The Fiber Bundle Model

Modeling Failure in Materials
1. Auflage 2015
ISBN: 978-3-527-41214-3
Verlag: WILEY-VCH

Buch, Englisch, 236 Seiten, Format (B × H): 175 mm x 252 mm, Gewicht: 712 g

Reihe: Statistical Physics of Fracture and Breakdown

Gathering research from physics, mechanical engineering, and statistics in a single resource for the first time, this text presents the background to the model, its theoretical basis, and applications ranging from materials science to earth science.

The authors start by explaining why disorder is important for fracture and then go on to introduce the fiber bundle model, backed by various different applications. Appendices present the necessary mathematical, computational and statistical background required.

The structure of the book allows the reader to skip some material that is too specialized, making this topic accessible to the engineering, mechanics and materials science communities, in addition to providing further reading for graduate students in statistical physics.

Autoren/Hrsg.

Hansen, Alex

Hemmer, Per Christian

Pradhan, Srutarshi

Fachgebiete

• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Werkstoffkunde, Materialwissenschaft: Forschungsmethoden

Inhaltsverzeichnis

Preface XIII

1 The Fiber Bundle Model 1

1.1 Rivets VersusWelding 1

1.1.1 What Are Models Good For? 3

1.2 Fracture and Failure: A Short Summary 4

1.3 The Fiber Bundle Model in Statistics 5

1.4 The Fiber Bundle Model in Physics 6

1.5 The Fiber Bundle Model in Materials Science 8

1.6 Structure of the Book 8

2 Average Properties 11

2.1 Equal Load Sharing versus Local Load Sharing 11

2.2 Strain-Controlled versus Force-Controlled Experiments 12

2.3 The Critical Strength 16

2.4 Fiber Mixtures 22

2.5 Non-Hookean Forces 24

2.5.1 Fibers with Random Slacks 24

2.5.2 Elastic–Plastic Model 25

3 Fluctuation Effects 27

3.1 Range of Force Fluctuations 28

3.2 The Maximum Bundle Strength 30

3.3 Avalanches 32

3.3.1 The Burst Distribution 33

3.3.1.1 The Forward Condition 35

3.3.1.2 The Backward Condition 36

3.3.1.3 Total Number and Average Size of Bursts 37

3.3.2 Asymptotic Burst Distribution: 5/2 Law 40

3.3.2.1 Asymptotic Burst Distribution: Nongeneric Cases 42

3.3.3 Inclusive Bursts 45

3.3.4 Forward Bursts 47

3.3.5 Avalanches as RandomWalks 49

3.3.5.1 The Exact RandomWalk 49

3.3.5.2 Asymptotic Burst Distribution via RandomWalks 51

3.3.6 Energy Release 53

3.3.6.1 High-Energy Asymptotics 53

3.3.6.2 Low-Energy Behavior 55

3.3.7 Failure Avalanches for Stepwise Load Increase 57

3.3.7.1 UniformThreshold Distribution 58

3.3.7.2 General Threshold Distribution 59

4 Local and Intermediate Load Sharing 63

4.1 The Local-Load-Sharing Model 64

4.1.1 Redistribution of Forces 66

4.1.2 Determining the Failure Sequence 67

4.1.3 Bundle Strength 68

4.1.4 Failure of First and Second Fibers 69

4.1.4.1 Other Threshold Distributions 75

4.1.4.2 Localization 76

4.1.5 Hole Size Distribution 78

4.1.5.1 De

Über Autor(innen)

Alex Hansen earned his Ph.D. from Cornell University in 1986. He was then Joliot-Curie fellow at the Ecole Normale Supérieure in Paris, followed by postdoctoral positions at the Universities of Cologne and Oslo. In 1992, Hansen became a CNRS scientist at the University of Rennes 1 in France. From 1994, he has been professor of physics at the Norwegian University of Science and Technology in Trondheim, Norway. Hansen is member of the Norwegian Academy of Science and Letters, the Royal Norwegian Society of Science and Letters and the

Norwegian Academy of Technical Sciences. He is Dr. honoris causa at the University of Rennes 1. Hansen chairs at present the Commission on Computational Physics of the International Union of Pure and Applied Physics, where he is also a vice president.

Per Christian Hemmer earned his doctorate from the Norwegian Institute of Technology in 1959. He was then NORDITA fellow in Copenhagen, followed by a postdoctoral position at The Rockefeller Institute, New York. In 1959 he was appointed professor of theoretical physics at the University of Trondheim, now the Norwegian University of Science and Technology. He has been dean of the faculty for general sciences at the university. Hemmer has been secretary of the Commission on Statistical Physics of the International Union of Pure and Applied Physics, as well as a vice president of the union. He is member of the Royal Norwegian Society of Science and Letters, the Norwegian Academy of Science and Letters, and the Norwegian Academy of Technical Sciences.

Srutarshi Pradhan completed his Ph.D. work at Saha Institute of Nuclear Physics, Kolkata, India in 2004 and earned his doctorate from Jadavpur University, Kolkata, India. He was then a postdoctoral fellow at the Norwegian University of Science and Technology for 4 years (2004-2007) with a fellowship from the Norwegian Research Council. In 2008 he was appointed as a research scientist at SINTEF Petroleum Research, Trondheim, Norway. Pradhan has been promoted to senior scientist position at SINTEF Petroleum Research in 2012.