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Probabilistic Mechanics of Quasibrittle Structures: Strength, Lifetime, and Size Effect [Kõva köide]

(University of Minnesota), (Northwestern University, Illinois)
  • Formaat: Hardback, 316 pages, kõrgus x laius x paksus: 254x178x19 mm, kaal: 790 g
  • Ilmumisaeg: 25-May-2017
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1107151708
  • ISBN-13: 9781107151703
Teised raamatud teemal:
Probabilistic Mechanics of Quasibrittle Structures: Strength, Lifetime, and Size EffectSuurem pilt
  • Formaat: Hardback, 316 pages, kõrgus x laius x paksus: 254x178x19 mm, kaal: 790 g
  • Ilmumisaeg: 25-May-2017
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1107151708
  • ISBN-13: 9781107151703
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781107151703.html
Märksõnad:
Quasibrittle (or brittle heterogeneous) materials are becoming increasingly important for modern engineering. They include concretes, rocks, fiber composites, tough ceramics, sea ice, bone, wood, stiff soils, rigid foams, glass, dental and biomaterials, as well as all brittle materials on the micro or nano scale. Their salient feature is that the fracture process zone size is non-negligible compared to the structural dimensions. This causes intricate energetic and statistical size effects and leads to size-dependent probability distribution of strength, transitional between Gaussian and Weibullian. The ensuing difficult challenges for safe design are vanquished in this book, which features a rigorous theory with detailed derivations yet no superfluous mathematical sophistication; extensive experimental verifications; and realistic approximations for design. A wide range of subjects is covered, including probabilistic fracture kinetics at nanoscale, multiscale transition, statistics of structural strength and lifetime, size effect, reliability indices, safety factors, and ramification to gate dielectrics breakdown.

Arvustused

'This new book provides a welcome addition to the very sparse collection of contemporary books that genuinely move the field of mechanics and materials forward. It does so by major steps of progress and consolidation, not just by incremental change. And its beneficial effects are not limited to mechanics and materials. Virtually all work is supported by experimental verification. There is an unusually large, detailed and illuminating summary of past work and references. Much of it is from the senior author's voluminous and well received contributions to the research literature. As is evident, this is a research oriented book. It is not for beginners. But for those interested in the topic and determined to diligently pursue it, then this book will prove to be an invaluable and indispensable resource. The authors seem to have been committed to work on some of the very hardest problems in existence and their progress is nothing short of remarkable.' Richard M. Christensen, Meccanica

Muu info

This book presents an experimentally validated probabilistic strength theory of structures made of concrete, composites, ceramics and other quasibrittle materials.
Foreword xiii
Preface xv
1 Introduction
1(21)
1.1 The Problem of Tail of Probability Distribution
1(2)
1.2 History in Brief
3(6)
1.2.1 Classical History
3(3)
1.2.2 Recent Developments
6(3)
1.3 Safety Specifications in Concrete Design Codes and Embedded Obstacles to Probabilistic Analysis
9(1)
1.4 Importance of Size Effect for Strength Statistics
10(2)
1.5 Power-Law Scaling in the Absence of Characteristic Length
12(2)
1.5.1 Nominal Strength of Structure and Size Effect
13(1)
1.6 Statistical and Deterministic Size Effects
14(1)
1.7 Simple Models for Deterministic Size Effects
14(5)
1.7.1 Type 1 Size Effect for Failures at Crack Initiation
