lecture4-material-properties-and-assemblies

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专业英语Propertiesofmaterials

Unit 7 Properties of materialsThe final strength of any material used in an engineering component depends on its mechanical and physical properties after it has been subjected to one or more different manufacturing processes. Also, there are several properties that determine the suitability of the material in its initial state for any particular manufacturing process. The initial strength of the virgin material is important, because that strength will affect the ease with which it can be deformed into its required shape and finally, its ability to resist loads during service. Factors which increase or decrease the strength of the starting material may be equally important. It may be desirable either to reduce its strength sufficiently to allow it to be formed into shape easily with the available machines, or alternatively to increase the final strength of the manufactured component and render it more serviceable . Strength is an imprecise term that may here be understood to indicate the ability of a material either to accept or to resist deformation.A similar argument applies to a rather more elusive property of any material, namely, its ductility, which is understood to mean the ability of a material to accept large amount of deformation (mainly tensile) without fracture. Again considering manufacturing processes, a large value of this parameter will obviously be beneficial. Many mental-working process are limited only by the available ductility of the material being working, so that the amount of deformation which can be imposed on the material has to be restricted to avoid fracture. There are, however, some manufacturing processes for which the opposite of ductility is beneficial. A suitable generic term for this property might be brittleness; for example, it is well-known that certain brittle materials are much easier to machine or shear than are ductile materials.It is mainly the interplay of the properties such as strength and ductility during fabrication that has influenced the technology of production. For example, it is common knowledge that most metals when heated will become softer and easier to deform. If thespeed of deformation is too great, however, this benefit will be lost and the material may become either too hard or so brittle that fast deformation will lead to fracture. The occurrence and magnitude of such effects as these depend in some way on the microstructure of the material, so a knowledge of the metallurgy of metals or the corresponding microscope structure of non-metal is necessary for any understanding of the broad subject of this book, namely the strength of materials. The aim of the initial discussion in this chapter is , in fact, to indicate those properties of materials which are important both during and after manufacture, to see why they are important and how they influence the manufacturing process. It is clearly necessary to have more precise terms than strength and ductility, and in this chapter some of the standard mechanical tests will be considered to see whether it is possible to define such concepts with more precision. Of course, to do this it is necessary also to have some knowledge of the mathematical theory of the plasticity or rheology of ideal substances.Once the various properties of importance in manufacture have been defined and understood, it is then possible to consider how this knowledge may be used to control the process and the product, and how these properties are affected by different production process. In this way it should be easier to decide the method of manufacture most able to suit a given component and material so as to give it the final shape, strength and properties required. Thus it can be understood why the subject traditionally entitled strength of material is so important, not only as it related to the final condition of the materials found in any engineering artifact, but also as it relates to the materials before they are formed into the final shapes.For example, it might be relevant to consider changing the shape or material of a manufactured component to suit the available production technique. Such questions are outside the scope of this book, and properly belong to the more specialized realms of design for manufacture or manufacturing engineering. In the final analysis any successful manufacturing process must be economically sound and high priorityshould always be given to economic factors. The costs of manufacture are important from the outset i.e. from the time a component is specified to fulfil a certain lifetime until its final inspection, testing, and guarantee. The whole manufacturing process entails both design and production of the component , particularly in the manner in which they affect the final strength of the material.There are several physical and chemical properties that influence the choice and treatment of materials in manufacture. An example of physical property is thermal conductivity which will affect the flow of heat with the body of the material whilst it is being deformed and therefore its rate of cooling and hardening. Similarly, a well-known example of an important chemical property is that of corrosion resistance. Its importance in the final product is obvious, and it may well be important during the manufacturing process too, because it can sometimes influence the formation of surface films which affect lubrication, or thermal and electrical conduction.。

