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The papers in this volume represent a considerable cross-section of the field of fracture mechanics, a testimony to the breadth of interest that Mel and Max Williams'friends share with them. Several are expanded versions of papers that were given in special sessions honoring them at the 1997 Ninth International Conference on Fracture Mechanics in Sydney, Australia. The subjects treated in this volume can be classified as follows: dynamic fracture problems as viewed primarily from a classical continuum point of view; analysis of relatively general crack geometrics; fracture problems of polymers and other relatively ductile materials; scaling rules that allow extension of results obtained at one size to be translated into behavior at different size scales; problems dealing with interactions that produce complex stress fields; fracture problems directly appropriate to composite materials; analysis of stress concentrations in anisotropic, elastic solids; and the problem of cracks in thin plates bending. This volume will be of interest to engineers and scientists working on all aspects of the physics and mechanics of fracture.

This volume contains two-page abstracts of the 698 papers presented at the “16th European Conference of Fracture,” (ECF16) held in Alexandroupolis, Greece, July 3-7, 2006. The accompanying CD attached at the back cover of the book contains the full length papers. The abstracts of the fifteen plenary lectures are included in the beginning of the book. The remaining 683 abstracts are arranged in 25 tracks and 35 special symposia/sessions with 303 and 380 abstracts, respectively. The papers of the tracks have been contributed from open call, while the papers of the symposia/sessions have been solicited by the respective organizers. Both tracks and symposia/sessions fall into two categories, namely, fracture of nanomaterials and structures and engineering materials and structures with 88 and 595 papers, respectively. Started in 1976, the European Conference of Fracture (ECF) takes place every two years in a European country. Its scope is to promote world-wide cooperation among scientists and engineers concerned with fracture and fatigue of solids. ECF16 was under the auspices of the European Structural Integrity Society (ESIS) and was sponsored by the American Society of Testing and Materials, the British Society for Stain Measurement, the Society of Experimental Mechanics, the Italian Society for Experimental Mechanics, and the Japanese Society of Mechanical Engineers. ECF16 focused in all aspects of structural integrity with the objective of improving the safety and performance of engineering structures, components, systems and their associated materials.

It is propitious that the 25th year of publication of the International Journal of Fracture should coincide with the opportunity to support the recognition by the Society of Engineer­ ing Science of the 65th birthday of the Founding Editor-in-Chief, Professor M.L. Williams. At its 24th Annual Meeting at the University of Utah in September 1987, the Organizing Committee of the Society chose to honor Professor Williams by reserving several sessions for contributions from his colleagues working in the mechanics of fracture and associated mechanical property-structure relationships. We are therefore pleased to welcome Professor E.S. Folias, Professor of Mechanical Engineering, University of Utah, and a member of the Editorial Committee as the Guest Editor for the first three issues of Volume 39 of the Journal. We have also noted that the University of Utah was one of the three homes for the Journal, sandwiched between the original home at the California Institute of Technology in 1965 and its current location at the University of Pittsburgh. In observing these dual anniversaries, the publishers not only enthusiastically support the presentation of these special papers, but also wish to extend to Professor Williams our own best wishes on his personal anniversary, and to thank him and all the authors, reviewers, and particularly M.e. Williams, J.L. Swedlow and the Regional Editors for their respective contributions as we observe this 25th milestone.

From time to time the International Journal of Fracture has presented matters thought to be of special interest to its readers. In previous special issues (December 1980 and April 1981), Dr H.W. Liu as Guest Editor presented a series of review papers dealing with fatigue processes and characteristics in metals and non-metals. Continuing this policy, which is consistent with our stated objectives, a second review dealing with time depen­ dence in the fracture process, including the effect of material inertia but essentially excluding very strong shock effects in solids, has been assembled under the generic term'dynamic fracture'. We hope that the ensuing state-of-the-art review will yield an instructive and timely product which readers will find useful. To assist us in presenting this subject, we have prevailed upon a well-known worker in dynamic fracture, Dr W.G. Knauss, Professor of Aeronautics and Applied Mechanics, California Institute of Technology to act as Guest Editor for this special double issue. On behalf of the editors and publisher, I wish to express our indebtedness to Professor Knauss and his invited authors for undertaking this special effort.

