This book is addressed to professionals active in the design and operation of power plants and those involved in supporting research and development activities in high temperature materials. Following an introduction, typical operating conditions of pressure vessels, pipe-line elements and turbine blades and vanes are described. This includes both steadystate and transient loading. Advanced problems are also covered, such as structural problems, associated with power plant materials, deformation and fracture at high temperatures. Distinctions are made between the processes of crack initiation and crack growth in conducting lifetime assessments. Failure prevention methods, thermal shock problems, details of damage analysis and the possibilities of life extension are also covered.

Intended for engineers from a variety of disciplines that deal with structural materials, this text describes the current state of knowledge of how fractures in materials form and propagate, leading to failure. The book begins by describing the fracture process at the two extremes of scale: first in the context of atomic structures, then in terms of a continuous elastic medium. Treating the fracture process in increasingly sophisticated ways, the book then considers plastic corrections and the procedures for measuring the toughness of materials. Practical considerations are then discussed, including crack propagation, geometry dependence, flaw density, mechanisms of failure by cleavage, the ductile-brittle transition, and continuum damage mechanics. The text concludes with discussions of generalized plasticity and the link between the microscopic and macroscopic aspects. The text is suitable for advanced undergraduates. Problems are provided at the end of each chapter.

In the preliminary stage of designing new structural hardware that must perform a given mission in a fluctuating load environment, there are several factors the designers should consider. Trade studies for different design configurations should be performed and, based on strength and weight considerations, among others, an optimum configuration selected. The selected design must be able to withstand the environment in question without failure. Therefore, a comprehen sive structural analysis that consists of static, dynamic, fatigue, and fracture is necessary to ensure the integrity of the structure. During the past few decades, fracture mechanics has become a necessary discipline for the solution of many structural problems. These problems include the prevention of failures resulting from preexisting cracks in the parent material, welds or that develop under cyclic loading environment during the life of the structure. The importance of fatigue and fracture in nuclear, pressure vessel, aircraft, and aerospace structural hardware cannot be overemphasized where safety is of utmost concern. This book is written for the designer and strength analyst, as well as for the material and process engineer who is concerned with the integrity of the structural hardware under load-varying environments in which fatigue and frac ture must be given special attention. The book is a result of years of both acade mic and industrial experiences that the principal author and co-authors have accumulated through their work with aircraft and aerospace structures."

A report from the RILEM Technical Committee 119. This text presents models and methods to determine thermal stresses and cracking risks in concrete. Possible influences on and causes of thermal cracking of concrete are discussed and cases of practical measures for avoiding cracking are detailed. The book should be of interest to concrete technologists; researchers on concrete structures and technology; prime building contractors and building authorities.

Modern fracture mechanics considers phenomena at many levels, macro and micro; it is therefore inextricably linked to methods of theoretical and mathematical physics. This book introduces these sophisticated methods in a straightforward manner. The methods are applied to several important phenomena of solid state physics which impinge on fracture mechanics: adhesion, defect nucleation and growth, dislocation emission, sintering, the electron beam effect and fractal cracks. The book shows how the mathematical models for such processes may be set up, and how the equations so formulated may be solved and interpreted. The many open problems which are encountered will provide topics for MSc and PhD theses in fracture mechanics, and in theoretical and experimental physics. As a supplementary text, the book can be used in graduate level courses on fracture mechanics, solid matter physics, and mechanics of solids, or in a special course on the application of fracture mechanics methods in solid matter physics.

The IUTAM Symposium on "Combustion in Supersonic Flows" was held in Poitiers at Ecole Nationale Superieure de Mecanique et d'Aerotechnique (ENSMA) from 2 to 6 october 1995. The Symposium was hosted by the Laboratoire de Combustion et de Detonique (UPR - CNRS 9028) and was attended by 60 delegates from 10 countries. The formal presentations and invited lectures were focused on four main topics, related to combustion in supersonic streams and practical issues relative to the development of new propulsion system: fundamental studies on premixed and unpremixed combustion, fluid dynamic aspects of supersonic combustion, practical system including Scramjet, Ramaccelerators and Pulsed Detonation Engines, application of detonation to propulsion. Invited lectures presenting the state of the art on these topics as well as available data base were delivered by professors Paul A. Libby from University of California at San Diego, Vladimir Sabel'nikov from TsAGI (Russia), Paul Clavin from IRPHE (Marseille, France) and Drs Shmuel Eidelman from SAlC (USA), Gunter Smeets from the French-German Institut of Saint-Louis and Bruno Deshaies from LCD (poi tiers, France).

