degree of Freedom....................................................................354 16.1.2 Constitutive Equation..............................................................................354 16.1.3 Determination of Φ(y, z)..........................................................................355 16.1.3.1 Local Equilibrium....................................................................355 16.1.3.2 External Boundary Condition..................................................356 16.1.3.3 Internal Boundary Conditions. .................................................356 16.1.3.4 Uniqueness of Function Φ........................................................356 16.1.4 Energy Interpretation...............................................................................357 16.2 Location of the Torsion Center..............................................................................358 16.2.1 Coordinates in Principal Axes..................................................................358 16.2.2 Summary of Results.................................................................................359 16.2.3 Flexion–Torsion Coupling........................................................................361 17 Bending of Thick Composite Plates..........................................................................363 17.1 Preliminary Remarks............................................................................................ 363 17.1.1 Transverse Normal Stress σz.................................................................... 363 17.1.2 Transverse Shear Stress τxz and τyz. ........................................................... 364 17.1.3 Assumptions.............................................................................................365 17.2 Displacement Field................................................................................................367 17.3 Strains.................................................................................................................. 369 17.4 Constitutive Equations......................................................................................... 369 17.4.1 Membrane Behavior................................................................................ 369 17.4.2 Bending Behavior.....................................................................................370 17.4.3 Transverse Shear Behavior........................................................................372 17.4.3.1 Transverse Shear Resultant Qx..................................................372 17.4.3.2 Transverse Shear Resultant Qy..................................................373 17.5 Equilibrium Relationships.....................................................................................373 17.5.1 Transverse Equilibrium............................................................................373 17.5.2 Equilibrium in Bending. ...........................................................................374
xvi ◾ Contents 17.6 Technical Formulation for Bending.......................................................................374 17.6.1 Stress Due to Bending..............................................................................375 17.6.1.1 Plane Stress Values. ...................................................................375 17.6.1.2 Transverse Shear Stress Values..................................................376 17.6.2 Characterization of Warping Increments in Bending ηx and ηy. ................376 17.6.3 Particular Cases....................................................................................... 377 17.6.3.1 Orthotropic Homogeneous Plate............................................. 377 17.6.3.2 Cylindrical Bending about x- or y-Axis. ....................................378 17.6.3.3 Multilayered Plate. ....................................................................379 17.6.3.4 Consequences.......................................................................... 380 17.6.4 Warping Functions.................................................................................. 380 17.6.4.1 Boundary Conditions.............................................................. 380 17.6.4.2 Interfacial Continuity...............................................................381 17.6.4.3 Formulation of Warping Functions..........................................381 17.6.5 Consequences.......................................................................................... 382 17.6.5.1 Expression of Transverse Shear Stress...................................... 382 17.6.5.2 Transverse Shear Coefficients. .................................................. 382 17.6.6 Energy Interpretation.............................................................................. 384 17.7 Examples...............................................................................................................385 17.7.1 Orthotropic Homogeneous Plate..............................................................385 17.7.2 Sandwich Plate........................................................................................ 387 17.7.2.1 Case of Two Orthotropic Materials......................................... 387 17.7.2.2 Warping Functions.................................................................. 388 17.7.2.3 Transverse Shear Stress............................................................ 389 17.7.2.4 Transverse Shear Coefficients. .................................................. 389 17.7.3 Conclusion.............................................................................................. 390 Section IV Applications 18 Applications Level 1..................................................................................................393 18.1 Simply Supported Sandwich Beam........................................................................393 18.2 Poisson Coefficient of a Unidirectional Layer....................................................... 396 18.3 Helicopter Blade................................................................................................... 397 18.4 Drive Shaft for Trucks.......................................................................................... 402 18.5 Flywheel in Carbon/Epoxy. .................................................................................. 408 18.6 Wing Tip Made of Carbon/Epoxy........................................................................410 18.7 Carbon Fiber Coated with Nickel. ........................................................................ 423 18.8 Tube Made of Glass/Epoxy under Pressure. .......................................................... 425 18.9 Filament-Wound Pressure Vessel: Winding Angle................................................ 428 18.10 Filament-Wound Pressure Vessel: Consideration of Openings in the Bottom Heads.......431 18.11 Determination of Fiber Volume Fraction by Pyrolysis...........................................435 18.12 Reversing Lever Made of Carbon/PEEK (Unidirectional and Short Fibers)......... 436 18.13 Glass/Resin Telegraph Pole................................................................................... 439 18.14 Unidirectional Layer of HR Carbon..................................................................... 443 18.15 Manipulator Arm for a Space Shuttle................................................................... 444
Contents ◾ xvii 19 Applications Level 2..................................................................................................449 19.1 Sandwich Beam: Simplified Calculation of the Shear Coefficient......................... 449 19.2 Procedure for a Laminate Calculation Program.....................................................451 19.3 Kevlar/Epoxy Laminates: Stiffness in Terms of the Direction of Load..................455 19.4 Residual Thermal Stress Due to the Laminate Curing Process..............................459 19.5 Thermoelastic Behavior of a Glass/Polyester Tube................................................ 462 19.6 Creep of a Polymeric Tube Reinforced by Filament Wound under Thermal Stress...... 465 19.7 First-Ply Failure of a Laminate: Ultimate Strength................................................471 19.8 Optimum Laminate for Isotropic Plane Stress.......................................................475 19.9 Laminate Made of Identical Layers of Balanced Fabric. .........................................481 19.10 Carbon/Epoxy Wing Spar.................................................................................... 484 19.11 Elastic Constants of a Carbon/Epoxy Unidirectional Layer, Based on Tensile Test. .......491 19.12 Sailboat Hull in Glass/Polyester. ...............................................................................492 19.13 Balanced Fabric Ply: Determination of the In-Plane Shear Modulus.....................498 19.14 Quasi-Isotropic Laminate..................................................................................... 499 19.15 Pure Torsion of Orthotropic Plate........................................................................ 502 19.16 Plate Made by Resin Transfer Molding . ............................................................... 506 19.17 Thermoelastic Behavior of a Balanced Fabric Ply...................................................512 20 Applications Level 3..................................................................................................523 20.1 Cylindrical Bonding..............................................................................................523 20.2 Double-Lap Bonded Joint. .....................................................................................528 20.3 Composite Beam with Two Layers........................................................................533 20.4 Buckling of a Sandwich Beam...............................................................................537 20.5 Shear Due to Bending in a Sandwich Beam......................................................... 540 20.6 Shear Due to Bending in a Composite Box Beam................................................ 544 20.7 Torsion Center of a Composite U-Beam............................................................... 547 20.8 Shear Due to Bending in a Composite I-Beam..................................................... 549 20.9 Polymeric Column Reinforced by Filament-Wound Fiberglass..............................553 20.10 Cylindrical Bending of a Thick Orthotropic Plate under Uniform Loading......... 563 20.11 Bending of a Sandwich Plate................................................................................ 564 20.12 Bending Vibration of a Sandwich Beam................................................................567 Appendix A: Stresses in the Plies of a Carbon/Epoxy Laminate Loaded in Its Plane........571 Appendix B: Buckling of Orthotropic Structures..............................................................585 Bibliography. ......................................................................................................................595 Index���������������������������������������������������������������������������������������������������������������������������������599
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xix Preface The developments in the field of composite materials since the last quarter of a century have made this area popular due to the breadth and universality of applications. The annual global growth rate of composites is 5%–6%, and tonnage, which was 8 million tonnes in 2010, could rise to 10 million tonnes by 2015—a growth driven by advances in the transportation and wind industries. The sector of composites is an area of business that is always evolving. The cost of composites is becoming increasingly competitive. For a quarter of a century, the price of high-performance composites used in aerospace declined by more than half to compete with sophisticated metal alloys. At the same time, the quality of semifinished products reached remarkable levels. For example, the unidirectional prepreg tapes carbon/epoxy have their widths defined within 0.2 mm, and their fiber volume content controlled within only a few fractions of a percent, with obvious consequences for the evolution of the quality of parts. The legislation on recyclability obligation also affects the composite activities. It leads to sig- nificant increases in research and development on topics concerning natural fibers and biodegrad- able polymers. The growth in the use of composites has been aided by the development of modern design and manufacturing methods for industrial components, which allow functional optimization based on multiple technical and economic criteria. A good knowledge of what already exists helps develop and use reliable numerical simulations for in-service behavior as well as for implementation during the manufacturing. The development of simulation tools is an important component of industrial development, in general, and in composite domains, in particular. Without trying to replace testing, these tools allow full exploitation of the experimental results in a much more complete manner, creating a powerful synergy that saves time and cost. This third edition has been updated to take into account this rapidly changing field as well as the emergence and development of additional areas, such as those of bio- and nanocomposites. The core of the book devoted to the methodical predesign of structural parts has been preserved. As in previous editions, we have considered only a limited number of significant reinforcements and have highlighted the specific features needed for predimensioning. This is, in fact, to limit the number of performance tables accompanying the text. Other reinforcements not detailed in this book can be readily adapted; the reader will find everything needed to use a spreadsheet in order to get the desired results. He or she may also download a dedicated free utility as indicated in the book. The chapters on composite beams of any cross-sectional shape and the chapter on laminated thick plates still retain their original character, both with regard to the proposed method and to the results.
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I will not have thee.) But the smiles that played upon her features as the lady vanished beneath the waters raised within the young man a hope that forbade him to despair by her refusal of him, and the recollection of which cheered him on his way home. His aged parent was made acquainted with his ill-success, and she suggested that his bread should next time be but slightly baked, as most likely to please the mysterious being of whom he had become enamoured. “Impelled by an irresistible feeling, the youth left his mother’s house early next morning, and with rapid steps he passed over the mountain. He was soon near the margin of the lake, and with all the impatience of an ardent lover did he wait with a feverish anxiety for the reappearance of the mysterious lady. “The sheep and goats browsed on the precipitous sides of the Fan; the cattle strayed amongst the rocks and large stones, some of which were occasionally loosened from their beds and suddenly rolled down into the lake; rain and sunshine alike came and passed away; but all were unheeded by the youth, so wrapped up was he in looking for the appearance of the lady. “The freshness of the early morning had disappeared before the sultry rays of the noon-day sun, which in its turn was fast verging towards the west as the evening was dying away and making room for the shades of night, and hope had well nigh abated of beholding once more the Lady of the Lake. The young man cast a sad and last farewell look over the water, and to his astonishment, beheld several cows walking along its surface. The sight of these animals caused hope to revive that they would be followed by another object far more pleasing; nor was he disappointed, for the maiden reappeared, and to his enraptured sight, even lovelier than ever. She approached the land, and he rushed to meet her in the water. A smile encouraged him to seize her hand; neither did she refuse the moderately baked bread he offered her; and after some persuasion she consented to become his bride, on condition that they should only live together until she received from him three blows without a cause,
“Tri ergyd diachos.” (Three causeless blows.) and if he ever should happen to strike her three such blows she would leave him for ever. To such conditions he readily consented and would have consented to any other stipulation, had it been proposed, as he was only intent on then securing such a lovely creature for his wife. “Thus the Lady of the Lake engaged to become the young man’s wife, and having loosened her hand for a moment she darted away and dived into the lake. His chagrin and grief were such that he determined to cast himself headlong into the deepest water, so as to end his life in the element that had contained in its unfathomed depths the only one for whom he cared to live on earth. As he was on the point of committing this rash act, there emerged out of the lake two most beautiful ladies, accompanied by a hoary-headed man of noble mien and extraordinary stature, but having otherwise all the force and strength of youth. This man addressed the almost bewildered youth in accents calculated to soothe his troubled mind, saying that as he proposed to marry one of his daughters, he consented to the union, provided the young man could distinguish which of the two ladies before him was the object of his affections. This was no easy task, as the maidens were such perfect counterparts of each other that it seemed quite impossible for him to choose his bride, and if perchance he fixed upon the wrong one all would be for ever lost. “Whilst the young man narrowly scanned the two ladies, he could not perceive the least difference betwixt the two, and was almost giving up the task in despair, when one of them thrust her foot a slight degree forward. The motion, simple as it was, did not escape the observation of the youth, and he discovered a trifling variation in the mode with which their sandals were tied. This at once put an end to the dilemma, for he, who had on previous occasions been so taken up with the general appearance of the Lady of the Lake, had also noticed the beauty of her feet and ankles, and on now recognising the peculiarity of her shoe-tie he boldly took hold of her hand.
“‘Thou hast chosen rightly,’ said her father, ‘be to her a kind and faithful husband, and I will give her, as a dowry, as many sheep, cattle, goats, and horses as she can count of each without heaving or drawing in her breath. But remember, that if you prove unkind to her at any time, and strike her three times without a cause, she shall return to me, and shall bring all her stock back with her.’” Such was the verbal marriage settlement, to which the young man gladly assented, and his bride was desired to count the number of sheep she was to have. She immediately adopted the mode of counting by fives, thus:—one, two, three, four, five—one, two, three, four, five; and as many times as possible in rapid succession, till her breath was exhausted. The same procession of reckoning had to determine the number of goat, cattle, and horses respectively; and in an instant the full number of each came out of the lake when called upon by the father. “The young couple were then married, by what ceremony was not stated, and afterwards went to reside at a farm called Esgair Llaethy, somewhat more than a mile from the Village of Myddfai, where they lived in prosperity and happiness for several years, and became the parents of three sons, who were beautiful children. “Once upon a time there was a christening to take place in the neighbourhood, to which the parents were specially invited. When the day arrived the wife appeared very reluctant to attend the christening, alleging that the distance was too great for her to walk. Her husband told her to fetch one of the horses which were grazing in an adjoining field. ‘I will,’ said she, ‘if you will bring me my gloves which I left in our house.’ He went to the house and returned with the gloves, and finding that she had not gone for the horse jocularly slapped her shoulder with one of them, saying, ‘go! go!’ (dos, dos), when she reminded him of the understanding upon which she consented to marry him:—That he was not to strike her without a cause; and warned him to be more cautious for the future.
“On another occasion, when they were together at a wedding in the midst of the mirth and hilarity of the assembled guests, who had gathered together from all the surrounding country, she burst into tears and sobbed most piteously. Her husband touched her on her shoulder and inquired the cause of her weeping: she said, ‘Now people are entering into trouble, and your troubles are likely to commence, as you have the second time stricken me without a cause.’ “Years passed on, and their children had grown up, and were particularly clever young men. In the midst of so many worldly blessings at home, the husband almost forgot that there remained only one causeless blow to be given to destroy the whole of his prosperity. Still he was watchful lest any trivial occurrence should take place which his wife must regard as a breach of their marriage contract. She told him, as her affection for him was unabated, to be careful that he would not, through some inadvertence, give the last and only blow, which, by an unalterable destiny over which she had no control, would separate them for ever. “It, however, so happened that one day they were together at a funeral, where, in the midst of the mourning and grief at the house of the deceased, she appeared in the highest and gayest spirits, and indulged in immoderate fits of laughter, which so shocked her husband that he touched her, saying: ‘Hush! hush! don’t laugh.’ She said that she laughed ‘because people when they die go out of trouble,’ and rising up she went out of the house, saying, ‘The last blow has been struck, our marriage contract is broken, and at an end! Farewell!’ Then she started off towards Esgair Llaethdy, where she called her cattle and other stock together, each by name. The cattle she called thus:— Mu wlfrech, Mu olfrech, gwynfrech, Pedair cae tonn-frech, Yr hen wynebwen. A’r las Geigen, Gyda’r Tarw gwyn O lys y Brenin;
A’r llo du bach, Sydd ar y bach, Dere dithe, yn iach adre! Brindled cow, white speckled, Spotted cow, bold freckled, The four field sward mottled, The old white-faced, And the grey Geigen, With the white Bull, From the court of the King; And the little black calf Tho’ suspended on the hook, Come thou also, quite well home.” They all immediately obeyed the summons of their mistress. The ‘little black calf,’ although it had been slaughtered, became alive again, and walked off with the rest of the stock at the command of the lady. This happened in the spring of the year, and there were from four oxen ploughing in one of the fields; to these she cried:— “Pedwar eidion glas sydd ar y maes, Deuwch chwithau yn iach adre! The four grey oxen, that are on the field, Come you also quite well home!” Away the whole of the live stock went with the Lady across Myddfai Mountain, towards the lake from whence they came, a distance of above six miles, where they disappeared beneath its waters, leaving no trace behind except a well-marked furrow, which was made by the plough the oxen drew after them into the lake, and which remains to this day as a testimony to the truth of this story.
