This book introduces laser pulse heating and thermal stress analysis in materials surface. Analytical temperature treatments and stress developed in the surface region are also explored. The book will help the reader analyze the laser induced stress in the irradiated region and presents solutions for the stress field. Detailed thermal stress analysis in different laser pulse heating situations and different boundary conditions are also presented. Written for surface engineers.

Problems of fatigue under multiaxial fatigue loads have been addressed in a very large number of research publications. The present publication is primarily a survey of biaxial fatigue under constant amplitude loading on metal specimens. It starts with the physical understanding of the fatigue phenomenon under biaxial fatigue loads. Various types of proportional and non-proportional biaxial fatigue loads and biaxial stress distributions in a material are specified. Attention is paid to the fatigue limit, crack nucleation, initial micro crack growth and subsequent macro-crack in different modes of crack growth. The interference between the upper and lower surfaces of a fatigue crack is discussed. Possibilities for predictions of biaxial fatigue properties are analysed with reference to the similarity concept. The significance of the present understanding for structural design problems is considered. The book is completed with a summary of major observations.

This book presents a multifunctional approach to the design of bulk nanostructured metals through severe plastic deformation (SPD). Materials engineering has traditionally involved selecting a suitable material for a given application. However, modern engineering frequently requires materials with a set of multifunctional, often conflicting properties: Enhanced mechanical properties need to be combined with improved physical (electrical, magnetic, etc.) and/or chemical (corrosion resistance, biocompatibility) properties. So disparate materials properties need to be engineered and optimized simultaneously. These requirements have created a paradigm shift in which the classical materials selection approach is replaced by design of material microstructures to achieve certain performance requirements, subject to constraints on individual properties such as strength, conductivity, and corrosion resistance. Written by researchers at the forefront of this new materials design approach, the present volume provides a comprehensive introduction to multifunctional design of bulk nanostructured materials, with applications ranging from hydrogen storage to construction engineering.

This Brief focuses on the synthesis, functionalization techniques, optical properties and biomedical application of gold nanostars (GNS). Various facilities of gold nanostars synthesis as well as functionalization of GNS with PEG, organic dyes, bioactive compounds are discussed. The authors discuss physical origin of the Localized Surface Plasmon Resonances and the way the nano-environment affects them. The implication of the LSPR of gold nanostars surface enhanced Raman scattering is also discussed. The emphasis has been done on the application of GNS for current and emerge needs of medicine, biology and pharmacy. Moreover, properties of gold nanostars as contrast agents for in vivo imaging and interaction of GNS with cells are also discussed in this Brief.

Friction Stir Casting Modification for Enhanced Structural Efficiency: A Volume in the Friction Stir Welding and Processing Book Series summarizes current research and applications of friction stir processing techniques for casting modification. Research in this area has shown significant benefit in terms of fatigue performance as a result of friction stir processing. This book addresses the latest research, providing readers with a summary of these results and new guidelines for designers.

Originally published in 1936, this book formed part of The Craftsman Series, which aimed to give secondary school age children an insight into 'the development of constructive activities in the sphere of material things'. The text is comprised of extracts from the complete version of The Din of a Smithy (1932) by J. A. R. Stevenson; these extracts are arranged into short chapters to form a coherent narrative. The narrative gives an account of how the author established his own smithy and became involved in the creation of decorative ironwork. Chapters also provide information on the various tools and processes involved in smithing. This is a highly readable book that will be of value to anyone with an interest in ironwork and books for schools.

Inorganic nanoparticles are among the most investigated objects nowadays, both in fundamental science and in various technical applications. In this book the physical properties of nanowires formed by nanoparticles with elongated shape, i.e. rod-like or wire-like, are described. The transition in the physical properties is analyzed for nanorods and nanowires consisting of spherical and rod-like nanoparticles. The physical properties of nanowires and elongated inorganic nanoparticles are reviewed too. The optical, electrical, magnetic, mechanical and catalytic properties of nanowires consisting of semiconductors, noble and various other metals, metal oxides properties and metal alloys are presented. The applications of nanorods and nanowires are discussed in the book.