The book explores the two opposite natural trends of composite systems: (i) order and structure emerging from heterogeneity and randomness, and (ii) instability and chaos arising from simple nonlinear rules. Providing insights into the rapidly growing field of complexity sciences, the book focuses on the role of complexity in fracture mechanics. It firstly discusses the occurrence of self-similarity and fractal patterns in deformation, damage, fracture, and fragmentation of heterogeneous materials and the apparent scaling of the nominal mechanical properties of disordered materials, as well as of the time-to-failure after fatigue and creep loading. Then the book addresses criticality in the acoustic emissions from damaged structures and tectonic faults. Further, it examines the snap-back instability in the structural behavior of relatively large composite structures in the framework of catastrophe theory, and lastly describes the transition toward chaos in the dynamics of cracked elements.

This book offers a comprehensive and timely review of the fracture behavior of bimaterial composites consisting of periodically connected components, i.e. of bimaterial composites possessing periodical cracks along the interface. It first presents an overview of the literature, and then analyzes the isotropic, anisotropic and piezoelectric/dielectric properties of bimaterial components, gradually increasing the difficulty of the solutions discussed up to the coupled electromechanical problems. While in the case of isotropic and anisotropic materials it covers the problems generated by an arbitrary set of cracks, for the piezoelectric materials it focuses on studying the influence of the electric permittivity of the crack's filler, using not only a simple, fully electrically permeable model, but also a physically realistic, semi-permeable model. Throughout the analyses, the effects of the contact of the crack faces are taken into account so as to exclude the physically unrealistic interpenetration of the composite components that are typical of the classical open model. Further, the book derives and examines the mechanical and electromechanical fields, stress and electric intensity factors in detail. Providing extensive information on the fracture processes taking place in composite materials, the book helps readers become familiar with mathematical methods of complex function theory for obtaining exact analytical solutions.

This book provides a state-of-the-art review of the fail-safe and damage tolerance approaches, allowing weight savings and increasing aircraft reliability and structural integrity.The application of the damage tolerance approach requires extensive know-how of the fatigue and fracture properties, corrosion strength, potential failure modes and non-destructive inspection techniques, particularly minimum detectable defect and inspection intervals. In parallel, engineering practice involving damage tolerance requires numerical techniques for stress analysis of cracked structures. These evolved from basic mode I evaluations using rough finite element approaches, to current 3D modeling based on energetic approaches as the VCCT, or simulation of joining processes. This book provides a concise introduction to this subject.

In this thesis, the author investigates experimentally and numericallythe fracture behavior of an electron beam welded joint made fromtwo butt S355 plates. The 2D Rousselier model, the Gurson-Tvergaard-Needleman (GTN) model and the cohesive zone model (CZM) wereadopted to predict the crack propagation of thick compact tension (CT)specimens. Advantages and disadvantages of the three mentioned modelsare discussed. The cohesive zone model is suggested as it is easy to usefor scientists & engineers because the CZM has less model parametersand can be used to simulate arbitrary crack propagation. The resultsshown in this thesis help to evaluate the fracture behavior of a metallicmaterial. A 3D optical deformation measurement system (ARAMIS) andthe synchrotron radiation-computed laminography (SRCL) techniquereveal for the first time the damage evolution on the surfaceof the sampleand inside a thin sheet specimen obtained from steel S355. Damageevolution by void initiation, growth and coalescence are visualized in2D and 3D laminographic images. Two fracture types, i.e., a flat crackpropagation originated from void initiation, growth and coalescenceand a shear coalescence mechanism are visualized in 2D and 3D imagesof laminographic data, showing the complexity of real fracture. Inthe dissertation, the 3D Rousselier model is applied for the first timesuccessfully to predict different microcrack shapes before shear cracksarise by defining the finite elements in front of the initial notch withinhomogeneous f0-values. The influence of the distribution of inclusionson the fracture shape is also discussed. For the analyzed material, ahomogeneous distribution of particles in the material provides thehighest resistance to fracture.

This book introduces readers to the application of fracture mechanics and mesomechanics to the analysis of the fracture behaviors of wood and bamboo. It presents a range of research methods to study the fracture behaviors of wood and bamboo, taking into account their various fracture mechanisms resulting from differences in their macroscopic and microscopic structures. It combines theoretical analysis with experiments, as well as various mathematical tools and experimental approaches. The research methods are illustrated by simple schematic diagrams, and the results obtained are largely presented as tables and figures, helping to make the book concise and compact. As such, it provides a valuable guide to the development of new biocomposites that possess exceptional strength and toughness properties and successfully overcome the shortcomings of biomaterials.