“What became of the affrighted ploughman—whether he was left on the field when the oxen set off, or whether he followed them to the lake, has not been handed down to tradition; neither has the fate of the disconsolate and half-ruined husband been kept in remembrance. But of the sons it is stated that they often wandered about the lake and its vicinity, hoping that their mother might be permitted to visit the face of the earth once more, as they had been apprised of her mysterious origin, her first appearance to their father, and the untoward circumstances which so unhappily deprived them of her maternal care. “In one of their rambles, at a place near Dol Howel, at the Mountain Gate, still called ‘Llidiad y Meddygon,’ (The Physician’s Gate), the mother appeared suddenly, and accosted her eldest son, whose name was Rhiwallon, and told him that his mission on earth was to be a benefactor to mankind by relieving them from pain and misery, through healing all manner of their diseases; for which purpose she furnished him with a bag full of medical prescriptions and instructions for the preservation of health. That by strict attention thereto he and his family would become for many generations the most skilful physicians in the country. Then, promising to meet him when her counsel was most needed, she vanished. But on several occasions she met her sons near the banks of the lake, and once she even accompanied them on their return home as far as a place still called ‘Pant-y- Meddygon,’ (The dingle of the Physicians) where she pointed out to them the various plants and herbs which grew in the dingle, and revealed to them their medicinal qualities or virtues; and the knowledge she imparted to them, together with their unrivalled skill, soon caused them to attain such celebrity that none ever possessed before them. And in order that their knowledge should not be lost, they wisely committed the same to writing for the benefit of mankind throughout all ages. And so ends the story of the Physicians of Myddfai, which had been handed down from one generation to another, thus:— “Yr hen wr llwyd o’r cornel, Gan ei dad a glywodd chwedel, A chan ei dad fy glywodd yntau,
Ac ar ei ol mi gofiais innau.” “The grey old man in the corner Of his father heard a story, Which from his father he had heard, And after them I have remembered.” The Physicians of Myddfai were Rhiwallon and his sons, Cadwgan, Gruffydd and Einion, who became Physicians to Rhys Gryg, Lord of Llandovery and Dynefor Castles, who lived in the early part of the thirteenth century. Rhys “gave them rank, lands, and privileges at Myddfai for their maintenance in the practice of their art and science, and the healing and benefit of those who should seek their help.” The fame of the celebrated Physicians was soon established over the whole country, and continued for centuries among their descendants; and the celebrated Welsh Poet Dafydd ap Gwilym, who flourished in the fourteenth century, says in one of his poems when alluding to these physicians:— “Meddyg, nis gwnai modd y gwnaeth Myddfai, o chai ddyn meddfaeth.” (A Physician he would not make As Myddfai made, if he had a mead fostered man.) Mr. Rees says that “of the above lands bestowed upon the Meddygon, there are two farms in the Myddfai parish still called “Llwyn Ifan Feddyg,” the Grove of Evan, the Physician, and “Llwyn Meredydd Feddyg” (the Grove of Meredydd the Physician). Esgair Llaethdy, mentioned in the foregoing legend, was formerly in the possession of the above descendants, and so was Ty-newydd, near Myddfai, which was purchased by Mr. Holford, of Cilgwyn, from the Rev. Charles Lloyd, vicar of Llandefalle, Breconshire, who married a daughter of one of the Meddygon, and had the living of Llandefalle from a Mr. Vaughan, who presented him to the same out of
gratitude, because Mr. Lloyd, wife’s father had cured him of a disease in the eye. As Mr. Lloyd succeeded to the above living in 1748, and died in 1800, it is probable that that skilful oculist was John Jones, who is mentioned in the following inscription on a tombstone at present fixed against the west end of Myddfai HERE Lieth the body of Mr. David Jones, of Mothvey, Surgeon, who was an honest, charitable and skilful man, He died September 14th, Anno Dom. 1719, aged 61. JOHN JONES, SURGEON, Eldest son of the said David Jones, departed this life the 25th of November, 1739, in the 4th year of his Age, and also lyes interred hereunder. These appear to have been the last of the Physicians who practised at Myddfai. The above John Jones resided for some time at Llandovery, and was a very eminent surgeon. One of his descendants, named John Lewis, lived at Cwmbran, Myddfai, at which place his great-grandson, Mr. John Jones, now resides. “Dr. Morgan Owen, Bishop of Llandaff, who died at Glasallt, parish of Myddfai, in 1645, was a descendant of the Meddygon, and an inheritor of much of their landed property in that parish, the bulk of which he bequeathed to his nephew, Morgan Owen, who died in 1667, and was succeeded by his son Henry Owen; and at the decease of the last of whose descendants, Roberts Lewis, Esqr., the estates became, through the will of one of the family, the property of the late D. A. S. Davies, Esqr., M.P., for Carmarthenshire. “Bishop Owen bequeathed to another nephew, Morgan ap Rees, son of Rees ap John, a descendant of the Meddygon, the farm of Rhyblid, and some other property. “Amongst other families who claim descent from the Physicians were the Bowens of Cwmydw, Myddfai, and Jones of Dollgarreg and Penrhock, in the same parish; the latter of whom are represented by Charles Bishop, of
Dollgarreg, Esqr., Clerk of the Peace for Carmarthenshire, and Thomas Bishop, of Brecon, Esqr. “Rees Williams, of Myddfai, is recorded as one of the Meddygon. His great grandson was the late Rice Williams, M.D., of Aberystwyth, who died May l6th, 1842, aged 85, and appears to have been the last, although not the least eminent of the Physicians descended from the mysterious Lady of Llyn y Fan.” Sir John Rhys mentions of another Dr. Williams also a descendant of the Lady of Llyn y Fan, who was living at Aberystwyth in 1881. It seems that there are several families in different parts of Wales who are said to have fairy blood coursing through their veins; and the noble Lady Bulkeley, who lived in North Wales, three or four generations was supposed to be descended from a Fairy lady who married a mortal. There is also a tradition that after the disappearance of the lady the disconsolate husband and his friends set to work to drain the lake in order to get at her, if possible; but as they were making a cutting into the bank a huge monster emerged from the water and threatened to drown the town of Brecon for disturbing him, saying:— “Os na cha’i lonydd yn fy lle Mi fodda, dre Byrhonddu!” (If I get no quiet in my place I shall drown the town of Brecon). so they had to give up draining the lake. There are extant several versions of the Myddfai Legend. In the “Cambro Briton” Vol. II., pages 313–315, we have a version in which it is stated that the farmer used to go near the lake and see some lambs he had bought at a fair, and that wherever he so went three most beautiful maidens appeared to
him from the lake. But whenever he tried to catch them they ran away into the lake, saying:— “Cras dy fara, Anhawdd ein dala.” (For thee who eatest baked bread It is difficult to catch us.) But one day a piece of moist bread came floating ashore, which he ate, and the next day he had a chat with the maidens. After a little conversation he proposed marriage to one of them, to which she consented, provided he could distinguish her from her sisters the day after. Then the story goes on very similar to Mr. Rees’ version which I have already given in full. In another beautiful version of the story which is given by Sikes in his “British Goblins,” it is said that an enamoured farmer had heard of the lake maiden, who rowed up and down the lake in a golden boat, with a golden oar. Her hair was long and yellow, and her face was pale and melancholy. In his desire to see this wondrous beauty, the farmer went on New Year’s Eve to the edge of the lake and in silence, awaited the coming of the first hour of the new year. It came, and there in truth was the maiden in her golden boat, rowing softly to and fro. Fascinated, he stood for hours beholding her, until the stars faded out of the sky, the moon sank behind the rocks, and the cold gray dawn drew nigh; and then the maiden began to vanish from his sight. Wild with passion, he cried aloud to the retreating vision, “Stay! Stay! Be my wife.” But the maiden only uttered a faint cry, and was gone. Night after night the young farmer haunted the shores of the lake, but the maiden returned no more. He became negligent of his person; his once robust form grew thin and wan; his face was a map of melancholy and despair. He went one day to consult a soothsayer who dwelt on the mountain, and this grave personage advised him to besiege the damsel’s heart with gifts of bread and cheese. This counsel commending itself strongly to his Welsh way of thinking, the former set out upon an assiduous course of casting his bread upon the waters—accompanied by cheese. He began on Mid-summer Eve
by going to the lake and dropping therein a large cheese and a loaf of bread. Night after night he continued to throw in loaves and cheeses, but nothing appeared in answer to his sacrifices. His hopes were set, however, on the approaching New Year’s Eve. The momentous night arrived at last. Clad in his best array, and armed with seven white loaves and his biggest and handsomest cheese, he set out once more for the lake. Then he waited till mid-night, and then slowly and solemnly dropped the seven loaves into the water, and with a sigh sent the cheese to keep them company. His persistence was at length rewarded. The Lake Lady came in her skiff to where he was, and gracefully stepped ashore. The story then proceeds as in the other versions. It was once a custom for people to go up to the lake on the first Sunday in August, when its water was supposed to be boiling; and Bishop Edwards, of St. Asaph, informed Professor Sir J. Rhys, that “an old woman from Myddfai, who is now, that is to say in January, 1881, about eighty years of age, tells me that she remembers thousands and thousands of people visiting the Lake of Little Fan on the first Sunday or Monday in August, and when she was young she often heard old men declare that at that time a commotion took place in the lake, and that its waters boiled, which was taken to herald the approach of the Lake Lady and her oxen.”—Celtic Folk Lore—page 15. A STUDENT WHO HAD FAILED TO PASS HIS EXAMINATIONS TAUGHT BY THE FAIRIES. Mr. John Jones, of Pontrhydfendigaid, an old man of over 95 years of age, related to me the following story about seven years ago:— In the 18th century there was a certain clergyman in North Cardiganshire, who was supposed to have been educated by the Fairies.
When he was a boy, his parents were very ambitious to see their son a clergyman, but, unfortunately, the lad either neglected his studies, or was a regular “blockhead,” and always failed to pass his college examinations, to the great regret and disappointment of his father and mother. One day, however, when the boy was roaming about the country (near the banks of the river Rheidol, as far as Mr. Jones could remember the story), he suddenly met three boys, or rather three little men who were not bigger than boys, who took him into some cave and led him along a subterranean passage into the land of the Fairies. The Fairies proved very kind to him, and when they heard his story, they undertook to help him to learn his lessons, so that in course of time he acquired a considerable knowledge of the classics. After spending a certain number of years very happily in Fairy Land, the young man returned to the world of mortals, and to the great joy of his parents passed his examinations now without the least difficulty, and in due time was ordained by the bishop, and became a vicar of a parish north of Aberystwyth, either Llanfihangel, Llancynfelin, or Eglwysfach. This tale seems to be a version of the Story of Elidorus, which Giraldus Cambrensis heard in the neighbourhood of Swansea during his “Itinerary through Wales,” with Archbishop Baldwin in the year 1188, which is as follows:— “A short time before our days, a circumstance worthy of note occurred in these parts, which Elidorus, a priest, most strenuously affirmed had befallen himself. When a youth of twelve years, and learning his letters, since, as Solomon says, “The root of learning is bitter, although the fruit is sweet,” in order to avoid the discipline and frequent stripes inflicted on him by his perceptor, he ran away, and concealed himself under the hollow bank of a river. After fasting in that situation for two days, two little men of pigmy stature appeared to him, saying, ‘If you come with us, we will lead you into a country full of delights and sports.’ “Assenting, and rising up, he followed his guides through a path, at first subterraneous and dark, into a most beautiful country, adorned with rivers and meadows, woods and plains, but obscure, and not illuminated with the full light of the sun.” All the days were cloudy, and the nights extremely dark, on account of the absence of the moon and stars. The boy was brought before the King, and introduced to
him in the presence of the court; who, having examined him for a long time, delivered him to his son, who was then a, boy. “These men were of the smallest stature, but very well proportioned in their make; they were all of a fair complexion, with luxuriant hair falling over their shoulders like that of women. “They had horses and greyhounds adapted to their size. “They neither ate flesh nor fish, but lived on milk diet, made up into messes with saffron. “They never took an oath, for they detested nothing so much as lies. “As often as they returned from our upper hemisphere, they reprobated our ambition, infidelities, and inconstances; they had no form of public worship, being strict lovers and reverers, as it seemed, of truth. “The boy frequently returned to our hemisphere, sometimes by the way he had first gone, sometimes by another; at first in company with other persons, and afterwards alone, and made himself known only to his mother, declaring to her the manners, nature and state of that people. “Being desired by her to bring a present of gold, with which that region abounded, he stole, while at play with the King’s son, the golden ball with which he used to divert himself, and brought it to his mother in great haste; and when he reached the door of his father’s house, but not unpursued, and was entering it in a great hurry, his foot stumbled on the threshold, and falling down into the room where his mother was sitting, the two pigmies seized the ball which had dropped from his hand, and departed, showing the boy every mark of contempt and derision. “On recovering from his fall, confounded with shame, and execrating the evil counsel of his mother, he returned by the usual track to the subterraneous road, but found no appearance of any passage, though he searched for it on the banks of the river for nearly the space of a year. “But since those calamities are often alleviated by time, which reason cannot mitigate, and length of time alone blunts the edge of our afflictions, and puts an end to many evils, the youth having been brought back by his friends and mother, and restored to his right way of thinking, and to his learning, in process of time attained the rank of priesthood. “Whenever David II., bishop of St. David’s, talked to him in his advanced state of life concerning this event, he could never relate the particulars without shedding tears. “He had made himself acquainted with the language of that nation, the words of which, in his younger days he used to recite, which, as the bishop often had informed me, were very conformable to the Greek idiom. “When they asked for water, they said
‘ydor ydorum,’ which meant bring water, for ‘ydor’ in their language, as well as in Greek, signifies water, from whence vessels for water are caller ‘udriai’; and ‘Dur’ (dwr) also, in the British language (Welsh) signifies water. “When they wanted salt they said, ‘Halgein ydorum,’ bring salt: salt is called ‘al’ in Greek, and ‘halen’ in British, for that language, from the length of time which the Britons (then called Trojans, and afterwards Britons, from Brito, their leader), remained in Greece after the destruction of Troy, became in many instances, similar to the Greek.... “If a scrupulous inquirer asks my opinion of the relation here inserted, I answer with Augustine, ‘that the Divine miracles are to be admired, not discussed.’ “Nor do I, by denial, place bounds to the Divine Power, nor, by assent, insolently extend what cannot be extended. “But I always call to mind the saying of St. Jerome: ‘You will find,’ says he, ‘Many things incredible and improbable, which nevertheless are true; for nature cannot in any respect prevail against the Lord of nature.’ “These things, therefore, and similar contingencies, I should place, according to the opinion of Augustine, among those particulars which are neither to be affirmed, nor too positively denied.” The above account is of the greatest interest, as it was written 700 years ago, and it also gives the opinion of one who lived in those days, of “these things, and similar contingencies.” It is possible that many of the Fairy Tales throughout the Kingdom, if not throughout the whole of Europe, have been founded on the story of Elidorus, the priest. THE SHEPHERD BOY AND THE FAIRIES OF FRENIFAWR. The following story appeared in the “Cambrian Superstitions,” by W. Howells, a little book published at Tipton in 1831:—
A stripling, of twelve or more years of age, was tending his father’s sheep on a small mountain called Frenifach, it was a fine morning in June, and he had just driven the sheep to their pasture for the day, when he looked at the top of Frenifawr to observe which way the morning fog declined, that he might judge the weather. If the fog on Frenifawr (a high mountain in Pembrokeshire, 10 miles from Cardigan) declines to the Pembrokeshire side, the peasants prognosticated fair, if on the Cardiganshire side foul weather. To his surprise the boy saw what seemed a party of soldiers sedulously engaged in some urgent affair; knowing there could not possibly be soldiers there so early, he with some alarm, looked more minutely, and perceived they were too diminutive for men; yet, thinking his eyesight had deceived him, he went to a more elevated situation, and discovered that they were the “Tylwyth Teg” (Fairies) dancing. He had often heard of them and had seen their rings in the neighbourhood, but not till then had the pleasure of seeing them; he once thought of running home to acquaint his parents, but judging they would be gone before he returned, and he be charged with a falsehood, he resolved to go up to them, for he had been informed that the fairies were very harmless, and would only injure those who attempted to discover their habitation, so by degrees he arrived within a short distance of the ring, where he remained some time observing their motions. They were of both sexes, and he described them as being the most handsome people he had ever seen, they also appeared enchantingly cheerful, as if inviting him to enter and join the dance. They did not all dance, but those who did, never deviated from the circle; some ran after one another with surprising swiftness, and others (females), rode on small white horses of the most beautiful form. Their dresses, although indescribably elegant, and surpassing the sun in radiance, varied in colour, some being white, others scarlet, and the males wore a red triplet cap, but the females some light head-dress, which waved fantastically with the slightest breeze. He had not remained long ere they made signs for him to enter, and he gradually drew nearer till at length he ventured to place one foot in the circle, which he had no sooner done than his ears were charmed
with the most melodious music, which moved him in the transport of the moment, to enter altogether; he was no sooner in than he found himself in a most elegant palace, glittering with gold and pearls; here he enjoyed every variety of pleasure, and had the liberty to range whatever he pleased, accompanied by kind attendants beautiful as the howries; and instead of “Tatws a llaeth,” buttermilk, or fresh boiled flummery, here were the choicest viands and the purest wine in abundance, brought in golden goblets inlaid with gems, sometimes by invisible agency, and at other times by the most beautiful virgins. He had only one restriction, and that was not to drink, upon any consideration (or it was told him it would be fatal to his happiness), from a certain well in the middle of the garden, which contained golden fishes and others of various colours. New objects daily attracts his attention, and new faces presented themselves to his view, surpassing, if possible those he had seen before; new pastimes were continually invented to charm him, but one day his hopes were blasted, and all his happiness fled in an instant. Possessing that innate curiosity nearly common to all, he, like our first parents transgressed, and plunged his hand into the well, when the fishes instantly disappeared, and, putting the water to his mouth, he heard a confused shriek run through the garden: in an instant after, the palace and all vanished away, and to his horror, he found himself in the very place where he first entered the ring, and the scenes around, with the same sheep grazing, were just as he had left them. He could scarcely believe himself, and hoped again, that he was in the magnificent fairy castle; he looked around, but the scene was too well known; his senses soon returned to their proper action, and his memory proved that, although he thought he had been absent so many years, he had been so only so many minutes. This tale bears a strange contrast as regards the time the boy thought he was away, to most of our fairy tales which represent those who had the pleasure of being with fairies as imagining they had been dancing only a few minutes, when they had been away for years.
FAIRY MUSIC AND DANCING. The Rev. Z. M. Davies, Vicar of Llanfihangel Genau’r Glyn, told me that he once heard an old man in the Vale of Aeron saying that when he was out late one night, he heard the Fairies singing, and that their music was so delightful that he listened to them for hours; and we find from many of the Fairy Tales that one of their chief occupation in their nightly revels was singing and dancing, and that they often succeeded in inducing men through the allurements of music to join their ranks. The beautiful old Welsh Air, “Toriad y Dydd” (Dawn of Day) is supposed to have been composed by the Fairies, and which they chanted just as the pale light in the east announced the approach of returning day. The following “Can y Tylwyth Teg,” or the Fairies’ song, was well-known once in Wales, and these mythical beings were believed to chant it whilst dancing merrily on summer nights. “O’r glaswellt glan a’r rhedyn mân, Gyfeillion dyddan, dewch. ‘E ddarfu’r nawn—mae’r lloer yn llawn, Y nos yn gyflawn gewch; O’r chwarau sydd ar dwyn y dydd, I’r Dolydd awn ar daith, Nyni sydd lon, ni chaiff gerbron, Farwolion ran o’n gwaith. “Canu, canu, drwy y nos, Dawnsio, dawnsio, ar waen y rhos, Yn ngoleuni’r lleuad dlos: Hapus ydym ni! Pawb o honom sydd yn llon, Heb un gofid dan ei fron: Canu, dawnsio, ar y ton—
Dedwydd ydym ni!” “From grasses bright, and bracken light, Come, sweet companions, come, The full moon shines, the sun declines. We’ll spend the night in fun; With playful mirth, we’ll trip the earth, To meadows green let’s go We’re full of joy, without alloy, Which mortals may not know. “Singing, singing, through the night, Dancing, dancing, with our might, Where the moon the moor doth light; Happy ever we! One and all of merry mein, Without sorrow are we seen, Singing, dancing, on the green: Gladsome ever we!” MR. EDWARD JONES, PENCWM, LLANRHYSTID, AND THE FAIRIES. Mr. Edward Jones, Pencwm, who only died about 8 years ago, was coming home from Lampeter one moonlight night, and when he came to the top of Trichrug hill, he saw the Fairies dancing in a field close to the road. When he was within a certain distance of them he felt as if his feet were almost lifted up from the ground, and his body so light that he could almost stand in the air.