Steels and computer-based modelling are fast growing fields in materials science as well as structural engineering, demonstrated by the large amount of recent literature. Steels: From Materials Science to Structural Engineering combines steels research and model development, including the application of modelling techniques in steels. The latest research includes structural engineering modelling, and novel, prototype alloy steels such as heat-resistant steel, nitride-strengthened ferritic/martensitic steel and low nickel maraging steel. Researchers studying steels will find the topics vital to their work. Materials experts will be able to learn about steels used in structural engineering as well as modelling and apply this increasingly important technique in their steel materials research and development.

This book helps designers and manufacturers to select and develop the most suitable and competitive steel structures, which are safe, fit for production and economic. An optimum design system is used to find the best characteristics of structural models, which guarantee the fulfilment of design and fabrication requirements and minimize the cost function. Realistic numerical models are used as main components of industrial steel structures. Chapter 1 containts some experiences with the optimum design of steel structures Chapter 2 treats some newer mathematical optimization methods. Chapter 3 gives formulae for fabrication times and costs. Chapters 4 deals with beams and columns. Summarizes the Eurocode rules for design. Chapter 5 deals with the design of tubular trusses. Chapter 6 gives the design of frame structures and fire-resistant design rules for a frame. In Chapters 7 some minimum cost design problems of stiffened and cellular plates and shells are worked out for cases of different stiffenings and loads. Chapter 8 gives a cost comparison of cylindrical and conical shells. The book contains a large collection of literatures and a subject list and a name index.

Micro Metal Forming, i. e. forming of parts and features with dimensions below 1 mm, is a young area of research in the wide field of metal forming technologies, expanding the limits for applying metal forming towards micro technology. The essential challenges arise from the reduced geometrical size and the increased lot size. In order to enable potential users to apply micro metal forming in production, information about the following topics are given: tribological behavior: friction between tool and work piece as well as tool wear mechanical behavior: strength and formability of the work piece material, durability of the work pieces size effects: basic description of effects occurring due to the fact, that the quantitative relation between different features changes with decreasing size process windows and limits for forming processes tool making methods numerical modeling of processes and process chains quality assurance and metrology All topics are discussed with respect to the questions relevant to micro metal forming. The description comprises information from actual research and the young history of this technology branch to be used by students, scientists and engineers in industry who already have a background in metal forming and like to expand their knowledge towards miniaturization. tribological behavior: friction between tool and work piece as well as tool wear mechanical behavior: strength and formability of the work piece material, durability of the work pieces size effects: basic description of effects occurring due to the fact, that the quantitative relation between different features changes with decreasing size process windows and limits for forming processes tool making methods numerical modeling of processes and process chains quality assurance and metrology All topics are discussed with respect to the questions relevant to micro metal forming. The description comprises information from actual research and the young history of this technology branch to be used by students, scientists and engineers in industry who already have a background in metal forming and like to expand their knowledge towards miniaturization.

These are the proceedings of the International Conference on Design, Fabrication and Economy of Metal Structures held on 24-26 April 2013 in Miskolc, Hungary which contain 99 papers covering: Structural optimization Thin-walled structures Stability Fatigue Frames Fire Fabrication Welding technology Applications Steel-concrete composite Special problems The authors are from 23 different countries, ensuring that the themes covered are of worldwide interest and importance. The International Institute of Welding (IIW), the International Society of Structural and Multidisciplinary Optimization (ISSMO), the TAMOP 4.2.1.B-10/2/KONV-2010-0001 project entitled "Increasing the quality of higher education through the development of research - development and innovation program at the University of Miskolc supported by the European Union, co-financed by the European Social Fund" and many other sponsors helped organizers to collect these valuable studies, the results of which will provoke discussion, and provide an important reference for civil and mechanical engineers, architects, researchers and structural designers and fabricators, as well as managers in a range of industries including building, transport, shipbuilding, aircraft, chemical and offshore engineering.