This book is based on 40 years of research and teaching in the fields of fracture mechanics and plasticity. It will bring students and engineers from various disciplines up to date on key concepts that have become increasingly important in the design of safety-relevant engineering structures in general and in modern lightweight structures in the transportation industry in particular. Primarily intended for graduate students in the engineering sciences and practicing structural engineers, it employs a multidisciplinary approach that comprises theoretical concepts, numerical methods, and experimental techniques. In addition, it includes a wealth of analytical and numerical examples, used to illustrate the applications of the concepts discussed.

This book covers a wide range of topics in fracture and damage mechanics. It presents historical perspectives as well as recent innovative developments, presented by peer reviewed contributions from internationally acknowledged authors. The volume deals with the modeling of fracture and damage in smart materials, current industrial applications of fracture mechanics, and it explores advances in fracture testing methods. In addition, readers will discover trends in the field of local approach to fracture and approaches using analytical mechanics. Scholars in the fields of materials science, engineering and computational science will value this volume which is dedicated to Meinhard Kuna on the occasion of his 65th birthday in 2015. This book incorporates the proceedings of an international symposium that was organized to honor Meinhard Kuna's contributions to the field of theoretical and applied fracture and damage mechanics.

This book offers a concise introduction to fatigue crack growth, based on practical examples. It discusses the essential concepts of fracture mechanics, fatigue crack growth under constant and variable amplitude loading and the determination of the fracture-mechanical material parameters. The book also introduces the analytical and numerical simulation of fatigue crack growth as well as crack initiation. It concludes with a detailed description of several practical case studies and some exercises. The target group includes graduate students, researchers at universities and practicing engineers.

This volume introduces a comprehensive theory of deformation and fracture to engineers and applied scientists. Here “comprehensive” means that the theory can describe all stages of deformation from elastic to plastic and plastic to fracturing stage on the same basis (equations). The comprehensive approach is possible because the theory is based on a fundamental physical principle called the local symmetry, or gauge invariance, as opposed to phenomenology.Professor Yoshida explains the gist of local symmetry (gauge invariance) intuitively so that engineers and applied physicists can digest it easily, rather than describing physical or mathematical details of the principle. The author also describes applications of the theory to practical engineering, such as nondestructive testing in particular, with the use of an optical interferometric technique called ESPI (Electronic Speckle-Pattern Interferometry).The book is not a manual of applications. Instead, it provides information on how to apply physical concepts to engineering applications.

A complete and comprehensive theory of failure is developed for homogeneous and isotropic materials. The full range of materials types are covered from very ductile metals to extremely brittle glasses and minerals. Two failure properties suffice to predict the general failure conditions under all states of stress. With this foundation to build upon, many other aspects of failure are also treated, such as extensions to anisotropic fiber composites, cumulative damage, creep and fatigue, and microscale and nanoscale approaches to failure.

This book summarizes research advances in micromechanics modeling of ductile fractures made in the past two decades. The ultimate goal of this book is to reach manufacturing frontline designers and materials engineers by providing a user-oriented, theoretical background of micromechanics modeling. Accordingly, the book is organized in a unique way, first presenting a vigorous damage percolation model developed by the authors over the last ten years. This model overcomes almost all difficulties of the existing models and can be used to completely accommodate ductile damage developments within a single-measure microstructure frame. Related void damage criteria including nucleation, growth and coalescence are then discussed in detail: how they are improved, when and where they are used in the model, and how the model performs in comparison with the existing models. Sample forming simulations are provided to illustrate the model's performance.