My informant, Mr. D. Morgan, Carpenter, Llanrhystid, added that Mr. Jones was an intelligent and educated man, who had travelled, and was far from being superstitious. A FARM SERVANT NEAR TREGARON, WHO SPENT A YEAR AND A DAY WITH THE FAIRIES. The following story appeared in “Cymru” for May, 1893, a Welsh Magazine, edited by Owen M. Edwards, M.A. It was written in Welsh by the late eminent Folk-Lorist, Mr. D. Lledrod Davies, and I translate it:— The farm-house called “Allt Ddu,” is situated about half-way between Pont Rhyd Fendigaid and Tregaron. It is said that two servant men went out of the house one evening in search for the cattle, which had gone astray. One of the men proceeded in one direction and the other in another way, so as to be more sure of finding the animals. But after wandering about for hours, one of the two servants came home, but whether he found the cattle or not it is not stated. However, he reached home safely; but the other man, his fellow-servant, came not, and after anxiously expecting him till a late hour of night, he began to feel very uneasy concerning his safety, fearing that the lad had accidentally fallen into some of the pits of the Gors Goch. Next morning came, but the servant came not home; and in vain did they long to hear the sound of his footsteps approaching the house as before. Then inquiries were made about him, and people went to try and find him, but all in vain. Days past and even weeks without hearing anything about him, till at last his relations began to suspect that his fellow servant had murdered him during the night they were out looking for the cattle. So the
servant was summoned before a Court of Justice, and accused of having murdered his fellow-servant on a certain night; but the young man, pleaded not guilty in a most decided manner, and as no witness could be found against him, the case was dismissed; but many people were still very suspicious of him, and the loss of his fellow servant continued to be a black spot on his character. However, it was decided at last to go to the “dyn hysbys,” (a wise man, or a conjurer)—a man of great repute in former days, —to consult with him, and to set the case before him exactly as it had happened. After going and explaining everything to the conjurer concerning the lost servant, he informed them that the young man was still alive. He then told them to go to a certain place at the same time of night, one year and a day from the time the man was lost, and that they should then and there see him. One year and a day at last passed away, and at that hour the family, and especially the servant, traced their steps to the particular spot pointed out by the conjuror, and there, to their great surprise, whom should they see within the Fairy Circle, dancing as merrily as any, but the lost servant. And now, according to the directions which had been given by the conjurer, the other servant took hold of the collar of the coat of the one who was dancing, and dragged him out of the circle, saying to him —“Where hast thou been lad?” But the lad’s first words were, “Did you find the cattle?” for he thought that he had been with the Fairies only for a few minutes. Then he explained how he entered the Fairy Circle, and how he was seized by them, but found their company so delightful that he thought he had been with them only for a few minutes. THE SERVANT GIRL WHO WAS LOST IN THE FAIRY CIRCLE.
The following is another of the tales recorded in “Ystraeon y Gwyll,” by the late D. Lledrod Davies:— “There lived in an old farm house on the banks of the Teivy, a respectable family, and in order to carry on the work of the farm successfully, they kept men servants and maid servants. One afternoon, a servant-man and a servant girl went out to look for the cows, but as they were both crossing a marshy flat, the man suddenly missed the girl, and after much shouting and searching, no sound of her voice could be heard replying. He then took home the cows, and informed the family of the mysterious disappearance of the servant maid which took place so suddenly. As the Fairies were suspected, it was resolved to go to the dyn hysbys (wise man). To him they went, and he informed them that the girl was with the Fairies, and that they could get her back from them, by being careful to go to a certain spot at the proper time at the end of a year and a day. They did as they were directed by the “wise man,” and to their great surprise, found the maid among the fairies dancing and singing with them, and seemed as happy as a fish in the water. Then they successfully drew her out of the ring, and they took her home safely. The master had been told by the “Wise Man” that the girl was not to be touched by iron, or she would disappear at once after getting her out of the ring. One day, however, when her master was about to start from home, and whilst he was getting the horse and cart ready, he asked the girl to assist him, which she did willingly; but as he was bridling the horse, the bit touched the girl and she disappeared instantly, and was never seen from that day forth. THE LITTLE SERVANT BOY AND THE BARM.
The following story was related to me by Mrs. Davies, Bryneithyn, in the neighbourhood of Ystrad Meurig, where the tale is well-known:— An old woman known as Nancy of Pen Gwndwn, kept a little boy servant, whom she sent one evening to the neighbouring village with a bottle to get some barm for her, and as he had to pass through a field which was frequented by the Fairies, he was told by the old woman to keep away from their circles or rings. The boy reached the village, got the barm, and in due time proceeded on his homeward journey, but did not reach home. Search was made for him in all directions, and people were able to trace his steps as far as the Fairies’ field, but no further, so it was evident that the Fairies had seized him. At the end of a year and a day, however, to the great surprise of everybody, the boy came home, entered the house, with the bottle of barm in hand, and handed it to the old woman as if nothing unusual had happened. The boy was greatly surprised when he was told that he had been away for twelve months and a day. Then he related how he fell in with the Fairies, whom he found such nice little men, and whose society was so agreeable that he lingered among them, as he thought, for a few minutes. A CARMARTHENSHIRE MAIDEN WHO GOT INTO A FAIRY RING. In the parish of Cynwil Elvet, there is a farmhouse called Fos Anna, a place which was known to the writer of this book once when a boy:— A servant girl at this farm once went rather late in the evening to look for the cows, and, unfortunately, got into the Fairy ring, and although she had been a long period without food she did not feel hungry.
IAGO AP DEWI AMONG THE FAIRIES SEVEN YEARS. A Carmarthenshire tradition names among those who lived for a period among the Fairies no less a person than the translator into Welsh of Bunyan’s “Pilgrim’s Progress.” “He was called Iago ap Dewi, and lived in the parish of Llanllawddog, in a cottage situated in the wood of Llangwyly. He was absent from the neighbourhood for a long period, and the universal belief among the peasantry was that Iago got out of bed one night to gaze on the starry sky, as he was accustomed (astrology being one of his favourite studies), and whilst thus occupied the Fairies, passing by, carried him away, and he dwelt with them seven years. Upon his return, he was questioned by many as to where he had been, but always avoiding giving them a reply.” A district famous for Fairies long ago was the parish of Llanedi in Carmarthenshire, and Mr. Williams, says in his “Llen Gwerin Sir Gaerfyrddin,” that an intelligent old man in that parish, named John Rees, gave him the following story of A MAN WHO WAS FOUND AMONG THE FAIRIES AT CAE CEFN PANTYDWR. This story which is similar to some of the tales I have already given as located in other parts is as follows:—
A certain man of Llanedi, on one occasion long ago, went away to another neighbourhood, leading by the “penwast” (collar) a very wild and unmanageable horse; and in order to be sure not to lose his hold of the animal, the man tied the end of the collar round the middle. So both man and horse went together and got lost. After much searching the horse was found without the collar, but nothing was heard of the man. After giving up searching for him as hopeless, they at last consulted a “Dyn Hysbys,” (a conjuror or a wise man). The wise man directed them to go on a certain night into a field known as Cae Cefn Pantydwr, about forty yards from the road where the Fairies could be seen dancing, and the lost man among them, with the “penwast” still around his waist, which would enable them to know him; and the way to get him out of the Fairy Ring was to watch him coming round in the dance, and take hold of the collar when an opportunity offered itself, and drag the man out boldly. They did so, and the man was rescued. Ever since then people dreaded going to that field after dark, especially children. In some parts of Carmarthenshire, Fairy Rings are known as “Rings y Gwr Drwg” (the rings of the Old Gentleman), suggesting that the Fairies had some connection with the evil one. SON OF LLECH Y DERWYDD AND THE FAIRIES. The writer of the following tale was the late Rev. Benjamin Williams (Gwynionydd), an eminent antiquarian, Folk-Lorist, and a bard, and it is to be found in Welsh in Y Brython, vol. III., page 460. It is evident that the scene of the story was West or Mid-Wales. Mr. Williams heard the tale from old people who believed in the truth of it:— “Yr oedd mab Llech y Derwydd yn unig blentyn ei rieni, ac hefyd yn etifedd y tyddyn. Yr oedd felly yn anwyl, ie, yn ddau lygad ei dad a’i fam.
“Yr oedd y pen gwas a mab y ty yn gyfeillion mynwesol iawn, fel dau frawd, ie, fel gyfeilliaid. Gan fod y mab a’r gwas y fath gyfeillion, byddai gwraig y ty bob amser yn darpar dillad i’r gwas yr un peth yn hollol ag i’r mab. Cwympodd y ddau gyfaill mewn serch a dwy ddynes ieuainc, brydferth, ac uchel eu parch yn yr ardal, a mawr oedd y boddineb yn Llech y Derwydd; ac yn fuan ymunodd y ddau bar mewn glan briodas, a mawr fu y rhialtwch ar yr amser. Cafodd y gwas le cyfleus i fyw ar dir Llech y Derwydd. Yn mhen tua haner blwyddyn ar ol priodi o’r mab, aeth ei gyfaill ac yntau allan i hela; enciliodd y deiliad i ryw gilfach lawn o anialwch, i edrych am helwriaeth; a dychwelodd yn y man at ei gyfaill, ond erbyn dyfod yno, nid oedd modd gweled y mab yn un man. Parhaodd i edrych o gwmpas am dro gan waeddi a chwibanu, ond dim un arwydd am ei gyfaill. Yn mhen tro aeth adref i Llech y Derwydd, gan ddysgwyl ei weled yno; ond ni wyddai neb ddim am dano. Mawr oedd y gofid yn y teulu drwy y nos; ac erbyn dranoeth yr oedd eu pryder yn llawer mwy. Aethpwyd i weled y fan lle y gwelodd ei gyfaill ef olaf. Wylai ei fam a’i wraig am y gwaethaf. Yr oedd y tad dipyn yn well na’i wraig a’i fam, ond edrychai yntau fel yn haner gwallgof. Edrychwyd ar y fan olaf y gwelodd y deiliad ef, ac er eu mawr syndod a’u gofid, canfyddasent gylch y Tylwyth Teg gerllaw y fan, a chofiodd y deiliad yn y man iddo glywed swn peroriaeth hudoliaethus iawn rywle ar y pryd. Penderfynwyd ar unwaith iddo fod mor anffodus a myned i gylch y Tylwyth, a chael ei gludo ymaith na wyddid i ba le. “Aeth wythnosau a misoedd gofidus heibio, a ganwyd mab i fab Llech y Derwydd; ond nid oedd y tad ieuanc yno i gael gweled ei blentyn, ac yr oedd hyny yn ofidus iawn gan yr hen bobl. Beth bynag, daeth y dyn bach i fyny yr un ddelw a’i dad, fel pe buasai wedi ei arlunio; a mawr ydoedd yng ngolwg ei daid a’i nain. Efe oedd pobpeth yno. Tyfodd i oedran gwr, a phriododd a merch landeg yn y gymydogaeth; ond nid oedd gair da i’r tylwyth eu bod yn bobl hawddgar. “Bu farw yr hen bobl, a bu farw y ferch-yng-nghyfraith hefyd. Ar ryw brydnawn gwyntog, ym mis Hydref, gwelai teulu Llech y Derwydd henafgwr tal, teneu, a’i farf a’i wallt fel yr eira, yr hwn a dybient ydoedd Iddew, yn dynesu yn araf araf at y ty. Hylldremiai y morwynion drwy y ffenestr, a chwarddai y feistress am ben yr ‘hen Iddew,’ gan godi y plant un
ar ol y llall i’w weled yn dyfod. Daeth at y drws, a daeth i mewn hefyd yn lled eofn, gan ofyn am ei rieni. Atebai y wraig ef yn daeog, a choeglyd anghyffredin, gan ddywedyd, ‘Beth oedd yr hen Iddew meddw yn dyfod yno,’ oblegid tybient ei fod wedi yfed, onid e ni fuasai yn siarad felly. Edrychai yr hen wr yn syn a phryderus iawn ar bob peth yn y ty, gan synu llawer; ond ar y plant bychain ar hyd y llawr y sylwai fwyaf. Edrychai yn llawn siomedigaeth a gofid. Dywedodd yr hanes i gyd, iddo fod allan yn hela ddoe, a’i fod yn awr yn dychwelyd. Dywedodd y wraig iddi glywed chwedl am dad ei gwr flynyddau cyn ei geni, ei fod wedi myned ar goll wrth hela; ond fod ei thad yn dywedyd wrthi nad gwir hyny, mai ei ladd a gafodd. Aeth y wraig yn anystywallt, ac yn llwyr o’i chof eisiau fod yr hen ‘Iddew’ yn myned allan. Cyffrodd yr hen wr, a dywedai mai efe ydoedd perchen y ty, ac y byddai raid iddo gael ei hawl. Aeth allan i weled ei feddianau, ac yn fuan i dy y deiliad. Er ei syndod, yr oedd pethau wedi newid yn fawr yno. Ar ol ymddiddan am dro a hen wr oedranus wrth y tan, edrychai y naill fwy fwy ar y llall. Dywedai yr hen wr beth fu tynged ei ben gyfaill, mab Llech y Derwydd. Siaradent yn bwyllog am bethau mebyd, ond yr oedd y cyfan fel breuddwyd. Beth bynag, penderfynodd yr hen wr yn y cornel mai ei hen gyfaill, mab Llech y Derwydd, oedd yr ymwelydd, wedi dychwelyd o wlad y Tylwyth Teg, ar ol bod yno haner can’ mlynedd. Credodd yr hen wr a’r farf wen ei dynged, a mawr y siarad a’r holi fu gan y naill y llall am oriau lawer. “Dywedai fod gwr Llech y Derwydd y diwrnod hwnw oddi cartref. Cafwyd gan yr hen ymwelydd fwyta bwyd; ond er mawr fraw, syrthiodd y bwytawr yn farw yn y fan. Nid oes hanes fod trengholiad wedi bod ar y corff; ond dywedai y chwedl mae yr achos oedd, iddo fwyta bwyd ar ol bod yn myd y Tylwyth Teg cyhyd. Mynodd ei hen gyfaill weled ei gladdu yn ochr ei deidiau. Bu melldith fyth, hyd y silcyn ach, yn Llech y Derwydd, o blegid sarugrwydd y wraig i’w thad-yng-nghyfraith, nes gwerthu y lle naw gwaith.” The above tale translated into English reads as follows:— “The son of Llech y Derwydd was the only child of his parents, and also the heir to the farm. He was, therefore, very dear to his father and mother, yea,
he was as the very light of their eyes. The son and the head servant man were more than bosom friends, they were like two brothers, or rather twins. As the son and the servant were such close friends, the farmer’s wife was in the habit of clothing them exactly alike. The two friends fell in love with two young handsome women who were highly respected in the neighbourhood. This event gave the old people great satisfaction, and ere long the two couples were joined in holy wedlock, and great was the merry- making on the occasion. The servant man obtained a convenient place to live in on the grounds of Llech y Derwydd. “About six months after the marriage of the son, he and the servant man went out to hunt. The servant penetrated to a ravine filled with brushwood to look for game, and presently returned to his friend, but by the time he came back the son was nowhere to be seen. He continued awhile looking about for his absent friend, shouting and whistling to attract his attention, but there was no answer to his calls. By and by he went home to Llech y Derwydd, expecting to find him there, but no one knew anything about him. Great was the grief of the family throughout the night, but it was even greater next day. They went to inspect the place where the son had last been seen. His mother and his wife wept bitterly, but the father had greater control over himself, still he appeared as half mad. They inspected the place where the servant man had last seen his friend, and, to their great surprise and sorrow, observed a Fairy ring close by the spot, and the servant recollected that he had heard seductive music somewhere about the time that he parted with his friend. “They came to the conclusion at once that the man had been so unfortunate as to enter the Fairy ring, and they conjectured that he had been transported no one knew where. Weary weeks and months passed away, and a son was born to the absent man. “The little one grew up the very image of his father, and very precious was he to his grandfather and grandmother. In fact, he was everything to them. He grew up to man’s estate and married a pretty girl in the neighbourhood, but her people had not the reputation of being kind-hearted. The old folks died, and also their daughter-in-law.
