Zehnder Fracture Mechanics

1. Auflage 2012
ISBN: 978-94-007-2595-9
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 62, 235 Seiten

Reihe: Lecture Notes in Applied and Computational Mechanics

Fracture mechanics is a vast and growing field. This book develops the basic elements needed for both fracture research and engineering practice. The emphasis is on continuum mechanics models for energy flows and crack-tip stress- and deformation fields in elastic and elastic-plastic materials. In addition to a brief discussion of computational fracture methods, the text includes practical sections on fracture criteria, fracture toughness testing, and methods for measuring stress intensity factors and energy release rates. Class-tested at Cornell, this book is designed for students, researchers and practitioners interested in understanding and contributing to a diverse and vital field of knowledge.

Alan Zehnder joined the faculty at Cornell University in 1988. Since then he has served in a number of leadership roles including Chair of the Department of Theoretical and Applied Mechanics, and Director of the Sibley School of Mechanical and Aerospace Engineering.  He teaches applied mechanics and his research topics focus on fracture, experimental mechanics and nonlinear dynamics of nanomechanical oscillators.  He was awarded the 1988 Rudolf Kingslake Medal and Prize for his Optical Engineering paper on optical methods in dynamic-fracture experimentation.

Autoren/Hrsg.

Zehnder, Alan T.

