Download or read book Measurement and Interpretation of Fracture Surface Fractal Dimension written by W. Drury and published by . This book was released on 1993 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of fractals in the analysis of fracture surfaces is increasingly being investigated in the hope that this concept may provide a means of characterizing these complex irregular surfaces. While the preliminary experimental evidence is interesting and encouraging, questions concerning the correct measurement and interpretation of fracture surface fractal dimension remain. This paper seeks to address these issues to the extent possible. In particular, it is noted that currently accepted techniques for measuring surface fractal dimension are flawed, and a new alternate technique based on vertical section profilometry is proposed. Important aspects of this new technique are that it is assumption-free and the required data are obtained by standard methods involving reasonable operator effort. Finally, possible interpretations of fractal results are briefly discussed, focusing on potential advantages of use of the entire "fractal plot" for developing a clearer understanding of surface geometry and the role of microstructure in the failure event.
Download or read book Fractal Surfaces written by John C. Russ and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author integrates discussions of fractal geometry, surface modeling techniques, and applications to real world problems to provide a comprehensive, accessible overview of the field. His work will equip researchers with the basic tools for measurement and interpretation of data, stimulating more work on these problems and, perhaps, leading to an understanding of the reasons that Nature has adopted this geometry to shape much of our world.
Download or read book Perimeter Yardstick Technique for Fracture Surface Fractal Analysis written by Gay Kendall and published by . This book was released on 1994 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Local fractal dimensions alpha(Chi, Epsilon), which are closely related to crowding indices of individual islands and lakes formed by sectioning of fracture surfaces produced in Charpy impact testing of a high-strength and high-toughness steel (ASTM A723) alloy, have been determined by perimeter- yardstick analysis. In this type of analysis, the perimeter of an island or lake on a fracture surface section is measured at several different magnifications, and Richardson's equation is employed to determine the fractal dimension of the island or lake. Perimeter-yardstick analysis, which had not previously been applied to fracture surface analysis, yielded alpha(Chi, Epsilon), values ranging from 1.17 to 1.40 (mean: 1.28, standard deviation: 0.08) for Charpy fracture islands and lakes in ASTM A723 steel for epsilon-values near 0.00013 cm. The mean alpha(Chi, Epsilon)-value is consistent with the (global) fractal dimension of 1.25 obtained by slit-island analysis of the same fracture surface sections-- a value typical of high-strength steel alloys previously studied. The island-to- island and lake-to-lake variations of the local fractal dimensions reflect real variations analogous to differences in the fractal dimensions of the coastlines of Norway and England. Either the fracture surfaces are fractally inhomogeneous or the range of alpha(Chi, Epsilon)-values determines limits on the variation of the global multifractal dimensions D(q) and a(q). Fractals, Fracture, Crowding indices, Slit-Island Method.
Download or read book Image Based Fractal Description of Microstructures written by J.M. Li and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal analysis has rapidly become an important field in materials science and engineering with broad applications to theoretical analysis and quantitative description of microstructures of materials. Fractal methods have thus far shown great potential in engineering applications in quantitative microscopic analysis of materials using commercial microscopes. This book attempts to introduce the fundamentals and the basis methods of fractal description of microstructures in combination with digital imaging and computer technologies. Basic concepts are given in the form of mathematical expressions. Detailed algorithms in practical applications are also provided. Fractal measurement, error analysis and fractal description of cluster growth, thin films and surfaces are emphasized in this book. Image-Based Fractal Description of Microstructures provides a comprehensive approach to materials characterization by fractal from theory to application.
Download or read book The Fracture of Brittle Materials written by Stephen W. Freiman and published by John Wiley & Sons. This book was released on 2019-01-07 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a modern, practical approach to the understanding and measurement procedures relevant to the fracture of brittle materials This book examines the testing and analysis of the fracture of brittle materials. Expanding on the measurement and analysis methodology contained in the first edition, it covers the relevant measurements (toughness and strength), material types, fracture mechanics, measurement techniques, reliability and lifetime predictions, microstructural considerations, and material/test selection processes appropriate for the analysis of the fracture behavior of brittle materials. The Fracture of Brittle Materials: Testing and Analysis, Second Edition summarizes the concepts behind the selection of a test procedure for fracture toughness and strength, and goes into detail on how the statistics of fracture can be used to assure reliability. It explains the importance of the role of microstructure in these determinations and emphasizes the use of fractographic analysis as an important tool in understanding why a part failed. The new edition includes a significant quantity of material related to the fracture of biomaterials, and features two new chapters—one on thermal shock, the other on the modeling of the fracture process. It also expands on a discussion of how to treat the statistics of fracture strength data to ensure reliability. Provides practical analysis of fracture toughness and strength Introduces the engineering and materials student to the basic concepts necessary for analyzing brittle fracture Contains new statistical analysis procedures to allow for the prediction of the safe design of brittle components Contains real-world examples to assist the reader in applying the concepts to their own research, material development, and quality-control needs The Fracture of Brittle Materials: Testing and Analysis, Second Edition is an important resource for all students, technicians, engineers, scientists, and researchers involved in the study, analysis, creation, or testing of ceramics.
Download or read book Estimation of Shear Strength Using Fractals as a Measure of Rock Fracture Roughness written by Paul C. McWilliams and published by . This book was released on 1993 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fractal Analysis written by Fernando Brambila and published by BoD – Books on Demand. This book was released on 2017-06-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.
Download or read book Fractography written by Derek Hull and published by Cambridge University Press. This book was released on 1999-09-23 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced 1999 text for those working in materials science and related inter-disciplinary subjects.
