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.

As Directors of this NATO Workshop, we welcome this opportunity to record formally our thanks to the NATO Scientific Affairs Division for making our meeting possible through generous financial support and encouragement. This meeting has two purposes: the first obvious one because we have collected scientists from East, far East and west to discuss new development in the field of fracture mechanics: the notch fracture mechanics. The second is less obvious but perhaps in longer term more important that is the building of bridges between scientists in the frame of a network called Without Walls Institute on Notch Effects in Fatigue and Fracture." Physical perception of notch effects is not so easy to understand as the presence of a geometrical discontinuity as a worst effect than the simple reduction of cross section. Notch effects in fatigue and fracture is characterised by the following fundamental fact: it is not the maximum local stress or stress which governs the phenomena of fatigue and fracture. The physic shows that a process volume is needed probably to store the necessary energy for starting and propagating the phenomenon. This is a rupture of the traditional "strength of material" school which always give the prior importance of the local maximum stress. This concept of process volume was strongly affirmed during this workshop.

Concrete has traditionally been known as a material used widely in the construction of roads, bridges and buildings. Since cost effectiveness has always been one of the more important aspects of design, concrete, when reinforced and/or prestressed, is finding more use in other areas of application such as floating marine structures, storage tanks, nuclear vessel containments and a host of other structures. Because of the demand for concrete to operate under different loading and environmen tal conditions, increasing attention has been paid to study concrete specimens and structure behavior. A subject of major concern is how the localized segregation of the constituents in concrete would affect its global behavior. The degree of nonhomogeneity due to material property and damage. by yielding and/or cracking depends on the size scale and loading rate under consideration. Segregation or clustering of aggregates at the macroscopic level will affect specimen behavior to a larger degree than it would to a large structure such as a dam. Hence, a knowledge of concrete behavior over a wide range of scale is desired. The parameters governing micro-and macro-cracking and the techniques for evaluating and observing the damage in concrete need to be better understood. This volume is intended to be an attempt in this direction. The application of Linear Elastic Fracture Mechanics to concrete is discussed in several of the chapters."

In this volume on the mechanics of fracture of Portland cement concrete, the general theme is the connection between microstructural phenomena and macroscopic models. The issues addressed include techniques for observation over a wide range of scales, the influence of .microcracking on common measures of strength and de formability , and ultimately, the relationship between microstructural changes in concrete under load and its resistance to cracking. It is now commonly accepted that, in past attempts to force-fit the behavior of concrete into the rules of linear elastic fracture mechanics, proper attention has not been paid to scale effects. Clearly, the relationships among specimen size, crack length and opening, and characteristic material fabric dimensions have been, in comparison to their counterparts in metals, ceramics, and rocks, abused in concrete. Without a fundamental understanding of these relationships, additional testing in search of the elusive, single measure of fracture toughness has spawned additional confusion and frustration. No one is in a better position to document this observation than Professor Mindess.

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.

An International Conference on the Application of Fracture Mechanics to Ma terials and Structures was held at the Hotel Kolpinghaus in Freiburg, West Ger many, June 20-24, 1983. It was attended by more than 250 participants from different countries which include Austria, Canada, Czechoslovakia, Democratic Republic of Germany, Denmark, Federal Republic of Germany, Finland, France, Greece, Hungary, Israel, Italy, Japan, Netherlands, Norway, People's Republic of China, Portugal, Sweden, Switzerland, United Kingdom, United States of America, USSR and Yugoslavia. Conference Co-Chairmen were Professor G. C. Sih, Lehigh University, Bethle hem, Pennsylvania, U. S. A., Dr. E. Sommer, Fraunhofer-Institut fur Werkstoff mechanik, Freiburg, FRG and Professor W. Dahl, Rheinisch-Westfalische Technische Hochschule, Aachen, FRG. Dr. Wenrich, as the representative of the Land Baden-WUrttemberg, delivered the opening address with the remarks that International Conferences can serve the means to further enhance the technology development of a country. He empha sized that the Federal Republic of Germany is presently in need of strengthening the engineering manpower in order to keep her in a competitive position. The Conference was officially cast off with the leading plenary lectures that under lined the theme of the technical lectures for the first day. This pattern was observed for the five-day meeting. The interplay between material and design re quirements was the theme and emphasized in many of the technical presentations that amounted to approximately ninety (90) papers."