The book contains an analysis of theoretical dependences, bottlenecks and limiting factors of a new technology used in both Consteel and shaft furnaces operating with flat bath. Performances obtained and potentialities of these furnaces are examined. Based on this analysis, a steel melting aggregate of the new type - fuel arc furnace FAF has been developed and offered. In comparison with the best modern electric arc furnaces of identical capacity the productivity of FAF is higher by 36% and electrical energy consumption is lower by a factor of 1.8. Environment characteristics are considerably improved.

New Edition Now Covers Recycling, Environmental Issues, and Analytical Determination Employing four decades of experience in the rare metal and rare earths industry, the authors of Extractive Metallurgy of Rare Earths, Second Edition present the entire subject of rare earth elements with depth and accuracy. This second edition updates the most important developments from the past 10 years. It emphasizes advances made in rare-earth materials processing (converting a rare-earth metal, alloy, or compound to a device-ready material), breakthroughs in the area of rare-earth separation, and now includes a chapter on the recycling of rare earth elements from magnets, batteries, and phosphors among others, covering both manufacturing scrap or materials in end of life devices. Essential to Your Collection This second edition presents comprehensive, detailed, and up-to-date coverage that includes: All aspects of rare earth extractive metallurgy A status of rare earth extraction from various world resources Flow sheets that can be used for rare earths separation, metal reduction, alloy making, refining and end product materials preparation Techniques of various rare earths recycling options An outline of environmental issues in rare earths mining and processing Methods of rare earths determination and analyses of components and impurities in rare earth materials Information extensively linked to primary literature with a complete listing of references A narration of the changing scenario of world rare earth resources and possibility of their exploitation An indispensable resource, Extractive Metallurgy of Rare Earths, Second Edition explains the many aspects of rare earth extractive metallurgy clearly and systematically. The text reveals process implementation possibilities and research opportunities, and considers potential solutions to the challenges impacting this rapidly changing industry.

This thesis deals with Rare Earth Elements (REE), especially with neodymium used in permanent magnets, from a very scientific basis by providing basic research data. Despite the fact that REE are newsworthy and very important elements for a considerable bandwidth of todays' technologies, accompanied by the monopolistic supply-situation and Chinese politics, there are inexplicable data discrepancies about REE which have been recognized frequently but usually have not been addressed accordingly. So this analysis started with the hypothesis that the four application areas, namely computer hard disk drives (HDD), mobile phones, wind turbines and e-mobility (automotive traction), account for about 80% of the global annual neodymium-demand. The research methodology was a laboratory analysis of the composition of used magnets for HDDs and mobile phones and a literature and official report analysis of wind turbine and automotive neodymium use. The result was amazing and the hypothesis had to be withdrawn as these four areas only account for about 20% of neodymium use. This result raises some questions concerning actual use and thus potential recycling options.

This book presents cutting-edge research on the design and development of novel, advanced high-strength, light-weight materials via the incorporation of novel reinforcements, namely, metallic amorphous alloys/bulk metallic glasses (BMG), in light metal matrix composites (LMMCs) based on Al and Mg. The book begins with an introduction to conventional ceramic reinforced light metal matrix composites, along with the major drawbacks which limit their application. Metallic amorphous alloys/Bulk Metallic Glasses (BMG) are new class of metallic materials that are distinctly differently from conventional metals/alloys in terms of their structure and thermal behavior, and exhibit extremely high strength (1 to 2 GPa) and large elastic strain limit (1 to 2%). Given these unique properties, upon their incorporation into Al/Mg-matrices, they provide superior interfacial properties, i.e. high degree of compatibility with the matrix due to their metallic nature when compared to conventional ceramic reinforcements, and thereby significantly enhance the mechanical performance of LMMCs. Amorphous/BMG reinforced LMMCs is an emerging research field and the existing literature is meager. This book discusses the various processing methods that would be suitable for these novel materials. A comparison of mechanical properties and strengthening mechanisms of amorphous/BMG reinforced composites with those of conventional ceramic composites is presented. Future research directions and wider research potential of the novel materials are discussed, and prospective applications are highlighted. For ease of understanding and comparison, appropriate schematics, tables, and figures are provided.