Inhaltsverzeichnis

1;Fracture Mechanics;4
1.1;Preface;6
1.1.1; References;6
1.2;Contents;8
1.3;Acronyms;12
2;Chapter 1: Introduction;16
2.1;1.1 Notable Fractures;16
2.2;1.2 Basic Fracture Mechanics Concepts;18
2.2.1;1.2.1 Small Scale Yielding Model;19
2.2.2;1.2.2 Fracture Criteria;19
2.3;1.3 Fracture Unit Conversions;20
2.4;1.4 Exercises;20
2.5; References;21
3;Chapter 2: Linear Elastic Stress Analysis of 2D Cracks;22
3.1;2.1 Notation;22
3.2;2.2 Introduction;22
3.3;2.3 Modes of Fracture;23
3.4;2.4 Mode III Field;23
3.4.1;2.4.1 Asymptotic Mode III Field;24
3.4.2;2.4.2 Full Field for Finite Crack in an In?nite Body;28
3.4.2.1;2.4.2.1 Complex Variables Formulation of Anti-Plane Shear;28
3.4.2.2;2.4.2.2 Solution to the Problem;29
3.5;2.5 Mode I and Mode II Fields;31
3.5.1;2.5.1 Review of Plane Stress and Plane Strain Field Equations;31
3.5.1.1;2.5.1.1 Plane Strain;31
3.5.1.2;2.5.1.2 Plane Stress;32
3.5.1.3;2.5.1.3 Stress Function;32
3.5.2;2.5.2 Asymptotic Mode I Field;32
3.5.2.1;2.5.2.1 Stress Field;32
3.5.2.2;2.5.2.2 Displacement Field;34
3.5.3;2.5.3 Asymptotic Mode II Field;36
3.6;2.6 Complex Variables Method for Mode I and Mode II Cracks;36
3.6.1;2.6.1 Westergaard Approach for Mode-I;37
3.6.2;2.6.2 Westergaard Approach for Mode-II;37
3.6.3;2.6.3 General Solution for Internal Crack with Applied Tractions;37
3.6.4;2.6.4 Full Stress Field for Mode-I Crack in an In?nite Plate;38
3.6.5;2.6.5 Stress Intensity Factor Under Remote Shear Loading;40
3.6.6;2.6.6 Stress Intensity Factors for Cracks Loaded with Tractions;41
3.6.7;2.6.7 Asymptotic Mode I Field Derived from Full Field Solution;41
3.6.8;2.6.8 Asymptotic Mode II Field Derived from Full Field Solution;43
3.6.9;2.6.9 Stress Intensity Factors for Semi-in?nite Crack;43
3.7;2.7 Some Comments;43
3.7.1;2.7.1 Three-Dimensional Cracks;44
3.8;2.8 Exercises;46
3.9; References;47
4;Chapter 3: Energy Flows in Elastic Fracture;48
4.1;3.1 Generalized Force and Displacement;48
4.1.1;3.1.1 Prescribed Loads;48
4.1.2;3.1.2 Prescribed Displacements;49
4.2;3.2 Elastic Strain Energy;50
4.3;3.3 Energy Release Rate, G;51
4.3.1;3.3.1 Prescribed Displacement;51
4.3.2;3.3.2 Prescribed Loads;52
4.3.3;3.3.3 General Loading;53
4.4;3.4 Interpretation of G from Load-Displacement Records;53
4.4.1;3.4.1 Multiple Specimen Method for Nonlinear Materials;53
4.4.2;3.4.2 Compliance Method for Linearly Elastic Materials;56
4.4.3;3.4.3 Applications of the Compliance Method;57
4.4.3.1;3.4.3.1 Determination of G in DCB Sample;57
4.4.3.2;3.4.3.2 Use of Compliance to Determine Crack Length;58
4.5;3.5 Crack Closure Integral for G;58
4.6;3.6 G in Terms of KI, KII, KIII for 2D Cracks That Grow Straight Ahead;62
4.6.1;3.6.1 Mode-III Loading;62
4.6.2;3.6.2 Mode I Loading;63
4.6.3;3.6.3 Mode II Loading;63
4.6.4;3.6.4 General Loading (2D Crack);63
4.7;3.7 Contour Integral for G (J-Integral);64
4.7.1;3.7.1 Two Dimensional Problems;64
4.7.2;3.7.2 Three-Dimensional Problems;66
4.7.3;3.7.3 Example Application of J-Integral;66
4.8;3.8 Exercises;67
4.9; References;69
5;Chapter 4: Criteria for Elastic Fracture;70
5.1;4.1 Introduction;70
5.2;4.2 Initiation Under Mode-I Loading;70
5.3;4.3 Crack Growth Stability and Resistance Curve;73
5.3.1;4.3.1 Loading by Compliant System;75
5.3.2;4.3.2 Resistance Curve;76
5.4;4.4 Mixed-Mode Fracture Initiation and Growth;78
5.4.1;4.4.1 Maximum Hoop Stress Theory;78
5.4.2;4.4.2 Maximum Energy Release Rate Criterion;80
5.4.3;4.4.3 Crack Path Stability Under Pure Mode-I Loading;81
5.4.4;4.4.4 Second Order Theory for Crack Kinking and Turning;84
5.5;4.5 Criteria for Fracture in Anisotropic Materials;85
5.6;4.6 Crack Growth Under Fatigue Loading;86
5.7;4.7 Stress Corrosion Cracking;89
5.8;4.8 Exercises;89
5.9; References;91
6;Chapter 5: Determining K and G;92
6.1;5.1 Analytical Methods;92
6.1.1;5.1.1 Elasticity Theory;92
6.1.1.1;5.1.1.1 Finite Crack in an In?nite Body;92
6.1.1.2;5.1.1.2 Semi-in?nite Crack in an In?nite Body;93
6.1.1.3;5.1.1.3 Array of Cracks Under Remote Loading;93
6.1.2;5.1.2 Energy and Compliance Methods;94
6.1.2.1;5.1.2.1 4-Point Bending Debond Specimen: Energy Method;94
6.2;5.2 Stress Intensity Handbooks and Software;95
6.3;5.3 Boundary Collocation;95
6.4;5.4 Computational Methods: A Primer;99
6.4.1;5.4.1 Stress and Displacement Correlation;99
6.4.1.1;5.4.1.1 Stress Correlation;99
6.4.1.2;5.4.1.2 Displacement Correlation;100
6.4.2;5.4.2 Global Energy and Compliance;100
6.4.3;5.4.3 Crack Closure Integrals;101
6.4.3.1;5.4.3.1 Nodal Release;101
6.4.3.2;5.4.3.2 Modi?ed Crack Closure Integral;102
6.4.4;5.4.4 Domain Integral;104
6.4.5;5.4.5 Crack Tip Singular Elements;105
6.4.6;5.4.6 Example Calculations;109
