This volume constitutes the Proceedings of the IUTAM Symposium on "Analytical and Computational Fracture Mechanics of Non-homogeneous Materials," held in Cardiff from 18th to 22nd June 2001. The Symposium was convened to address and place on record topical issues in analytical and computational aspects of the fracture of non-homogeneous materials as they are approached by specialists in mechanics, materials science and related fields. The expertise represented in the Symposium was accordingly very wide, and many of the world's greatest authorities in their respective fields participated. Given the extensive range and scale of non-homogeneous materials, it had to be focussed to enhance the quality and impact of the Symposium. The range of non-homogeneous materials was limited to those that are inhomogeneous at the macroscopic level and/or exhibit strain softening. The issues of micro to macro scaling were not excluded even within this restricted range which covered materials such as rock, concrete, ceramics and composites on the one hand, and, on the other, those metallic materials whose ductile fracture is strongly influenced by the presence of inhomogeneities. The Symposium remained focussed on fundamental research issues of practical significance. These issues have many common features among seemingly disparate non-homogeneous materials.

Materials of micro-/nanometer dimensions have aroused remarkable interest, motivated by the diverse utility of unconventional mechanical and electronic properties distinguished from the bulk counterpart and various industrial applications such as electronic/optic devices and MEMS/NEMS. The size of their elements is now, ultimately, approaching nanometer and atomic scales. Since the conventional theory of "fracture mechanics" is based on the continuum-body approximation, its applicability to the nanoscale components is questionable owing to the discreteness of atoms. Moreover, for describing the fracture behavior of atomic components, it is necessary to understand not only the mechanical parameters (e.g., stress and strain) but also the fracture criterion in the atomic scale. This book systematically provides recent understanding of unusual fracture behaviors in nano/atomic elements (nanofilms, nanowires, etc.) and focuses on the critical initiation and propagation of interface crack and the mechanical instability criteria of atomic structures through the introduction of state-of-the-art experimental and theoretical techniques. It covers the fundamentals and the applicability of top-down (conventional fracture mechanics to nanoscale) and bottom-up (atomistic mechanics, including quantum mechanical effects) concepts. This second edition of Fracture Nanomechanics newly includes dramatic advances in unconventional fracture mechanics in nanofilms, extraordinary fatigue mechanics and mechanisms in nanometals, and a new area of multiphysics properties in nanoelements.

This monograph presents recent research findings on fracture properties and behavior of the composites, and their damage and cracking process under both quasi-static and impact loading conditions. Theoretical treatment, experimental investigation and numerical simulation aspects of the mechanics of composites, including sandwich structures are included.

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.

Intended for engineers, researchers, and graduate students dealing with materials science, structural design, and nondestructive testing and evaluation, this book represents a continuation of the author's "Fracture Mechanics" (1997). It will appeal to a variety of audiences: The discussion of design codes and procedures will be of use to practicing engineers, particularly in the nuclear, aerospace, and pipeline industries; the extensive bibliography and discussion of recent results will make it a useful reference for academic researchers; and graduate students will find the clear explanations and worked examples useful for learning the field. The book begins with a general treatment of fracture mechanics in terms of material properties and loading and provides up-to-date reviews of the ductile-britttle transition in steels and of methods for analyzing the risk of fracture. It then discusses the dynamics of fracture and creep in homogeneous and isotropic media, including discussions of high-loading-rate characteristics, the behavior of stationary cracks in elastic media under stress, and the propagation of cracks in elastic media. This is followed by an analysis of creep and crack initiation and propagation, describing, for example, the morphology and incubation times of crack initiation and growth and the effects of high temperatures. The book concludes with treatments of cycling deformation and fatigue, creep-fatigue fractures, and crack initiation and propagation. Problems at the end of each chapter serve to reinforce and test the student's knowledge and to extend some of the discussions in the text. Solutions to half of the problems are provided.

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.

Fatigue Design of Marine Structures provides students and professionals with a theoretical and practical background for fatigue design of marine structures including sailing ships, offshore structures for oil and gas production, and other welded structures subject to dynamic loading such as wind turbine structures. Industry expert Inge Lotsberg brings more than forty years of experience in design and standards-setting to this comprehensive guide to the basics of fatigue design of welded structures. Topics covered include laboratory testing, S-N data, different materials, different environments, stress concentrations, residual stresses, acceptance criteria, non-destructive testing, improvement methods, probability of failure, bolted connections, grouted connections, and fracture mechanics. Featuring twenty chapters, three hundred diagrams, forty-seven example calculations, and resources for further study, Fatigue Design of Marine Structures is intended as the complete reference work for study and practice.