Composites offer great promise as light weight and strong materials for high performance structures. One of the major advantages of these materials as compared with metals is the basic way in which heterogeneity resist crack extension. In a fiber/matrix composite system, the fibers tend to cause cracks to form at closer spacing and delay the formation of a large crack. The enhancement of local failure such as fiber breaking, matrix cracking and interface debonding further reduces the energy level which might have otherwise reached the point of catastrophic failure. Even though substantial tests have been made on composite materials, little has been gained in the understanding and development of a predic tive procedure for composite failure. There are fundamental difficulties associated with incorporating the nonhomogeneous and anisotropic prop erties of the composite into the continuum mechanics analysis. Additional uncertainties arise from voids and defects that are introduced in the composite during manufacturing. Even a small quantity of mechanical imperfections can cause a marked influence on the composite strength. Moreover, the interface properties between the fibers and matrix or bonded laminae can also affect the load transmission characteristics significantly. It would be impossible to establish predictive procedures for composite failure unless realistic guidelines could be developed to control the manufacturing quality of composite systems."

This book was written to serve as both a professional's overview of the entire field of fatigue and fracture mechanics as it is currently practiced, and as an introduction to the application of the Fracture Mechanics of Ductile Metals (FMDM) theory. Particular benefits include: Application of fracture mechanics concepts to metallic structure, composites, welds and bolted joints. Extensive discussion of two welding techniques currently used in aerospace and aircraft structure, with emphasis given to state-of-the-art friction stir welding techniques. Life assessment of welded and bolted joints, with example problems. Damage tolerance and durability assessment of composites, not found in any other book published in this area. Presentation of Elastic-Plastic Fracture Mechanics (EPFM). Application of multi-specimen and single-specimen techniques to obtain fracture properties. Introduction to Fracture Mechanics of Ductile Metals (FMDM) theory to determine residual strength capability of structural metals. Discussion of techniques to determine the material fracture toughness properties without the need for laboratory testing. This is the first single text to present applications of fatigue and fracture mechanics to metals and composites and also include practical applications and example problems. It will be an essential reference for researchers, practitioners, and students alike.

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 this book a systematic discussion of crack problems in elastic-plastic materials is presented. The state of the art in fracture mechanics research and assessment of cracks is documented, with the help of analytic, asymptotic methods as well as finite element computations. After a brief introduction to fracture mechanics, the two-parameter concept for stationary cracks is studied in addition to the issues in three-dimensional crack fields under coupling with strong out-of-plane effects. Cracks along interfaces and crack growth problems under mixed mode conditions are also treated. A systematic study of stress singularities for different notches is accompanied by detailed finite element computations.

This is not just another book on fracture mechanics. In recent years, there have been many books published on this subject in an attempt to assess the state of the art and its applications. The majority of the work dealt with energy release rate or critical stress intensity factor and is applicable only to fracture toughness testing. The main reason for this restriction is that the energy release concept cannot easily be extended to mixed mode fracture that occurs in practice as the rule rather than the exception. Cracks will normally curve or turn because the direction of loading can change as a function of time. Their directions of growth cannot be assumed as an a priori and must be determined from a pre-assumed criterion. Analysts are still perplexed with selecting an appropriate fracture criterion because it requires much discernment and judgement. Criteria which often appeared valid for idealized situations are quickly dis credited when encountering more complex physical phenomena. Moreover, the claim of generality cannot be justified on the basis of agreement between theory and experiment for a few simple examples."

Within the last two decades fracture theory has been one of the most rapidly advancing fields of continuous media mechanics. Noteworthy suc cess has been achieved in linear fracture mechanics where the propagation of the macrocrack in elastic materials is under study. However, fracture of materials is by no means a simple process since it involves fracture of structural elements ranging from atomic sizes to macrocracks. To obtain all information about how and why materials fail, all stages of the process must be studied. For a long time both mechanical engineers and physicists have been concerned with the problem of the fracture of solids. Unfortunately, most of their work has been independent of the others. To solve the problem not only requires the minds and work of mechanical engineers and physicists but chemists and other specialists must be consulted as well. In this book we will consider some conclusions of the "physical" and "mechanical" schools acquired by the A. F. Joffe Physics-Technical Institute of the USSR Academy of Sciences in Leningrad and the Institute of Polymer Mechanics of Latvian SSR Academy of Sciences in Riga. The methods for studying the phenomena of fracture applied at both Institutes are different yet complimentary to one another; the materials tested are also sometimes different."