Designing new structural materials, extending lifetimes and guarding against fracture in service are among the preoccupations of engineers, and to deal with these they need to have command of the mechanics of material behaviour. This ought to reflect in the training of students. In this respect, the first volume of this work deals with elastic, elastoplastic, elastoviscoplastic and viscoelastic behaviours; this second volume continues with fracture mechanics and damage, and with contact mechanics, friction and wear. As in Volume I, the treatment links the active mechanisms on the microscopic scale and the laws of macroscopic behaviour. Chapter I is an introduction to the various damage phenomena. Chapter II gives the essential of fracture mechanics. Chapter III is devoted to brittle fracture, chapter IV to ductile fracture and chapter V to the brittle-ductile transition. Chapter VI is a survey of fatigue damage. Chapter VII is devoted to hydrogen embrittlement and to environment assisted cracking, chapter VIII to creep damage. Chapter IX gives results of contact mechanics and a description of friction and wear mechanisms. Finally, chapter X treats damage in non metallic materials: ceramics, glass, concrete, polymers, wood and composites. The volume includes many explanatory diagrams and illustrations. A third volume will include exercises allowing deeper understanding of the subjects treated in the first two volumes.

Fracture Mechanics of Piezoelectric and Ferroelectric Solids presents a systematic and comprehensive coverage of the fracture mechanics of piezoelectric/ferroelectric materials, which includes the theoretical analysis, numerical computations and experimental observations. The main emphasis is placed on the mechanics description of various crack problems such static, dynamic and interface fractures as well as the physical explanations for the mechanism of electrically induced fracture.The book is intended for postgraduate students, researchers and engineers in the fields of solid mechanics, applied physics, material science and mechanical engineering.Dr. Daining Fang is a professor at the School of Aerospace, Tsinghua University, China; Dr. Jinxi Liu is a professor at the Department of Engineering Mechanics, Shijiazhuang Railway Institute, China.

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.

In the preliminary stage of designing new structural hardware to perform a given mission in a fluctuating load environment, there are several factors that the designer 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 withstand the environment in question without failure. Therefore, a comprehensive structural analysis that consists of static, dynamic, fatigue, and fracture is necessary to ensure the integrity of the structure. Engineers must also consider the feasibility of fabricating the structural hardware in the material selection process. During the past few decades, fracture mechanics has become a necessary discipline for the solution of many structural problems in which the survivability of structure containing pre-existing flaws is of great interest. These problems include structural failures resulting from cracks that are inherent in the material, or defects that are introduced in the part due to improper handling or rough machining, that must be assessed through fracture mechanics concepts.

As the shift from the Metal Age progresses, materials engineers and materials scientists seek new analytical and design methods to create stronger and more reliable materials. Based on extensive research and developmental work done at the author's multi-disciplinary material laboratory, this graduate-level and professional reference addresses the relationship between fracture mechanisms (macroscale) and the microscopic, with the goal of explaining macroscopic fracture behavior based on a microscopic fracture mechanism. A careful fusion of mechanics and materials science, this text and monograph systematically considers an array of materials, from metals through ceramics and polymers, and demonstrates lab-tested strategies to develop desirable high-temperature materials for technological applications.

This book focuses on the mechanisms and underlying mechanics of failure in various classes of materials such as metallic, ceramic, polymeric, composite and bio-material. Topics include tensile and compressive fracture, crack initiation and growth, fatigue and creep rupture in metallic materials, matrix cracking and delamination and environmental degradation in polymeric composites, failure of bio-materials such as prosthetic heart valves and prosthetic hip joints, failure of ceramics and ceramic matrix composites, failure of metallic matrix composites, static and dynamic buckling failure, dynamic excitations and creep buckling failure in structural systems. Chapters are devoted to failure mechanisms that are characteristic of each of the materials. The work also provides the basic elements of fracture mechanics and studies in detail several niche topics such as the effects of toughness gradients, variable amplitude loading effects in fatigue, small fatigue cracks, and creep induced brittleness. Furthermore, the book reviews a large number of experimental results on these failure mechanisms. The book will benefit structural and materials engineers and researchers seeking a “birds-eye” view of possible failure mechanisms in structures along with the associated failure and structural mechanics.

The aim of the book is to present, in a novel and unified fashion, the elements of Mechanics in Material Space or Configurational Mechanics, with applications to fracture and defect mechanics. This mechanics, in contrast to Newtonian mechanics in physical space, is concerned with defects such as cracks and dislocations, which are embedded in the material and might move in it. The level is kept accessible to any engineer, scientist or graduate student possessing some knowledge of calculus and partial differential equations, and working in the various areas where rational use of materials is essential.

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.