The book presents twelve state of the art contributions in the field of numerical modeling of materials subjected to large strain, high strain rates, large pressure and high stress triaxialities, organized into two sections. The first part is focused on high strain rate-high pressures such as those occurring in impact dynamics and shock compression related phenomena, dealing with material response identification, advanced modeling incorporating microstructure and damage, stress waves propagation in solids and structures response under impact. The latter part is focused on large strain-low strain rates applications such as those occurring in technological material processing, dealing with microstructure and texture evolution, material response at elevated temperatures, structural behavior under large strain and multi axial state of stress.

Presents a new physical and mathematical theory of irreversible deformations and ductile fracture of metals that acknowledges the continuous change in the structure of materials during deformation and the accumulation of deformation damage. Plastic deformation, viscous destruction, evolution of structure, creep processes, and long-term strength of metals and stress relaxation are described in the framework of a unified approach and model. The author then expands this into a mathematical model for determining the mechanical characteristics of quasi-samples of standard mechanical properties in deformed semi-finished products.

This unified guide brings together the underlying principles, and predictable material responses, that connect metals, polymers, brittle solids and energetic materials as they respond to extreme external stresses. Previously disparate scientific principles, concepts and terminology are combined within a single theoretical framework, across different materials and scales, to provide all the tools necessary to understand, and calculate, the responses of materials and structures to extreme static and dynamic loading. Real-world examples illustrate how material behaviours produce a component response, enabling recognition - and avoidance - of the deformation mechanisms that contribute to mechanical failure. A final synoptic chapter presents a case study of extreme conditions brought about by the infamous Chicxulub impact event. Bringing together simple concepts from diverse fields into a single, accessible, rigorous text, this is an indispensable reference for all researchers and practitioners in materials science, mechanical engineering, physics, physical chemistry and geophysics.

This the third volume of six from the Annual Conference of the Society for Experimental Mechanics, 2010, brings together 56 chapters on Time-Dependent Constitutive Fracture and Failure. It presents early findings from experimental and computational investigations on Time Dependent Materials including contributions on Thermal and Mechanical Characterization, Coupled Experimental and Computational Analysis of Fracture Path Selection, Procedures for Mixed Mode Fracture Testing of Bonded Beams, and Experimental Study of Voids in High Strength Aluminum Alloys.

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.

The Second International Symposium on Defects, Fracture and Fatigue took place at Mont Gabriel, Quebec, Canada, May 30 to June 5, 1982, and was organized by the Mechanical Engineering Department of McGill University and Institute of Fracture and Solid Mechanics, Lehigh University. The Co-Chairmen of the Sympo- sium were Professor G. C. Sih of Lehigh University and Professor J. W. Provan of McGill University. Among those who served on the Organizing Committee were G. C. Sih (Co-Chairman), J. W. Provan (Co-Chairman), H. Mughrabi, H. Zorski, R. Bullough, M. Matczynski, G. Barenblatt and G. Caglioti. As a result of the interest expressed at the First Symposium that was held in October 1980, in Po- land, the need for a follow-up meeting to further explore the phenomena of mate- rial damage became apparent. Among the areas considered were dislocations, per- sistent-slip-bands, void creation, microcracking, microstructure effects, micro/ macro fracture mechanics, ductile fracture criteria, fatigue crack initiation and propagation, stress and failure analysis, deterministic and statistical crack models, and fracture control. This wide spectrum of topics attracted researchers and engineers in solid state physics, continuum mechanics, applied mathematics, metallurgy and fracture mechanics from many different countries. This spectrum is also indicative of the interdisciplinary character of material damage that must be addressed at the atomic, microscopic and macroscopic scale level.