This is the proceedings of the IUTAM Symposium on Creep in Structures, held at Nagoya, 3-7 April 2000, which is the 5th one of this series of the IUTAM Symposia organized every then years since 1960. The present proceedings contains 48 innovative papers presented at the 5th Symposium, in which 91 participants from 15 countries participated to consolidate the development of creep research since 1990 and to discuss the new horizons in this fundamental field of applied mechanics in the coming century. the papers contained deal with (1) physical and microstructural process of creep, viscoplasticity and creep damage related to their modeling, (2) elaborated constitutive equations of time-dependent deformation and damage, (3) creep damage and fracture of engineering materials and structures, (4) computational modeling, simulation, analysis and design of structures in creep, and (5) creep of polymers, composites, and heterogeneous materials. This volume is useful for researchers and graduate course students in the relevant fields. The field of optical WDM networks has experienced widespread attention and growth in recent years.

It is weH known that the traditional failure criteria cannot adequately explain failures which occur at a nominal stress level considerably lower than the ultimate strength of the material. The current procedure for predicting the safe loads or safe useful life of a structural member has been evolved around the discipline oflinear fracture mechanics. This approach introduces the concept of a crack extension force which can be used to rank materials in some order of fracture resistance. The idea is to determine the largest crack that a material will tolerate without failure. Laboratory methods for characterizing the fracture toughness of many engineering materials are now available. While these test data are useful for providing some rough guidance in the choice of materials, it is not clear how they could be used in the design of a structure. The understanding of the relationship between laboratory tests and fracture design of structures is, to say the least, deficient. Fracture mechanics is presently at astandstill until the basic problems of scaling from laboratory models to fuH size structures and mixed mode crack propagation are resolved. The answers to these questions require some basic understanding ofthe theory and will not be found by testing more specimens. The current theory of fracture is inadequate for many reasons. First of aH it can only treat idealized problems where the applied load must be directed normal to the crack plane.

Thematerialsusedinmanufacturingtheaerospace, aircraft, automobile, andnuclear parts have inherent aws that may grow under uctuating load environments during the operational phase of the structural hardware. The design philosophy, material selection, analysis approach, testing, quality control, inspection, and manufacturing are key elements that can contribute to failure prevention and assure a trouble-free structure. To have a robust structure, it must be designed to withstand the envir- mental load throughout its service life, even when the structure has pre-existing aws or when a part of the structure has already failed. If the design philosophy of the structure is based on the fail-safe requirements, or multiple load path design, partial failure of a structural component due to crack propagation is localized and safely contained or arrested. For that reason, proper inspection technique must be scheduled for reusable parts to detect the amount and rate of crack growth, and the possible need for repairing or replacement of the part. An example of a fail-sa- designed structure with crack-arrest feature, common to all aircraft structural parts, is the skin-stiffened design con guration. However, in other cases, the design p- losophy has safe-life or single load path feature, where analysts must demonstrate that parts have adequate life during their service operation and the possibility of catastrophic failure is remote. For example, all pressurized vessels that have single load path feature are classi ed as high-risk parts. During their service operation, these tanks may develop cracks, which will grow gradually in a stable mann

These proceedings gather a selection of peer-reviewed papers presented at the 7th International Conference on Fracture Fatigue and Wear (FFW 2018), held at Ghent University, Belgium on 9-10 July 2018. The contributions, prepared by international scientists and engineers, cover the latest advances in and innovative applications of fracture mechanics, fatigue of materials, tribology and wear of materials. The book is intended for academics, including graduate students and researchers, as well as industrial practitioners working in the areas of fracture fatigue and wear.