Fracture mechanics is a vast and growing field. This book develops the basic elements needed for both fracture research and engineering practice. The emphasis is on continuum mechanics models for energy flows and crack-tip stress- and deformation fields in elastic and elastic-plastic materials. In addition to a brief discussion of computational fracture methods, the text includes practical sections on fracture criteria, fracture toughness testing, and methods for measuring stress intensity factors and energy release rates. Class-tested at Cornell, this book is designed for students, researchers and practitioners interested in understanding and contributing to a diverse and vital field of knowledge.

Concerned with the fundamental concepts and methods of fracture mechanics and micromechanics, Fracture Mechanics primarily focuses on the mechanical description of the fracture process; however, material specific aspects are also discussed. The presentation of continuum mechanical and phenomenological foundations is followed by an introduction into classical failure hypotheses. A major part of the book is devoted to linear elastic and elastic-plastic fracture mechanics. Further subjects are creep fracture, dynamic fracture mechanics, damage mechanics, probabilistic fracture mechanics, failure of thin films and fracture of piezoelectric materials. The book also contains an extensive introduction into micromechanics. Self-contained and well-illustrated, this text serves as a graduate-level text and reference.

Micromechanisms of Fracture and Fatigue forms the culmination of 20 years of research in the field of fatigue and fracture. It discusses a range of topics and comments on the state of the art for each. The first part is devoted to models of deformation and fracture of perfect crystals. Using various atomistic methods, the theoretical strength of solids under simple and complex loading is calculated for a wide range of elements and compounds, and compared with experimental data. The connection between the onset of local plasticity in nanoindentation tests and the ideal shear strength is analysed using a multi-scale approach. Moreover, the nature of intrinsic brittleness or ductility of perfect crystal lattices is demonstrated by the coupling of atomistic and mesoscopic approaches, and compared with brittle/ductile behaviour of engineering materials. The second part addresses extrinsic sources of fracture toughness of engineering materials, related to their microstructure and microstructurally-induced crack tortuosity. Micromechanisms of ductile fracture are also described, in relation to the fracture strain of materials. Results of multilevel modelling, including statistical aspects of microstructure, are used to explain remarkable phenomena discovered in experiments. In the third part of the book, basic micromechanisms of fatigue cracks propagation under uniaxial and multiaxial loading are discussed on the basis of the unified mesoscopic model of crack tip shielding and closure, taking both microstructure and statistical effects into account. Applications to failure analysis are also outlined, and an attempt is made to distinguish intrinsic and extrinsic sources of materials resistance to fracture. Micromechanisms of Fracture and Fatigue provides scientists, researchers and postgraduate students with not only a deep insight into basic micromechanisms of fracture behaviour of materials, but also a number of engineering applications.

The First African InterQuadrennial ICF Conference “AIQ-ICF2008” on Damage and Fracture Mechanics – Failure Analysis of Engineering Materials and Structures”, Algiers, Algeria, June 1–5, 2008 is the first in the series of InterQuadrennial Conferences on Fracture to be held in the continent of Africa. During the conference, African researchers have shown that they merit a strong reputation in international circles and continue to make substantial contributions to the field of fracture mechanics. As in most countries, the research effort in Africa is und- taken at the industrial, academic, private sector and governmental levels, and covers the whole spectrum of fracture and fatigue. The AIQ-ICF2008 has brought together researchers and engineers to review and discuss advances in the development of methods and approaches on Damage and Fracture Mechanics. By bringing together the leading international experts in the field, AIQ-ICF promotes technology transfer and provides a forum for industry and researchers of the host nation to present their accomplishments and to develop new ideas at the highest level. International Conferences have an important role to play in the technology transfer process, especially in terms of the relationships to be established between the participants and the informal exchange of ideas that this ICF offers.

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 manner.

Fiber Reinforced Plastics (FRP) are widely used for the design of load-bearing structures. Life time prediction based on failure analysis is therefore essential for many applications in Aeronautics, Automotive and Civil Engineering. Analysis of Failure in Fiber Polymer Laminates presents Alfred Puck´s failure model, which, among several other theories, predicts fracture limits best and describes the failure phenomena in FRP most realistically – as confirmed within the “World-wide Failure Exercise”. Using Puck´s model the composite engineer can follow the gradual failure process in a laminate and deduce from the results of the analysis how to improve the laminate design. This capability distinguishes the model from other phenomenological and global models. It thus reduces the number of required component tests and iteration loops in the design process and paves the way to sorely needed software for crash-simulation of FRP-structures.