“One windy afternoon in the month of October, the family of Llech y Derwydd saw a tall thin old man with beard and hair as white as snow, who they thought was a Jew approaching slowly, very slowly, towards the house. The servant girls stared mockingly through the window at him, and their mistress laughed unfeelingly at the ‘old Jew,’ and lifted the children up, one after the other, to get a sight of him as he neared the house. “He came to the door, and entered the house boldly enough, and inquired after his parents. The mistress answered him in a surly and unusually contemptuous manner and wished to know ‘What the drunken old Jew wanted there,’ for they thought he must have been drinking or he would never have spoken in the way he did. The old man looked at everything in the house with surprise and bewilderment, but the little children about the floor took his attention more than anything else. His looks betrayed sorrow and deep disappointment. He related his whole history, that yesterday he had gone out to hunt, and that now he had returned. The mistress told him that she had heard a story about her husband’s father, which occurred before she was born, that he had been lost whilst hunting, but that her father had told her that the story was not true, but that he had been killed. The woman became uneasy and angry that the old ‘Jew’ did not depart. The old man was roused, and said that the house was his, and that he would have his rights. He went to inspect his possessions, and shortly afterwards directed his steps to the servant’s house. To his surprise he saw that things were greatly changed. After conversing awhile with an aged man who sat by the fire, they carefully looked each other in the face, and the old man by the fire related the sad history of his lost friend, the son of Llech y Derwydd. “They conversed together deliberately on the events of their youth, but all seemed like a dream. However, the old man in the corner came to the conclusion that his visitor was his old friend, the son of Llech y Derwydd, returned from the land of the Fairies, after spending there fifty years. “The old man with the white beard believed the story related by his friend, and long was the talk and many were the questions which the one gave to the other. The visitor was informed that the master of Llech y Derwydd was from home that day, and he was persuaded to eat some food; but to the
horror of all, when he had done so, he instantly fell down dead. We are not informed that an inquest was held over the body; but the tale relates that the cause of the man’s sudden death was that he ate food after having been so long in the land of the Fairies. His old friend insisted on the dead man being buried with his ancestors. The rudeness of the mistress of Llech y Derwydd to her father-in-law brought a curse upon the place and family, ‘hyd y silcyn ach,’ and her offence was not expiated until the farm had been sold nine times.” TAFFY AP SION OF PENCADER AMONG THE FAIRIES. The following Fairy Legend appeared in “British Goblins,” page 75:— Taffy ap Sion, the shoemaker’s son, living near Pencader, Carmarthenshire, was a lad who many years ago entered the Fairy circle on the mountain hard by there, and having danced a few minutes as he supposed, chanced to step out. He was then astonished to find that the scene which had been so familiar was now quite strange to him. Here were roads and houses he had never seen, and in place of his father’s humble cottage there now stood a fine stone farmhouse. About him were lovely cultivated fields instead of the barren mountain he was accustomed to. ‘Ah,’ thought he, ‘this is some Fairy trick to deceive my eyes. It is not ten minutes since I stepped into that circle, and now when I step out they have built my father a new house! Well, I only hope it is real; anyhow, I’ll go and see.’ So he started off by a path he knew instinctively, and suddenly struck against a very solid hedge. He rubbed his eyes, felt the hedge with his fingers, scratched his head, felt the hedge again, ran a thorn into his fingers and cried out, ‘Wbwb’ this is no Fairy hedge anyhow, nor, from the age of the thorns, was it grown in a few minutes’ time! So he climbed over it and walked on. ‘Here was I born,’ said he, as he entered the farmyard, staring
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  • 5. Composite Materials Design and Applications 3rd Edition Gay Digital Instant Download Author(s): Gay, Daniel ISBN(s): 9781466584877, 1466584874 Edition: 3 File Details: PDF, 19.84 MB Year: 2014 Language: english
  • 6. K19063 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 2 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK an informa business www.taylorandfrancisgroup.com COMPOSITE MATERIALS COMPOSITE MATERIALS COMPOSITE MATERIALS T H I R D E D I T I O N THIRD EDITION T H I R D E D I T I O N Design and Applications Design and Applications Design and Applications Daniel Gay Gay K19063 6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 2 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK an informa business www.taylorandfrancisgroup.com Composite materials Composite materials Composite materials T h i r d E d i T i o n Third EdiTion T h i r d E d i T i o n design and Applications design and Applications design and Applications daniel Gay Gay “This book covers the topics related to the mechanics of composite ma- terials in a very simple way. ... it is addressed to graduate and under- graduate students as well as to practical engineers who want to en- hance their knowledge and learn the guidelines of the use of composite materials. ... This book is...a good classroom material...[and] a good reference.” —Dr. Pierre Rahme, University of Notre Dame, Indiana, USA Considered to have contributed greatly to the pre-sizing of composite structures, Composite Materials: Design and Applications is a popular reference book for designers of heavily loaded composite parts. Fully updated to mirror the exponential growth and development of compos- ites, this English-language Third Edition: • Contains all-new coverage of nanocomposites and biocomposites • reflects the latest manufacturing processes and applications in the aerospace, automotive, naval, wind turbine, and sporting goods industries • Provides a design method to define composite multilayered plates under loading, along with all numerical information needed for implementation • Proposes original study of composite beams of any section shapes and thick-laminated composite plates, leading to technical formula- tions that are not found in the literature • Features numerous examples of the pre-sizing of composite parts, processed from industrial cases and reworked to highlight key in- formation • includes test cases for the validation of computer software using finite elements Consisting of three main parts, plus a fourth on applications, Composite Materials: Design and Applications, Third Edition features a technical level that rises in difficulty as the text progresses, yet each part still can be explored independently. While the heart of the book, devoted to the methodical pre-design of structural parts, retains its original character, the contents have been significantly rewritten, restructured, and expand- ed to better illustrate the types of challenges encountered in modern engineering practice. Materials Science/Mechanical Engineering “This book covers the topics related to the mechanics of composite ma- terials in a very simple way. ... It is addressed to graduate and un- dergraduate students as well as to practical engineers who want to enhance their knowledge and learn the guidelines of the use of compos- ite materials. ... This book is...good classroom material...[and] a good reference.” —Dr. Pierre Rahme, University of Notre Dame, Indiana, USA Considered to have contributed greatly to the pre-sizing of composite structures, Composite Materials: Design and Applications is a popular reference book for designers of heavily loaded composite parts. Fully updated to mirror the exponential growth and development of compos- ites, this English-language Third Edition: • Contains all-new coverage of nanocomposites and biocomposites • Reflects the latest manufacturing processes and applications in the aerospace, automotive, naval, wind turbine, and sporting goods industries • Provides a design method to define composite multilayered plates under loading, along with all numerical information needed for implementation • Proposes original study of composite beams of any section shapes and thick-laminated composite plates, leading to technical formula- tions that are not found in the literature • Features numerous examples of the pre-sizing of composite parts, processed from industrial cases and reworked to highlight key in- formation • Includes test cases for the validation of computer software using finite elements Consisting of three main parts, plus a fourth on applications, Composite Materials: Design and Applications, Third Edition features a technical level that rises in difficulty as the text progresses, yet each part still can be explored independently. While the heart of the book, devoted to the methodical pre-design of structural parts, retains its original character, the contents have been significantly rewritten, restructured, and expand- ed to better illustrate the types of challenges encountered in modern engineering practice. Materials Science/Mechanical Engineering ISBN: 978-1-4665-8487-7 9 781466 584877 90000
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  • 9. Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business Composite materials T h i r d E d i T i o n design and Applications daniel Gay
  • 10. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20140611 International Standard Book Number-13: 978-1-4665-8488-4 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
  • 11. v Contents Preface.................................................................................................................................xix Acknowledgments...............................................................................................................xxi Author.............................................................................................................................. xxiii Section I  PRINCIPLES OF CONSTRUCTION 1 Composite Materials: Interest and Physical Properties. ................................................3 1.1 What Is a Composite Material?................................................................................ 3 1.1.1 Broad Definition......................................................................................... 3 1.1.2 Main Features. ............................................................................................. 4 1.2 Fibers and Matrices.................................................................................................. 4 1.2.1 Fibers........................................................................................................... 4 1.2.1.1 Definition.................................................................................... 4 1.2.1.2 Principal Fiber Materials............................................................. 5 1.2.1.3 Relative Importance of Different Fibers in Applications.............. 6 1.2.2 Materials for Matrices. ................................................................................. 7 1.3 What Can Be Made Using Composite Materials?.................................................... 7 1.4 A Typical Example of Interest. .................................................................................. 9 1.5 Some Examples of Classical Design Replaced by Composite Solutions. ...................10 1.6 Main Physical Properties.........................................................................................10 2 Manufacturing Processes............................................................................................17 2.1 Molding Processes...................................................................................................17 2.1.1 Contact Molding........................................................................................17 2.1.2 Compression Molding................................................................................18 2.1.3 Vacuum Molding. .......................................................................................18 2.1.4 Resin Injection Molding.............................................................................19 2.1.5 Injection Molding with Prepreg................................................................. 20 2.1.6 Foam Injection Molding. ........................................................................... 20 2.1.7 Molding of Hollow Axisymmetric Components........................................ 20 2.2 Other Forming Processes. ....................................................................................... 22 2.2.1 Sheet Forming........................................................................................... 22 2.2.2 Profile Forming......................................................................................... 23 2.2.3 Forming by Stamping................................................................................ 23
  • 12. vi ◾ Contents 2.2.4 Preforming by Three-Dimensional Assembly............................................. 24 2.2.4.1 Example: Carbon/Carbon......................................................... 24 2.2.4.2 Example: Silicon/Silicon............................................................ 24 2.2.5 Automated Tape Laying and Fiber Placement. ........................................... 24 2.2.5.1 Necessity of Automation. ........................................................... 24 2.2.5.2 Example. .................................................................................... 24 2.2.5.3 Example. .....................................................................................25 2.2.5.4 Example: Robots and Software for AFP—Automatic Fiber Placement Coriolis Composites (FRA)..............................25 2.3 Practical Considerations on Manufacturing Processes............................................ 26 2.3.1 Acronyms.................................................................................................. 26 2.3.2 Cost Comparison...................................................................................... 27 3 Ply Properties..............................................................................................................29 3.1 Isotropy and Anisotropy......................................................................................... 29 3.1.1 Isotropic Materials......................................................................................31 3.1.2 Anisotropic Material.................................................................................. 32 3.2 Characteristics of the Reinforcement–Matrix Mixture............................................33 3.2.1 Fiber Mass Fraction................................................................................... 34 3.2.2 Fiber Volume Fraction............................................................................... 34 3.2.3 Mass Density of a Ply.................................................................................35 3.2.4 Ply Thickness..............................................................................................35 3.3 Unidirectional Ply.................................................................................................. 36 3.3.1 Elastic Modulus......................................................................................... 36 3.3.2 Ultimate Strength of a Ply......................................................................... 38 3.3.3 Examples................................................................................................... 39 3.3.4 Examples of High-Performance Unidirectional Plies..................................41 3.4 Woven Ply...............................................................................................................41 3.4.1 Forms of Woven Fabrics.............................................................................41 3.4.2 Elastic Modulus of Fabric Layer................................................................ 42 3.4.3 Examples of Balanced Fabric/Epoxy.......................................................... 43 3.5 Mats and Reinforced Matrices. ................................................................................45 3.5.1 Mats...........................................................................................................45 3.5.2 Example: A Summary of Glass/Epoxy Layers.............................................45 3.5.3 Microspherical Fillers.................................................................................45 3.5.4 Other Classical Reinforcements. ................................................................ 48 3.6 Multidimensional Fabrics....................................................................................... 49 3.6.1 Example: A Four-Dimensional Architecture of Carbon Reinforcement..... 49 3.6.2 Example: Three-Dimensional Carbon/Carbon Components..................... 50 3.7 Metal Matrix Composites....................................................................................... 50 3.7.1 Some Examples. ......................................................................................... 50 3.7.2 Unidirectional Fibers/Aluminum Matrix. ...................................................52 3.8 Biocomposite Materials...........................................................................................53 3.8.1 Natural Plant Fibers...................................................................................53 3.8.1.1 Natural Fibers. ............................................................................53 3.8.1.2 Pros............................................................................................53
  • 13. Contents ◾ vii 3.8.1.3 Cons...........................................................................................53 3.8.1.4 Examples................................................................................... 54 3.8.2 Natural Vegetable Fiber–Reinforced Composites...................................... 54 3.8.2.1 Mechanical Properties............................................................... 54 3.8.2.2 Biodegradable Matrices............................................................. 54 3.8.3 Manufacturing Processes........................................................................... 56 3.8.3.1 With Thermosetting Resins....................................................... 56 3.8.3.2 With Thermoplastic Resins.........................................................57 3.9 Nanocomposite Materials........................................................................................57 3.9.1 Nanoreinforcement. ....................................................................................57 3.9.1.1 Nanoreinforcement Shapes.........................................................57 3.9.1.2 Properties of Nanoreinforcements. ............................................. 58 3.9.2 Nanocomposite Material............................................................................61 3.9.3 Mechanical Applications........................................................................... 62 3.9.3.1 Improvement in Mechanical Properties..................................... 62 3.9.3.2 Further Examples of Nonmechanical Applications.................... 64 3.9.4 Manufacturing of Nanocomposite Materials............................................. 64 3.10 Tests....................................................................................................................... 66 4 Sandwich Structures. ...................................................................................................69 4.1 What Is a Sandwich Structure?. .............................................................................. 69 4.1.1 Their Properties Are Surprising. ................................................................. 69 4.1.2 Constituent Materials................................................................................ 70 4.2 Simplified Flexure. .................................................................................................. 71 4.2.1 Stress......................................................................................................... 71 4.2.2 Displacements........................................................................................... 72 4.2.2.1 Contributions of bending moment M and of shear force T .... 72 4.2.2.2 Example: A Cantilever Sandwich Structure............................... 73 4.3 Some Special Features of Sandwich Structures........................................................74 4.3.1 Comparison of Mass for the Same Flexural Rigidity 〈EI〉..........................74 4.3.2 Deterioration by Buckling of Sandwich Structures.....................................74 4.3.2.1 Global Buckling........................................................................ 75 4.3.2.2 Local Buckling of the Skins....................................................... 75 4.3.3 Other Types of Damage.............................................................................76 4.4 Manufacturing and Design Problems......................................................................76 4.4.1 Example of Core Material: Honeycomb.....................................................76 4.4.2 Shaping Processes...................................................................................... 77 4.4.2.1 Machining................................................................................. 77 4.4.2.2 Deformation.............................................................................. 77 4.4.2.3 Some Other Considerations. ...................................................... 77 4.4.3 Inserts and Attachment Fittings................................................................ 78 4.4.4 Repair of Laminated Facings..................................................................... 79 4.5 Nondestructive Inspection. ..................................................................................... 80 4.5.1 Main Nondestructive Inspection Methods................................................ 80 4.5.2 Acoustic Emission Testing..........................................................................81
  • 14. viii ◾ Contents 5 Conception: Design and Drawing...............................................................................85 5.1 Drawing a Composite Part......................................................................................85 5.1.1 Specific Properties......................................................................................85 5.1.2 Guide Values of Presizing.......................................................................... 86 5.1.2.1 Material Characteristics............................................................. 86 5.1.2.2 Design Factors........................................................................... 88 5.2 Laminate................................................................................................................ 88 5.2.1 Unidirectional Layers and Fabrics............................................................. 88 5.2.1.1 Unidirectional Layer. ................................................................. 88 5.2.1.2 Fabrics....................................................................................... 89 5.2.2 Correct Ply Orientation............................................................................. 89 5.2.3 Laminate Drawing Code........................................................................... 90 5.2.3.1 Standard Orientations............................................................... 90 5.2.3.2 Laminate Middle Plane............................................................. 90 5.2.3.3 Description of the Stacking Order............................................. 93 5.2.3.4 Midplane Symmetry.................................................................. 93 5.2.3.5 Specific Case of Balanced Fabrics.............................................. 94 5.2.3.6 Technical Minimum. ................................................................. 95 5.2.4 Arrangement of Plies................................................................................. 96 5.2.4.1 Proportion and Number of Plies................................................ 96 5.2.4.2 Example of Pictorial Representation.......................................... 97 5.2.4.3 Case of Sandwich Structure....................................................... 97 5.3 Failure of Laminates............................................................................................... 98 5.3.1 Damages. ................................................................................................... 98 5.3.1.1 Types of Failure......................................................................... 98 5.3.1.2 Note: Classical Maximum Stress Criterion Shows Its Limits...........................................................................99 5.3.2 Most Frequently Used Criterion: Tsai–Hill Failure Criterion.................. 100 5.3.2.1 Tsai–Hill Number.................................................................... 100 5.3.2.2 Notes........................................................................................101 5.3.2.3 How to Determine the Stress Components σℓ, σt, and τℓt in Each Ply...............................................................................101 5.4 Presizing of the Laminate......................................................................................102 5.4.1 Modulus of Elasticity—Deformation of a Laminate. ................................102 5.4.1.1 Varying Proportions of Plies.....................................................102 5.4.1.2 Example of Using Tables..........................................................103 5.4.2 Case of Simple Loading............................................................................103 5.4.3 Complex Loading Case: Approximative Proportions According to Orientations.........................................................................................109 5.4.3.1 When the Normal and Tangential (Shear) Loads Are Applied Simultaneously............................................................109 5.4.3.2 Example. ...................................................................................114 5.4.3.3 Note.........................................................................................117 5.4.4 Complex Loading Case: Optimum Composition of a Laminate. ..............119 5.4.4.1 Optimum Laminate.................................................................119 5.4.4.2 Example. .................................................................................. 122
