Statistical Physics of Fracture, Breakdown, and Earthquake E-Book

Soumyajyoti Biswas

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Serie: Statistical Physics of Fracture and Breakdown
• Sprache: Englisch

Seitenzahl: 558

Veröffentlichungsjahr: 2015

Beschreibung

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.

Leseprobe

CONTENTS

Cover

Title page

Book Series: Statistical Physics of Fracture and Breakdown

Preface

Notations

1 Introduction

2 Mechanical and Fracture Properties of Solids

2.1 Mechanical Response in Materials

2.2 Ductile, Quasi-brittle, and Brittle Materials

2.3 Ductile and Brittle Fracture

3 Crystal Defects and Disorder in Lattice Models

3.1 Point Defects

3.2 Line Defects

3.3 Planar Defects

3.4 Lattice Defects: Percolation Theory

3.5 Summary

4 Nucleation and Extreme Statistics in Brittle Fracture

4.1 Stress Concentration Around Defect

4.2 Strength of Brittle Solids: Extreme Statistics

4.3 Extreme Statistics in Fiber Bundle Models of Brittle Fracture

4.4 Extreme Statistics in Percolating Lattice Model of Brittle Fracture

4.5 Molecular Dynamics Simulation of Brittle Fracture

4.6 Summary

5 Roughness of Fracture Surfaces

5.1 Roughness Properties in Fracture

5.2 Molecular Dynamics Simulation of Fractured Surface

5.3 Summary

6 Avalanche Dynamics in Fracture

6.1 Probing Failure with Acoustic Emissions

6.2 Dynamics of Fiber Bundle Model

6.3 Interpolations of Global and Local Load Sharing Fiber Bundle Models

6.4 Random Threshold Spring Model

6.5 Summary

7 Subcritical Failure of Heterogeneous Materials

7.1 Time of Failure Due to Creep

7.2 Dynamics of Strain Rate

7.3 Summary

8 Dynamics of Fracture Front

8.1 Driven Fluctuating Line

8.2 Fracture Front Propagation in Fiber Bundle Models

8.3 Hydraulic Fracture

8.4 Summary

9 Dislocation Dynamics and Ductile Fracture

9.1 Nonlinearity in Materials

9.2 Deformation by Slip

9.3 Slip by Dislocation Motion

9.4 Plastic Strain due to Dislocation Motion

9.5 When Does a Dislocation Move?

9.6 Ductile–Brittle Transition

9.7 Theoretical Work on Ductile–Brittle Transition

10 Electrical Breakdown Analogy of Fracture

10.1 Disordered Fuse Network

10.2 Numerical Simulations of Random Fuse Network

10.3 Dielectric Breakdown Problem

10.4 Summary

11 Earthquake as Failure Dynamics

11.1 Earthquake Statistics: Empirical Laws

11.2 Spring-block Models of Earthquakes

11.3 Cellular Automata Models of Earthquakes

11.4 Equivalence of Interface and Train Models

11.5 Summary

12 Overview and Outlook

A Percolation

A.1 Critical Exponent: General Examples

A.2 Percolation Transition

A.3 Renormalization Group (RG) Scheme

B Real-space RG for Rigidity Percolation

C Fiber Bundle Model

C.1 Universality Class of the Model

C.2 Brittle to Quasi-brittle Transition and Tricritical Point

D Quantum Breakdown

E Fractals

F Two-fractal Overlap Model

F.1 Renormalization Group Study: Continuum Limit

F.2 Discrete Limit

G Microscopic Theories of Friction

G.1 Frenkel-Kontorova Model

G.2 Two-chain Model

References

Index

End User License Agreement

List of Tables

Chapter 02

Table 2.1 Comparison of fracture properties of brittle and ductile materials.

Chapter 07

Table 10.1 Theoretical estimates

for the fuse failure exponent

.

Table 10.2 Theoretical estimates for the dielectric breakdown exponent

.

