Brocks Plasticity and Fracture

1. Auflage 2018
ISBN: 978-3-319-62752-6
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 244, 189 Seiten

Reihe: Solid Mechanics and Its Applications

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.

Autoren/Hrsg.

Brocks, Wolfgang

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Nomenclature;11
4;1 Introduction;19
4.1;Abstract;19
4.2;References;20
5;2 Concepts of Fracture Mechanics;22
5.1;Abstract;22
5.2;2.1 The Energy Approach of Griffith;24
5.3;2.2 The Stress-Intensity Approach of Irwin;26
5.4;2.3 Determination of SIFs;30
5.4.1;2.3.1 Cracked Cylinders;32
5.4.2;2.3.2 Semi-elliptical Surface Crack;34
5.5;References;37
6;3 Phenomenological Theory of Time- and Rate-Independent Plasticity;39
6.1;Abstract;39
6.2;3.1 Uniaxial Tensile Test;40
6.3;3.2 Generalisation to Triaxial Stress States;41
6.4;3.3 Isotropic Yielding;45
6.4.1;3.3.1 The Yield Condition of Tresca;46
6.4.2;3.3.2 The Theory of Von Mises, Prandtl and Reuß;48
6.4.3;3.3.3 Example: Pressure Vessel;49
6.5;3.4 Deformation Theory of Plasticity;51
6.6;References;53
7;4 Extension of LEFM for Small-Scale Yielding;55
7.1;Abstract;55
7.2;4.1 The Equivalent Elastic Crack (Mode I);55
7.3;4.2 Crack Tip Opening Displacement (CTOD);58
7.4;4.3 Shape of the Plastic Zone;58
7.5;4.4 The Models of Barenblatt and Dugdale;61
7.6;References;64
8;5 Elastic-Plastic Fracture Mechanics;65
8.1;Abstract;65
8.2;5.1 The J-Integral;65
8.2.1;5.1.1 Definition and Path Independence;65
8.2.2;5.1.2 J as Energy Release Rate;70
8.2.3;5.1.3 The Three-Dimensional J;73
8.2.4;5.1.4 Extensions for Multi-phase Materials, Body Forces, Surface Tractions and Thermal Loading;75
8.2.5;5.1.5 Resistance Curves Against Ductile Crack Extension;77
8.2.6;5.1.6 Application and Validity of Resistance Curves;79
8.3;5.2 Asymptotic Solution of Stress and Strain Fields in Mode I;81
8.3.1;5.2.1 The Boundary Value Problem;81
8.3.2;5.2.2 Singular Crack Tip Fields;82
8.3.3;5.2.3 J-Integral as Crack-Tip Intensity;85
8.3.4;5.2.4 Crack Tip Opening Displacement;86
8.3.5;5.2.5 Validity of the HRR Solution;86
8.4;5.3 Extended and Alternative Concepts;88
8.4.1;5.3.1 Dissipation Rate;88
8.4.2;5.3.2 J-Integral for Cyclic Plasticity;90
8.4.3;5.3.3 CTOD and CTOA;92
8.4.4;5.3.4 Assessment Procedures;93
8.5;References;96
9;6 Solutions for Fully Plastic Conditions;101
9.1;Abstract;101
9.2;6.1 Plastic Collapse and Limit Load Theorems;102
9.2.1;6.1.1 Drucker’s Postulates of Stability;102
9.2.2;6.1.2 Plastic Limit State (Collapse): Definitions and Theorems;104
9.3;6.2 Example of a Statically Admissible Stress Field;108
9.4;6.3 Slip Line Theory;113
9.4.1;6.3.1 Basic Equations for Plane-Strain Conditions;113
9.4.2;6.3.2 Cauchy’s Initial Value Problem;114
9.4.3;6.3.3 The Characteristics of Plane Strain Flow;116
9.4.4;6.3.4 Generation of Slip-Line Fields—Boundary Conditions;118
9.4.5;6.3.5 Examples of Notched Structures;121
9.5;References;123
10;7 Determination of Fracture Parameters;125
10.1;Abstract;125
10.2;7.1 Numerical Methods: Crack Driving Forces;125
10.2.1;7.1.1 FE Meshes for Structures with Cracks;126
10.2.2;7.1.2 Energy Release Rate and J-Integral;128
10.2.3;7.1.3 Stress Intensity Factors;129
10.2.4;7.1.4 Path (Domain) Dependence of J in Incremental Plasticity;132
10.3;7.2 Test Methods and Standards: Material Resistance;135
10.3.1;7.2.1 Standard Terminology;135
10.3.2;7.2.2 Linear-Elastic Plane-Strain Fracture Toughness;137
10.3.3;7.2.3 Measurement of Fracture Toughness in EPFM;138
10.3.4;7.2.4 Crack Extension in Thin Structures;139
10.4;References;140
11;8 Damage and Fracture;143
11.1;Abstract;143
11.2;8.1 Phenomena and Models;144
11.3;8.2 Local and Micromechanical Approaches;146
11.3.1;8.2.1 Brittle Fracture and Cleavage;146
11.3.2;8.2.2 Ductile Damage und Fracture;150
11.3.3;8.2.3 The Concept of Representative Volume Elements;152
11.4;8.3 Porous Metal Plasticity;154
11.4.1;8.3.1 Gurson Model;154
11.4.2;8.3.2 Rousselier Model;158
11.4.3;8.3.3 Length Scales and Local Instability;159
11.5;8.4 Continuum Damage Mechanics;159
11.6;8.5 Parameter Identification;162
11.7;References;164
12;9 The Cohesive Model;167
12.1;Abstract;167
12.2;9.1 The Cohesive Zone;168
12.3;9.2 Cohesive Laws;170
12.3.1;9.2.1 Shapes of Traction-Separation Laws;170
12.3.2;9.2.2 Significance of Initial Compliance;173
12.3.3;9.2.3 Unloading and Reloading;174
12.3.4;9.2.4 Mixed Mode;175
12.3.5;9.2.5 Cohesive Laws and Damage;177
12.3.6;9.2.6 Triaxiality Dependence of Cohesive Parameters;178
12.4;9.3 Applications;179
12.4.1;9.3.1 Crack Extension in Thin Panels and Shells;180
12.4.2;9.3.2 Crack Path Branching;181
12.5;9.4 Advancements;182
12.6;References;184
13;Index;187