APPLIED FRACTURE MECHANICS doc

APPLIED FRACTURE

MECHANICS

Edited by Alexander Belov

Applied Fracture Mechanics

http://dx.doi.org/10.5772/2823

Edited by Alexander Belov

Contributors

A. Yu. Belov, Lucas Máximo Alves, Luiz Alkimin de Lacerda, Karl-Johan Söderholm, Ilya I.

Kudish, Kunio Asai, Sylwester Kłysz, Andrzej Leski, Narciso Acuña-González, Jorge A. González￾Sánchez, Luis R. Dzib-Pérez, Aarón Rivas-Menchi, Dino A. Araneo, Francesco D’Auria, Ľubomír

Gajdoš, Martin Šperl, Mahmood Sameezadeh, Hassan Farhangi, A. Guedri, Y. Djebbar, Moe.

Khaleel, A. Zeghloul, Ruslizam Daud, Ahmad Kamal Ariffin, Shahrum Abdullah, Al Emran Ismail

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First published December, 2012

Printed in Croatia

A free online edition of this book is available at www.intechopen.com

Additional hard copies can be obtained from [email protected]

Applied Fracture Mechanics, Edited by Alexander Belov

p. cm.

ISBN 978-953-51-0897-9

Contents

Preface IX

Section 1 Computational Methods of Fracture Mechanics 1

Chapter 1 Higher Order Weight Functions

in Fracture Mechanics of Multimaterials 3

A. Yu. Belov

Chapter 2 Foundations of Measurement Fractal

Theory for the Fracture Mechanics 19

Lucas Máximo Alves

Chapter 3 Fractal Fracture Mechanics

Applied to Materials Engineering 67

Lucas Máximo Alves and Luiz Alkimin de Lacerda

Section 2 Fracture of Biological Tissues 107

Chapter 4 Fracture of Dental Materials 109

Karl-Johan Söderholm

Section 3 Fracture Mechanics Based Models of Fatigue 143

Chapter 5 Fracture Mechanics Based Models of Structural

and Contact Fatigue 145

Ilya I. Kudish

Chapter 6 Fracture Mechanics Analysis of Fretting Fatigue

Considering Small Crack Effects, Mixed Mode,

and Mean Stress Effect 177

Kunio Asai

Chapter 7 Good Practice for Fatigue Crack

Growth Curves Description 197

Sylwester Kłysz and Andrzej Leski

VI Contents

Chapter 8 Early Corrosion Fatigue Damage on Stainless Steels Exposed

to Tropical Seawater: A Contribution from Sensitive

Electrochemical Techniques 229

Narciso Acuña-González, Jorge A. González-Sánchez,

Luis R. Dzib-Pérez and Aarón Rivas-Menchi

Section 4 Fracture Mechanics Aspects of Power Engineering 261

Chapter 9 Methodology for Pressurized Thermal Shock Analysis

in Nuclear Power Plant 263

Dino A. Araneo and Francesco D’Auria

Section 5 Developments in Civil and Mechanical Engineering 281

Chapter 10 Evaluating the Integrity of Pressure

Pipelines by Fracture Mechanics 283

Ľubomír Gajdoš and Martin Šperl

Chapter 11 Fracture Analysis of Generator Fan Blades 311

Mahmood Sameezadeh and Hassan Farhangi

Chapter 12 Structural Reliability Improvement Using In-Service

Inspection for Intergranular Stress Corrosion

of Large Stainless Steel Piping 331

A. Guedri, Y. Djebbar, Moe. Khaleel and A. Zeghloul

Chapter 13 Interacting Cracks Analysis

Using Finite Element Method 359

Ruslizam Daud, Ahmad Kamal Ariffin,

Shahrum Abdullah and Al Emran Ismail

Preface

Knowledge accumulated in the science of fracture can be considered as an intellectual

heritage of humanity. Already at the end of Palaeolithic Era humans made first

observations on cleavage of flint and applied them to produce sharp stone axes and

other tools. The coming of Industrial Era with its attributes in the form of skyscrapers,

jumbo jets, giant cruise ships, or nuclear power plants increased probability of large

scale accidents and made deep understanding of the laws of fracture a question of

survival. In the 20th century fracture mechanics has evolved into a mature discipline

of science and engineering and became an important aspect of engineering education.

At present, our understanding of fracture mechanisms is developing rapidly and

numerous new insights gained in this field are, to a significant degree, defining the

face of contemporary engineering science. The power of modern supercomputers

substantially increases the reliability of fracture mechanics based predictions, making

fracture mechanics an indispensable tool in engineering design. Today fracture

mechanics faces a range of new problems, which is too vast to be discussed

comprehensively in a short Preface.