material science class 托福听力

material science class 托福听力Material Science Class: A Journey into the World of MaterialsIntroductionWelcome to the exciting world of material science! In this article, wewill embark on a journey into the class of material science, exploring the nature of materials, their properties, and the fascinating applications they have in our everyday lives. Join us as we delve into this captivating subject and unravel the mysteries behind the objects that surround us.Understanding MaterialsMaterials are the building blocks of our world. They can be found in everything we see and touch, from the clothes we wear to the devices we use. Material science is a field that studies the composition, structure, properties, and behavior of different materials. By understanding materials at a fundamental level, scientists can manipulate and design new materials to meet specific requirements.The Structure of MaterialsMaterials have intricate structures that determine their properties and behavior. Atoms are the basic units of matter, and they arrange themselvesin various patterns to form solids, liquids, or gases. In material science, we focus primarily on the study of solids. The arrangement of atoms in solids can be amorphous, where there is no long-range order, or crystalline, where atoms are arranged in a repeating pattern known as a crystal lattice.Properties of MaterialsMaterials possess a wide range of properties that make them suitable for specific applications. These properties include mechanical properties (such as strength, hardness, and elasticity), thermal properties (such as conductivity and expansion), electrical properties (such as conductivity and resistivity), optical properties (such as transparency and reflectivity), and many more. Understanding these properties allows engineers to select the most suitable materials for different products and industries.Materials ClassificationMaterials can be classified into various categories based on their composition and properties. Some common classifications include metals, polymers, ceramics, and composites. Metals are known for their high strength and conductivity, whereas polymers exhibit flexibility and low density. Ceramics are known for their high melting points and resistance to heat and chemicals. Composites are materials made by combining two or more different materials, often resulting in enhanced properties.Material TestingIn material science class, students get hands-on experience with material testing techniques. These tests are conducted to determine the physical and mechanical properties of materials. Common material testing methods include tensile testing, hardness testing, impact testing, and thermal analysis. By analyzing the data obtained from these tests, scientists can evaluate the suitability of materials for specific applications and identify any potential weaknesses or areas for improvement.Applications of Material ScienceMaterial science plays a crucial role in numerous industries and applications. It is used in the development of new and improved materials for aerospace, automotive, construction, electronics, and healthcare industries, among others. For example, the development of lightweight and strong materials have revolutionized the aerospace industry, allowing for more efficient and eco-friendly aircraft. Advances in material science have also led to the development of electronic devices with faster processing speeds and improved reliability.Future PerspectivesAs technology continues to advance, material science will undoubtedly play an even more significant role. The demand for new materials with improved properties will drive research and innovation in the field. Nanomaterials, for instance, are emerging as a promising area of study. These materials exhibit unique properties at the nanoscale and have the potential to revolutionize various industries. The future of material science holds exciting possibilities, opening doors to new discoveries and breakthroughs.ConclusionIn conclusion, material science is an intriguing class that offers insights into the world of materials. By understanding their composition, structure, properties, and behavior, we can harness the power of materials to create innovative and sustainable solutions for numerous industries. As we progress through this class, let us embrace the wonders of material science and appreciate the impact it has on shaping our modern world.。

CEL-L04-Techniques

• No inflow
• Outflow
• Zero pressure
• Nonreflecting
• Non-uniform pressure
• User interface
*EULERIAN BOUNDARY, INFLOW = FREE / VOID / NONE, OUTFLOW = FREE/ NONREFLECTING/ ZERO PRESSURE/ NONUNIFORM PRESSURE
L4.7
ICs, BCs, and Loads
• The default behavior on Eulerian boundaries when no boundary conditions are defined is free inflow and free outflow. • Other Eulerian boundary conditions include • Inflow • Void
• Default outflow behavior
• OUTFLOW=NONREFLECTING
• Models an unbounded domain in which the region of interest is small in size compared to the surrounding medium. • This condition is approximate in that it does not provide perfect transmission of energy out of the mesh except in the case of plane body waves impinging orthogonally on the boundary in an isotropic medium.

新世纪高等院校英语专业本科生系列教材《综合教程3》Unit3

children from a friend’s house, where the letter carrier
takes his van up and down every driveway on a street.
Detailed Reading
8 We will go through the most extraordinary contortions to save ourselves from walking. Sometimes it’s almost ludicrous. The other day I was waiting to bring home one of my children from a piano lesson when a car stopped outside a post office, and a man about my age popped out and dashed inside. He was in the post office for about three or four minutes, and then came out, got in the car and drove exactly 16 feet (I had nothing better to do, so I paced it off) to the general store next door.
2. What’s the secret of success of that factory? The product and their manufacturing process are one unit. Automation, technology and skilled human labor combine to build the Porsche 911. And the factory runs like a precision machine.

材料科学与工程第四版部分翻译

P2Material science is the investigation of the relationship among processing, structure, properties, and performance of materials.材料科学是研究材料的加工，组织性能和功能之间关系的学科（材料与工程之间的关系可以用图一的四面体来表示）P2The discipline of materials science involves investigating the relationships that exist between the structures and properties of materials.材料科学是研究材料的结构和性能之间的关系的学科In contrast, materials engineering is, on the basis of these structure-property correlations, designing or engineering the structure of a material to produce a predetermined set of properties. 而材料加工是在材料组织和性能关系的基础上，对材料的组织进行设计，以获得一系列预定的性能P5 Semiconductors have electrical properties that are intermediate between the electrical conductors and insulators. Furthermore, the electrical characteristics of these materials are extremely sensitive to the presence of minute concentrations of impurity atoms, which concentrations may be controlled over very small spatial regions. The semiconductors have made possible the advent of integrated circuitry that has totally revolutionized the electronics and computer industries.半导体有介于电导体和绝缘体之间的性能。