15(1)
1.7.2 Type 2 Size Effect for Structures with Deep Cracks or Notches
16(3)
1.8 Probability Distributions of Strength of Ductile and Brittle Structures
19(3)
2 Review of Classical Statistical Theory of Structural Strength and Structural Safety, and of Statistics Fundamentals
22(13)
2.1 Weakest-Link Model
22(1)
2.2 Weibull Theory
23(1)
2.3 Scaling of Weibull Theory and Pure Statistical Size Effect
24(2)
2.4 Equivalent Number of Elements
26(1)
2.5 Stability Postulate of Extreme Value Statistics
27(1)
2.6 Distributions Ensuing from Stability Postulate
28(2)
2.7 Central Limit Theorem and Strength Distribution of Ductile Structures
30(2)
2.8 Failure Probability When Both the Strength and Load Are Random, and Freudenthal Integral
32(3)
3 Review of Fracture Mechanics and Deterministic Size Effect in Quasibrittle Structures
35(24)
3.1 Linear Elastic Fracture Mechanics
35(2)
3.2 Cohesive Crack Model
37(3)
3.3 Crack Band Model
40(4)
3.4 Nonlocal Damage Models and Lattice-Particle Model
44(2)
3.5 Overcoming Instability of Tests of Post-Peak Softening of Fiber-Polymer Composites
46(1)
3.6 Dimensional Analysis of Asymptotic Size Effects
47(3)
3.7 Second-Order Asymptotic Properties of Cohesive Crack or Crack Band Models
50(1)
3.8 Types of Size Effect Distinguished by Asymptotic Properties
51(1)
3.9 Derivation of Quasibrittle Deterministic Size Effect from Equivalent LEFM
52(4)
3.9.1 Type 2 Size Effect
53(1)
3.9.2 Type 1 Size Effect
54(2)
3.10 Nonlocal Weibull Theory for Mean Response
56(1)
3.11 Combined Energetic-Statistical Size Effect Law and Bridging of Type 1 and 2 Size Effects
57(2)
4 Failure Statistics of Nanoscale Structures
59(12)
4.1 Background of Modeling of Nanoscale Fracture
59(1)
4.2 Stress-Driven Fracture of Nanoscale Structures
60(5)
4.3 Probability Distribution of Fatigue Strength at Nanoscale
65(1)
4.4 Random Walk Aspect of Failure of Nanoscale Structures
66(5)
5 Nano--Macroscale Bridging of Probability Distributions of Static and Fatigue Strengths
71(29)
5.1 Chain Model
72(1)
5.2 Fiber-Bundle Model for Static Strength
73(15)
5.2.1 Brittle Bundle
74(5)
5.2.2 Plastic Bundle
79(2)
5.2.3 Softening Bundle with Linear Softening Behavior
81(3)
5.2.4 Bundle with General Softening Behavior and Nonlocal Interaction
84(4)
5.3 Fiber-Bundle Model for Fatigue Strength
88(4)
5.4 Hierarchical Model for Static Strength
92(5)
5.5 Hierarchical Model for Fatigue Strength
97(3)
6 Multiscale Modeling of Fracture Kinetics and Size Effect under Static and Cyclic Fatigue
100(19)
6.1 Previous Studies of Fracture Kinetics
100(2)
6.2 Fracture Kinetics at Nanoscale
102(1)
6.3 Multiscale Transition of Fracture Kinetics for Static Fatigue
103(3)
6.4 Size Effect on Fracture Kinetics under Static Fatigue
106(2)
6.5 Multiscale Transition of Fracture Kinetics under Cyclic Fatigue
108(4)
6.6 Size Effect on Fatigue Crack Growth Rate and Experimental Evidence
112(5)
6.7 Microplane Model for Size Effect on Fatigue Kinetics under General Loading
117(2)
7 Size Effect on Probability Distributions of Strength and Lifetime of Quasibrittle Structures
119(20)
7.1 Probability Distribution of Structural Strength
119(3)
7.2 Probability Distribution of Structural Lifetime
122(7)
7.2.1 Creep Lifetime
122(5)
7.2.2 Fatigue Lifetime
127(2)
7.3 Size Effect on Mean Structural Strength
129(4)
7.4 Size Effects on Mean Structural Lifetimes and Stress-Life Curves
133(3)
7.5 Effect of Temperature on Strength and Lifetime Distributions
136(3)
8 Computation of Probability Distributions of Structural Strength and Lifetime
139(22)
8.1 Nonlocal Boundary Layer Model for Strength and Lifetime Distributions
139(5)
8.2 Computation by Pseudo-random Placing of RVEs
144(2)
8.3 Approximate Closed-Form Expression for Strength and Lifetime Distributions
146(6)
