Statistical Physics of Fracture and Breakdown in Disordered Systems

by Chakrabarti, Bikas K.; Benguigui, L. Gilles

• ISBN13: 9780198520566
• ISBN10: 0198520565
• Format: Hardcover
• Copyright: 1997-12-04
• Publisher: Clarendon Press

Summary

Under extreme conditions the mechanical or electrical properties of solids tend to destabilize, leading to failure or breakdown. These instabilities often nucleate or spread from disorders in the structure of the solid. This book by two experts in the field investigates current techniques for modeling these failure and breakdown processes. It illustrates the basic modeling principles through a series of computer and laboratory simulations and 'table top' experiments. The book centers on three important case studies: electrical failures like fuse and dielectric breakdown; mechanical fractures; and earthquakes, which exhibit dynamic failure. The material will interest all graduate students and researchers studying disordered systems, whether their focus is the mechanical failure of solids, the electrical breakdown of conductors, or earthquake mechanics.

Table of Contents

1 Introduction	1	(29)
1.1 Breakdown of disordered solids and dynamic frictional failures	1	(3)
1.2 A brief introduction to some theoretical ideas and models	4	(26)
1.2.1 A brief summary of percolation theory	5	(15)
1.2.2 Stress concentration and statistics of extremes	20	(7)
1.2.3 Self-organised criticality and sandpile models	27	(3)
2 Electrical breakdown in disordered solids	30	(50)
2.1 Introduction	30	(3)
2.2 The fuse problem	33	(28)
2.2.1 Qualitative analysis	33	(3)
2.2.2 Quantitative analysis: most probable failure current and distribution	36	(9)
2.2.3 Numerical simulations and experimental results	45	(3)
2.2.4 Other kinds of disorder: distribution of the failure threshold	48	(4)
2.2.5 The shortest path and the electromigration fuse model	52	(4)
2.2.6 Effects of temperature, AC fields and nonlinearity	56	(5)
2.3 The dielectric breakdown problem	61	(17)
2.3.1 Qualitative analysis	61	(1)
2.3.2 Duality in two dimensions	61	(3)
2.3.3 Lattice percolation	64	(3)
2.3.4 Continuum percolation	67	(1)
2.3.5 The shortest path	67	(1)
2.3.6 Dielectric breakdown with tunnelling bonds	68	(2)
2.3.7 Numerical simulations and experimental results	70	(8)
2.4 Conclusions	78	(2)
3 Fracture strength of disordered solids	80	(48)
3.1 Introduction	80	(2)
3.2 Fracture strength of a perfect solid containing a single crack	82	(9)
3.2.1 Stress concentration	84	(2)
3.2.2 Griffith's energy balance concept	86	(2)
3.2.3 Experimental and computer simulational verifications of Griffith's law	88	(3)
3.3 Fracture strength of brittle solids with small disorder and rough cracks	91	(4)
3.3.1 Griffith's law for fractal crack surfaces	92	(2)
3.3.2 Experimental observations	94	(1)
3.4 Fracture strength of strongly disordered solids	95	(11)
3.4.1 Estimates for the fracture exponent and comparisons with experiment	96	(9)
3.4.2 Brittleness and plastic yield	105	(1)
3.5 Fracture strength distribution	106	(7)
3.5.1 Extreme statistics and strength distribution	106	(3)
3.5.2 Comparisons with computer simulational and experimental results	109	(4)
3.6 Fracture strength scaling in systems with random breaking thresholds	113	(4)
3.6.1 Models with random spring constants	114	(1)
3.6.2 Models with random breaking strengths	114	(3)
3.7 Dynamics of fracture	117	(9)
3.7.1 Fracture propagation velocity	117	(2)
3.7.2 Large propagation velocity and morphology of fractured surfaces	119	(2)
3.7.3 Elastic precursor effects of complete fracture	121	(5)
3.8 Dynamic annealed impurity and self-organised criticality in fracture	126	(1)
3.9 Summary and conclusions	127	(1)
4 Earthquakes in model systems	128	(22)
4.1 Introduction	128	(2)
4.2 Burridge-Knopoff stick-slip model of earthquakes	130	(10)
4.2.1 Laboratory simulation model	130	(3)
4.2.2 Computer simulation model	133	(2)
4.2.3 Numerical studies and results	135	(5)
4.3 Self-organised criticality and cellular automata models of earthquakes	140	(3)
4.4 Earthquake fault patterns and percolation model of earthquakes	143	(2)
4.5 Precursors of self-organised criticality and earthquakes	145	(4)
4.5.1 Pulse response of the sandpile model	146	(2)
4.5.2 Response of the Burridge-Knopoff model to localised periodic pulses	148	(1)
4.6 Summary and conclusions	149	(1)
References	150	(9)
Index	159