人教版高中英语必修四-Unit-4-Body-L精选全文完整版

可编辑修改精选全文完整版高中英语教学设计教学过程设计活动内容StepII导入A. Group Discussion The Different Ways of Communication ( 3 min )Hold an activity of group discussion among the class on the question “What are the different ways of ofcommunicating in daily life?”Divide the class in to 8 groups, and give them 2 minutes for discussion about the above question. After discussion, several students will be asked to express their ideas. The teacher will add their answers around the circle.Blackboard Design (板书设计)In the center of the circle ,there will be the words “different ways of communicating …” and the teacher will aid their answers around the circle. They are also supposed to give an example for their answers.Possible Answers AreBy talking, speaking, phoning, writing letters, sending e-mails, using gestures, etcB. The Teacher ’s Categorizing of The Students ’ Answers ( 1 min )In this step, the teacher will try to help the students to categorize their answers, making them know that body language is as important a way as spoken or written language in communication.Blackboard Design (板书设计)Step 2介绍身势语的重要性A.Telling Students the Story of Tai Lihua and Making Them Know theImportance of Body Language in Her Life ( 3 min )1.Present the pictures of Thousands of Hands Kwan-yin , and ask the students whether they know thegirl who dances in the front.2. Tell the students tell life story of Tai Lihua and ask them the question “What are the key factors for her success in her life?”writingtypi ngSpoken languageWritten languageBody language gesturingspeakingringingverballanguageNon-verballanguageThe life story of Tai LihuaHer name is Tai Lihua（邰丽华）. She is called a Fairy of Peach blossom(桃花仙子) by people. You knowshe is a deaf girl, but she is a wise, diligent, charming and energetic girl. She studied very hard and got two degrees of bachelors in university. She was famous as an artist for her wonderful performance. She is deafand dumb. But how did she get that great achievement and became a successful person? She loves life very much. We should learn from her spirit. Besides her hard working, body language plays a very importantpart in her life. We are all healthy people, sometimes we can use body language to express ourselves. Sowe should pay more attention to learning body languages.B.Showing the Students the Science Report of the Importance Body Language, Making Them Know That Body Language Is As Important For Us As ForDisabled Person Like Tai Lihua. ( 1 min )Some psychologist believe that we communicate 65% of our ideas and feelings without words! The shapeof our bodies and faces, the movements and gestures we make, the clothes we wear, how near we stand to each other and whether we touch each other…all these communicate. we must study all these types of information if we want to truly understand what other people are saying.Step 3介绍不同类型的身势语() ( step 3 will use around 5 min )A. Showing the Students The Four Types of Body LanguageGestureFacial expressionEye contactPostureB. Guessing The Meaning of GesturesThe teacher show the students a series of pictures of a man using different gestures, and the students are supposed to say their meaning.C. Acting Out By GesturesThe teacher show the students some English words and ask them to act them out together by usinggestures.D. Chasing the Right WordThe teacher will show the students a series of pictures describing different facial expressions and askthe students to choose the right word for each.Victory! Ok !Be quiet! You!Threatening No. sixThank you ！ Congratulations!E. Matching the Right Interpretation Of the EyesThe teacher will present students several pictures of eyes and ask the students to match the right interpretation.Facial expressionanger fear joy sorrow contempt轻视surprise disgust 厌恶What do you see in the eyes below?That’s a problem. I need to thinkfor while.a whileIt’s you! Let’s have a duel!That’s horrible! I’m terrified!The next minute,you’re a dead body!I’m in great sorrown ess…I won’t give up! We’ll soon winback!F. Guessing The Meaning of Postures in Real ContextI’m listening carefully!What do we know from their posture?Nice to meet you!This woman is listening to your ideas…You meet this man for the first time…Give me a little time!I’m still thinking!You are asking this womanTo finish her work as soon as possible…You are asking this woman ”Have you got any good idea?” …I give up!OK!You are asking help from this woman…You are saying “Will you give up!”…G. Matching the Right Meaning of the Given Posturesnervous Bite your nails and fondle hair agreement Nod the head up and downBe not interested Look away or yawn.Do not believe Roll your eyes and turn your head away. angry Frown and turn your back to sb disagreement Shake the headStep 4给身势语下定义A．Finishing the First Question of Warming-up Part ( 3 min )The teacher will ask the students to discuss the question with your partner and try to find what the people in the pictures are communicating.B.Giving Definition To Body Language ( 2 min )The teacher will guide the students to give a general definition to body language.Body languageis a form of non-verbal communication.uses movements or positions of our body to show other people what we are thinking or feeling.mainly includes gesture, facial expression, eye contact, posture four forms.Step 5练习运用身势语A.Acting Out the Following words ( 4 min )This exercise is based on the second question of warming-up part. Two students will be chose to the frontof the class, and each of them will choose five words to act. After their action, other students will try to guess which word they have acted.•Hello!•Goodbye!•Go away!•Expensive!•I’m surprised!•I’m tired•I’m confused!•Good luck•I’m delighted!•I’m upset!•I’m sad!•I forgot!•You are great!•I’m curious!•I ate too much!•Come here!B．Acting Out the Dialogue on Page 67 ( 10 min )The student will work in groups of two to finish the speaking task of this unit on page 67. They are required to use appropriate body language as they are making dialogues. After their pairwork, volunteers will make their dialogue before the whole class.Step 6介绍身势语的文化多样性A．Showing the Cultural Difference in Body Language With Examples ( 2 min )America OKJapan moneyFrance zeroBrazilGermanyrudeB ． Presenting the Students the Major Greeting Customs in the World ( 2 min )Person and country Suitable greeting A man from ColumbiaTo a man: same as for a womanTo a woman: touches her shoulder and kissesher on the cheekA woman from BritainTo a man: not to close, shake hands To a woman: shake hands, will get closeA man from JapanTo a man: bowsTo a woman: bowsA man from CanadaTo a man: shake handsTo a woman: shake hands or kisses on both cheeks if knownA woman from FranceTo a man: shake hands, kisses twice on the cheekTo a woman: same to someone she knowsA man from the Middle East or some Muslim countriesTo a man:comes close, shakes handsTo a woman:nodsC. Discussion On the Question That If There is a Division of Good or Bad of the Different Meaning of The Same Body Language Under Different Culture.The students will have 3 minutes for discussion and after that some of them will represent their group to share their idea with the whole class.Step Role Play ( 8 min )USA Nigeria rude Germany Japanone“great”or “good job”。

