Plasticity and Fracture (eBook)

Wolfgang Brocks (Autor)

eBook Download: PDF

2017 | 1st ed. 2018
XVIII, 173 Seiten
Springer International Publishing (Verlag)
978-3-319-62752-6 (ISBN)

Infos

This book is based on 40 years of research and teaching in the fields of fracture mechanics and plasticity. It will bring students and engineers from various disciplines up to date on key concepts that have become increasingly important in the design of safety-relevant engineering structures in general and in modern lightweight structures in the transportation industry in particular. Primarily intended for graduate students in the engineering sciences and practicing structural engineers, it employs a multidisciplinary approach that comprises theoretical concepts, numerical methods, and experimental techniques. In addition, it includes a wealth of analytical and numerical examples, used to illustrate the applications of the concepts discussed.

Inhalt

Preface 6
Contents 8
Nomenclature 11
1 Introduction 19
Abstract 19
References 20
2 Concepts of Fracture Mechanics 22
Abstract 22
2.1 The Energy Approach of Griffith 24
2.2 The Stress-Intensity Approach of Irwin 26
2.3 Determination of SIFs 30
2.3.1 Cracked Cylinders 32
2.3.2 Semi-elliptical Surface Crack 34
References 37
3 Phenomenological Theory of Time- and Rate-Independent Plasticity 39
Abstract 39
3.1 Uniaxial Tensile Test 40
3.2 Generalisation to Triaxial Stress States 41
3.3 Isotropic Yielding 45
3.3.1 The Yield Condition of Tresca 46
3.3.2 The Theory of Von Mises, Prandtl and Reuß 48
3.3.3 Example: Pressure Vessel 49
3.4 Deformation Theory of Plasticity 51
References 53
4 Extension of LEFM for Small-Scale Yielding 55
Abstract 55
4.1 The Equivalent Elastic Crack (Mode I) 55
4.2 Crack Tip Opening Displacement (CTOD) 58
4.3 Shape of the Plastic Zone 58
4.4 The Models of Barenblatt and Dugdale 61
References 64
5 Elastic-Plastic Fracture Mechanics 65
Abstract 65
5.1 The J-Integral 65
5.1.1 Definition and Path Independence 65
5.1.2 J as Energy Release Rate 70
5.1.3 The Three-Dimensional J 73
5.1.4 Extensions for Multi-phase Materials, Body Forces, Surface Tractions and Thermal Loading 75
5.1.5 Resistance Curves Against Ductile Crack Extension 77
5.1.6 Application and Validity of Resistance Curves 79
5.2 Asymptotic Solution of Stress and Strain Fields in Mode I 81
5.2.1 The Boundary Value Problem 81
5.2.2 Singular Crack Tip Fields 82
5.2.3 J-Integral as Crack-Tip Intensity 85
5.2.4 Crack Tip Opening Displacement 86
5.2.5 Validity of the HRR Solution 86
5.3 Extended and Alternative Concepts 88
5.3.1 Dissipation Rate 88
5.3.2 J-Integral for Cyclic Plasticity 90
5.3.3 CTOD and CTOA 92
5.3.4 Assessment Procedures 93
References 96
6 Solutions for Fully Plastic Conditions 101
Abstract 101
6.1 Plastic Collapse and Limit Load Theorems 102
6.1.1 Drucker’s Postulates of Stability 102
6.1.2 Plastic Limit State (Collapse): Definitions and Theorems 104
6.2 Example of a Statically Admissible Stress Field 108
6.3 Slip Line Theory 113
6.3.1 Basic Equations for Plane-Strain Conditions 113
6.3.2 Cauchy’s Initial Value Problem 114
6.3.3 The Characteristics of Plane Strain Flow 116
6.3.4 Generation of Slip-Line Fields—Boundary Conditions 118
6.3.5 Examples of Notched Structures 121
References 123
7 Determination of Fracture Parameters 125
Abstract 125
7.1 Numerical Methods: Crack Driving Forces 125
7.1.1 FE Meshes for Structures with Cracks 126
7.1.2 Energy Release Rate and J-Integral 128
7.1.3 Stress Intensity Factors 129
7.1.4 Path (Domain) Dependence of J in Incremental Plasticity 132
7.2 Test Methods and Standards: Material Resistance 135
7.2.1 Standard Terminology 135
7.2.2 Linear-Elastic Plane-Strain Fracture Toughness 137
7.2.3 Measurement of Fracture Toughness in EPFM 138
7.2.4 Crack Extension in Thin Structures 139
References 140
8 Damage and Fracture 143
Abstract 143
8.1 Phenomena and Models 144
8.2 Local and Micromechanical Approaches 146
8.2.1 Brittle Fracture and Cleavage 146
8.2.2 Ductile Damage und Fracture 150
8.2.3 The Concept of Representative Volume Elements 152
8.3 Porous Metal Plasticity 154
8.3.1 Gurson Model 154
8.3.2 Rousselier Model 158
8.3.3 Length Scales and Local Instability 159
8.4 Continuum Damage Mechanics 159
8.5 Parameter Identification 162
References 164
9 The Cohesive Model 167
Abstract 167
9.1 The Cohesive Zone 168
9.2 Cohesive Laws 170
9.2.1 Shapes of Traction-Separation Laws 170
9.2.2 Significance of Initial Compliance 173
9.2.3 Unloading and Reloading 174
9.2.4 Mixed Mode 175
9.2.5 Cohesive Laws and Damage 177
9.2.6 Triaxiality Dependence of Cohesive Parameters 178
9.3 Applications 179
9.3.1 Crack Extension in Thin Panels and Shells 180
9.3.2 Crack Path Branching 181
9.4 Advancements 182
References 184
Index 187

Produkt-Details

• Erscheint lt. Verlag: 16.8.2017
• Reihe/Serie: Solid Mechanics and Its Applications
• Reihe/Serie: Solid Mechanics and Its Applications
• Zusatzinfo: XVIII, 173 p. 75 illus.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Cohesive model • damage mechanics • Elasto-plastic fracture mechanics • inelastic deformations • Numerical simulations
• ISBN-10: 3-319-62752-X / 331962752X
• ISBN-13: 978-3-319-62752-6 / 9783319627526