6.4.6.1;5.4.6.1 Displacement Correlation and Domain Integral with 1/4 Point Elements;110
6.4.6.2;5.4.6.2 Global Energy;110
6.4.6.3;5.4.6.3 Modi?ed Crack Closure Integral;111
6.5;5.5 Experimental Methods;112
6.5.1;5.5.1 Strain Gauge Method;113
6.5.2;5.5.2 Photoelasticity;115
6.5.3;5.5.3 Digital Image Correlation;116
6.5.4;5.5.4 Thermoelastic Method;118
6.6;5.6 Exercises;120
6.7; References;121
7;Chapter 6: Fracture Toughness Tests;123
7.1;6.1 Introduction;123
7.2;6.2 ASTM Standard Fracture Test;124
7.2.1;6.2.1 Test Samples;124
7.2.2;6.2.2 Equipment;126
7.2.3;6.2.3 Test Procedure and Data Reduction;126
7.3;6.3 Interlaminar Fracture Toughness Tests;127
7.3.1;6.3.1 The Double Cantilever Beam Test;127
7.3.1.1;6.3.1.1 Geometry and Test Procedure;127
7.3.1.2;6.3.1.2 Data Reduction Methods;128
7.3.1.3;6.3.1.3 Example Results;130
7.3.2;6.3.2 The End Notch Flexure Test;131
7.3.3;6.3.3 Single Leg Bending Test;132
7.4;6.4 Indentation Method;134
7.5;6.5 Chevron-Notch Method;136
7.5.1;6.5.1 KIVM Measurement;137
7.5.2;6.5.2 KIV Measurement;138
7.5.3;6.5.3 Work of Fracture Approach;139
7.6;6.6 Wedge Splitting Method;141
7.7;6.7 K-R Curve Determination;144
7.7.1;6.7.1 Specimens;144
7.7.2;6.7.2 Equipment;145
7.7.2.1;6.7.2.1 Optical Measurement of Crack Length;145
7.7.2.2;6.7.2.2 Compliance Method for Crack Length;145
7.7.2.3;6.7.2.3 Other Methods for Crack Length;145
7.7.3;6.7.3 Test Procedure and Data Reduction;147
7.7.3.1;6.7.3.1 By Measurement of Load and Crack Length;147
7.7.3.2;6.7.3.2 By Measurement of Load and Compliance;147
7.7.3.3;6.7.3.3 Indirect Approach Using Monotonic Load-Displacement Data;148
7.7.4;6.7.4 Sample K-R curve;148
7.8;6.8 Exercises;148
7.9; References;149
8;Chapter 7: Elastic Plastic Fracture: Crack Tip Fields;151
8.1;7.1 Introduction;151
8.2;7.2 Strip Yield (Dugdale) Model;151
8.2.1;7.2.1 Effective Crack Length Model;157
8.3;7.3 A Model for Small Scale Yielding;158
8.4;7.4 Introduction to Plasticity Theory;160
8.5;7.5 Anti-plane Shear Cracks in Elastic-Plastic Materials in SSY;164
8.5.1;7.5.1 Stationary Crack in Elastic-Perfectly Plastic Material;164
8.5.2;7.5.2 Stationary Crack in Power-Law Hardening Material;168
8.5.3;7.5.3 Steady State Growth in Elastic-Perfectly Plastic Material;170
8.5.4;7.5.4 Transient Crack Growth in Elastic-Perfectly Plastic Material;174
8.6;7.6 Mode-I Crack in Elastic-Plastic Materials;176
8.6.1;7.6.1 Stationary Crack in a Power Law Hardening Material;176
8.6.1.1;7.6.1.1 Deformation Theory (HRR Field);176
8.6.1.2;7.6.1.2 Incremental Theory;179
8.6.2;7.6.2 Slip Line Solutions for Rigid Plastic Material;179
8.6.2.1;7.6.2.1 Introduction to Plane Strain Slip Line Theory;179
8.6.2.2;7.6.2.2 Plane-Strain, Semi-in?nite Crack;181
8.6.2.3;7.6.2.3 Plane-Stress, Semi-in?nite Crack;183
8.6.3;7.6.3 Large Scale Yielding (LSY) Example;183
8.6.4;7.6.4 SSY Plastic Zone Size and Shape;184
8.6.5;7.6.5 CTOD-J Relationship;186
8.6.6;7.6.6 Growing Mode-I Crack;187
8.6.7;7.6.7 Three Dimensional Aspects;191
8.6.8;7.6.8 Effect of Finite Crack Tip Deformation on Stress Field;193
8.7;7.7 Exercises;195
8.8; References;196
9;Chapter 8: Elastic Plastic Fracture: Energy and Applications;198
9.1;8.1 Energy Flows;198
9.1.1;8.1.1 When Does G=J?;198
9.1.2;8.1.2 General Treatment of Crack Tip Contour Integrals;199
9.1.3;8.1.3 Crack Tip Energy Flux Integral;201
9.1.3.1;8.1.3.1 Global Path Independence for Steady State Crack Growth;201
9.1.3.2;8.1.3.2 Energy Flux as Gamma->0;202
9.1.3.3;8.1.3.3 Energy Flux for Gamma Outside Plastic Zone;202
9.1.3.4;8.1.3.4 Thermal Field Visualization of Energy Flow;204
9.2;8.2 Fracture Toughness Testing for Elastic-Plastic Materials;206
9.2.1;8.2.1 Samples and Equipment;206
9.2.2;8.2.2 Procedure and Data Reduction;207
9.2.2.1;8.2.2.1 Test Procedure;207
9.2.2.2;8.2.2.2 Data Reduction;208
9.2.2.3;8.2.2.3 Validation of Results;209
9.2.3;8.2.3 Examples of J-R Data;210
9.3;8.3 Calculating J and Other Ductile Fracture Parameters;210
9.3.1;8.3.1 Computational Methods;211
9.3.2;8.3.2 J Result Used in ASTM Standard JIC Test;213
9.3.2.1;8.3.2.1 Rigid Plastic Material;215
9.3.2.2;8.3.2.2 Elastic Material;215
9.3.2.3;8.3.2.3 Elastic-Plastic Material;215
9.3.3;8.3.3 Engineering Approach to Elastic-Plastic Fracture Analysis;215
9.3.3.1;8.3.3.1 Sample Calculation;217
9.4;8.4 Fracture Criteria and Prediction;218
9.4.1;8.4.1 J Controlled Crack Growth and Stability;218
9.4.2;8.4.2 J-Q Theory;220
9.4.3;8.4.3 Crack Tip Opening Displacement, Crack Tip Opening Angle;223
9.4.4;8.4.4 Cohesive Zone Model;226
9.4.4.1;8.4.4.1 Cohesive Zone Embedded in Elastic Material;228
9.4.4.2;8.4.4.2 Cohesive Zone Embedded in Elastic-Plastic Material;229
9.5; References;231
10;Index;233