This volume contains the edited version of lectures and selected research contributions presented at the NATO ADVANCED STUDY INSTITUTE on MECHANICAL BEHA VI OUR OF MATERIALS AT HIGH TEMPERATURE, held in Sesimbra, Portugal, 12th-22nd September 1995, and organized by 1ST-Lisbon Institute of Technology, PortugaL The Institute was attended by 88 participants, including 15 lecturers from 17 countries including five CP countries. The lecturers were leading scientists and technologists from universities, research institutions and industry. The students were mainly young PhD students and junior academic or research staff with postgraduate qualifications (MSc or PhD). Fourteen students were from the five CP countries. The students presented research papers or posters during the Institute reporting the current progress of their research projects. A total of thirty three lectures, ten research papers and fifty posters were presented. This book does not contain the poster presentations and seven research papers were selected for publication. All the sessions were very active and quite extensive discussions on scientific aspects took place during the Institute. The Advanced Study Institute provided a forum for interaction among scientists and engineers from different areas of research, and young researchers.

This book is concerned with the numerical solution of crack problems. The techniques to be developed are particularly appropriate when cracks are relatively short, and are growing in the neighbourhood of some stress raising feature, causing a relatively steep stress gradient. It is therefore practicable to represent the geometry in an idealised way, so that a precise solution may be obtained. This contrasts with, say, the finite element method in which the geometry is modelled exactly, but the subsequent solution is approximate, and computationally more taxing. The family of techniques presented in this book, based loosely on the pioneering work of Eshelby in the late 1950's, and developed by Erdogan, Keer, Mura and many others cited in the text, present an attractive alternative. The basic idea is to use the superposition of the stress field present in the unfiawed body, together with an unknown distribution of 'strain nuclei' (in this book, the strain nucleus employed is the dislocation), chosen so that the crack faces become traction-free. The solution used for the stress field for the nucleus is chosen so that other boundary conditions are satisfied. The technique is therefore efficient, and may be used to model the evolution of a developing crack in two or three dimensions. Solution techniques are described in some detail, and the book should be readily accessible to most engineers, whilst preserving the rigour demanded by the researcher who wishes to develop the method itself.

An Introduction to Fatigue in Metals and Composites provides a balanced treatment of the phenomenon of fatigue in metals, nonmetals and composites with polymeric, metallic and ceramic matrices. The applicability of the safe life philosophy of design is examined for each of the materials. Attention is also focused on the stable crack growth phase of fatigue and differences in the operative mechanisms for the various classes of materials are considered. The impacts of these differences on the development of damage tolerance strategies are examined. Among topics discussed are; variable amplitude loading with tensile and compressive overload; closure obstruction; bridging mechanisms; mixed mode states; small cracks; delamination mechanisms and environmental conditions. The arrangement and presentation of the topics are such that An Introduction to Fatigue in Metals and Composites can serve as a course text for mechanical, civil, aeronautical and astronautical engineering and material science courses as well as a reference for engineers who are concerned with fatigue testing and aircraft, automobile and engine design.

Failures of many mechanical components in service result from fatigue. The cracks which grow may either originate from some pre-existing macroscopic defect, or, if the component is of high integrity but highly stressed, a region of localized stress concentration. In turn, such concentrators may be caused by some minute defect, such as a tiny inclusion, or inadvertent machining damage. Another source of surface damage which may exist between notionally 'bonded' components is associated with minute relative motion along the interface, brought about usually be cyclic tangential loading. Such fretting damage is quite insidious, and may lead to many kinds of problems such as wear, but it is its influence on the promotion of embryo cracks with which we are concerned here. When the presence of fretting is associated with decreased fatigue performance the effect is known as fretting fatigue. Fretting fatigue is a subject drawing equally on materials science and applied mechanics, but it is the intention in this book to concentrate attention entirely on the latter aspects, in a search for the quantification of the influence of fretting on both crack nucleation and propagation. There have been very few previous texts in this area, and the present volume seeks to cover five principal areas; (a) The modelling of contact problems including partial slip under tangentialloading, which produces the surface damage. (b) The modelling of short cracks by rigorous methods which deal effectively with steep stress gradients, kinking and closure. (c) The experimental simulation of fretting fatigue.

All materials contain numerous defects, such as microcracks, microvoids, inhomogeneities, dislocations, etc., which precede possible fracture. Thus mathematical modeling becomes necessary. This volume contains some introductory material, aspects of fracture mechanics, the theory of crystal defects, computational micromechanics, and the heterogenization methodology.