This book equips a reader with knowledge necessary for critical analysis of innovations in electric arc furnaces and helps to select the most effective ones and for their successful implementation. The book also covers general issues related to history of development, current state and prospects of steelmaking in Electric Arc Furnaces. Therefore, it can be useful for everybody who studies metallurgy, including students of colleges and universities. The modern concepts of mechanisms of Arc Furnace processes are discussed in the book at the level sufficient to solve practical problems: To help readers lacking knowledge required in the field of heat transfer as well as hydro-gas dynamics, it contains several chapters which provide the required minimum of information in these fields of science. In order to better assess different innovations, the book describes experience of the application of similar innovations in open-hearth furnaces and oxygen converters. Some promising ideas on key issues regarding intensification of the heat, which are of interest for developers of new processes and equipment for Electric Arc Furnaces, are also the concern of the book It should be noted, that carrying out the simplified calculations as distinct from using "off the shelf" programs greatly promotes comprehensive understanding of physical basics of processes and effects produced by various factors. This book gives numerous examples of such calculations performed by means of simplified methods and formulas. Getting familiar with material in this book will allow the reader to perform required calculations on his / her own without any difficulties.

Laser shock processing (LSP) is a new and promising surface treatment technique for improving the fatigue durability, corrosion, wear resistance and other mechanical properties of metals and alloys. During LSP, the generated shock wave can introduce a deep compressive residual stress into the material, due to its high-pressure (GPa-TPa), ultra-fast (several tens nanoseconds), ultra-high strain-rate and high-energy. The overall properties and behavior of metal materials subjected to LSP were significantly improved because a refined surface layer was successfully obtained. Nevertheless, up to now, a clear scenery between micro-structure and macro-property of the refined surface layer, especially formation of sub-micrometer grains from coarse grains during severe plastic deformation, is still pending. Therefore, the basic studies of the underlying mechanism for grain refinement by ultra-high strain-rate presented in this book becomes more and more crucial.

The fundamental properties of deep luminescence centres in Si associated with transition metals such as Cu, Ag, Au, and Pt have been a focus of interest for decades, both as markers for these deleterious contaminants, and also in the quest for efficient Si-based light emission. This dissertation presents the results of ultra-high resolution photoluminescence studies of these centres in specially prepared, highly enriched 28-Si samples. The greatly improved spectral resolution due to this enrichment led to the discovery of isotopic fingerprints. These fingerprints have revealed that the detailed constituents of all of the centres previously studied had been identified incorrectly. They also revealed the existence of several different families of impurity complexes containing either four or five atoms chosen from Li, Cu, Ag, Au, and Pt. These centres' constituents have been determined, together with no-phonon transition energies, no-phonon isotope shifts, local vibrational mode energies, and the isotope shifts of the local vibrational mode energies. The data presented here for these centres should prove useful for the currently sought theoretical explanations of their formation, stability, and properties.

High Interstitial Stainless Austenitic Steels is of interest to all engineers and resaerchers working with stainless steel, either at universities or R&D departments in Industry. The new applications described appeal to design engineers while procees engineers find interesting challenges. These novel steels enter more and more industrial applications. Their development is presented by this book in its entirety, starting from the electronic scale of components. This makes it particlularly attractive to Materials Scientists and Metal Physicists.

Die Casting: An Analytical Approach will refresh knowledge of the governing laws of the fluid dynamics that have an effect on die cast die and die cast process design. It will be bought by product designers that design die cast parts and die cast die and process engineers and designers.

Machining of Metal Matrix Composites provides the fundamentals and recent advances in the study of machining of metal matrix composites (MMCs). Each chapter is written by an international expert in this important field of research. Machining of Metal Matrix Composites gives the reader information on machining of MMCs with a special emphasis on aluminium matrix composites. Chapter 1 provides the mechanics and modelling of chip formation for traditional machining processes. Chapter 2 is dedicated to surface integrity when machining MMCs. Chapter 3 describes the machinability aspects of MMCs. Chapter 4 contains information on traditional machining processes and Chapter 5 is dedicated to the grinding of MMCs. Chapter 6 describes the dry cutting of MMCs with SiC particulate reinforcement. Finally, Chapter 7 is dedicated to computational methods and optimization in the machining of MMCs. Machining of Metal Matrix Composites can serve as a useful reference for academics, manufacturing and materials researchers, manufacturing and mechanical engineers, and professionals involved with MMC applications. It can also be used to teach modern manufacturing engineering or as a textbook for advanced undergraduate and postgraduate engineering courses in machining, manufacturing or materials.