8.4 Analysis of Strength Statistics of Beams under Flexural Loading
152(2)
8.5 Optimum Fits of Strength and Lifetime Histograms
154(7)
8.5.1 Optimum Fits of Strength Histograms
154(3)
8.5.2 Optimum Fits of Histograms of Creep Lifetime
157(2)
8.5.3 Optimum Fits of Histograms of Fatigue Lifetime
159(2)
9 Indirect Determination of Strength Statistics of Quasibrittle Structures
161(16)
9.1 Relation between Mean Size Effect Curve and Probability Distribution of RVE Strength
161(3)
9.2 Experimental Verification
164(5)
9.2.1 Description of Experiments
164(2)
9.2.2 Analysis of Test Results
166(3)
9.3 Determination of Large-Size Asymptotic Properties of the Size Effect Curve
169(1)
9.4 Comparison with the Histogram Testing Method
170(1)
9.5 Problems with the Three-Parameter Weibull Distribution of Strength
171(5)
9.5.1 Theoretical Argument
171(1)
9.5.2 Evidence from Histogram Testing
172(1)
9.5.3 Mean Size Effect Analysis
173(3)
9.6 Alternative Proof of Strength Distribution of an RVE Based on Stability Postulate and Atomistic Analysis
176(1)
10 Statistical Distribution and Size Effect on Residual Strength after Sustained Load
177(16)
10.1 Nanomechanics Based Relation between Monotonic Strength and Residual Strength of One RVE
178(2)
10.2 Analysis of Residual Strength Degradation for One RVE
180(1)
10.3 Probability Distribution of Residual Strength
181(2)
10.3.1 Formulation of Statistics of Residual Strength for One RVE
181(1)
10.3.2 Formulation of Residual Strength cdf of Geometrically Similar Structures of Different Sizes
182(1)
10.4 Comparison among Strength, Residual Strength, and Lifetime Distributions
183(1)
10.5 Experimental Validation
184(5)
10.5.1 Optimum Fits of Strength and Residual Strength Histograms of Borosilicate Glass
184(2)
10.5.2 Optimum Fits of Strength Histograms and Prediction of Lifetime and Mean Residual Strength for Unidirectional Glass/Epoxy Composites
186(2)
10.5.3 Prediction of Strength Degradation Curve for Soda-Lime Silicate Glasses
188(1)
10.6 Comparison of Size Effects on Mean Strength, Residual Strength, and Lifetime
189(4)
11 Size Effect on Reliability Indices and Safety Factors
193(17)
11.1 Size Effect on the Cornell Reliability Index
194(3)
11.2 Size Effect on the Hasofer-Lind Reliability Index
197(2)
11.3 Approximate Equation for Scaling of Safety Factors
199(3)
11.4 Analysis of Failure Statistics of the Malpasset Arch Dam
202(8)
11.4.1 Model Description
203(1)
11.4.2 Discussion of Cornell and Hasofer-Lind Indices
204(3)
11.4.3 Discussion of Central and Nominal Safety Factors
207(3)
12 Crack Length Effect on Scaling of Structural Strength and Type 1 to 2 Transition
210(8)
12.1 Type 1 Size Effect in Terms of Boundary Strain Gradient
211(2)
12.2 Universal Size Effect Law
213(2)
12.3 Verification of the Universal Size Effect Law by Comprehensive Fracture Tests
215(3)
13 Effect of Stress Singularities on Scaling of Structural Strength
218(21)
13.1 Strength Scaling of Structures with a V-Notch under Mode 1 Loading
218(5)
13.1.1 Energetic Scaling of Strength of Structures with Strong Stress Singularities
219(1)
13.1.2 Generalized Finite Weakest-Link Model
220(3)
13.2 Numerical Simulation of Mode I Fracture of Beams with a V-Notch
223(5)
13.2.1 Model Description
223(1)
13.2.2 Results and Discussion
224(4)
13.3 Scaling of Fracture of Bimaterial Hybrid Structures
228(6)
13.3.1 Energetic Scaling with Superposed Multiple Stress Singularities
229(3)
13.3.2 Finite Weakest-Link Model for Failure of Bimaterial Interface
232(2)
13.4 Numerical Analysis of Bimaterial Fracture
234(5)
13.4.1 Description of Analysis
234(2)
13.4.2 Results and Discussion
236(3)
14 Lifetime of High-k Gate Dielectrics and Analogy with Failure Statistics of Quasibrittle Structures
239(18)
14.1 Deviation of Lifetime Histograms of High-k Dielectrics from the Weibull Distribution