  • 15. Contents ◾ ix 5.4.4.3 Example. ...................................................................................125 5.4.4.4 Notes....................................................................................... 126 5.4.5 Notes for Practical Use Concerning Laminates....................................... 127 5.4.5.1 Specific Aspects for the Design of Laminates. .......................... 127 5.4.5.2 Delaminations......................................................................... 128 5.4.5.3 Why Is Fatigue Resistance So Good?. .......................................129 5.4.5.4 Laminated Tubes......................................................................133 6 Conception: Fastening and Joining...........................................................................135 6.1 Riveting and Bolting.............................................................................................135 6.1.1 Local Loss of Strength..............................................................................135 6.1.1.1 Knock-Down Factor.................................................................135 6.1.1.2 Causes of Hole Degradation.................................................... 136 6.1.2 Main Failure Modes in Bolted Joints of Composite Materials..................138 6.1.3 Sizing of the Joint.....................................................................................138 6.1.3.1 Recommended Values. ..............................................................138 6.1.3.2 Evaluation of Magnified Stress Values......................................140 6.1.4 Riveting....................................................................................................140 6.1.5 Bolting. .....................................................................................................141 6.1.5.1 Example of Bolted Joint............................................................141 6.1.5.2 Tightening of the bolt..............................................................143 6.2 Bonding. ................................................................................................................143 6.2.1 Adhesives Used.........................................................................................143 6.2.2 Geometry of the Bonded Joints................................................................145 6.2.3 Sizing of the Bonding Surface Area..........................................................146 6.2.3.1 Strength of adhesive. ................................................................146 6.2.3.2 Design......................................................................................147 6.2.3.3 Stress in Bonded Areas.............................................................148 6.2.3.4 Example of single-lap adhesive joint......................................150 6.2.4 Case of Bonded Joint with Cylindrical Geometry. ....................................150 6.2.4.1 Bonded Circular Flange. ...........................................................150 6.2.4.2 Tubes Fitted and Bonded into One Another.............................150 6.2.5 Examples of Bonding. ...............................................................................150 6.2.5.1 Laminates.................................................................................150 6.3 Inserts. ...................................................................................................................152 6.3.1 Case of Sandwich Parts. ............................................................................152 6.3.2 Case of Parts under Uniaxial Loads..........................................................154 7 Composite Materials and Aerospace Construction...................................................155 7.1 Aircraft..................................................................................................................155 7.1.1 Composite Components in Aircraft. .........................................................155 7.1.2 Allocation of Composites Depending on Their Nature.............................156 7.1.2.1 Glass/Epoxy, Kevlar/Epoxy......................................................156 7.1.2.2 Carbon/Epoxy..........................................................................157 7.1.2.3 Boron/Epoxy............................................................................157 7.1.2.4 Honeycombs. ............................................................................157 7.1.3 Few Comments........................................................................................158
  • 16. x ◾ Contents 7.1.4 Specific Aspects of Structural Strength.....................................................158 7.1.5 Large Transport Aircraft. ..........................................................................159 7.1.5.1 Example. ...................................................................................159 7.1.5.2 How to Determine the Benefits................................................159 7.1.5.3 Example: Civil Transport Aircraft A380-800, Airbus (EUR) ...................................................................... 161 7.1.5.4 Example: Civil Transport Aircraft B 787-800, Boeing (USA). ....................................................................161 7.1.5.5 Example: Civil Transport Aircraft A350-900, Airbus (EUR)................................................................... 163 7.1.6 Regional Aircraft and Business Jets..........................................................165 7.1.6.1 Example: Regional Aircraft ATR 72-600, EADS (EUR), Alenia (ITA) ............................................................................165 7.1.6.2 Example: Business Aircraft Falcon, Dassault Aviation (FRA). ......165 7.1.6.3 Example: Cargo Aircraft WK2 and Suborbital Space Plane SST2, Scaled Composites (USA)–Virgin Group (UK).............166 7.1.7 Light Aircraft...........................................................................................168 7.1.7.1 Trends......................................................................................168 7.1.7.2 Aircraft with Tractor Propeller.................................................168 7.1.7.3 Aircraft with Pusher Propeller..................................................169 7.1.7.4 Modern Glider Planes. ..............................................................170 7.1.8 Fighter Aircraft.........................................................................................170 7.1.9 Architecture and Manufacture of Composite Aircraft Parts.....................171 7.1.9.1 Sandwich Design......................................................................171 7.1.9.2 Rib-Stiffened Panels.................................................................173 7.1.10 Braking Systems.......................................................................................178 7.2 Helicopters............................................................................................................179 7.2.1 Situation...................................................................................................179 7.2.2 Composite Areas. ......................................................................................180 7.2.2.1 Example: Helicopter EC 145 T2, Airbus-Helicopter (EUR).....180 7.2.2.2 Example: Helicopter X4, Thales–Safran (FRA), Airbus-Helicopter (EUR)���������������������������������������������������������180 7.2.3 Blades.......................................................................................................181 7.2.3.1 Design of a Main Rotor Blade..................................................181 7.2.3.2 Advantages...............................................................................181 7.2.3.3 Consequences...........................................................................181 7.2.4 Rotor Hub................................................................................................183 7.2.4.1 Example: Rotor Hub Starflex, Eurocopter (FRA–GER)...........183 7.2.4.2 Example: Rotor Hub Spheriflex, Eurocopter (FRA–GER).......184 7.2.5 Other Working Composite Parts..............................................................184 7.3 Airplane Propellers................................................................................................186 7.3.1 Propellers for Conventional Aerodynamics...............................................186 7.3.1.1 Example: Propeller Blade, Hamilton Sundstrand (USA)– Ratier Figeac (FRA)�����������������������������������������������������������������186 7.3.1.2 Example: Airplane with Tilt Rotors, V-22 Osprey Bell Boeing (USA) and Dowty Propellers (UK)�����������������������������187 7.3.2 High-Speed Propellers..............................................................................188
  • 17. Contents ◾ xi 7.4 Aircraft Reaction Engine.......................................................................................190 7.4.1 Employed Materials..................................................................................190 7.4.2 Refractory Composites.............................................................................191 7.4.2.1 Specific Features.......................................................................191 7.4.2.2 Fibers........................................................................................191 7.4.2.3 Matrices. ...................................................................................192 7.4.2.4 Applications. .............................................................................192 7.4.2.5 Example: Jet Engine Leap®, CFM International, General Electric (USA)–SNECMA (FRA) �����������������������������193 7.5 Space Applications.................................................................................................194 7.5.1 Satellites...................................................................................................194 7.5.2 Propellant Tanks and Pressure Vessels......................................................195 7.5.3 Nozzles.....................................................................................................196 7.5.4 Other Composite Components for Space Application..............................198 7.5.4.1 For Engines..............................................................................198 7.5.4.2 For Thermal Protection. ............................................................198 7.5.4.3 For Energy Storage.................................................................. 200 8 Composite Materials for Various Applications..........................................................203 8.1 Comparative Importance of Composites in Applications. ..................................... 203 8.1.1 Relative Importance in terms of Mass and Market Value........................ 204 8.1.2 Mass of Composites Implemented According to the Geographical Area............................................................................. 205 8.1.3 Average Prices.......................................................................................... 205 8.2 Composite Materials and Automotive Industry.................................................... 206 8.2.1 Introduction............................................................................................ 206 8.2.1.1 Example: Golf Model, Volkswagen (GER).............................. 206 8.2.1.2 Relative Weight Importance of Materials................................ 207 8.2.2 Composite Parts...................................................................................... 208 8.2.2.1 Brief Reminder........................................................................ 208 8.2.2.2 Current Functional Design. ..................................................... 208 8.2.2.3 Notable Composite Components. .............................................210 8.2.2.4 Notes........................................................................................212 8.2.2.5 Use of Natural Fibers. ...............................................................213 8.2.3 Research and Development......................................................................214 8.2.3.1 Structure..................................................................................215 8.2.3.2 Mechanical Parts......................................................................215 8.2.4 Motor Racing...........................................................................................216 8.3 Wind Turbines......................................................................................................217 8.3.1 Components.............................................................................................217 8.3.2 Manufacturing Processes..........................................................................218 8.4 Composites and Shipbuilding. ...............................................................................219 8.4.1 Competition.............................................................................................219 8.4.1.1 Example: Ocean-Going Maxi-Trimaran.................................. 220 8.4.1.2 Example: Single Scull.............................................................. 222 8.4.1.3 Example: Surfboard. ................................................................ 223 8.4.2 Vessels..................................................................................................... 223
  • 18. xii ◾ Contents 8.5 Sports and Leisure................................................................................................ 223 8.5.1 Skis.......................................................................................................... 223 8.5.1.1 Equipment of a Skier............................................................... 223 8.5.1.2 Main Components of a Ski...................................................... 224 8.5.2 Bicycles.................................................................................................... 225 8.5.2.1 Machine.................................................................................. 226 8.5.2.2 Other Specific Equipments...................................................... 226 8.5.3 Tennis Rackets........................................................................................ 226 8.6 Diverse Applications............................................................................................. 226 8.6.1 Pressure Gas Bottle.................................................................................. 226 8.6.2 Bogie Frame............................................................................................ 227 8.6.3 Tubes for Offshore Installations. .............................................................. 227 8.6.4 Biomechanical Applications. .................................................................... 228 8.6.5 Cable Car................................................................................................ 229 Section II  Mechanical Behavior of Laminated Materials    9 Anisotropic Elastic Medium......................................................................................233 9.1 Some Reminders. ...................................................................................................233 9.1.1 Continuum Mechanics.............................................................................233 9.1.2 Number of Distinct φijkℓ Terms............................................................... 234 9.2 Orthotropic Material............................................................................................ 236 9.3 Transversely Isotropic Material............................................................................. 236 10 Elastic Constants of Unidirectional Composites. ......................................................239 10.1 Longitudinal Modulus Eℓ..................................................................................... 239 10.2 Poisson Coefficient................................................................................................241 10.3 Transverse Modulus Et......................................................................................... 242 10.4 Shear Modulus Gℓt............................................................................................. 244 10.5 Thermoelastic Properties. .......................................................................................245 10.5.1 Isotropic Material: Recall.........................................................................245 10.5.2 Case of Unidirectional Composite........................................................... 246 10.5.2.1 Coefficient of Thermal Expansion along the Direction ℓ......... 246 10.5.2.2 Coefficient of Thermal Expansion along the Transverse Direction t................................................................................247 10.5.3 Thermomechanical Behavior of a Unidirectional Layer........................... 248 11 Elastic Constants of a Ply in Any Direction..............................................................249 11.1 Flexibility Coefficients...........................................................................................249 11.2 Stiffness Coefficients. .............................................................................................255 11.3 Case of Thermomechanical Loading. .....................................................................257 11.3.1 Flexibility Coefficients..............................................................................257 11.3.2 Stiffness Coefficients. ................................................................................259 12 Mechanical Behavior of Thin Laminated Plates.......................................................263 12.1 Laminate with Midplane Symmetry..................................................................... 263 12.1.1 Membrane Behavior................................................................................ 263 12.1.1.1 Loadings.................................................................................. 263 12.1.1.2 Displacement Field.................................................................. 264
  • 19. Contents ◾ xiii 12.1.2 Apparent Elastic Moduli of the Laminate. ................................................267 12.1.3 Consequence: Practical Determination of a Laminate Subject to Membrane Loading..............................................................................267 12.1.3.1 Givens of the Problem..............................................................267 12.1.3.2 Principle of Calculation........................................................... 268 12.1.3.3 Calculation Procedure............................................................. 269 12.1.4 Flexure Behavior...................................................................................... 272 12.1.4.1 Displacement Field.................................................................. 272 12.1.4.2 Loadings.................................................................................. 273 12.1.4.3 Notes........................................................................................275 12.1.5 Consequence: Practical Determination of a Laminate Subject to Flexure......278 12.1.6 Simplified Calculation for Bending......................................................... 278 12.1.6.1 Apparent Failure Strength in Bending..................................... 278 12.1.6.2 Apparent Flexure Modulus...................................................... 279 12.1.7 Thermomechanical Loading Case. ........................................................... 280 12.1.7.1 Membrane Behavior................................................................ 280 12.1.7.2 Behavior under Bending.......................................................... 283 12.2 Laminate without Midplane Symmetry................................................................ 283 12.2.1 Coupled Membrane–Flexure Behavior.................................................... 283 12.2.2 Case of Thermomechanical Loading. ....................................................... 285 Section III  Justifications, Composite Beams, and Thick Laminated Plates 13 Elastic Coefficients....................................................................................................289 13.1 Elastic Coefficients for an Orthotropic Material................................................... 289 13.1.1 Reminders............................................................................................... 289 13.1.2 Elastic Behavior Equation in Orthotropic Axes....................................... 290 13.2 Elastic Coefficients for a Transverse Isotropic Material......................................... 292 13.2.1 Elastic Behavior Equation. ....................................................................... 292 13.2.2 Rotation about an Orthotropic Transverse Axis...................................... 295 13.2.2.1 Problem................................................................................... 295 13.2.2.2 Technical Form....................................................................... 300 13.3 Case of a Ply......................................................................................................... 302 14 Damage in Composite Parts: Failure Criteria...........................................................303 14.1 Damage in Composite Parts................................................................................. 303 14.1.1 Industrial Emphasis of the Problem......................................................... 303 14.1.1.1 Causes of Damage................................................................... 303 14.1.1.2 Diversity of Composite Parts................................................... 304 14.1.2 Influence of Manufacturing Process........................................................ 304 14.1.2.1 Example: Injected Part with Short Fibers. ................................ 305 14.1.2.2 Example: Parts with Pronounced Curvatures.......................... 305 14.1.3 Typical Area and Singularities in a Same Part......................................... 305 14.1.4 Degradation Process within the Typical Area.......................................... 306 14.1.4.1 Example: Composite Short Fiber Plate.................................... 306 14.1.4.2 Example: Laminate Consisting of Unidirectional Plies............ 307
  • 20. xiv ◾ Contents 14.2 Form of a Failure Criterion....................................................................................310 14.2.1 Features of a Failure Criterion..................................................................310 14.2.1.1 Failure Criterion Is a Design Tool. ............................................310 14.2.1.2 Many Criteria...........................................................................310 14.2.2 General Form of a Failure Criterion.........................................................310 14.2.2.1 Development of a Criterion......................................................310 14.2.2.2 Case of an Orthotropic Material. ..............................................311 14.2.3 Linear Failure Criterion............................................................................312 14.2.3.1 Example: Plane State of Stress in an Orthotropic Material.......312 14.2.3.2 Example: Maximum Stress Failure Criterion............................313 14.2.3.3 Note: Maximum Eligible Strain Criterion................................313 14.2.4 Quadratic Failure Criterion......................................................................314 14.2.4.1 General Form...........................................................................314 14.2.4.2 Specific Case of Plane Stress.....................................................314 14.2.4.3 Note: Simplified Form for the Quadratic Criterion..................315 14.3 Tsai–Hill Failure Criterion....................................................................................316 14.3.1 Isotropic Material: The von Mises Criterion.............................................316 14.3.1.1 Material Is Elastic and Isotropic...............................................316 14.3.1.2 Notes........................................................................................318 14.3.2 Orthotropic Material: Tsai–Hill Criterion. .............................................. 320 14.3.2.1 Notes....................................................................................... 320 14.3.2.2 Case of a Transversely Isotropic Material..................................321 14.3.2.3 Case of Unidirectional Ply under In-Plane Loading................ 323 14.3.3 Evolution of Strength Properties of a Unidirectional Ply Depending on the Direction of Solicitation���������������������������������������������������������������324 14.3.3.1 Tensile and Compressive Strength............................................324 14.3.3.2 Shear Strength..........................................................................325 15 Bending of Composite Beams of Any Section Shape. ................................................327 15.1 Bending of Beams with Isotropic Phases and Plane of Symmetry......................... 328 15.1.1 Degrees of Freedom..................................................................................329 15.1.1.1 Equivalent Stiffnesses...............................................................329 15.1.1.2 Longitudinal Displacement......................................................329 15.1.1.3 Rotation of the Section.............................................................329 15.1.1.4 Elastic Center.......................................................................... 330 15.1.1.5 Transverse Displacement along y Direction............................. 330 15.1.1.6 Transverse Displacement along z Direction..............................331 15.1.2 Perfect Bonding between the Phases.........................................................332 15.1.2.1 Displacements..........................................................................332 15.1.2.2 Strains......................................................................................332 15.1.2.3 Stress........................................................................................333 15.1.3 Equilibrium Relationships........................................................................333 15.1.3.1 Longitudinal Equilibrium........................................................333 15.1.3.2 Transverse Equilibrium........................................................... 334 15.1.3.3 Moment Equilibrium...............................................................335