This book is a collection of 13 chapters, divided into five sections primarily according

to the field of application of the fracture mechanics methodology. Assignment of the

chapters to the sections only indicates the main contents of a chapter because some

chapters are interdisciplinary and cover different aspects of fracture.

In section "Computational Methods" the topics comprise discussion of computational

and mathematical methods, underlying fracture mechanics applications, namely, the

weight function formalism of linear fracture mechanics (chapter 1) as well as the fractal

geometry based formulation of the fracture mechanics laws (chapter 2). These chapters

attempt to overview the complex mathematical concepts in the form intelligible to a

broad audience of scientists and engineers. The fractal models of fracture are further

applied (chapter 3) to analyze experimental data in terms of fractal geometry.

Section "Fracture of Biological Tissues" focuses on discussion on the strength of

biological tissues, in particular, on human teeth tissues such as enamel and dentin

(chapter 4). On the basis of the structure-property relation analysis for the biological

tissues the perspective directions for the development of artificial restorative materials

for dentistry are formulated.

X Preface

Section "Fracture Mechanics Based Models of Fatigue" reminds that the phenomenon

of fatigue still remains an important direction in fracture mechanics and attracts

considerable attention of researches and engineers. The chapters presented here show

efficacy of the traditional statistical approach and its improved versions in description

of structural fatigue (chapter 5), fretting fatigue (chapter 6), and in fitting experimental

fatigue crack growth curves (chapter 7). Even more complicated case of fatigue,

namely the fatigue of steal in natural seawater at temperatures of tropical climates, is

discussed with an account of the role of electrochemical processes (chapter 8).

Section “Fracture Mechanics Aspects of Power Engineering” contains one chapter

(chapter 9) dealing with application of fracture mechanics to the problems of safety

and lifetime of nuclear reactor components, primarily reactor pressure vessels with

emphasis on pressurized thermal shock events.

Section “Developments in Civil and Mechanical Engineering” deals with fracture

mechanics analysis of large scale engineering structures, including various pipelines

(chapters 10 and 12), generator fan blades (chapter 11), or of some more general

industrial failures (chapter 13).

The topics of this book cover a wide range of directions for application of fracture

mechanics analysis in materials science, medicine, and engineering (power,

mechanical, and civil). In many cases the reported experience of the authors with

commercial engineering software may be also of value to engineers applying such

codes. The book is intended for mechanical and civil engineers, and also to material

scientists from industry, research, or education.

Alexander Belov

Institute of Crystallography

Russian Academy of Sciences

Moscow

Russia

Section 1

Computational Methods of Fracture Mechanics

Chapter 1

Higher Order Weight Functions in Fracture

Mechanics of Multimaterials

A. Yu. Belov

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/55360

1. Introduction

The quantities characterizing near-tip fields of cracks are generally recognized to play a crucial

role in both linear and nonlinear fracture mechanics. Among various methods developed to

analyze the structure of the near-tip fields, the weight function technique of Bueckner [4, 6]

based on Betti’s reciprocity theorem turned out to be especially promising. The concept of

higher-order weight functions in mechanics of elastic cracks was introduced by Sham [20, 21]

as an extension of the weight function approach. A historical introduction into the existing

alternative formulations of the weight function theory and a review of its earlier development

can be found in the papers by Belov and Kirchner [28, 31]. The theory of weight functions

treats the stress intensity factor K, which is a coefficient normalizing the stress singularity

σ = K/(2πr)1/2 at the crack tip, as a linear functional of loadings applied to an elastic body.

The kernel of the functional is however independent of loadings and, in this sense, universal

for the given body geometry and crack configuration. To emphasize this fact, Bueckner [4]

suggested that the kernel to be called ’universal weight function’. The weight functions play

the role of influence functions for stress intensity factors, since the weight function value

at a point situated inside the body or at its surface (including crack faces) is equal to the

stress intensity factor, which is due to the unit concentrated force applied at this point. The

weight function based functionals can be constructed not only for external forces but also for

the dislocation distributions described by the dislocation density tensor, as it was shown by

Kirchner [14]. The objective of the weight function theory is not to compute complete stress

distributions in cracked bodies for an arbitrary loading, but to express only one parameter K

characterizing the strength of the near-tip stress field as a functional (weighted average) of

the loading. In particular, in the simplest case of a cracked body subjected to only surface

loadings the functional has the form of a contour integral. However, in order to apply the

weight function theory to practical situations, the kernel of the functional has to be evaluated

and this can be done by solving a special elasticity problem, for instance, numerically by

a finite element method. The stress singularities are inherent not only to cracks. Sharp

©2012 Belov, licensee InTech. This is an open access chapter distributed under the terms of the Creative

Commons Attribution License (http://creativecommons.org/licenses/by/3.0),which permits unrestricted

use, distribution, and reproduction in any medium, provided the original work is properly cited.

Chapter 1