This book consists of a collection of lectures prepared for a short course on "Fracture Mechanics Methodology" sponsored by the Advisory Group for Aerospace Research and Development (AGARD), part of the North Atlantic Treaty Organization (NATO). The course was organized jointly by Professor George C. Sih of the Institute of Fracture and Solid Mechanics at Lehigh University in the United States and Professor Luciano Faria from Centro de Mecanica e de Materiais das Universidade de Lisboa in Portugal. It was held in Lisbon from June 1 to 4, 1981. Dr. Robert Badaliance from the McDonnell Aircraft Company in St. Louis and Dr. Oscar Orringer from the Depart ment of Transportation in Cambridge are the other US lecturers while Professor Carlos Moura Branco from Portugal also lectured. The audience consisted of engineers from the Portuguese industry with a large portion from the aeronautical sector and others who are particularly interested to apply the fracture mechanics discipline for analyzing the integrity of structural components and fracture control methods. Particular. emphases were given to the fundamentals of fracture mechanics as applied to aircraft structures."

Fatigue and Fracture Reliability Engineering is an attempt to present an integrated and unified approach to reliability determination of fatigue and fracture behaviour, incorporating probability, statistics and other related areas. A series of original and practical approaches, are suggested in Fatigue and Fracture Reliability Engineering, including new techniques in determining fatigue and fracture performances. It also carries out an investigation into static and fatigue properties, and into the failure mechanisms of unnotched and notched CFR composite laminates with different lay-ups to optimize the stacking sequence effect. Further benefits include: a novel convergence-divergence counting procedure to extract all load cycles from a load history of divergence-convergence waves; practical scatter factor formulae to determine the safe fatigue crack initiation and propagation lives from the results of a single full-scale test of a complete structure; and a nonlinear differential kinetic model for describing the dynamical behaviour of an atom at a fatigue crack tip. Fatigue and Fracture Reliability Engineering is intended for practising engineers in marine, civil construction, aerospace, offshore, automotive and chemical industries. It is also useful reading for researchers on doctoral programmes, and is appropriate for advanced undergraduate and postgraduate programmes in any mechanically-oriented engineering discipline.

Contents:
Part 1 Fundamentals: introduction to Cartesian tensors; stress; strain. Part 2 Useful constitutive laws: behaviour of engineering materials; linear elastic behaviour; introduction to linear viscoelastic behaviour; creep; plasticity; boundary value problems. Part 3 Applications to simple structural members: flexure of beams; torsion of shafts; plane strain; plane stress.

This proceedings contains contributions to the series of seminars held in Vienna (1992), Miskolc, Hungary (1993 and 1994) and Vienna (1995) and provides a valuable resource for those concerned with the teaching of fracture and fatigue. It presents a wide range of approaches relevant to course and curriculum development. It is aimed particularly at those concerned with graduate and post-graduate education. This book should be of interest to lecturers and researchers in the field of mechanics of materials, especially related to mechanical and structural engineering.

Invited international contributions to this exciting new research field are included in this volume. It contains the specially selected papers from 45 key specialists given at the Symposium held under the auspices of the prestigious International Union of Theoretical and Applied Mechanics at Turin in October 1994.

Derived from the invited IUTAM Symposium in September 1993, this volume's contributions discuss recent advances in fracture mechanics, studies of concrete, rock, ceramics and other brittle disordered materials at micro and structural levels. It draws together research and new applications in continuum, damage and fracture mechanics approaches.

This book deals with the new developments and application of the geometric method to the nonlinear stability problem for thin non-elastic shells. A.V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicityly the asymptotic formulas for the upper and lower critical loads. The geometric method by Pogorelov is one of the most importanty analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the post critical form of a deformed shell surface, successfully applied to a direct variational approach to the nonlinear shell stability problems. Until now, most of Pogorelov's monographs were written in Russian, which limited the diffusion of his ideas among the international scientific community. The present book is intended to assist and encourage the researchers in this field to apply the geometric method and the related results to everyday engineering practice. Further developments of the geometric method are carried out in this book and are directed to stability of thin shells in the case of elastic anisotropy, elastic anisotropy with linear memory and elasto-plastic properties of the shell material. This book is intended to serve both as a textbook for post-graduate students in structural engineering and applied mathematics, and as a revference monograph for academic and industrial researchers.