  • 21. Contents ◾ xv 15.1.4 Constitutive Equations............................................................................ 336 15.1.5 Technical Formulation.............................................................................337 15.1.5.1 Assumptions.............................................................................337 15.1.5.2 Expression of Normal Stress.....................................................337 15.1.5.3 Expression of Shear Stress.........................................................338 15.1.5.4 Shear Coefficient for the Section. ............................................. 340 15.1.6 Energy Interpretation.............................................................................. 342 15.1.6.1 Energy Due to Normal Stress σxx. ............................................ 342 15.1.6.2 Energy Due to Shear Stress τ. .................................................. 343 15.1.7 Extension to the Dynamic Case.............................................................. 344 15.2 Case of Beams of Any Cross Section (Asymmetric).............................................. 346 15.2.1 Technical Formulation............................................................................ 347 15.2.2 Notes........................................................................................................351 16 Torsion of Composite Beams of Any Section Shape..................................................353 16.1 Uniform Torsion. ...................................................................................................353 16.1.1 Torsional Degree of Freedom....................................................................354 16.1.2 Constitutive Equation..............................................................................354 16.1.3 Determination of Φ(y, z)..........................................................................355 16.1.3.1 Local Equilibrium....................................................................355 16.1.3.2 External Boundary Condition..................................................356 16.1.3.3 Internal Boundary Conditions. .................................................356 16.1.3.4 Uniqueness of Function Φ........................................................356 16.1.4 Energy Interpretation...............................................................................357 16.2 Location of the Torsion Center..............................................................................358 16.2.1 Coordinates in Principal Axes..................................................................358 16.2.2 Summary of Results.................................................................................359 16.2.3 Flexion–Torsion Coupling........................................................................361 17 Bending of Thick Composite Plates..........................................................................363 17.1 Preliminary Remarks............................................................................................ 363 17.1.1 Transverse Normal Stress σz.................................................................... 363 17.1.2 Transverse Shear Stress τxz and τyz. ........................................................... 364 17.1.3 Assumptions.............................................................................................365 17.2 Displacement Field................................................................................................367 17.3 Strains.................................................................................................................. 369 17.4 Constitutive Equations......................................................................................... 369 17.4.1 Membrane Behavior................................................................................ 369 17.4.2 Bending Behavior.....................................................................................370 17.4.3 Transverse Shear Behavior........................................................................372 17.4.3.1 Transverse Shear Resultant Qx..................................................372 17.4.3.2 Transverse Shear Resultant Qy..................................................373 17.5 Equilibrium Relationships.....................................................................................373 17.5.1 Transverse Equilibrium............................................................................373 17.5.2 Equilibrium in Bending. ...........................................................................374
  • 22. xvi ◾ Contents 17.6 Technical Formulation for Bending.......................................................................374 17.6.1 Stress Due to Bending..............................................................................375 17.6.1.1 Plane Stress Values. ...................................................................375 17.6.1.2 Transverse Shear Stress Values..................................................376 17.6.2 Characterization of Warping Increments in Bending ηx and ηy. ................376 17.6.3 Particular Cases....................................................................................... 377 17.6.3.1 Orthotropic Homogeneous Plate............................................. 377 17.6.3.2 Cylindrical Bending about x- or y-Axis. ....................................378 17.6.3.3 Multilayered Plate. ....................................................................379 17.6.3.4 Consequences.......................................................................... 380 17.6.4 Warping Functions.................................................................................. 380 17.6.4.1 Boundary Conditions.............................................................. 380 17.6.4.2 Interfacial Continuity...............................................................381 17.6.4.3 Formulation of Warping Functions..........................................381 17.6.5 Consequences.......................................................................................... 382 17.6.5.1 Expression of Transverse Shear Stress...................................... 382 17.6.5.2 Transverse Shear Coefficients. .................................................. 382 17.6.6 Energy Interpretation.............................................................................. 384 17.7 Examples...............................................................................................................385 17.7.1 Orthotropic Homogeneous Plate..............................................................385 17.7.2 Sandwich Plate........................................................................................ 387 17.7.2.1 Case of Two Orthotropic Materials......................................... 387 17.7.2.2 Warping Functions.................................................................. 388 17.7.2.3 Transverse Shear Stress............................................................ 389 17.7.2.4 Transverse Shear Coefficients. .................................................. 389 17.7.3 Conclusion.............................................................................................. 390 Section IV Applications 18 Applications Level 1..................................................................................................393 18.1 Simply Supported Sandwich Beam........................................................................393 18.2 Poisson Coefficient of a Unidirectional Layer....................................................... 396 18.3 Helicopter Blade................................................................................................... 397 18.4 Drive Shaft for Trucks.......................................................................................... 402 18.5 Flywheel in Carbon/Epoxy. .................................................................................. 408 18.6 Wing Tip Made of Carbon/Epoxy........................................................................410 18.7 Carbon Fiber Coated with Nickel. ........................................................................ 423 18.8 Tube Made of Glass/Epoxy under Pressure. .......................................................... 425 18.9 Filament-Wound Pressure Vessel: Winding Angle................................................ 428 18.10 Filament-Wound Pressure Vessel: Consideration of Openings in the Bottom Heads.......431 18.11 Determination of Fiber Volume Fraction by Pyrolysis...........................................435 18.12 Reversing Lever Made of Carbon/PEEK (Unidirectional and Short Fibers)......... 436 18.13 Glass/Resin Telegraph Pole................................................................................... 439 18.14 Unidirectional Layer of HR Carbon..................................................................... 443 18.15 Manipulator Arm for a Space Shuttle................................................................... 444
  • 23. Contents ◾ xvii 19 Applications Level 2..................................................................................................449 19.1 Sandwich Beam: Simplified Calculation of the Shear Coefficient......................... 449 19.2 Procedure for a Laminate Calculation Program.....................................................451 19.3 Kevlar/Epoxy Laminates: Stiffness in Terms of the Direction of Load..................455 19.4 Residual Thermal Stress Due to the Laminate Curing Process..............................459 19.5 Thermoelastic Behavior of a Glass/Polyester Tube................................................ 462 19.6 Creep of a Polymeric Tube Reinforced by Filament Wound under Thermal Stress...... 465 19.7 First-Ply Failure of a Laminate: Ultimate Strength................................................471 19.8 Optimum Laminate for Isotropic Plane Stress.......................................................475 19.9 Laminate Made of Identical Layers of Balanced Fabric. .........................................481 19.10 Carbon/Epoxy Wing Spar.................................................................................... 484 19.11 Elastic Constants of a Carbon/Epoxy Unidirectional Layer, Based on Tensile Test. .......491 19.12 Sailboat Hull in Glass/Polyester. ...............................................................................492 19.13 Balanced Fabric Ply: Determination of the In-Plane Shear Modulus.....................498 19.14 Quasi-Isotropic Laminate..................................................................................... 499 19.15 Pure Torsion of Orthotropic Plate........................................................................ 502 19.16 Plate Made by Resin Transfer Molding . ............................................................... 506 19.17 Thermoelastic Behavior of a Balanced Fabric Ply...................................................512 20 Applications Level 3..................................................................................................523 20.1 Cylindrical Bonding..............................................................................................523 20.2 Double-Lap Bonded Joint. .....................................................................................528 20.3 Composite Beam with Two Layers........................................................................533 20.4 Buckling of a Sandwich Beam...............................................................................537 20.5 Shear Due to Bending in a Sandwich Beam......................................................... 540 20.6 Shear Due to Bending in a Composite Box Beam................................................ 544 20.7 Torsion Center of a Composite U-Beam............................................................... 547 20.8 Shear Due to Bending in a Composite I-Beam..................................................... 549 20.9 Polymeric Column Reinforced by Filament-Wound Fiberglass..............................553 20.10 Cylindrical Bending of a Thick Orthotropic Plate under Uniform Loading......... 563 20.11 Bending of a Sandwich Plate................................................................................ 564 20.12 Bending Vibration of a Sandwich Beam................................................................567 Appendix A: Stresses in the Plies of a Carbon/Epoxy Laminate Loaded in Its Plane........571 Appendix B: Buckling of Orthotropic Structures..............................................................585 Bibliography. ......................................................................................................................595 Index���������������������������������������������������������������������������������������������������������������������������������599
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  • 25. xix Preface The developments in the field of composite materials since the last quarter of a century have made this area popular due to the breadth and universality of applications. The annual global growth rate of composites is 5%–6%, and tonnage, which was 8 million tonnes in 2010, could rise to 10 million tonnes by 2015—a growth driven by advances in the transportation and wind industries. The sector of composites is an area of business that is always evolving. The cost of composites is becoming increasingly competitive. For a quarter of a century, the price of high-performance composites used in aerospace declined by more than half to compete with sophisticated metal alloys. At the same time, the quality of semifinished products reached remarkable levels. For example, the unidirectional prepreg tapes carbon/epoxy have their widths defined within 0.2 mm, and their fiber volume content controlled within only a few fractions of a percent, with obvious consequences for the evolution of the quality of parts. The legislation on recyclability obligation also affects the composite activities. It leads to sig- nificant increases in research and development on topics concerning natural fibers and biodegrad- able polymers. The growth in the use of composites has been aided by the development of modern design and manufacturing methods for industrial components, which allow functional optimization based on multiple technical and economic criteria. A good knowledge of what already exists helps develop and use reliable numerical simulations for in-service behavior as well as for implementation during the manufacturing. The development of simulation tools is an important component of industrial development, in general, and in composite domains, in particular. Without trying to replace testing, these tools allow full exploitation of the experimental results in a much more complete manner, creating a powerful synergy that saves time and cost. This third edition has been updated to take into account this rapidly changing field as well as the emergence and development of additional areas, such as those of bio- and nanocomposites. The core of the book devoted to the methodical predesign of structural parts has been preserved. As in previous editions, we have considered only a limited number of significant reinforcements and have highlighted the specific features needed for predimensioning. This is, in fact, to limit the number of performance tables accompanying the text. Other reinforcements not detailed in this book can be readily adapted; the reader will find everything needed to use a spreadsheet in order to get the desired results. He or she may also download a dedicated free utility as indicated in the book. The chapters on composite beams of any cross-sectional shape and the chapter on laminated thick plates still retain their original character, both with regard to the proposed method and to the results.
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  • 27. I will not have thee.) But the smiles that played upon her features as the lady vanished beneath the waters raised within the young man a hope that forbade him to despair by her refusal of him, and the recollection of which cheered him on his way home. His aged parent was made acquainted with his ill-success, and she suggested that his bread should next time be but slightly baked, as most likely to please the mysterious being of whom he had become enamoured. “Impelled by an irresistible feeling, the youth left his mother’s house early next morning, and with rapid steps he passed over the mountain. He was soon near the margin of the lake, and with all the impatience of an ardent lover did he wait with a feverish anxiety for the reappearance of the mysterious lady. “The sheep and goats browsed on the precipitous sides of the Fan; the cattle strayed amongst the rocks and large stones, some of which were occasionally loosened from their beds and suddenly rolled down into the lake; rain and sunshine alike came and passed away; but all were unheeded by the youth, so wrapped up was he in looking for the appearance of the lady. “The freshness of the early morning had disappeared before the sultry rays of the noon-day sun, which in its turn was fast verging towards the west as the evening was dying away and making room for the shades of night, and hope had well nigh abated of beholding once more the Lady of the Lake. The young man cast a sad and last farewell look over the water, and to his astonishment, beheld several cows walking along its surface. The sight of these animals caused hope to revive that they would be followed by another object far more pleasing; nor was he disappointed, for the maiden reappeared, and to his enraptured sight, even lovelier than ever. She approached the land, and he rushed to meet her in the water. A smile encouraged him to seize her hand; neither did she refuse the moderately baked bread he offered her; and after some persuasion she consented to become his bride, on condition that they should only live together until she received from him three blows without a cause,
  • 28. “Tri ergyd diachos.” (Three causeless blows.) and if he ever should happen to strike her three such blows she would leave him for ever. To such conditions he readily consented and would have consented to any other stipulation, had it been proposed, as he was only intent on then securing such a lovely creature for his wife. “Thus the Lady of the Lake engaged to become the young man’s wife, and having loosened her hand for a moment she darted away and dived into the lake. His chagrin and grief were such that he determined to cast himself headlong into the deepest water, so as to end his life in the element that had contained in its unfathomed depths the only one for whom he cared to live on earth. As he was on the point of committing this rash act, there emerged out of the lake two most beautiful ladies, accompanied by a hoary-headed man of noble mien and extraordinary stature, but having otherwise all the force and strength of youth. This man addressed the almost bewildered youth in accents calculated to soothe his troubled mind, saying that as he proposed to marry one of his daughters, he consented to the union, provided the young man could distinguish which of the two ladies before him was the object of his affections. This was no easy task, as the maidens were such perfect counterparts of each other that it seemed quite impossible for him to choose his bride, and if perchance he fixed upon the wrong one all would be for ever lost. “Whilst the young man narrowly scanned the two ladies, he could not perceive the least difference betwixt the two, and was almost giving up the task in despair, when one of them thrust her foot a slight degree forward. The motion, simple as it was, did not escape the observation of the youth, and he discovered a trifling variation in the mode with which their sandals were tied. This at once put an end to the dilemma, for he, who had on previous occasions been so taken up with the general appearance of the Lady of the Lake, had also noticed the beauty of her feet and ankles, and on now recognising the peculiarity of her shoe-tie he boldly took hold of her hand.
  • 29. “‘Thou hast chosen rightly,’ said her father, ‘be to her a kind and faithful husband, and I will give her, as a dowry, as many sheep, cattle, goats, and horses as she can count of each without heaving or drawing in her breath. But remember, that if you prove unkind to her at any time, and strike her three times without a cause, she shall return to me, and shall bring all her stock back with her.’” Such was the verbal marriage settlement, to which the young man gladly assented, and his bride was desired to count the number of sheep she was to have. She immediately adopted the mode of counting by fives, thus:—one, two, three, four, five—one, two, three, four, five; and as many times as possible in rapid succession, till her breath was exhausted. The same procession of reckoning had to determine the number of goat, cattle, and horses respectively; and in an instant the full number of each came out of the lake when called upon by the father. “The young couple were then married, by what ceremony was not stated, and afterwards went to reside at a farm called Esgair Llaethy, somewhat more than a mile from the Village of Myddfai, where they lived in prosperity and happiness for several years, and became the parents of three sons, who were beautiful children. “Once upon a time there was a christening to take place in the neighbourhood, to which the parents were specially invited. When the day arrived the wife appeared very reluctant to attend the christening, alleging that the distance was too great for her to walk. Her husband told her to fetch one of the horses which were grazing in an adjoining field. ‘I will,’ said she, ‘if you will bring me my gloves which I left in our house.’ He went to the house and returned with the gloves, and finding that she had not gone for the horse jocularly slapped her shoulder with one of them, saying, ‘go! go!’ (dos, dos), when she reminded him of the understanding upon which she consented to marry him:—That he was not to strike her without a cause; and warned him to be more cautious for the future.
  • 30. “On another occasion, when they were together at a wedding in the midst of the mirth and hilarity of the assembled guests, who had gathered together from all the surrounding country, she burst into tears and sobbed most piteously. Her husband touched her on her shoulder and inquired the cause of her weeping: she said, ‘Now people are entering into trouble, and your troubles are likely to commence, as you have the second time stricken me without a cause.’ “Years passed on, and their children had grown up, and were particularly clever young men. In the midst of so many worldly blessings at home, the husband almost forgot that there remained only one causeless blow to be given to destroy the whole of his prosperity. Still he was watchful lest any trivial occurrence should take place which his wife must regard as a breach of their marriage contract. She told him, as her affection for him was unabated, to be careful that he would not, through some inadvertence, give the last and only blow, which, by an unalterable destiny over which she had no control, would separate them for ever. “It, however, so happened that one day they were together at a funeral, where, in the midst of the mourning and grief at the house of the deceased, she appeared in the highest and gayest spirits, and indulged in immoderate fits of laughter, which so shocked her husband that he touched her, saying: ‘Hush! hush! don’t laugh.’ She said that she laughed ‘because people when they die go out of trouble,’ and rising up she went out of the house, saying, ‘The last blow has been struck, our marriage contract is broken, and at an end! Farewell!’ Then she started off towards Esgair Llaethdy, where she called her cattle and other stock together, each by name. The cattle she called thus:— Mu wlfrech, Mu olfrech, gwynfrech, Pedair cae tonn-frech, Yr hen wynebwen. A’r las Geigen, Gyda’r Tarw gwyn O lys y Brenin;
  • 31. A’r llo du bach, Sydd ar y bach, Dere dithe, yn iach adre! Brindled cow, white speckled, Spotted cow, bold freckled, The four field sward mottled, The old white-faced, And the grey Geigen, With the white Bull, From the court of the King; And the little black calf Tho’ suspended on the hook, Come thou also, quite well home.” They all immediately obeyed the summons of their mistress. The ‘little black calf,’ although it had been slaughtered, became alive again, and walked off with the rest of the stock at the command of the lady. This happened in the spring of the year, and there were from four oxen ploughing in one of the fields; to these she cried:— “Pedwar eidion glas sydd ar y maes, Deuwch chwithau yn iach adre! The four grey oxen, that are on the field, Come you also quite well home!” Away the whole of the live stock went with the Lady across Myddfai Mountain, towards the lake from whence they came, a distance of above six miles, where they disappeared beneath its waters, leaving no trace behind except a well-marked furrow, which was made by the plough the oxen drew after them into the lake, and which remains to this day as a testimony to the truth of this story.