In the last few years, a significant increase in applications of MMCs has taken place, particularly in the areas of automotive, aerospace, electronics, and recreation. These include continuous fiber reinforced MMCs for cables in power transmission, high temperature superconducting wires, particulate MMCs in civilian aircraft and automotive applications, and high volume fraction, high thermal conductivity substrates for electronic packaging. Nevertheless, as with any novel material systems, there is a lack of fundamental understanding on the part of practicing engineers and designers. This book would seek to address these issues, in a thorough and cohesive manner, as well as to provide students and scientists with a basic understanding of MMCs. This book will emphasize the synergistic relationships among processing, structure, and properties of metal matrix composites.

The concept of virtual manufacturing has been developed in order to increase the industrial performances, being one of the most ef cient ways of reducing the m- ufacturing times and improving the quality of the products. Numerical simulation of metal forming processes, as a component of the virtual manufacturing process, has a very important contribution to the reduction of the lead time. The nite element method is currently the most widely used numerical procedure for s- ulating sheet metal forming processes. The accuracy of the simulation programs used in industry is in uenced by the constitutive models and the forming limit curves models incorporated in their structure. From the above discussion, we can distinguish a very strong connection between virtual manufacturing as a general concept, ?nite element method as a numerical analysis instrument and constitutive laws,aswellas forming limit curves as a speci city of the sheet metal forming processes. Consequently, the material modeling is strategic when models of reality have to be built. The book gives a synthetic presentation of the research performed in the eld of sheet metal forming simulation during more than 20 years by the members of three international teams: the Research Centre on Sheet Metal Forming-CERTETA (Technical University of Cluj-Napoca, Romania); AutoForm Company from Zurich, Switzerland and VOLVO automotive company from Sweden. The rst chapter presents an overview of different Finite Element (FE) formu- tions used for sheet metal forming simulation, now and in the past.

One of the key aspects of this volume is to cut across the traditional taxonomy of disciplines in the study of alloys. Hence there has been a deliberate attempt to integrate the different approaches taken towards alloys as a class of materials in different fields, ranging from geology to metallurgical engineering. The emphasis of this book is to highlight commonalities between different fields with respect to how alloys are studied. The topics in this book fall into several themes, which suggest a number of different classification schemes. We have chosen a scheme that classifies the papers in the volume into the categories Microstructural Considerations, Ordering, Kinetics and Diffusion, Magnetic Considerations and Elastic Considerations. The book has juxtaposed apparently disparate approaches to similar physical processes, in the hope of revealing a more dynamic character of the processes under consideration. This monograph will invigorate new kinds of discussion and reveal challenges and new avenues to the description and prediction of properties of materials in the solid state and the conditions that produce them.