239(3)
14.2 Breakdown Probability
242(7)
14.2.1 Analogy with Strength of Quasibrittle Structures
242(2)
14.2.2 Application to Dielectric Breakdown
244(1)
14.2.3 Microscopic Statistical Models
245(3)
14.2.4 Breakdown Voltage Distribution
248(1)
14.3 Breakdown Lifetime under Constant Voltage
249(2)
14.3.1 Relation between Lifetime and Breakdown Voltage
249(1)
14.3.2 Microscopic Physics
250(1)
14.3.3 Probability Distribution of Breakdown Lifetime
251(1)
14.4 Breakdown Lifetime under Unipolar AC Voltage
251(1)
14.5 Experimental Validation
252(3)
14.5.1 Breakdown under Constant Gate Voltage Stress
252(3)
14.5.2 Breakdown under Unipolar AC Voltage Stress
255(1)
14.6 Size Effect on Mean Breakdown Lifetime
255(2)
Appendix A Power-Law Scaling of Boundary Value Problems 257(3)
Appendix B Proof of Transitional Size Effects of Types 1 and 2 by Dimensional Analysis and Asymptotic Matching up to Second Order 260(4)
Appendix C Proof of Small-Size Asymptotics of Cohesive Crack Model up to Second Order 264(5)
References 269(22)
Author Index 291(6)
Subject Index 297
Zdenek P. Bazant received his PhD from the Czechoslovak Academy of Sciences in 1963.He joined Northwestern University, Illinois in 1969, where he has been W. P. Murphy Professor since 1990 and simultaneously McCormick Institute Professor since 2002, and Director of the Center for Geomaterials (19817). He is a member of the US National Academy of Sciences, the US National Academy of Engineering, the American Academy of Arts and Sciences, and the Royal Society of London, as well as the Austrian Academy of Sciences, the Engineering Academy of the Czech Republic, the Italian National Academy, the Spanish Royal Academy of Engineering, the Istituto Lombardo, Milan, the Academia Europaea, London, and the European Academy of Sciences and Arts. Bazant is an Honorary Member of the American Society of Civil Engineers (ASCE), the American Society of Mechanical Engineers (ASME), the American Concrete Institute, and RILEM (International Union of Laboratories and Experts in Construction Materials, Systems and Structures), Paris. He has received the Austrian Cross of Honor for Science and Art, First Class, 7 honorary doctorates, ASME Timoshenko, Nadai and Warner Medals, the ASCE von Karman, Newmark, Biot, Mindlin and Croes Medals and Lifetime Achievement Award, the Society of Engineering Science William Prager Medal, and the RILEM L'Hermite Medal, among others. He is the author of Scaling of Structural Strength (2002), Inelastic Analysis of Structures (with Milan Zirásek, 2001), Fracture and Size Effect in Concrete and Other Quasibrittle Materials (with Jaime Planas, 1997), Stability of Structures (with Luigi Cedolin, 2010) and Concrete at High Temperatures (with Maurice F. Kaplan, 1996). In 2015, ASCE established ZP Baant Medal for Failure and Damage Prevention. He is one of the original top 100 ISI Highly Cited Scientists in Engineering (www.ISIhighlycited.com). Jia-Liang Le is currently Associate Professor of Civil, Environmental, and Geo-Engineering at the University of Minnesota. He obtained his Bachelor (First Class Honors) in civil engineering from the National University of Singapore (NUS) in 2003, a Master of Engineering from NUS in 2005, and a PhD in structural mechanics from Northwestern University, Illinois in 2010. He received the Undergraduate Faculty Award from the University of Minnesota, the Best Paper Award of the 48th US Rock Mechanics/Geomechanics Symposium, and the 2015 Young Investigator Award from the US Army Research Office. His research interests include fracture mechanics, probabilistic mechanics, scaling, and structural reliability. He has authored three book chapters and more than forty refereed journal articles.