Fatigue of engineering materials is a very complicated process that is difficult to accurately describe and predict. It is no doubt nowadays, that a fatigue of real materials should be regarded as a random phenomenon and analyzed by use of stochastic theory. This volume of the lectures sumarises the latest achievements in stochastic modelling and analysis of fatigue. The lectures cover the following important aspects of modern analysis of fatigue: methodology of stochastic modelling of fatigue, tools for characterization of random fatigue loads, physical and mechanical aspects of random fatigue, basic stochastic models for fatigue and the estimation of fatigue reliability of specific structural systems.

This text includes coverage of the following topics: stress-induced crack path in Aji granite under tensile stress; relation of fracture resistance to fabric for granitic rocks; and the mechanisms of finite brittle strain.

These volumes contain contributions from a conference on the themes of measurement and prediction of residual stress in railroad rails. The subtitle, Effects of rail integrity and railroad economics', expresses an ultimate goal of reducing technical results to practical knowledge of interest to transportation engineers. Volume I contains elements of practical railway experience, laboratory tests, including experimental strees analysis, and theoretical evaluations of residual stress, crack propagation, and rail fracture. Observations of the effects of residual stress on rails in service, field tests, and laboratory experiments and recounted in the first three chapters of the volume. Experiments in which samples of new rail are subjected to precisely controlled rolling contact loads under laboratory conditions are dealt with in Chapters 4 and 5. Chapter 6 describes a method for programming loads on compact tension specimens to stimulate the stress intensity factor history of an internal transverse crack in rail head. Chapter 7 outlines a method for setting rail inspection intervals in service, based on what is presently known about the behaviour of transverse cracks in the rail head. The remainder of the volume deals with experimental stress analysis. Chapter 8 describes an elaborate procedure for combining stair change and length to evaluate internal stress distribution, and several other measurement techniques are also evaluated as possible alternates. Chapter 9 discusses the neutron diffraction method and its recent application to rail. Chapter 10 summarizes a technique based on MoirA(c) interferometry and reports on the first step in the developments of rail stress measurementprocedure based on this alternate. Chapter 13 concludes the experimental contributions with a summary of some typical measurements of the residual stress states in rails from several different producers and service environments in Europe. The reader will find that a reasonable qualitative picture of the rail residual stress field emerges from the experimental stress analyses. However, the details always vary from one rail to another, and there are sufficient differences to prevent the drawing of general quantitative conclusions from the experimental work alone. Theoretical and numerical analyses' are presented in Volume II, in the hope that models based on solid mechanics can correlate the experimental stress measurements and lead to a better understanding of the effects of residual stress upon crack propagation, fracture, and ultimately the economics of rail in the modern railroad environment.

Material technology has become so diversified in theories and the construction of novel microstructures that the researchers and practitioners are drifting further apart. This book is based on material presented at an International Symposium in Xanthi, Greece in July 1989. The symposium attracted a group of individual engineers and scientists from the East and West who tackled the question of why particular manipulations of a given material have particular effects. Emphasis is laid on the strain energy function because of the versatile role it plays in mechanics and physics. It has been used successfully not only in predicting the failure of solids but also in formulating constitutive relations in continuum mechanics. The material presented falls within the areas of: Fundamentals of Strain Energy Density, Damage Analysis on Strain Energy Density, Strain Energy Density as Failure Criterion, Applications, and Composites.

Theory of Elasticity and Stress Concentration Yukitaka Murakami, Kyushu University, Japan A comprehensive guide to elasticity and stress concentration Theory of Elasticity and Stress Concentration comprehensively covers elasticity and stress concentration and demonstrates how to apply the theory to practical engineering problems. The book presents a new approach to the topic without the need for complicated mathematics, and the principles and meaning of stress concentration are covered without reliance on numerical analysis. The book consists of two parts: Part I - Theory of Elasticity and Part II - Stress Concentration. Part I treats the theory of elasticity from the viewpoint of helping the reader to comprehend the essence of it. Part II treats the principle and meaning of stress concentration and guides the reader to a better understanding of it. Throughout the book, many useful and interesting applications of the basic new way of thinking are presented and explained. Key features: * Unique approach to the topics. * Encourages the readers to acquire the new way of thinking and engineering judgement. * Includes examples, problems and solutions. This book provides essential reading for researchers and practitioners in the structural and mechanical engineering industries.