What can be added to the fracture mechanics of metal fatigue that has not already been said since the 1900s? From the view point of the material and structure engineer, there are many aspects of failure by fatigue that are in need of attention, particularly when the size and time of the working components are changed by orders of magnitude from those considered by st traditional means. The 21 century marks an era of technology transition where structures are made larger and devices are made smaller, rendering the method of destructive testing unpractical. While health monitoring entered the field of science and engineering, the practitioners are discovering that the correlation between the signal and the location of interest depends on a priori knowledge of where failure may initiate. This information is not easy to find because the integrity of the physical system will change with time. Required is software that can self-adjust in time according to the monitored data. In this connection, effective application of health monitoring can use a predictive model of fatigue crack growth. Earlier fatigue crack growth models assumed functional dependence on the maximum stress and the size of the pre-existing crack or defect. Various possibilities were examined in the hope that the data could be grouped such that linear interpolation would apply.

Concerned with the fundamental concepts and methods of fracture mechanics and micromechanics, Fracture Mechanics primarily focuses on the mechanical description of fracture processes; however, material specific aspects are also discussed. The presentation of continuum mechanical and phenomenological foundations is followed by an introduction into classical failure hypotheses. A major part of the book is devoted to linear elastic and elastic-plastic fracture mechanics. Further subjects are creep fracture, dynamic fracture mechanics, damage mechanics, probabilistic fracture mechanics, failure of thin films and fracture of piezoelectric materials. The book also contains an extensive introduction into micromechanics. Self-contained and well-illustrated, this text serves as a graduate-level text and reference. The 2nd revised edition has been expanded and complemented by numerous problems and figures.

“As a general principle natural selection is continually trying to economise every part of the organisation. ” That was Charles Darwin, writing over 100 years ago about e- ciency innature. Naturalmaterialsareremarkably ef?cient. Byef?cient wemeanthat they ful?l the complex requirements posed by the way plants and animals function, and that they do so using as little material as possible. Many of these requirements are mechanical in nature: the need to support static and dynamic loads created by the mass of the organism or by wind loading, the need to store and release elastic energy, the need to?ex through large angles, the need to resist buckling and fracture, and to survive damage. Few optimisation algorithms have been more successful than that of “survival of the?ttest”. The structural materials of nature exemplify this op- misation; even today, few man-made materials do better than those of nature in the function that they?ll. And of all the remarkable properties of natural materials, one is truly exceptional – that of the ability for self-repair. One recurring goal of material development has been to emulate the materials of nature. Among these, the most illusive is that of self-repair. In approaching this it is well to be aware of the nature of the differences that separate the structural materials of man and those of nature.

Residual Stress Measurement and the Slitting Method provides complete coverage of the slitting method with new results in analysis, computation and estimation. It discusses different roles of residual stresses from the fracture mechanics perspective. Covering both near-surface and through-thickness residual stress measurements, the book serves as a reference tool for graduate students, researchers and practicing engineers. The authors include discussions on the general expressions for residual stresses acting on the site of a slit, the analysis based on fracture mechanics solutions and finite element computations, the estimations using continuous and piecewise functions with and without least squares fit, examples of residual stress measurement and error analysis, the measurement of stress intensity factors, and many more timely topics. With more than 130 figures, Residual Stress Measurement and the Slitting Method provides detailed formulations and examples of compliance functions, weighted least squares fit and convergence test in stress estimation, and computer programs to facilitate the implementation of the slitting method. This book is an invaluable reference for professionals and researchers in the field.

This book is an outgrowth of my involvement in two groups of research in solid mechanics, created in 1960 for the French nuclear energy program. At this time, it was decided that France, as a no-oil reservoir country, must be powered by nuclear energy, which represents today 80% of the total - tional energy supply. Long before the construction of the first nuclear plant at Fessenheim in 1973, Electricité de France (EdF) created its first solid mechanics laboratory, appointed researchers and sent them to the universities or abroad in order to learn about theories and new methods of assessment of the safety of structures. Working at EdF, I was training in Professor Jean Mandel's laboratory at Ecole Polytechnique (LMS), Paris. My friend René Labbens, working at Framatome (the builder of nuclear plants) was training at the Lehigh University, under the guidance of professors G. R. Irwin and G. C. Sih. We had to work hard, both academically at the u- versities laboratories and performing engineering tasks for our employer. This dual position was a great chance for many of us, since we discovered that real industrial problems are the source of new subjects and research problems to be solved by theoreticians in the universities and conversely we immediately knew if our theoretical work was good or not for appli- tions as revealed in our daily works conducted for our industrial employer.