The International Conference on Fracture Mechanics in Engineering Applica tion convened at the r ational Aeronautical Laboratory (NAL) in Bangalore, India, March 26-30, 1979, with the presence of approximately 400 scientists and engi neers. The participants included individuals from all parts of India, United States of America, United Kingdom, Japan, Holland, France, Hong Kong, Korea, Sweden and Poland. The Conference was organized jointly by NAL, Bangalore;and Lehigh University, USA. Various organizations in India have also supported the Conference most generously. Professor S. Dhawan, Director of the Indian Institute of Science and Secre tary of Department of Space, delivered the inaugural speech. He said that the advance of science was the precondition of the development and survival of human society in the modern world. "It is true that in recent times, science and tech nology - and their practitioners - have been subjected to much public scrutiny, debate and severe criticism." On the other hand, the depletion of non-renewable resources, degradation of the natural environment and a host of other problems had been laid at the door of technology and science. One cannot deny that funda mental advances in the physics and chemistry of the structure of matter had led to spectacular engineering progress. Advanced technologies like nuclear energy and space exploration were but expression of the central role of computors, elec tronics, optics, polymers, etc., and all of these were heavily dependent on the successful application of material science and technology."

This International Conference on Analytical and Experimental Fracture Me chanics was organized jointly by the Centro Sperimentale Metallurgico, S. p. A. , Lehigh University and Italsider S. p. A. It took place at the Hotel Midas Palace in Rome, Italy, during 23-27 June, 1980. There were more than 150 attendees from 19 different countries: Australia, Austria, Belgium, Canada, People's Re public of China, Czechoslovakia, Finland, Federal Republic of Germany, Hungary, Israel, Italy, Japan, The Netherlands, Poland, Switzerland, Turkey, UK, USA and USSR. Dr. G. M. Costa from Finsider officially opened the Conference and gave the Welcome Address. More than 70 technical papers were presented at three con current sessions. There were six plenary lectures that helped to integrate the diverse efforts, e. g. , analytical fracture mechanics, testing methods, metallur gical effects, corrosion fatigue, dynamic crack propagation and weldments of in dividual researchers. In addition to providing an overall view of the current status of fracture mechanics technology, particular emphasis was given to methods of controlling fracture in gas pipeline structures. The members of the Organizing Committee made a special effort to organize a panel discussion on the application of fracture mechanics technology to the safe design of large diameter pipelines. Dr. Michele Civallero from Italsider and Professor George C. Sih from Lehigh University served as panel Co-Chairmen and delivered survey lectures to stimulate questions from the audience.

This book, based on the analogy between contact mechanics and fracture mechanics proposed by the author twenty years ago, starts with a treatment of the surface energy and tension of solids and surface thermodynamics. The essential concepts of fracture mechanics are presented with emphasis on the thermodynamic aspects. Readers will find complete analytical results and detailed calculations for cracks submitted to pressure distributions and the Dugdale model. Contact mechanics and the contact and adherence of rough solids are also covered.

Many approaches have been proposed to solve the problem of finding the optic flow field of an image sequence. Three major classes of optic flow computation techniques can discriminated (see for a good overview Beauchemin and Barron IBeauchemin19951): gradient based (or differential) methods; phase based (or frequency domain) methods; correlation based (or area) methods; feature point (or sparse data) tracking methods; In this chapter we compute the optic flow as a dense optic flow field with a multi scale differential method. The method, originally proposed by Florack and Nielsen [Florack1998a] is known as the Multiscale Optic Flow Constrain Equation (MOFCE). This is a scale space version of the well known computer vision implementation of the optic flow constraint equation, as originally proposed by Horn and Schunck [Horn1981]. This scale space variation, as usual, consists of the introduction of the aperture of the observation in the process. The application to stereo has been described by Maas et al. [Maas 1995a, Maas 1996a]. Of course, difficulties arise when structure emerges or disappears, such as with occlusion, cloud formation etc. Then knowledge is needed about the processes and objects involved. In this chapter we focus on the scale space approach to the local measurement of optic flow, as we may expect the visual front end to do. 17. 2 Motion detection with pairs of receptive fields As a biologically motivated start, we begin with discussing some neurophysiological findings in the visual system with respect to motion detection.