From time to time the International Journal of Fracture has presented matters thought to be of special interest to its readers. The last special topic review was presented by Drs W.G. Knauss and AJ. Rosakis as Guest Editors in four issues, January-April 1990, under the general title of Non Linear Fracture. It contained sections on damage mechanisms, interfaces and creep, time depen dence, and continuum plasticity insofar as they affect the mechanisms of the fracture process. Continuing this policy, which is consistent with our stated objectives, the two September issues deal with the behavior of concrete and cementious materials during fracture initiation and propagation. We hope that the ensuing state-of-the-art review will yield another instructive and timely product which readers will find useful. To assist us in presenting this subject, we have prevailed upon a well-known international expert in concrete behavior, Dr. Z.P. Bazant, Walter P. Murphy Professor of Civil Engineering, of Northwes tern University to act as Guest Editor. On behalf of the editors and publishers, I wish to thank Professor BaZant and his invited authors for undertaking this special effort. M.L. WILLIAMS Pittsburgh, Pennsylvania Editor-in-Chief September 1991 International Journal of Fracture 51: ix-xv, 1991. Z.P. Bafant (ed.), Current Trends in Concrete Fracture Research.

The purpose of this book is to present, describe and demonstrate the use of numerical methods in solving crack problems in fracture mechanics. The text concentrates, to a large extent, on the application of the Boundary Element Method (BEM) to fracture mechanics, although an up-to-date account of recent advances in other numerical methods such as the Finite Element Method is also presented. The book is an integrated presentation of modem numerical fracture mechanics, it contains a compilation of the work of many researchers as well as accounting for some of authors' most recent work on the subject. It is hoped that this book will bridge the gap that exists between specialist books on theoretical fracture mechanics on one hand, and texts on numerical methods on the other. Although most of the methods presented are the latest developments in the field of numerical fracture mechanics, the authors have also included some simple techniques which are essential for understanding the physical principles that govern crack problems in general. Different numerical techniques are described in detail and where possible simple examples are included, as well as test results for more complicated problems. The book consists of six chapters. The first chapter initially describes the historical development of theoretical fracture mechanics, before proceeding to present the basic concepts such as energy balance, stress intensity factors, residual strength and fatigue crack growth as well as briefly describing the importance of stress intensity factors in corrosion and residual stress cracking.

Recognized authors contributed to this collection of original papers from all fields of research in continuum mechanics. Special emphasis is given to time dependent and independent permanent deformations, damage and fracture. Part of the contributions is dedicated to current efforts in describing material behavior with regard to, e.g., anisotropy, thermal effects, softening, ductile and brittle fracture, porosity and granular structure. Another part deals with numerical aspects arising from the implementation of material laws in the calculations of forming processes, soil mechanics and structural mechanics. Applications of theory and numerical methods belong to the following areas: Comparison with experimental results from material testing, metal forming under thermal and dynamic conditions, failure by damage, fracture and localized deformation modes. The variety of treated topics provides a survery of the actual research in these fields; therefore, the book is addressed to those interested in special problems of continuum mechanics as well as to those interested in a general knowledge.

The assessment of crack initiation and/or propagation has been the subject of many past discussions on fracture mechanics. Depending on how the chosen failure criterion is combined with the solution of a particular theory of continuum mechanics, the outcome could vary over a wide range. Mod elling of the material damage process could be elusive if the scale level of observation is left undefined. The specification of physical dimension alone is not sufficient because time and temperature also play an intimate role. It is only when the latter two variables are fixed that failure predictions can be simplified. The sudden fracture of material with a pre-existing crack is a case in point. Barring changes in the local temperature,* the energy released to create a unit surface area of an existing crack can be obtained by considering the change in elastic energy of the system before and after crack extension. Such a quantity has been referred to as the critical energy release rate, G e, or stress intensity factor, K Ie. Other parameters, such as the crack opening displacement (COD), path-independent J-integral, etc. , have been proposed; their relation to the fracture process is also based on the energy release concept. These one-parameter approaches, however, are unable simultaneously to account for the failure process of crack initiation, propagation and onset of rapid fracture. A review on the use of G, K I, COD, J, etc. , has been made by Sih [1,2].