  • 32. “What became of the affrighted ploughman—whether he was left on the field when the oxen set off, or whether he followed them to the lake, has not been handed down to tradition; neither has the fate of the disconsolate and half-ruined husband been kept in remembrance. But of the sons it is stated that they often wandered about the lake and its vicinity, hoping that their mother might be permitted to visit the face of the earth once more, as they had been apprised of her mysterious origin, her first appearance to their father, and the untoward circumstances which so unhappily deprived them of her maternal care. “In one of their rambles, at a place near Dol Howel, at the Mountain Gate, still called ‘Llidiad y Meddygon,’ (The Physician’s Gate), the mother appeared suddenly, and accosted her eldest son, whose name was Rhiwallon, and told him that his mission on earth was to be a benefactor to mankind by relieving them from pain and misery, through healing all manner of their diseases; for which purpose she furnished him with a bag full of medical prescriptions and instructions for the preservation of health. That by strict attention thereto he and his family would become for many generations the most skilful physicians in the country. Then, promising to meet him when her counsel was most needed, she vanished. But on several occasions she met her sons near the banks of the lake, and once she even accompanied them on their return home as far as a place still called ‘Pant-y- Meddygon,’ (The dingle of the Physicians) where she pointed out to them the various plants and herbs which grew in the dingle, and revealed to them their medicinal qualities or virtues; and the knowledge she imparted to them, together with their unrivalled skill, soon caused them to attain such celebrity that none ever possessed before them. And in order that their knowledge should not be lost, they wisely committed the same to writing for the benefit of mankind throughout all ages. And so ends the story of the Physicians of Myddfai, which had been handed down from one generation to another, thus:— “Yr hen wr llwyd o’r cornel, Gan ei dad a glywodd chwedel, A chan ei dad fy glywodd yntau,
  • 33. Ac ar ei ol mi gofiais innau.” “The grey old man in the corner Of his father heard a story, Which from his father he had heard, And after them I have remembered.” The Physicians of Myddfai were Rhiwallon and his sons, Cadwgan, Gruffydd and Einion, who became Physicians to Rhys Gryg, Lord of Llandovery and Dynefor Castles, who lived in the early part of the thirteenth century. Rhys “gave them rank, lands, and privileges at Myddfai for their maintenance in the practice of their art and science, and the healing and benefit of those who should seek their help.” The fame of the celebrated Physicians was soon established over the whole country, and continued for centuries among their descendants; and the celebrated Welsh Poet Dafydd ap Gwilym, who flourished in the fourteenth century, says in one of his poems when alluding to these physicians:— “Meddyg, nis gwnai modd y gwnaeth Myddfai, o chai ddyn meddfaeth.” (A Physician he would not make As Myddfai made, if he had a mead fostered man.) Mr. Rees says that “of the above lands bestowed upon the Meddygon, there are two farms in the Myddfai parish still called “Llwyn Ifan Feddyg,” the Grove of Evan, the Physician, and “Llwyn Meredydd Feddyg” (the Grove of Meredydd the Physician). Esgair Llaethdy, mentioned in the foregoing legend, was formerly in the possession of the above descendants, and so was Ty-newydd, near Myddfai, which was purchased by Mr. Holford, of Cilgwyn, from the Rev. Charles Lloyd, vicar of Llandefalle, Breconshire, who married a daughter of one of the Meddygon, and had the living of Llandefalle from a Mr. Vaughan, who presented him to the same out of
  • 34. gratitude, because Mr. Lloyd, wife’s father had cured him of a disease in the eye. As Mr. Lloyd succeeded to the above living in 1748, and died in 1800, it is probable that that skilful oculist was John Jones, who is mentioned in the following inscription on a tombstone at present fixed against the west end of Myddfai HERE Lieth the body of Mr. David Jones, of Mothvey, Surgeon, who was an honest, charitable and skilful man, He died September 14th, Anno Dom. 1719, aged 61. JOHN JONES, SURGEON, Eldest son of the said David Jones, departed this life the 25th of November, 1739, in the 4th year of his Age, and also lyes interred hereunder. These appear to have been the last of the Physicians who practised at Myddfai. The above John Jones resided for some time at Llandovery, and was a very eminent surgeon. One of his descendants, named John Lewis, lived at Cwmbran, Myddfai, at which place his great-grandson, Mr. John Jones, now resides. “Dr. Morgan Owen, Bishop of Llandaff, who died at Glasallt, parish of Myddfai, in 1645, was a descendant of the Meddygon, and an inheritor of much of their landed property in that parish, the bulk of which he bequeathed to his nephew, Morgan Owen, who died in 1667, and was succeeded by his son Henry Owen; and at the decease of the last of whose descendants, Roberts Lewis, Esqr., the estates became, through the will of one of the family, the property of the late D. A. S. Davies, Esqr., M.P., for Carmarthenshire. “Bishop Owen bequeathed to another nephew, Morgan ap Rees, son of Rees ap John, a descendant of the Meddygon, the farm of Rhyblid, and some other property. “Amongst other families who claim descent from the Physicians were the Bowens of Cwmydw, Myddfai, and Jones of Dollgarreg and Penrhock, in the same parish; the latter of whom are represented by Charles Bishop, of
  • 35. Dollgarreg, Esqr., Clerk of the Peace for Carmarthenshire, and Thomas Bishop, of Brecon, Esqr. “Rees Williams, of Myddfai, is recorded as one of the Meddygon. His great grandson was the late Rice Williams, M.D., of Aberystwyth, who died May l6th, 1842, aged 85, and appears to have been the last, although not the least eminent of the Physicians descended from the mysterious Lady of Llyn y Fan.” Sir John Rhys mentions of another Dr. Williams also a descendant of the Lady of Llyn y Fan, who was living at Aberystwyth in 1881. It seems that there are several families in different parts of Wales who are said to have fairy blood coursing through their veins; and the noble Lady Bulkeley, who lived in North Wales, three or four generations was supposed to be descended from a Fairy lady who married a mortal. There is also a tradition that after the disappearance of the lady the disconsolate husband and his friends set to work to drain the lake in order to get at her, if possible; but as they were making a cutting into the bank a huge monster emerged from the water and threatened to drown the town of Brecon for disturbing him, saying:— “Os na cha’i lonydd yn fy lle Mi fodda, dre Byrhonddu!” (If I get no quiet in my place I shall drown the town of Brecon). so they had to give up draining the lake. There are extant several versions of the Myddfai Legend. In the “Cambro Briton” Vol. II., pages 313–315, we have a version in which it is stated that the farmer used to go near the lake and see some lambs he had bought at a fair, and that wherever he so went three most beautiful maidens appeared to
  • 36. him from the lake. But whenever he tried to catch them they ran away into the lake, saying:— “Cras dy fara, Anhawdd ein dala.” (For thee who eatest baked bread It is difficult to catch us.) But one day a piece of moist bread came floating ashore, which he ate, and the next day he had a chat with the maidens. After a little conversation he proposed marriage to one of them, to which she consented, provided he could distinguish her from her sisters the day after. Then the story goes on very similar to Mr. Rees’ version which I have already given in full. In another beautiful version of the story which is given by Sikes in his “British Goblins,” it is said that an enamoured farmer had heard of the lake maiden, who rowed up and down the lake in a golden boat, with a golden oar. Her hair was long and yellow, and her face was pale and melancholy. In his desire to see this wondrous beauty, the farmer went on New Year’s Eve to the edge of the lake and in silence, awaited the coming of the first hour of the new year. It came, and there in truth was the maiden in her golden boat, rowing softly to and fro. Fascinated, he stood for hours beholding her, until the stars faded out of the sky, the moon sank behind the rocks, and the cold gray dawn drew nigh; and then the maiden began to vanish from his sight. Wild with passion, he cried aloud to the retreating vision, “Stay! Stay! Be my wife.” But the maiden only uttered a faint cry, and was gone. Night after night the young farmer haunted the shores of the lake, but the maiden returned no more. He became negligent of his person; his once robust form grew thin and wan; his face was a map of melancholy and despair. He went one day to consult a soothsayer who dwelt on the mountain, and this grave personage advised him to besiege the damsel’s heart with gifts of bread and cheese. This counsel commending itself strongly to his Welsh way of thinking, the former set out upon an assiduous course of casting his bread upon the waters—accompanied by cheese. He began on Mid-summer Eve
  • 37. by going to the lake and dropping therein a large cheese and a loaf of bread. Night after night he continued to throw in loaves and cheeses, but nothing appeared in answer to his sacrifices. His hopes were set, however, on the approaching New Year’s Eve. The momentous night arrived at last. Clad in his best array, and armed with seven white loaves and his biggest and handsomest cheese, he set out once more for the lake. Then he waited till mid-night, and then slowly and solemnly dropped the seven loaves into the water, and with a sigh sent the cheese to keep them company. His persistence was at length rewarded. The Lake Lady came in her skiff to where he was, and gracefully stepped ashore. The story then proceeds as in the other versions. It was once a custom for people to go up to the lake on the first Sunday in August, when its water was supposed to be boiling; and Bishop Edwards, of St. Asaph, informed Professor Sir J. Rhys, that “an old woman from Myddfai, who is now, that is to say in January, 1881, about eighty years of age, tells me that she remembers thousands and thousands of people visiting the Lake of Little Fan on the first Sunday or Monday in August, and when she was young she often heard old men declare that at that time a commotion took place in the lake, and that its waters boiled, which was taken to herald the approach of the Lake Lady and her oxen.”—Celtic Folk Lore—page 15. A STUDENT WHO HAD FAILED TO PASS HIS EXAMINATIONS TAUGHT BY THE FAIRIES. Mr. John Jones, of Pontrhydfendigaid, an old man of over 95 years of age, related to me the following story about seven years ago:— In the 18th century there was a certain clergyman in North Cardiganshire, who was supposed to have been educated by the Fairies.
  • 38. When he was a boy, his parents were very ambitious to see their son a clergyman, but, unfortunately, the lad either neglected his studies, or was a regular “blockhead,” and always failed to pass his college examinations, to the great regret and disappointment of his father and mother. One day, however, when the boy was roaming about the country (near the banks of the river Rheidol, as far as Mr. Jones could remember the story), he suddenly met three boys, or rather three little men who were not bigger than boys, who took him into some cave and led him along a subterranean passage into the land of the Fairies. The Fairies proved very kind to him, and when they heard his story, they undertook to help him to learn his lessons, so that in course of time he acquired a considerable knowledge of the classics. After spending a certain number of years very happily in Fairy Land, the young man returned to the world of mortals, and to the great joy of his parents passed his examinations now without the least difficulty, and in due time was ordained by the bishop, and became a vicar of a parish north of Aberystwyth, either Llanfihangel, Llancynfelin, or Eglwysfach. This tale seems to be a version of the Story of Elidorus, which Giraldus Cambrensis heard in the neighbourhood of Swansea during his “Itinerary through Wales,” with Archbishop Baldwin in the year 1188, which is as follows:— “A short time before our days, a circumstance worthy of note occurred in these parts, which Elidorus, a priest, most strenuously affirmed had befallen himself. When a youth of twelve years, and learning his letters, since, as Solomon says, “The root of learning is bitter, although the fruit is sweet,” in order to avoid the discipline and frequent stripes inflicted on him by his perceptor, he ran away, and concealed himself under the hollow bank of a river. After fasting in that situation for two days, two little men of pigmy stature appeared to him, saying, ‘If you come with us, we will lead you into a country full of delights and sports.’ “Assenting, and rising up, he followed his guides through a path, at first subterraneous and dark, into a most beautiful country, adorned with rivers and meadows, woods and plains, but obscure, and not illuminated with the full light of the sun.” All the days were cloudy, and the nights extremely dark, on account of the absence of the moon and stars. The boy was brought before the King, and introduced to
  • 39. him in the presence of the court; who, having examined him for a long time, delivered him to his son, who was then a, boy. “These men were of the smallest stature, but very well proportioned in their make; they were all of a fair complexion, with luxuriant hair falling over their shoulders like that of women. “They had horses and greyhounds adapted to their size. “They neither ate flesh nor fish, but lived on milk diet, made up into messes with saffron. “They never took an oath, for they detested nothing so much as lies. “As often as they returned from our upper hemisphere, they reprobated our ambition, infidelities, and inconstances; they had no form of public worship, being strict lovers and reverers, as it seemed, of truth. “The boy frequently returned to our hemisphere, sometimes by the way he had first gone, sometimes by another; at first in company with other persons, and afterwards alone, and made himself known only to his mother, declaring to her the manners, nature and state of that people. “Being desired by her to bring a present of gold, with which that region abounded, he stole, while at play with the King’s son, the golden ball with which he used to divert himself, and brought it to his mother in great haste; and when he reached the door of his father’s house, but not unpursued, and was entering it in a great hurry, his foot stumbled on the threshold, and falling down into the room where his mother was sitting, the two pigmies seized the ball which had dropped from his hand, and departed, showing the boy every mark of contempt and derision. “On recovering from his fall, confounded with shame, and execrating the evil counsel of his mother, he returned by the usual track to the subterraneous road, but found no appearance of any passage, though he searched for it on the banks of the river for nearly the space of a year. “But since those calamities are often alleviated by time, which reason cannot mitigate, and length of time alone blunts the edge of our afflictions, and puts an end to many evils, the youth having been brought back by his friends and mother, and restored to his right way of thinking, and to his learning, in process of time attained the rank of priesthood. “Whenever David II., bishop of St. David’s, talked to him in his advanced state of life concerning this event, he could never relate the particulars without shedding tears. “He had made himself acquainted with the language of that nation, the words of which, in his younger days he used to recite, which, as the bishop often had informed me, were very conformable to the Greek idiom. “When they asked for water, they said
  • 40. ‘ydor ydorum,’ which meant bring water, for ‘ydor’ in their language, as well as in Greek, signifies water, from whence vessels for water are caller ‘udriai’; and ‘Dur’ (dwr) also, in the British language (Welsh) signifies water. “When they wanted salt they said, ‘Halgein ydorum,’ bring salt: salt is called ‘al’ in Greek, and ‘halen’ in British, for that language, from the length of time which the Britons (then called Trojans, and afterwards Britons, from Brito, their leader), remained in Greece after the destruction of Troy, became in many instances, similar to the Greek.... “If a scrupulous inquirer asks my opinion of the relation here inserted, I answer with Augustine, ‘that the Divine miracles are to be admired, not discussed.’ “Nor do I, by denial, place bounds to the Divine Power, nor, by assent, insolently extend what cannot be extended. “But I always call to mind the saying of St. Jerome: ‘You will find,’ says he, ‘Many things incredible and improbable, which nevertheless are true; for nature cannot in any respect prevail against the Lord of nature.’ “These things, therefore, and similar contingencies, I should place, according to the opinion of Augustine, among those particulars which are neither to be affirmed, nor too positively denied.” The above account is of the greatest interest, as it was written 700 years ago, and it also gives the opinion of one who lived in those days, of “these things, and similar contingencies.” It is possible that many of the Fairy Tales throughout the Kingdom, if not throughout the whole of Europe, have been founded on the story of Elidorus, the priest. THE SHEPHERD BOY AND THE FAIRIES OF FRENIFAWR. The following story appeared in the “Cambrian Superstitions,” by W. Howells, a little book published at Tipton in 1831:—
  • 41. A stripling, of twelve or more years of age, was tending his father’s sheep on a small mountain called Frenifach, it was a fine morning in June, and he had just driven the sheep to their pasture for the day, when he looked at the top of Frenifawr to observe which way the morning fog declined, that he might judge the weather. If the fog on Frenifawr (a high mountain in Pembrokeshire, 10 miles from Cardigan) declines to the Pembrokeshire side, the peasants prognosticated fair, if on the Cardiganshire side foul weather. To his surprise the boy saw what seemed a party of soldiers sedulously engaged in some urgent affair; knowing there could not possibly be soldiers there so early, he with some alarm, looked more minutely, and perceived they were too diminutive for men; yet, thinking his eyesight had deceived him, he went to a more elevated situation, and discovered that they were the “Tylwyth Teg” (Fairies) dancing. He had often heard of them and had seen their rings in the neighbourhood, but not till then had the pleasure of seeing them; he once thought of running home to acquaint his parents, but judging they would be gone before he returned, and he be charged with a falsehood, he resolved to go up to them, for he had been informed that the fairies were very harmless, and would only injure those who attempted to discover their habitation, so by degrees he arrived within a short distance of the ring, where he remained some time observing their motions. They were of both sexes, and he described them as being the most handsome people he had ever seen, they also appeared enchantingly cheerful, as if inviting him to enter and join the dance. They did not all dance, but those who did, never deviated from the circle; some ran after one another with surprising swiftness, and others (females), rode on small white horses of the most beautiful form. Their dresses, although indescribably elegant, and surpassing the sun in radiance, varied in colour, some being white, others scarlet, and the males wore a red triplet cap, but the females some light head-dress, which waved fantastically with the slightest breeze. He had not remained long ere they made signs for him to enter, and he gradually drew nearer till at length he ventured to place one foot in the circle, which he had no sooner done than his ears were charmed
  • 42. with the most melodious music, which moved him in the transport of the moment, to enter altogether; he was no sooner in than he found himself in a most elegant palace, glittering with gold and pearls; here he enjoyed every variety of pleasure, and had the liberty to range whatever he pleased, accompanied by kind attendants beautiful as the howries; and instead of “Tatws a llaeth,” buttermilk, or fresh boiled flummery, here were the choicest viands and the purest wine in abundance, brought in golden goblets inlaid with gems, sometimes by invisible agency, and at other times by the most beautiful virgins. He had only one restriction, and that was not to drink, upon any consideration (or it was told him it would be fatal to his happiness), from a certain well in the middle of the garden, which contained golden fishes and others of various colours. New objects daily attracts his attention, and new faces presented themselves to his view, surpassing, if possible those he had seen before; new pastimes were continually invented to charm him, but one day his hopes were blasted, and all his happiness fled in an instant. Possessing that innate curiosity nearly common to all, he, like our first parents transgressed, and plunged his hand into the well, when the fishes instantly disappeared, and, putting the water to his mouth, he heard a confused shriek run through the garden: in an instant after, the palace and all vanished away, and to his horror, he found himself in the very place where he first entered the ring, and the scenes around, with the same sheep grazing, were just as he had left them. He could scarcely believe himself, and hoped again, that he was in the magnificent fairy castle; he looked around, but the scene was too well known; his senses soon returned to their proper action, and his memory proved that, although he thought he had been absent so many years, he had been so only so many minutes. This tale bears a strange contrast as regards the time the boy thought he was away, to most of our fairy tales which represent those who had the pleasure of being with fairies as imagining they had been dancing only a few minutes, when they had been away for years.
  • 43. FAIRY MUSIC AND DANCING. The Rev. Z. M. Davies, Vicar of Llanfihangel Genau’r Glyn, told me that he once heard an old man in the Vale of Aeron saying that when he was out late one night, he heard the Fairies singing, and that their music was so delightful that he listened to them for hours; and we find from many of the Fairy Tales that one of their chief occupation in their nightly revels was singing and dancing, and that they often succeeded in inducing men through the allurements of music to join their ranks. The beautiful old Welsh Air, “Toriad y Dydd” (Dawn of Day) is supposed to have been composed by the Fairies, and which they chanted just as the pale light in the east announced the approach of returning day. The following “Can y Tylwyth Teg,” or the Fairies’ song, was well-known once in Wales, and these mythical beings were believed to chant it whilst dancing merrily on summer nights. “O’r glaswellt glan a’r rhedyn mân, Gyfeillion dyddan, dewch. ‘E ddarfu’r nawn—mae’r lloer yn llawn, Y nos yn gyflawn gewch; O’r chwarau sydd ar dwyn y dydd, I’r Dolydd awn ar daith, Nyni sydd lon, ni chaiff gerbron, Farwolion ran o’n gwaith. “Canu, canu, drwy y nos, Dawnsio, dawnsio, ar waen y rhos, Yn ngoleuni’r lleuad dlos: Hapus ydym ni! Pawb o honom sydd yn llon, Heb un gofid dan ei fron: Canu, dawnsio, ar y ton—
  • 44. Dedwydd ydym ni!” “From grasses bright, and bracken light, Come, sweet companions, come, The full moon shines, the sun declines. We’ll spend the night in fun; With playful mirth, we’ll trip the earth, To meadows green let’s go We’re full of joy, without alloy, Which mortals may not know. “Singing, singing, through the night, Dancing, dancing, with our might, Where the moon the moor doth light; Happy ever we! One and all of merry mein, Without sorrow are we seen, Singing, dancing, on the green: Gladsome ever we!” MR. EDWARD JONES, PENCWM, LLANRHYSTID, AND THE FAIRIES. Mr. Edward Jones, Pencwm, who only died about 8 years ago, was coming home from Lampeter one moonlight night, and when he came to the top of Trichrug hill, he saw the Fairies dancing in a field close to the road. When he was within a certain distance of them he felt as if his feet were almost lifted up from the ground, and his body so light that he could almost stand in the air.
  • 45. My informant, Mr. D. Morgan, Carpenter, Llanrhystid, added that Mr. Jones was an intelligent and educated man, who had travelled, and was far from being superstitious. A FARM SERVANT NEAR TREGARON, WHO SPENT A YEAR AND A DAY WITH THE FAIRIES. The following story appeared in “Cymru” for May, 1893, a Welsh Magazine, edited by Owen M. Edwards, M.A. It was written in Welsh by the late eminent Folk-Lorist, Mr. D. Lledrod Davies, and I translate it:— The farm-house called “Allt Ddu,” is situated about half-way between Pont Rhyd Fendigaid and Tregaron. It is said that two servant men went out of the house one evening in search for the cattle, which had gone astray. One of the men proceeded in one direction and the other in another way, so as to be more sure of finding the animals. But after wandering about for hours, one of the two servants came home, but whether he found the cattle or not it is not stated. However, he reached home safely; but the other man, his fellow-servant, came not, and after anxiously expecting him till a late hour of night, he began to feel very uneasy concerning his safety, fearing that the lad had accidentally fallen into some of the pits of the Gors Goch. Next morning came, but the servant came not home; and in vain did they long to hear the sound of his footsteps approaching the house as before. Then inquiries were made about him, and people went to try and find him, but all in vain. Days past and even weeks without hearing anything about him, till at last his relations began to suspect that his fellow servant had murdered him during the night they were out looking for the cattle. So the
  • 46. servant was summoned before a Court of Justice, and accused of having murdered his fellow-servant on a certain night; but the young man, pleaded not guilty in a most decided manner, and as no witness could be found against him, the case was dismissed; but many people were still very suspicious of him, and the loss of his fellow servant continued to be a black spot on his character. However, it was decided at last to go to the “dyn hysbys,” (a wise man, or a conjurer)—a man of great repute in former days, —to consult with him, and to set the case before him exactly as it had happened. After going and explaining everything to the conjurer concerning the lost servant, he informed them that the young man was still alive. He then told them to go to a certain place at the same time of night, one year and a day from the time the man was lost, and that they should then and there see him. One year and a day at last passed away, and at that hour the family, and especially the servant, traced their steps to the particular spot pointed out by the conjuror, and there, to their great surprise, whom should they see within the Fairy Circle, dancing as merrily as any, but the lost servant. And now, according to the directions which had been given by the conjurer, the other servant took hold of the collar of the coat of the one who was dancing, and dragged him out of the circle, saying to him —“Where hast thou been lad?” But the lad’s first words were, “Did you find the cattle?” for he thought that he had been with the Fairies only for a few minutes. Then he explained how he entered the Fairy Circle, and how he was seized by them, but found their company so delightful that he thought he had been with them only for a few minutes. THE SERVANT GIRL WHO WAS LOST IN THE FAIRY CIRCLE.
