Table Of Content

Modern Applied Fracture Mechanics Modern Applied Fracture Mechanics Cameron Coates Valmiki Sooklal MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. First edition published 2022 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN CRC Press is an imprint of Taylor & Francis Group, LLC © 2022 Taylor & Francis Group, LLC Reasonable efforts have been made to publish reliable data and information, but the authors and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. 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For works that are not available on CCC please contact [email protected] Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging‑in‑Publication Data Names: Coates, Cameron, author. | Sooklal, Valmiki, author. Title: Modern applied fracture mechanics / Cameron Coates, Valmiki Sooklal. Description: First edition. | Boca Raton : CRC Press, [2022] | Includes bibliographical references and index. | Identifiers: LCCN 2021055513 (print) | LCCN 2021055514 (ebook) | ISBN 9780367501259 (hardback) | ISBN 9780367509880 (paperback) | ISBN 9781003052050 (ebook) Subjects: LCSH: Fracture mechanics. Classification: LCC TA409 .C63 2022 (print) | LCC TA409 (ebook) | DDC 620.1/126--dc23/ eng/20220105 LC record available at https://lccn.loc.gov/2021055513LC ebook record available at https://lccn.loc.gov/2021055514 ISBN: 978-0-367-50125-9 (hbk) ISBN: 978-0-367-50988-0 (pbk) ISBN: 978-1-003-05205-0 (ebk) DOI: 10.1201/9781003052050 Typeset in Times by SPi Technologies India Pvt Ltd (Straive) Dedication To June, Nia, Kimani, Naomi, late brother Mark, sister Camille, and my parents Clinton (late) and Ava Coates of Ensom City, Jamaica, for their encouragement, faith, and support. Cameron W. Coates To my wife Tina and my parents Donna and Karamchand of Arouca, Trinidad and Tobago, for their love and support in all my endeavors. Val Sooklal Contents Preface .....................................................................................................................xiii Authors .....................................................................................................................xv Chapter 1 Fracture Mechanics ..............................................................................1 Objectives .............................................................................................1 1.1 Historical to Recent Failures .....................................................1 1.2 The Need for Fracture Mechanics and Their Applications ........5 1.3 Materials Science Review ..........................................................5 1.4 Dislocations and Plasticity ........................................................5 1.5 Isotropy vs. Anisotropy ..............................................................6 1.6 State of Stress and Strain Concepts ...........................................6 1.7 Stress-Based Approach ..............................................................7 1.8 The Fracture Mechanics Approach ............................................9 1.9 Linear Elastic vs. Elastic Plastic Fracture Mechanics .............10 1.10 Fracture of Metals ....................................................................11 1.11 Fracture of Nonmetals .............................................................13 1.12 Software Use in Fracture Mechanics .......................................14 Review and Practice Problems ...........................................................15 Elementary Mechanics of Materials Problems ...................................16 References ..........................................................................................18 Chapter 2 Fundamentals of Linear Elastic Fracture Mechanics: Basic ..............21 Objectives ...........................................................................................21 2.1 Early Theoretical Foundations .................................................21 2.2 Stress Concentration ................................................................23 2.3 Plane Strain or Plane Stress Problems .....................................27 2.4 Stress Intensity Factor .............................................................28 2.4.1 K and Global Behavior ...............................................28 2.4.2 Flaw Shape .................................................................30 2.4.3 Multiplicity of Geometry Factor, Y ............................31 2.4.4 Stress Intensity vs. Stress Concentration Factor ........31 2.5 Finite Size Correction ..............................................................32 2.6 Superposition ...........................................................................34 2.7 Fracture Toughness ..................................................................37 2.8 The Singularity Zone and the Plastic Zone .............................41 2.9 Effective Fracture Toughness ..................................................43 2.9.1 Criteria for LEFM Validity .........................................44 2.10 Fracture Toughness and Other Properties ................................47 2.10.1 Fracture Toughness and Strength ...............................47 vii viii Contents 2.10.2 Fracture Toughness vs. Temperature ..........................48 2.10.3 Fracture Toughness vs. Strain Rate ............................48 2.11 Industry Applications ...............................................................49 2.11.1 Hydraulic Proof Test to Determine K .......................49 Ic 2.11.2 Fracture Toughness vs. Tensile Strength ....................49 2.12 Review and Material Assumptions ..........................................51 Problems .............................................................................................52 References ..........................................................................................53 Chapter 3 Energy Approaches .............................................................................55 3.1 Introduction .............................................................................55 3.2 Griffith’s Theory ......................................................................55 3.3 Driving Force and Resistance to Crack Growth ......................59 3.4 R-Curve Behavior ....................................................................62 3.5 Strain Energy Density ..............................................................64 3.6 The J-Integral ...........................................................................70 3.7 Crack Tip Opening Displacement (CTOD) .............................75 3.8 Applications .............................................................................77 Problems .............................................................................................80 References ..........................................................................................81 Chapter 4 Applications .......................................................................................83 4.1 Fatigue Failures .......................................................................83 4.1.1 Fatigue Fundamentals .................................................83 4.1.1.1 S-N Curves ..................................................85 4.1.1.2 Fatigue Fracture Surface .............................88 4.1.2 Industry Applications .................................................91 4.1.2.1 Case Study 1: XFEM Simulation of Fatigue Crack Growth in a Welded Joint of a Pressure Vessel With a Reinforcement Ring Weldment ...................91 4.1.2.2 Case Study 2: Effect of Additional Holes on the Transient Thermal Fatigue Life of a Gas Turbine Casing ......................93 4.2 Failure Assessment Diagrams ..................................................96 4.3 Applications in Failure Analysis............................................100 4.3.1 Fundamentals of Failure Analysis ............................100 4.3.1.1 Tensile Overload .......................................100 4.3.1.2 Torsion Overload ......................................101 4.3.1.3 Bending Overload .....................................104 4.3.2 Industry Applications ...............................................104 4.3.2.1 Case Study 3: Failure of a 40-inch Diameter Crude Oil Pipeline ....................104 Contents ix 4.3.2.2 Case Study 4: Failure Study of the Railway Rail Serviced for Heavy Cargo Trains ..............................................107 4.4 Non-Destructive Testing ........................................................109 4.4.1 Ultrasonic Testing .....................................................109 4.4.2 Eddy Current Testing ................................................110 4.4.3 Magnetic Flux Leakage ............................................110 4.4.4 Radiographic Testing ................................................111 4.4.5 Liquid Penetrant Testing...........................................112 Problems ...........................................................................................113 References ........................................................................................114 Chapter 5 Further Fracture Mechanics Applications ........................................117 Objectives .........................................................................................117 5.1 Design Approaches to Prevent Failure ..................................117 5.1.1 Safe-Life ...................................................................117 5.1.2 Fail-Safe Approach ...................................................119 5.1.3 Fail Safe vs. Safe Life ..............................................119 5.2 Damage Tolerance Analysis ..................................................119 5.2.1 Safety Assurance Slow Crack Growth vs. Fail Safe ....................................................................120 5.2.2 Residual Strength Curve ...........................................121 5.2.3 Inspectability ............................................................122 5.2.4 Crack Growth Retardation ........................................123 5.2.5 The Wheeler Retardation Model ..............................124 5.2.6 Initial Steps in the Damage Tolerance Process .........124 5.3 Leak Before Burst (LBB) ......................................................128 5.3.1 Elliptical Crack Growth Behavior ............................129 5.4 Summary ................................................................................133 Problems ...........................................................................................134 References ........................................................................................135 Chapter 6 Experimental Methods .....................................................................137 6.1 Measurement of Fracture Toughness .....................................137 6.1.1 Specimen Type .........................................................137 6.1.2 Specimen Orientation ...............................................137 6.1.3 Measurement Apparatus ...........................................140 6.1.4 Specimen Preparation ...............................................141 6.1.5 K Testing ...................................................................141 6.1.6 Interpretation of Results ...........................................142 6.1.7 J Testing....................................................................145 6.1.7.1 The Basic Method .....................................145 6.1.7.2 Resistance Curve Method .........................147