Mechanics of Fatigue addresses the range of topics concerning damage, fatigue, and fracture of engineering materials and structures. The core of this resource builds upon the synthesis of micro- and macro-mechanics of fracture. In micromechanics, both the modeling of mechanical phenomena on the level of material structure and the continuous approach are based on the use of certain internal field parameters characterizing the dispersed micro-damage. This is referred to as continuum damage mechanics. The author develops his own theory for macromechanics, called analytical fracture mechanics. This term means the system cracked body - loading or loading device - is considered as a mechanical system and the tools of analytical (rational) mechanics are applied thoroughly to describe crack propagation until the final failure. Chapter discuss: preliminary information on fatigue and engineering methods for design of machines and structures against failures caused by fatigue fatigue crack nucleation, including microstructural and continuous models theory of fatigue crack propagation fatigue crack growth in linear elastic materials subject to dispersed damage fatigue cracks in elasto-plastic material, including crack growth retardation due to overloading as well as quasistationary approximation fatigue and related phenomena in hereditary solids application of the theory fatigue crack growth considering environmental factors unidirectional fiber composites with ductile matrix and brittle, initially continuous fibers laminate composites Mechanics of Fatigue serves students dealing with mechanical aspects of fatigue, conducting research in fracture mechanics, structural safety, mechanics of composites, as well as modern branches of mechanics of solids and structures.

It is difficult to do justice to fracture mechanics in a textbook, for the subject encompasses so many disciplines. A general survey of the field would serve no purpose other than give a collection of references. The present book by Professor E. E. Gdoutos is refreshing because it does not fall into the esoteric tradition of outlining equations and results. Basic ideas and underlying principles are clearly explained as to how they are used in application. The presentations are concise and each topic can be understood by advanced undergraduates in material science and continuum mechanics. The book is highly recommended not only as a text in fracture mechanics but also as a reference to those interested in the general aspects of failure analysis. In addition to providing an in-depth review of the analytical methods for evaluating the fundamental quantities used in linear elastic fracture mechanics, various criteria are discussed re: O. ecting their limitations and applications. Par ticular emphases are given to predicting crack initiation, subcritical growth and the onset of rapid fracture from a single criterion. Those models in which it is assumed that the crack extends from tip to tip rely on the specific surface energy concept. The differences in the global and energy states before and after crack extension were associated with the energy required to create a unit area of crack surface. Applications were limited by the requirement of self-similar crack growth."

This book provides an up-to-date knowledge on theory and experimental results of rate-dependent fracture processes in metallic materials. The objective is to expose the current status of a growing branch of fracture mechanics called generally "Dynamic Fracture." Crack dynamics takes into account not only the effects of inertia but also rate sensitivity of a material under consideration. This volume has been prepared by four leading authorities in fracture dynamics: D.R. Curran, J.F. Kalthoff, J.R. Klepaczko and F. Nilsson. A broad range of problem is covered: dynamic fracture theory, application of dynamic fracture mechanics, dynamic crack inition and microstatistical fracture mechanics in dynamic fracture. The book in its present format may serve as a text supplement in lecturing on fracture mechanics. On the other hand, it may serve as an instructional aid in engineering of fracture prevention.

This book is about the use of fracture mechanics for the solution of practical problems; academic rigor is not at issue and dealt with only in as far as it improves insight and understanding; it often concerns secondary errors in engineering. Knowledge of (ignorance of) such basic input as loads and stresses in practical cases may cause errors far overshadowing those introduced by shortcomings of fracture mechanics and necessary approximations; this is amply demonstrated in the text. I have presented more than three dozen 40-hour courses on fracture mechanics and damage tolerance analysis, so that I have probably more experience in teaching the subject than anyone else. I learned more than the students, and became cognizant of difficulties and of the real concerns in applications. In particular I found, how a subject should be explained to appeal to the practicing engineer to demonstrate that his practical problem can indeed be solved with engineering methods. This experience is reflected in the presenta tions in this book. Sufficient background is provided for an understanding of the issues, but pragamatism prevails. Mathematics cannot be avoided, but they are presented in a way that appeals to insight and intuition, in lieu of formal derivations which would show but the mathematical skill of the writer."

This book is about the use of fracture mechanics for the solution of practical problems; academic rigor is not at issue and dealt with only in as far as it improves insight and understanding; it often concerns secondary errors in engineering. Knowledge of (ignorance of) such basic input as loads and stresses in practical cases may cause errors far overshadowing those introduced by shortcomings of fracture mechanics and necessary approximations; this is amply demonstrated in the text. I have presented more than three dozen 40-hour courses on fracture mechanics and damage tolerance analysis, so that I have probably more experience in teaching the subject than anyone else. I learned more than the students, and became cognizant of difficulties and of the real concerns in applications. In particular I found, how a subject should be explained to appeal to the practicing engineer to demonstrate that his practical problem can indeed be solved with engineering methods. This experience is reflected in the presenta tions in this book. Sufficient background is provided for an understanding of the issues, but pragamatism prevails. Mathematics cannot be avoided, but they are presented in a way that appeals to insight and intuition, in lieu of formal derivations which would show but the mathematical skill of the writer."