Download or read book Metallography past Present and Future written by George F. Vander Voort and published by ASTM International. This book was released on 1993 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamics of Fractal Surfaces written by Fereydoon Family and published by World Scientific. This book was released on 1991 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last few years there has been an explosion of activity in the field of the dynamics of fractal surfaces, which, through the convergence of important new results from computer simulations, analytical theories and experiments, has led to significant advances in our understanding of nonequilibrium surface growth phenomena. This interest in surface growth phenomena has been motivated largely by the fact that a wide variety of natural and industrial processes lead to the formation of rough surfaces and interfaces. This book presents these developments in a single volume by bringing together the works containing the most important results in the field.The material is divided into chapters consisting of reprints related to a single major topic. Each chapter has a general introduction to a particular aspect of growing fractal surfaces. These introductory parts are included in order to provide a scientific background to the papers reproduced in the main part of the chapters. They are written in a pedagogical style and contain only the most essential information. The contents of the reprints are made more accessible to the reader as they are preceded by a short description of what the editors find to be the most significant results in the paper.
Download or read book Factors Affecting Accuracy and Precision in Measuring Material Surfaces written by Jason A. Griggs and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The fractal dimensions of material surfaces are of interest because they can be related to material performance. Such surfaces include the fracture surfaces of broken specimens, surfaces abraded by airborne particles, and surfaces upon which coatings of another material have been applied. Scientists who study the fracture surfaces of failed medical implants stand to benefit greatly from fractal analysis. The origin of failure is often damaged or lost during retrieval of a failed implant, and evaluation of the undamaged portions of the fracture surface by relying on the self-similarity property of fractals may allow one to deduce the conditions that were present at the failure origin at the moment of failure. If the analysis of material surfaces will be used as an engineering tool, then it is important to identify the analysis methods that yield the most precise and accurate estimates of surface dimension. Eleven algorithms for calculating the surface dimension are compared. A method for correcting the bias of dimension estimates is presented. The sources of error involved in atomic force microscopy, optical microscopy, mechanical sectioning, and fabrication of specimen replicas are discussed.
Download or read book Fractals written by Benoit Mandelbrot and published by Echo Point Books & Media. This book was released on 2020-02-25 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the Hidden Mathematics of Modern Geometry Fractals, the never-ending geometric-mathematical patterns existing throughout nature, are revealed in the shapes of continents, galaxies, snowflakes, and grains of sand. In this fascinating and seminal volume, renowned pioneering-mathematician Benoit B. Mandelbrot explains his work on fractal geometry, mathematically translating the description of these complex shapes of nature. Until Mandelbrot developed the concept of fractal geometry in the 1960s and 70s, most mathematicians believed these irregular shapes were too fragmented and amorphous to be described mathematically. Mandelbrot's revolutionary concept brought order to a variety of seemingly unsolvable problems in physics, biology, and financial markets. Broad in application, this groundbreaking work will inform not just mathematicians, but anyone that appreciates the natural elegance of patterns made manifest. Featuring illustrations of mathematically defined shapes, Mandelbrot describes how geometric patterns relate to every aspect of the physical world around us.
Download or read book Failure Analysis of Engineering Structures written by V. Ramachandran and published by ASM International. This book was released on 2005 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Printbegrænsninger: Der kan printes 10 sider ad gangen og max. 40 sider pr. session
Download or read book Fractals in Geophysics written by SCHOLZ and published by Birkhäuser. This book was released on 2013-11-22 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 131 (1989), No. 1
Download or read book Fractals and Dynamic Systems in Geoscience written by Jörn H. Kruhl and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry allows the description of natural patterns and the establishment and testing of models of pattern formation. In particular, it is a tool for geoscientists. The aim of this volume is to give an overview of the applications of fractal geometry and the theory of dynamic systems in the geosciences. The state of the art is presented and the reader obtains an impression of the variety of fields for which fractal geometry is a useful tool and of the different methods of fractal geometry which can be applied. In addition to specific information about new applications of fractal geometry in structural geology, physics of the solid earth, and mineralogy, proposals and ideas about how fractal geometry can be applied in the reader's field of studies will be put forward.
Download or read book Rock Fractures and Fluid Flow written by National Research Council and published by National Academies Press. This book was released on 1996-08-27 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific understanding of fluid flow in rock fracturesâ€"a process underlying contemporary earth science problems from the search for petroleum to the controversy over nuclear waste storageâ€"has grown significantly in the past 20 years. This volume presents a comprehensive report on the state of the field, with an interdisciplinary viewpoint, case studies of fracture sites, illustrations, conclusions, and research recommendations. The book addresses these questions: How can fractures that are significant hydraulic conductors be identified, located, and characterized? How do flow and transport occur in fracture systems? How can changes in fracture systems be predicted and controlled? Among other topics, the committee provides a geomechanical understanding of fracture formation, reviews methods for detecting subsurface fractures, and looks at the use of hydraulic and tracer tests to investigate fluid flow. The volume examines the state of conceptual and mathematical modeling, and it provides a useful framework for understanding the complexity of fracture changes that occur during fluid pumping and other engineering practices. With a practical and multidisciplinary outlook, this volume will be welcomed by geologists, petroleum geologists, geoengineers, geophysicists, hydrologists, researchers, educators and students in these fields, and public officials involved in geological projects.
Download or read book Quantitative Methods in Fractography written by Bernard M. Strauss and published by ASTM International. This book was released on 1990 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt:
