Statistical Physics of Fracture, Breakdown, and Earthquake

In this book, the authors bring together basic ideas from fracture mechanics and statistical physics, classical theories, simulation and experimental results to make the statistical physics aspects of fracture more accessible.
They explain fracture-like phenomena, highlighting the role of disorder and heterogeneity from a statistical physical viewpoint. The role of defects is discussed in brittle and ductile fracture, ductile to brittle transition, fracture dynamics, failure processes with tension as well as compression: experiments, failure of electrical networks, self-organized critical models of earthquake and their extensions to capture the physics of earthquake dynamics. The text also includes a discussion of dynamical transitions in fracture propagation in theory and experiments, as well as an outline of analytical results in fiber bundle model dynamics
With its wide scope, in addition to the statistical physics community, the material here is equally accessible to engineers, earth scientists, mechanical engineers, and material scientists. It also serves as a textbook for graduate students and researchers in physics.

Auteur

Soumyajyoti Biswas got his PhD in 2015 for works carried out at Saha Institute of Nuclear Physics. He has been a postdoctoral fellow at the Institute of Mathematical Sciences, Chennai until March 2015. Presently he is a postdoctoral fellow at the Earthquake Research Institute, University of Tokyo.

Purusattam Ray is professor in Physics at the Institute of Mathematical Sciences (IMSC), Chennai and an adjunct professor of Homi Bhabha National Institute (HBNI), Mumbai. He received his Ph.D. from Calcutta University in 1989. He was then SERC research fellow at the University of Manchester, England and subsequently Max Planck fellow at the MPI for Polymer Studies in Mainz and at the University of Mainz, Germany. He has made major contributions in the study of statistical physics of fracture. He annually organizes the International workshop on fracture and breakdown processes.

Bikas K. Chakrabarti is a senior professor of theoretical condensed matter physics at the Saha Institute of Nuclear Physics (SINP), Kolkata, and a visiting professor of economics at the Indian Statistical Institute, Kolkata, India. He received his doctorate in physics from Calcutta University in 1979 (for research at SINP). Following postdoctoral positions at Oxford University and Cologne University, he joined SINP in 1983. His main research interests include physics of fracture, quantum glasses, etc., and the interdisciplinary sciences of optimization, brain modeling, and econophysics. He has written several books and reviews on these topics.

Contenu

Series Editors' Preface XIII

Preface XV

Notations XVII

1 Introduction 1

2 Mechanical and Fracture Properties of Solids 7

2.1 Mechanical Response in Materials 8

2.1.1 Elastic and Plastic Regions 8

2.1.2 Linear Elastic Region 9

2.1.3 Nonlinear Plastic Region 10

2.2 Ductile, Quasi-brittle, and Brittle Materials 11

2.3 Ductile and Brittle Fracture 11

2.3.1 Macroscopic Features of Ductile and Brittle Fractures 12

2.3.2 Microscopic Features of Ductile and Brittle Fractures 14

3 Crystal Defects and Disorder in LatticeModels 17

3.1 Point Defects 17

3.2 Line Defects 18

3.3 Planar Defects 20

3.4 Lattice Defects: PercolationTheory 22

3.5 Summary 25

4 Nucleation and Extreme Statistics in Brittle Fracture 27

4.1 Stress Concentration Around Defect 27

4.1.1 Griffith'sTheory of Crack Nucleation in Brittle Fracture 30

4.2 Strength of Brittle Solids: Extreme Statistics 32

4.2.1 Weibull and Gumbel Statistics 32

4.3 Extreme Statistics in Fiber Bundle Models of Brittle Fracture 34

4.3.1 Fiber Bundle Model 34

4.3.1.1 Strength of the Local Load Sharing Fiber Bundles 35

4.3.1.2 Crossover from Extreme to Self-averaging Statistics in the Model 35

4.4 Extreme Statistics in Percolating Lattice Model of Brittle Fracture 37

4.5 Molecular Dynamics Simulation of Brittle Fracture 39

4.5.1 Comparisons with Griffith's Theory 39

4.5.2 Simulation of Highly Disordered Solids 41

4.6 Summary 42

5 Roughness of Fracture Surfaces 45

5.1 Roughness Properties in Fracture 45

5.1.1 Self-affine Scaling of Fractured Surfaces 46

5.1.2 Out-of-plane Fracture Roughness 47

5.1.3 Distribution of Roughness: Mono- and Multi-affinity 49

5.1.3.1 Nonuniversal Cases 50

5.1.3.2 Anisotropic Scaling 54

5.1.4 In-plane Roughness of Fracture Surfaces 56

5.1.4.1 Waiting Time Distributions in Crack Propagation 60

5.1.5 Effect of Probe Size 62

5.1.6 Effect of Spatial Correlation and Anisotropy 65

5.2 Molecular Dynamics Simulation of Fractured Surface 66

5.3 Summary 68

6 Avalanche Dynamics in Fracture 69

6.1 Probing Failure with Acoustic Emissions 70

6.2 Dynamics of Fiber Bundle Model 74

6.2.1 Dynamics Around Critical Load 77

6.2.2 Dynamics at Critical Load 81

6.2.3 Avalanche Statistics of Energy Emission 81

6.2.4 Precursors of Global Failure in the Model 82

6.2.5 Burst Distribution: Crossover Behavior 84

6.2.6 Abrupt Rupture and Tricritical Point 85

6.2.7 Disorder in Elastic Modulus 87

6.3 Interpolations of Global and Local Load Sharing Fiber Bundle Models 88

6.3.1 Power-law Load Sharing 89

6.3.2 Mixed-mode Load Sharing 90

6.3.3 Heterogeneous Load Sharing 92

6.3.3.1 Dependence on Loading Process 93

6.3.3.2 Results in One Dimension 94

6.3.3.3 Results in Two Dimensions 96

6.3.3.4 Comparison with Mixed Load Sharing Model 101

6.4 RandomThreshold Spring Model 101

6.5 Summary 107

7 Subcritical Failure of Heterogeneous Materials 111

7.1 Time of Failure Due to Creep 111

7.1.1 Fluctuating Load 112

7.1.2 Failure Due to Fatigue in Fiber Bundles 119

7.1.3 Creep Rupture Propagation in Rheological Fiber Bundles 122

7.1.3.1 Modification for Local Load Sharing Scheme 126

7.2 Dynamics of Strain Rate 129

7.3 Summary 134

8 Dynamics of Fracture Front 135

8.1 Driven Fluctuating Line 135

8.1.1 Variation of Universality Class 140

8.1.2 Depinning with Constant Volume 142

8.1.3 Infinite-range Elastic Force with Local Fluctuations 144 8.2 Fracture Front Propagation in ...