大学英语教材4三单元课文

大学英语教材4三单元课文Unit 4: Money MattersText: Managing Your Finances in CollegeIn today's lesson, we will explore the third unit of the university English textbook, which focuses on an essential aspect of life for college students: managing finances. As we all know, effective financial management plays a crucial role in our lives, especially during our time at university. Therefore, it is essential to develop necessary skills and knowledge to handle our finances responsibly. In this text, we will discuss various strategies for managing money as a college student.1. Understanding Your ExpensesBefore we delve into specific techniques for managing money, it is vital to have a clear understanding of the various expenses we may encounter as college students. These expenses include tuition fees, accommodation costs, textbooks, transportation, meals, and personal expenses. By being aware of the types of expenses we will encounter, we can make informed decisions about budgeting and prioritizing our spending.2. Creating a BudgetOne of the key steps in effectively managing finances is creating a budget. A budget serves as a roadmap to guide our spending and ensure that we do not overspend or accumulate unnecessary debts. When creating a budget, we should consider our income, including any allowances, part-time jobs, or financial aid. We should also identify our fixed expenses, such asrent and tuition, as well as our variable expenses, like meals and entertainment. By categorizing our expenses, we can allocate funds accordingly and make adjustments as needed.3. Prioritizing ExpensesIn college, it is essential to prioritize expenses to make the most of limited financial resources. Prioritizing involves distinguishing between necessary and discretionary expenses. Necessary expenses, such as tuition and rent, should be given priority, while discretionary expenses, such as eating out or purchasing luxury items, can be reduced or eliminated altogether. By developing this habit, we can ensure that our financial resources are utilized effectively and enable us to save for future goals.4. Seeking Financial AidMany universities offer various financial aid options that can help alleviate the financial burden on students. It is essential to research and explore all available options, such as scholarships, grants, and work-study programs. Applying for financial aid can provide additional support, allowing us to focus on our studies without excessive financial stress.5. Developing Saving HabitsIn addition to managing day-to-day expenses, it is important to develop saving habits. Saving money regularly, no matter how small the amount, can contribute to long-term financial stability. Setting aside a portion of our income or any unexpected money can help build an emergency fund or save for future goals, such as post-graduation plans or further education. Bycultivating this habit early on, we can develop a strong financial foundation for the future.6. Seeking Financial AdviceIf we encounter financial difficulties or feel unsure about managing our finances effectively, it is crucial to seek advice from professionals or financial advisors. Universities often have resources, such as financial counseling services, which provide guidance and support in money management. These professionals can help us understand complex financial concepts, create personalized budgets, and offer strategies for overcoming financial challenges.ConclusionIn conclusion, managing finances is a skill that college students should prioritize and develop. Understanding our expenses, creating a budget, prioritizing expenses, seeking financial aid, developing saving habits, and seeking advice when needed are all crucial steps in effectively managing our money. By following these strategies and continuously educating ourselves on personal finance, we can navigate our college years financially and set a solid foundation for our future financial success.。