Theuseoflasersinmaterialsprocessinghasbecomewidespreadinrecent years,sothatanunderstandingofthenatureofheatandmasstransferin thisbranchofmoderntechnologyisofincreasingimportance. Theaimofthe authorsofthisbookistoconcentrateonthephysicalprocesses;thesecanbe developedfromamathematicalpointofview,orfromdirectexperimental- derivedobservation. Thetwoapproachesarecomplementary;eachcanprovide insightsandthesynthesisofthetwocanleadtoaverypowerfulunderstanding oftheprocessesinvolved. Mathematicalmodellingofphysicalprocesseshas hadanimportantroletoplayinthedevelopmentoftechnologyoverthe centuriesandparticularlysointhelastonehundredand?ftyyearsorso. Itcanbearguedthatitismoreimportanttodaythaneverbeforesincethe availabilityofhigh-speedcomputersallowsaccuratenumericalsimulationof industrialprocessesatafractionofthecostofthecorrespondingexperiments. Thisisoneaspectofmathematicalmodelling,highpro?leandmuchvalued, butitisnottheonlyone. Inthepastmathematicalmodellinghadtorelyonqualitativeinves- gation,veryspecialanalyticalsolutions,orinaccurateandtime-consuming calculationsperformedwithlittleinthewayoftabulatedormechanical assistance. Logtablesandsliderulesarestillrememberedbypeopleworking today,thoughtherearesurelyfewwhoregrettheirdisappearance. Thevalueanddistinctivefunctionofmethodsbasedontheanalytical approachisnowbecomingmuchclearer,nowthattheyarenolongerexpected toproducedetailedimitationsofwhathappensinrealexperimentsofind- trialprocesses,afunctionnowful?lledmostlybynumericalmethods,c- sideredbelow. Theemphasistodayisontheirabilitytocon?rmandextend ourunderstandingofthebasicphysicalmechanismsinvolvedintheprocesses of interest. These are essential for any intelligent use of numerical simulation. Theargumentaboutthevalueofteachingpeoplehowtodoarithmetic themselveswithouttheaidofacalculatorseemstobepassingintohistory, vi Preface butitisanimportantoneandprovidesasimpleanalogy. Ifsomeonedoes nothaveafeelingfornumbersandthewayarithmeticworks,theywillalltoo easilyfailtospotanerrorproducedbyamachine. Computersarenotinfallible -andneitherarethosewhobuildorprogramthem. Computersarenow takingonlessmundanemathematicaltasksandthesamecontroversiesare appearinginconnectionwithalgebraicmanipulation. Equally,andwitheven greaterpenaltiesintermsofcostintheeventoferrors,thesameconsiderations applytonumericalsimulationofmajorindustrialprocesses. Awarenessofthe analyticalsolutionscanbeinvaluableindistinguishingtherightfromthe wrong,i. e. forthepractitionertounderstandthebasisofthework,andto haveanideaofthekindsofoutcomesthatareplausible-andtorecognise thosewhicharenot. Thephrase"mathematicalmodelling"is,however,ambiguous,perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance,leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms,aimedatthegenerationofunderstandingofcomplex interconnectedprocesses,ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat,withsu?cientcare,anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook,butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput,itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition,thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly,leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways,theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused,butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually,agreewiththemordisputethem vigorously,anddevelopthemfurther,wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden...1 1. 1 MathematicsanditsApplication...1 1. 2 FormulationinTermsofPartialDi?erentialEquations...3 1. 2. 1 LengthScales...3 1. 2. 2 ConservationEquationsandtheirGeneralisations...4 1. 2. 3 GoverningEquationsofGeneralised ConservationType...7 1. 2. 4 Gauss'is,however,ambiguous,perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance,leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms,aimedatthegenerationofunderstandingofcomplex interconnectedprocesses,ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat,withsu?cientcare,anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook,butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput,itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition,thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly,leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways,theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused,butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually,agreewiththemordisputethem vigorously,anddevelopthemfurther,wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden...1 1. 1 MathematicsanditsApplication...1 1. 2 FormulationinTermsofPartialDi?erentialEquations...3 1. 