Wood Fracture Characterization provides a guide to the application of modern fracture mechanics concepts to wood materials used in structural engineering, which commonly involve discontinuities and irregularities. The authors cover the tests, data reduction schemes and numerical methods devised for wood structural applications, based on cohesive zone analysis, and used to validate experimental-based methodologies. Five detailed Case Studies are included to link theory with engineering practice. This important new text explains the basics of fracture mechanics, and extends them as needed to cover the special behaviour of an anisotropic wood materials.

Five laboratories from France, Hungary and the Czech Republic have solved a Project supported fmancially by NATO within the Science for Peace Program (under Nr. 972655) for three years. The project, titled Fracture ResistanceofSteelsfor Containers of Spent Nuclear Fuel, was focused (i) on the generation of data needed for the qualification procedure of a new container introduced by Skoda Nuclear Machinery and (ii) on a number of topics of scientific nature associated with the interesting field of transferability of fracture mechanical data-, It has been found during numerous conference presentations of project results that the knowledge developed within the project would be more attractive when published in a more comprehensive form. This was the reason why the final project workshop was arranged as a meeting of project collaborators and contributing invited experts working in very similar field. The main scope of the final project workshop, titled Transferability of Fracture Mechanical Data and held in Brno from 5 to 6 November 200I, was to bring together project collaborators with a number of invited international experts, both covering the spectrum of topics solved within the project and reviewing the project results in the presence ofthese specialists. A totalof34 colleagues from 7 European countries and the USA participated in the workshop.

This book brings together scientists from diverse research communities to focus on four different aspects of fracture - instability dynamics, scaling/fractal geometry, the brittle/ductile transition, and fracture at interfaces. In each case, theoretical issues, as well as experimental and computer-simulated techniques, are addressed. Materials of interest range from ceramics to thin films, multilayer structures, composites and bulk crystals. Topics include: brittle/ductile behavior and crack tip processes; dislocations - theory/simulation approaches; fracture at interfaces - the role of impurities; fracture in ceramics and composites; dynamic instabilities in fracture; fractals and scaling in fracture; and friction, wear and peel processes.

In this second edition, which is the result of numerous revisions, updates and additions, the authors cover the basic concepts of fracture mechanics for both the linear elastic and elastic-plastic regimes. The fracture mechanics parameters K, G, J and CTOD are treated in a basic manner along with the text methods to determine critical values. The development of failure assessment based on elastic-plastic fracture mechanics is reflected in a comprehensive treatment. Three chapters are devoted to the fracture mechanics characterisation of crack growth. Fatigue crack growth is extensively treated and attention is paid to the important topic of the initiation and growth of short fatigue cracks. Furthermore, sustained load fracture and dynamic crack growth are discussed, including various test techniques, e.g. the determination of the crack arrest toughness. Finally, there are two chapters dealing with mechanisms of fracture and the ways in which actual material behaviour influences the fracture mechanics characterisation of crack growth. This textbook is intended primarily for engineering students. It will be useful to practising engineers as well, since it provides the background to s

Modern Solid Mechanics considers phenomena at many levels, ranging from nano size at atomic scale through the continuum level at millimeter size to large structures at the tens of meter scale. The deformation and fracture behavior at these various scales are inextricably related to interdisciplinary methods derived from applied mathematics, physics, chemistry, and engineering mechanics. This book, in honor of James R. Rice, contains articles from his colleagues and former students that bring these sophisticated methods to bear on a wide range of problems. Articles discussing problems of deformation include topics of dislocation mechanics, second particle effects, plastic yield criterion on porous materials, hydrogen embrittlement, solid state sintering, nanophases at surfaces, adhesion and contact mechanics, diffuse instability in geomaterials, and percolation in metal deformation. In the fracture area, the topics include: elastic-plastic crack growth, dynamic fracture, stress intensity and J-integral analysis, stress-corrosion cracking, and fracture in single crystal, piezoelectric, composite and cementitious materials. The book will be a valuable resource for researchers in modern solid mechanics and can be used as reference or supplementary text in mechanical and civil engineering, applied mechanics, materials science, and engineering graduate courses on fracture mechanics, elasticity, plasticity, mechanics of materials or the application of solid mechanics to processing, and reliability of life predictions.

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.

The principal objective of this book is to relate the random distributions of defects and material strength on the microscopic scale with the deformation and residual strength of materials on the macroscopic scale. To reach this goal the authors considered experimental, analytical and computational models on atomic, microscopic and macroscopic scales.