  • 47. The following is another of the tales recorded in “Ystraeon y Gwyll,” by the late D. Lledrod Davies:— “There lived in an old farm house on the banks of the Teivy, a respectable family, and in order to carry on the work of the farm successfully, they kept men servants and maid servants. One afternoon, a servant-man and a servant girl went out to look for the cows, but as they were both crossing a marshy flat, the man suddenly missed the girl, and after much shouting and searching, no sound of her voice could be heard replying. He then took home the cows, and informed the family of the mysterious disappearance of the servant maid which took place so suddenly. As the Fairies were suspected, it was resolved to go to the dyn hysbys (wise man). To him they went, and he informed them that the girl was with the Fairies, and that they could get her back from them, by being careful to go to a certain spot at the proper time at the end of a year and a day. They did as they were directed by the “wise man,” and to their great surprise, found the maid among the fairies dancing and singing with them, and seemed as happy as a fish in the water. Then they successfully drew her out of the ring, and they took her home safely. The master had been told by the “Wise Man” that the girl was not to be touched by iron, or she would disappear at once after getting her out of the ring. One day, however, when her master was about to start from home, and whilst he was getting the horse and cart ready, he asked the girl to assist him, which she did willingly; but as he was bridling the horse, the bit touched the girl and she disappeared instantly, and was never seen from that day forth. THE LITTLE SERVANT BOY AND THE BARM.
  • 48. The following story was related to me by Mrs. Davies, Bryneithyn, in the neighbourhood of Ystrad Meurig, where the tale is well-known:— An old woman known as Nancy of Pen Gwndwn, kept a little boy servant, whom she sent one evening to the neighbouring village with a bottle to get some barm for her, and as he had to pass through a field which was frequented by the Fairies, he was told by the old woman to keep away from their circles or rings. The boy reached the village, got the barm, and in due time proceeded on his homeward journey, but did not reach home. Search was made for him in all directions, and people were able to trace his steps as far as the Fairies’ field, but no further, so it was evident that the Fairies had seized him. At the end of a year and a day, however, to the great surprise of everybody, the boy came home, entered the house, with the bottle of barm in hand, and handed it to the old woman as if nothing unusual had happened. The boy was greatly surprised when he was told that he had been away for twelve months and a day. Then he related how he fell in with the Fairies, whom he found such nice little men, and whose society was so agreeable that he lingered among them, as he thought, for a few minutes. A CARMARTHENSHIRE MAIDEN WHO GOT INTO A FAIRY RING. In the parish of Cynwil Elvet, there is a farmhouse called Fos Anna, a place which was known to the writer of this book once when a boy:— A servant girl at this farm once went rather late in the evening to look for the cows, and, unfortunately, got into the Fairy ring, and although she had been a long period without food she did not feel hungry.
  • 49. IAGO AP DEWI AMONG THE FAIRIES SEVEN YEARS. A Carmarthenshire tradition names among those who lived for a period among the Fairies no less a person than the translator into Welsh of Bunyan’s “Pilgrim’s Progress.” “He was called Iago ap Dewi, and lived in the parish of Llanllawddog, in a cottage situated in the wood of Llangwyly. He was absent from the neighbourhood for a long period, and the universal belief among the peasantry was that Iago got out of bed one night to gaze on the starry sky, as he was accustomed (astrology being one of his favourite studies), and whilst thus occupied the Fairies, passing by, carried him away, and he dwelt with them seven years. Upon his return, he was questioned by many as to where he had been, but always avoiding giving them a reply.” A district famous for Fairies long ago was the parish of Llanedi in Carmarthenshire, and Mr. Williams, says in his “Llen Gwerin Sir Gaerfyrddin,” that an intelligent old man in that parish, named John Rees, gave him the following story of A MAN WHO WAS FOUND AMONG THE FAIRIES AT CAE CEFN PANTYDWR. This story which is similar to some of the tales I have already given as located in other parts is as follows:—
  • 50. A certain man of Llanedi, on one occasion long ago, went away to another neighbourhood, leading by the “penwast” (collar) a very wild and unmanageable horse; and in order to be sure not to lose his hold of the animal, the man tied the end of the collar round the middle. So both man and horse went together and got lost. After much searching the horse was found without the collar, but nothing was heard of the man. After giving up searching for him as hopeless, they at last consulted a “Dyn Hysbys,” (a conjuror or a wise man). The wise man directed them to go on a certain night into a field known as Cae Cefn Pantydwr, about forty yards from the road where the Fairies could be seen dancing, and the lost man among them, with the “penwast” still around his waist, which would enable them to know him; and the way to get him out of the Fairy Ring was to watch him coming round in the dance, and take hold of the collar when an opportunity offered itself, and drag the man out boldly. They did so, and the man was rescued. Ever since then people dreaded going to that field after dark, especially children. In some parts of Carmarthenshire, Fairy Rings are known as “Rings y Gwr Drwg” (the rings of the Old Gentleman), suggesting that the Fairies had some connection with the evil one. SON OF LLECH Y DERWYDD AND THE FAIRIES. The writer of the following tale was the late Rev. Benjamin Williams (Gwynionydd), an eminent antiquarian, Folk-Lorist, and a bard, and it is to be found in Welsh in Y Brython, vol. III., page 460. It is evident that the scene of the story was West or Mid-Wales. Mr. Williams heard the tale from old people who believed in the truth of it:— “Yr oedd mab Llech y Derwydd yn unig blentyn ei rieni, ac hefyd yn etifedd y tyddyn. Yr oedd felly yn anwyl, ie, yn ddau lygad ei dad a’i fam.
  • 51. “Yr oedd y pen gwas a mab y ty yn gyfeillion mynwesol iawn, fel dau frawd, ie, fel gyfeilliaid. Gan fod y mab a’r gwas y fath gyfeillion, byddai gwraig y ty bob amser yn darpar dillad i’r gwas yr un peth yn hollol ag i’r mab. Cwympodd y ddau gyfaill mewn serch a dwy ddynes ieuainc, brydferth, ac uchel eu parch yn yr ardal, a mawr oedd y boddineb yn Llech y Derwydd; ac yn fuan ymunodd y ddau bar mewn glan briodas, a mawr fu y rhialtwch ar yr amser. Cafodd y gwas le cyfleus i fyw ar dir Llech y Derwydd. Yn mhen tua haner blwyddyn ar ol priodi o’r mab, aeth ei gyfaill ac yntau allan i hela; enciliodd y deiliad i ryw gilfach lawn o anialwch, i edrych am helwriaeth; a dychwelodd yn y man at ei gyfaill, ond erbyn dyfod yno, nid oedd modd gweled y mab yn un man. Parhaodd i edrych o gwmpas am dro gan waeddi a chwibanu, ond dim un arwydd am ei gyfaill. Yn mhen tro aeth adref i Llech y Derwydd, gan ddysgwyl ei weled yno; ond ni wyddai neb ddim am dano. Mawr oedd y gofid yn y teulu drwy y nos; ac erbyn dranoeth yr oedd eu pryder yn llawer mwy. Aethpwyd i weled y fan lle y gwelodd ei gyfaill ef olaf. Wylai ei fam a’i wraig am y gwaethaf. Yr oedd y tad dipyn yn well na’i wraig a’i fam, ond edrychai yntau fel yn haner gwallgof. Edrychwyd ar y fan olaf y gwelodd y deiliad ef, ac er eu mawr syndod a’u gofid, canfyddasent gylch y Tylwyth Teg gerllaw y fan, a chofiodd y deiliad yn y man iddo glywed swn peroriaeth hudoliaethus iawn rywle ar y pryd. Penderfynwyd ar unwaith iddo fod mor anffodus a myned i gylch y Tylwyth, a chael ei gludo ymaith na wyddid i ba le. “Aeth wythnosau a misoedd gofidus heibio, a ganwyd mab i fab Llech y Derwydd; ond nid oedd y tad ieuanc yno i gael gweled ei blentyn, ac yr oedd hyny yn ofidus iawn gan yr hen bobl. Beth bynag, daeth y dyn bach i fyny yr un ddelw a’i dad, fel pe buasai wedi ei arlunio; a mawr ydoedd yng ngolwg ei daid a’i nain. Efe oedd pobpeth yno. Tyfodd i oedran gwr, a phriododd a merch landeg yn y gymydogaeth; ond nid oedd gair da i’r tylwyth eu bod yn bobl hawddgar. “Bu farw yr hen bobl, a bu farw y ferch-yng-nghyfraith hefyd. Ar ryw brydnawn gwyntog, ym mis Hydref, gwelai teulu Llech y Derwydd henafgwr tal, teneu, a’i farf a’i wallt fel yr eira, yr hwn a dybient ydoedd Iddew, yn dynesu yn araf araf at y ty. Hylldremiai y morwynion drwy y ffenestr, a chwarddai y feistress am ben yr ‘hen Iddew,’ gan godi y plant un
  • 52. ar ol y llall i’w weled yn dyfod. Daeth at y drws, a daeth i mewn hefyd yn lled eofn, gan ofyn am ei rieni. Atebai y wraig ef yn daeog, a choeglyd anghyffredin, gan ddywedyd, ‘Beth oedd yr hen Iddew meddw yn dyfod yno,’ oblegid tybient ei fod wedi yfed, onid e ni fuasai yn siarad felly. Edrychai yr hen wr yn syn a phryderus iawn ar bob peth yn y ty, gan synu llawer; ond ar y plant bychain ar hyd y llawr y sylwai fwyaf. Edrychai yn llawn siomedigaeth a gofid. Dywedodd yr hanes i gyd, iddo fod allan yn hela ddoe, a’i fod yn awr yn dychwelyd. Dywedodd y wraig iddi glywed chwedl am dad ei gwr flynyddau cyn ei geni, ei fod wedi myned ar goll wrth hela; ond fod ei thad yn dywedyd wrthi nad gwir hyny, mai ei ladd a gafodd. Aeth y wraig yn anystywallt, ac yn llwyr o’i chof eisiau fod yr hen ‘Iddew’ yn myned allan. Cyffrodd yr hen wr, a dywedai mai efe ydoedd perchen y ty, ac y byddai raid iddo gael ei hawl. Aeth allan i weled ei feddianau, ac yn fuan i dy y deiliad. Er ei syndod, yr oedd pethau wedi newid yn fawr yno. Ar ol ymddiddan am dro a hen wr oedranus wrth y tan, edrychai y naill fwy fwy ar y llall. Dywedai yr hen wr beth fu tynged ei ben gyfaill, mab Llech y Derwydd. Siaradent yn bwyllog am bethau mebyd, ond yr oedd y cyfan fel breuddwyd. Beth bynag, penderfynodd yr hen wr yn y cornel mai ei hen gyfaill, mab Llech y Derwydd, oedd yr ymwelydd, wedi dychwelyd o wlad y Tylwyth Teg, ar ol bod yno haner can’ mlynedd. Credodd yr hen wr a’r farf wen ei dynged, a mawr y siarad a’r holi fu gan y naill y llall am oriau lawer. “Dywedai fod gwr Llech y Derwydd y diwrnod hwnw oddi cartref. Cafwyd gan yr hen ymwelydd fwyta bwyd; ond er mawr fraw, syrthiodd y bwytawr yn farw yn y fan. Nid oes hanes fod trengholiad wedi bod ar y corff; ond dywedai y chwedl mae yr achos oedd, iddo fwyta bwyd ar ol bod yn myd y Tylwyth Teg cyhyd. Mynodd ei hen gyfaill weled ei gladdu yn ochr ei deidiau. Bu melldith fyth, hyd y silcyn ach, yn Llech y Derwydd, o blegid sarugrwydd y wraig i’w thad-yng-nghyfraith, nes gwerthu y lle naw gwaith.” The above tale translated into English reads as follows:— “The son of Llech y Derwydd was the only child of his parents, and also the heir to the farm. He was, therefore, very dear to his father and mother, yea,
  • 53. he was as the very light of their eyes. The son and the head servant man were more than bosom friends, they were like two brothers, or rather twins. As the son and the servant were such close friends, the farmer’s wife was in the habit of clothing them exactly alike. The two friends fell in love with two young handsome women who were highly respected in the neighbourhood. This event gave the old people great satisfaction, and ere long the two couples were joined in holy wedlock, and great was the merry- making on the occasion. The servant man obtained a convenient place to live in on the grounds of Llech y Derwydd. “About six months after the marriage of the son, he and the servant man went out to hunt. The servant penetrated to a ravine filled with brushwood to look for game, and presently returned to his friend, but by the time he came back the son was nowhere to be seen. He continued awhile looking about for his absent friend, shouting and whistling to attract his attention, but there was no answer to his calls. By and by he went home to Llech y Derwydd, expecting to find him there, but no one knew anything about him. Great was the grief of the family throughout the night, but it was even greater next day. They went to inspect the place where the son had last been seen. His mother and his wife wept bitterly, but the father had greater control over himself, still he appeared as half mad. They inspected the place where the servant man had last seen his friend, and, to their great surprise and sorrow, observed a Fairy ring close by the spot, and the servant recollected that he had heard seductive music somewhere about the time that he parted with his friend. “They came to the conclusion at once that the man had been so unfortunate as to enter the Fairy ring, and they conjectured that he had been transported no one knew where. Weary weeks and months passed away, and a son was born to the absent man. “The little one grew up the very image of his father, and very precious was he to his grandfather and grandmother. In fact, he was everything to them. He grew up to man’s estate and married a pretty girl in the neighbourhood, but her people had not the reputation of being kind-hearted. The old folks died, and also their daughter-in-law.
  • 54. “One windy afternoon in the month of October, the family of Llech y Derwydd saw a tall thin old man with beard and hair as white as snow, who they thought was a Jew approaching slowly, very slowly, towards the house. The servant girls stared mockingly through the window at him, and their mistress laughed unfeelingly at the ‘old Jew,’ and lifted the children up, one after the other, to get a sight of him as he neared the house. “He came to the door, and entered the house boldly enough, and inquired after his parents. The mistress answered him in a surly and unusually contemptuous manner and wished to know ‘What the drunken old Jew wanted there,’ for they thought he must have been drinking or he would never have spoken in the way he did. The old man looked at everything in the house with surprise and bewilderment, but the little children about the floor took his attention more than anything else. His looks betrayed sorrow and deep disappointment. He related his whole history, that yesterday he had gone out to hunt, and that now he had returned. The mistress told him that she had heard a story about her husband’s father, which occurred before she was born, that he had been lost whilst hunting, but that her father had told her that the story was not true, but that he had been killed. The woman became uneasy and angry that the old ‘Jew’ did not depart. The old man was roused, and said that the house was his, and that he would have his rights. He went to inspect his possessions, and shortly afterwards directed his steps to the servant’s house. To his surprise he saw that things were greatly changed. After conversing awhile with an aged man who sat by the fire, they carefully looked each other in the face, and the old man by the fire related the sad history of his lost friend, the son of Llech y Derwydd. “They conversed together deliberately on the events of their youth, but all seemed like a dream. However, the old man in the corner came to the conclusion that his visitor was his old friend, the son of Llech y Derwydd, returned from the land of the Fairies, after spending there fifty years. “The old man with the white beard believed the story related by his friend, and long was the talk and many were the questions which the one gave to the other. The visitor was informed that the master of Llech y Derwydd was from home that day, and he was persuaded to eat some food; but to the
  • 55. horror of all, when he had done so, he instantly fell down dead. We are not informed that an inquest was held over the body; but the tale relates that the cause of the man’s sudden death was that he ate food after having been so long in the land of the Fairies. His old friend insisted on the dead man being buried with his ancestors. The rudeness of the mistress of Llech y Derwydd to her father-in-law brought a curse upon the place and family, ‘hyd y silcyn ach,’ and her offence was not expiated until the farm had been sold nine times.” TAFFY AP SION OF PENCADER AMONG THE FAIRIES. The following Fairy Legend appeared in “British Goblins,” page 75:— Taffy ap Sion, the shoemaker’s son, living near Pencader, Carmarthenshire, was a lad who many years ago entered the Fairy circle on the mountain hard by there, and having danced a few minutes as he supposed, chanced to step out. He was then astonished to find that the scene which had been so familiar was now quite strange to him. Here were roads and houses he had never seen, and in place of his father’s humble cottage there now stood a fine stone farmhouse. About him were lovely cultivated fields instead of the barren mountain he was accustomed to. ‘Ah,’ thought he, ‘this is some Fairy trick to deceive my eyes. It is not ten minutes since I stepped into that circle, and now when I step out they have built my father a new house! Well, I only hope it is real; anyhow, I’ll go and see.’ So he started off by a path he knew instinctively, and suddenly struck against a very solid hedge. He rubbed his eyes, felt the hedge with his fingers, scratched his head, felt the hedge again, ran a thorn into his fingers and cried out, ‘Wbwb’ this is no Fairy hedge anyhow, nor, from the age of the thorns, was it grown in a few minutes’ time! So he climbed over it and walked on. ‘Here was I born,’ said he, as he entered the farmyard, staring
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