Simplified fracture mechanics based assessment methods are widely used by the industry to determine the structural integrity significance of postulated cracks, manufacturing flaws, service-induced cracking or suspected degradation of engineering components under normal and abnormal service loads. In many cases, welded joints are the regions most likely to contain original fabrication defects or cracks initiating and growing during service operation. Various procedures provide upper bound residual stress profiles for various classes of welded joints that can be used in fracture assessments, but these often give very conservative results. Recently, the option to use more realistic profiles has been adopted, but only where such profiles are based on finite element residual stress simulations supported by detailed residual stress measurements. Rapid advances in the capability of residual stress measurement techniques, such as the contour and deep hole drilling techniques as well as the neutron and synchrotron X-ray diffraction methods, now readily allow residual stresses and strains to be mapped on defined planes within a structure. The contents of this book have been grouped into three topic areas covering theoretical /numerical and experimental analyses of residual stress and its effects on fatigue and fracture.

Dynamic fracture in solids has attracted much attention for over a century from engineers as well as physicists due both to its technological interest and to inherent scientific curiosity. Rapidly applied loads are encountered in a number of technical applications. In some cases such loads might be applied deliberately, as for example in problems of blasting, mining, and comminution or fragmentation; in other cases, such dynamic loads might arise from accidental conditions. Regardless of the origin of the rapid loading, it is necessary to understand the mechanisms and mechanics of fracture under dynamic loading conditions in order to design suitable procedures for assessing the susceptibility to fracture. Quite apart from its repercussions in the area of structural integrity, fundamental scientific curiosity has continued to play a large role in engendering interest in dynamic fracture problems In-depth coverage of the mechanics, experimental methods, practical applications Summary of material response of different materials Discussion of unresolved issues in dynamic fracture

Fracture Mechanics is a graduate level text/professional reference that describes the analytical methods used to derive stress and strain functions related to fracture mechanics. The focus of the book will be on modeling and problem solving as tools to be used in interpreting the meaning of a mathematical solution for a particular engineering problem or situation. Once this is accomplished, the reader should be able to think mathematically, foresee metallurgically the significance of microstructural parameters on properties, analyze the mechanical behavior of materials, and recognize realistically how dangerous a crack is in a stressed structure, which may fail catastrophically. This book differs from others in that the subject matter is organized around the modeling and predicating approaches that are used to explain the detrimental effects of crack growth events. Thus, this book will take a more practical approach and make it especially useful as a basic reference for professional engineers.

Shock-induced dynamic fracture of solids is of practical importance in many areas of materials science, chemical physics, engineering, and geophysics. This book, by an international roster of authors, comprises a systematic account of the current state of research in the field, integrating the large amount of work done in the former Soviet Union with the work done in the West. Topics covered include: Wave propagation, experimental techniques and measurements, spallation of materials of different classes (metals, ceramics, glasses, polymers), constitutive models of fracture processes, and computer simulations.

When asked to start teaching a course on engineering fracture mechanics, I realized that a concise textbook, giving a general oversight of the field, did not exist. The explanation is undoubtedly that the subject is still in a stage of early development, and that the methodologies have still a very limited applicability. It is not possible to give rules for general application of fracture mechanics concepts. Yet our comprehension of cracking and fracture beha viour of materials and structures is steadily increasing. Further developments may be expected in the not too distant future, enabling useful prediction of fracture safety and fracture characteristics on the basis of advanced fracture mechanics procedures. The user of such advanced procedures m\lst have a general understanding of the elementary concepts, which are provided by this volume. Emphasis was placed on the practical application of fracture mechanics, but it was aimed to treat the subject in a way that may interest both metallurgists and engineers. For the latter, some general knowledge of fracture mechanisms and fracture criteria is indispensable for an apprecia­ tion of the limita tions of fracture mechanics. Therefore a general discussion is provided on fracture mechanisms, fracture criteria, and other metal­ lurgical aspects, without going into much detail. Numerous references are provided to enable a more detailed study of these subjects which are still in a stage of speculative treatment.