List of Illustrations

Chapter 01

Figure 1.1 Leonardo di ser Piero da Vinci (1452–1519): da Vinci was a diversely talented person and a leader of the Italian Renaissance movement. He displayed his talent in many areas of arts and science. Best known as a painter (for his famous Mona Lisa, The Last Supper, Virgin of the rocks to name a few), he was also a great engineering designer. However, apart from his well-known inventions and sketches, comparatively less known is his contribution to fracture mechanics. In his experiment titled “Testing the strengths of iron wires of various lengths,” he suspended a basket by an iron wire and slowly added sand to it from a pot hanging adjacent to the basket. The failure point of the wire was noted for its different lengths. In his own words (translated by Parsons, 1939): “The object of this test is to find the load an iron wire can carry. Attach an iron wire 2 braccia long to something which will firmly support it, then attach a basket or similar container to the wire and feed into the basket some fine sand through a small hole placed at the end of the hopper. A spring is fixed so that it will close the hole as soon as the wire breaks. The basket is not upset while falling, since it falls through a very short distance. The weight of sand and the location of the fracture of the wire are to be recorded. The test is repeated several times to check the results. Then a wire of 1/2 the previous length is tested and the additional weight it carries is recorded; then a wire of 1/4 length is tested and so forth, noting the ultimate strength and the location of the fracture.” As we will see in Section 4.2, because of the extreme nature of the breaking statistics, the strength of solids decrease with their volume typically as

.

Figure 1.2 Galileo Galilei (1564–1642): Galileo was an Italian physicist and astronomer who is called the “Father of Modern Science” to honor his many contributions to our present-day understanding of science. Particularly, he produced telescopic evidence of phases of Venus, the four largest satellite of Jupiter, sun spots, and also confirmed the earlier ideas of Copernicus and Kepler that the earth and other planets move around the sun. Because of his conflicting views with the church, he was put under house arrest for the last part of his life. There he wrote his famous book “Two new sciences,” where he described his works on the two sciences “kinematics” and “strength of matter.” There he had observed (see discussions in Section 4.2) the size effects of fracture and described how the natural sizes are limited by their own strengths. In his own words: “From what has already been demonstrated, you can plainly see the impossibility of increasing the size of structures to vast dimensions either in art or in nature; likewise the impossibility of building ships, palaces, or temples of enormous size in such a way that their oars, yards, beams, iron-bolts, and, in short, all their other parts will hold together; nor can nature produce trees of extraordinary size because the branches would break down under their own weight; so also it would be impossible to build up the bony structures of men, horses, or other animals so as to hold together and perform their normal functions if these animals were to be increased enormously in height; for this increase in height can be accomplished only by employing a material which is harder and stronger than usual, or by enlarging the size of the bones, thus changing their shape until the form and appearance of the animals suggest a monstrosity.” [From: http://ebooks.adelaide.edu.au/g/galileo/dialogues/chapter2.html]

Chapter 02

Figure 2.1 Stress–strain curve showing the variation of stress with strain.

Figure 2.2 Stress–strain curve for ductile and brittle materials.

Figure 2.3 Sir Nevill Francis Mott (1905–1996) won the Nobel Prize in Physics for his works on electronic structure of magnetic and disordered systems along with Phillip Anderson and J. H. Van Vleck in 1977. In addition to his excellent contribution to this field, he has also done significant research on fracture of solids and fragmentations (the figure shows the first page of his article on fragmentation). For these, he won also the A. A. Griffith Medal and Prize in 1973. The above excerpt is from Mott (1948).

Figure 2.4 (a) Cup-and-cone ductile fracture surface and (b) sharp brittle fracture surface.

Figure 2.5 Crack propagation in ductile (a) and brittle (b) materials.

Figure 2.6 Difference in crack tip for ductile and brittle materials.

Figure 2.7 Different stages of ductile fracture.

Chapter 03

Figure 3.1 Point defects. (a) Vacancy; (b) Interstitial; (c) Impurity atom.

Figure 3.2 Geometry and Burgers vector in edge dislocation.

Figure 3.3 Geometry and Burgers vector in screw dislocation.

Figure 3.4 Schematic diagram of grain boundaries and grains with different crystallographic orientations.

Figure 3.5 Schematic diagram of a microcrack formed due to breaking of atomic bonds.

Figure 3.6 Sample below and above the percolation threshold.

Figure 3.7 (a) Clusters in site percolation. (b) Clusters in bond percolation.

Chapter 04

Figure 4.1 The schematic diagram of a conductor having an elliptical defect.

Figure 4.2 Alan Arnold Griffith (1893–1963) was a mechanical engineer with a doctorate degree from Liverpool university in 1915. Among his many contributions such as developing the basis of jet engine, he is mostly remembered for his work on strength of brittle materials. He formulated the idea of fracture propagation from an energy balance principle, known as Griffith's criterion. It states that fracture propagates through a medium when the cost to form the surface area is compensated by the strain energy released. The work was published in Griffith (1921), the first page of which is shown in the figure with their kind permission.