2. 1 LengthScales...3 1. 2. 2 ConservationEquationsandtheirGeneralisations...4 1. 2. 3 GoverningEquationsofGeneralised ConservationType...7 1. 2. 4 Gauss'Theuseoflasersinmaterialsprocessinghasbecomewidespreadinrecent years,sothatanunderstandingofthenatureofheatandmasstransferin thisbranchofmoderntechnologyisofincreasingimportance. Theaimofthe authorsofthisbookistoconcentrateonthephysicalprocesses;thesecanbe developedfromamathematicalpointofview,orfromdirectexperimental- derivedobservation. Thetwoapproachesarecomplementary;eachcanprovide insightsandthesynthesisofthetwocanleadtoaverypowerfulunderstanding oftheprocessesinvolved. Mathematicalmodellingofphysicalprocesseshas hadanimportantroletoplayinthedevelopmentoftechnologyoverthe centuriesandparticularlysointhelastonehundredand?ftyyearsorso. Itcanbearguedthatitismoreimportanttodaythaneverbeforesincethe availabilityofhigh-speedcomputersallowsaccuratenumericalsimulationof industrialprocessesatafractionofthecostofthecorrespondingexperiments. Thisisoneaspectofmathematicalmodelling,highpro?leandmuchvalued, butitisnottheonlyone. Inthepastmathematicalmodellinghadtorelyonqualitativeinves- gation,veryspecialanalyticalsolutions,orinaccurateandtime-consuming calculationsperformedwithlittleinthewayoftabulatedormechanical assistance. Logtablesandsliderulesarestillrememberedbypeopleworking today,thoughtherearesurelyfewwhoregrettheirdisappearance. Thevalueanddistinctivefunctionofmethodsbasedontheanalytical approachisnowbecomingmuchclearer,nowthattheyarenolongerexpected toproducedetailedimitationsofwhathappensinrealexperimentsofind- trialprocesses,afunctionnowful?lledmostlybynumericalmethods,c- sideredbelow. Theemphasistodayisontheirabilitytocon?rmandextend ourunderstandingofthebasicphysicalmechanismsinvolvedintheprocesses of interest. These are essential for any intelligent use of numerical simulation. Theargumentaboutthevalueofteachingpeoplehowtodoarithmetic themselveswithouttheaidofacalculatorseemstobepassingintohistory, vi Preface butitisanimportantoneandprovidesasimpleanalogy. Ifsomeonedoes nothaveafeelingfornumbersandthewayarithmeticworks,theywillalltoo easilyfailtospotanerrorproducedbyamachine. Computersarenotinfallible -andneitherarethosewhobuildorprogramthem. Computersarenow takingonlessmundanemathematicaltasksandthesamecontroversiesare appearinginconnectionwithalgebraicmanipulation. Equally,andwitheven greaterpenaltiesintermsofcostintheeventoferrors,thesameconsiderations applytonumericalsimulationofmajorindustrialprocesses. Awarenessofthe analyticalsolutionscanbeinvaluableindistinguishingtherightfromthe wrong,i. e. forthepractitionertounderstandthebasisofthework,andto haveanideaofthekindsofoutcomesthatareplausible-andtorecognise thosewhicharenot. Thephrase"mathematicalmodelling"is,however,ambiguous,perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance,leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms,aimedatthegenerationofunderstandingofcomplex interconnectedprocesses,ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat,withsu?cientcare,anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook,butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput,itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition,thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly,leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways,theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused,butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually,agreewiththemordisputethem vigorously,anddevelopthemfurther,wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden...1 1. 1 MathematicsanditsApplication...1 1. 2 FormulationinTermsofPartialDi?erentialEquations...3 1. 2. 1 LengthScales...3 1. 2. 2 ConservationEquationsandtheirGeneralisations...4 1. 2. 3 GoverningEquationsofGeneralised ConservationType...7 1. 2. 4 Gauss'sLaw...10 1. 3 BoundaryandInterfaceConditions...11 1. 3. 1 GeneralisedConservationConditions...11 1. 3. 2 TheKinematicConditioninFluidDynamics...13 1. 4 Fick'sLaws...15 1. 5 Electromagnetism...15 1. 5. 1 Maxwell'sEquations...15 1. 5. 2 Ohm'sLaw...18 References...19 2SimulationofLaserCutting WolfgangSchulz,MarkusNiessen,UrsEppelt,KerstinKowalick...21 2. 1 Introduction...22 2. 1. 1 PhysicalPhenomenaandExperimentalObservation...23 2. 2 MathematicalFormulationandAnalysis...26 2. 2. 1 TheOne-PhaseProblem...29 2. 2. 2 TheTwo-PhaseProblem...42 2. 2. 3 Three-PhaseProblem...51 2. 3 Outlook...64 2. 4 Acknowledgements...65 References...65 x Contents 3KeyholeWelding:TheSolidandLiquidPhases AlexanderKaplan...71 3. 1 HeatGenerationandHeatTransfer...71 3. 1. 1 Absorption...