1999 Material properties and flow modes in pneumatic conveying

Ž.Powder Technology1041999157–163 r locate r powtec Material properties and flow modes in pneumatic conveyingR.PanDepartment of Mechanical Engineering,The UniÕersity of Newcastle,UniÕersity DriÕe,Callaghan,NSW2308,AustraliaReceived28May1998;received in revised form4February1999;accepted4February1999AbstractWhen bulk solid materials are transported in conventional pneumatic conveying systems,three flow modes have been observed.These Ž.Ž.Ž.are:i smooth transition from dilute-to fluidised dense-phase,ii dilute-phase,unstable-zone and slug-flow and iii dilute-phase only. The flow mode for a bulk solid material is totally dependant on material properties,in particular,those properties which involve Ž.particle r air interaction e.g.,permeability,air retention and ually,the particle r air interaction characteristics are a function of basic particle properties,such as particle size,size distribution,density and shape.Loose-poured bulk density also is a function of these basic particle properties.Therefore,there should be a relationship between the loose-poured bulk density and the particle r air interaction characteristics.Based on experimental results and theoretical analysis,a new flow mode diagram is developed for the purpose of selecting suitable flow mode for a particular material.Based on the developed flow mode diagram,the bulk solid materialsŽ.can be classified into three groups PC1,PC2and PC3,characterised simply by loose-poured bulk density and median particle diameter. Materials in group PC1can be transported smoothly and gently from dilute-to fluidised dense-phase.Materials in group PC2can be transported in dilute-phase,unstable zone or slug-flow and materials in group PC3are conveyed in dilute-phase only.A good accuracy is achieved when many test results with the observed flow modes are superimposed on the developed flow mode diagram.q1999Published by Elsevier Science S.A.All rights reserved.Keywords:Pneumatic conveying;Flow modes;Bulk solid materials1.IntroductionPneumatic conveying of bulk solid materials is well established in industry.Numerous bulk solid materialsŽwith dramatically different particle properties e.g.,size,. size distribution,shape,density and surface hardness are being transported pneumatically.When bulk solid materi-als are transported in conventional pneumatic conveyingŽ.systems,three flow modes:i smooth transition fromŽ.dilute-to fluidised dense-phase,ii dilute-phase,un-Ž.stable-zone and slug-flow and iii dilute-phase only,are observed.Since the conveyed materials have great influ-Ž.w x ences on flow modes or system performance1–3,it isŽ. quite important to identify in which flow mode s the materials can be conveyed when designing pneumatic con-veying systems.Usually,the following procedures are employed fre-quently for the purpose of selecting suitable flow modes for the materials.The most commonly used procedure is to undertake a series of tests with a representative sample of material in a pilot size rig.The flow mode of the material can be determined and quantified easily from the test results.However,this procedure can be a labour intensive, time consuming and costly process.Therefore,it is evident that the development of smaller scale and bench type tests to assist in this assessment is desirable.w x To date,the Dixon slugging diagram4based onw xGeldart fluidisation classifications5has been used widely for this purpose.The Dixon slugging diagram,charac-terised by the density difference between particle and air and the median particle diameter,is divided into four Ž.categories A,B,C and D.The location of a product on the slugging diagram will give some indication of its potential conveyability and flow mode.However,test work w x6,7has shown that the well known Geldart classifications used to categorise the fluidisation behaviour of particulate materials are not satisfactory for choosing the flow modes for bulk solid materials in pneumatic conveying,neither is the closely related Dixon slugging diagram.The flow mode for a bulk solid material is largely determined by the material properties,in particular,thoseŽproperties which involve particle r air interaction e.g.,per-.w x meability,air retention and de-aeration1–3.The parti-cle r air interaction characteristics usually are a function of()R.Pan r Powder Technology1041999157–163 158basic particle properties,especially such as particle size,size distribution,density,shape and hardness.The loose-poured bulk density also is a function of these basicparticle properties.Therefore,there should be a relation-ship between the loose-poured bulk density and the parti-cle r air interaction characteristics.Based on experimental results and theoretical analysis,a new flow mode diagram characterised simply by loose-poured bulk density and median particle diameter is devel-oped for the purpose of selecting suitable flow mode for aparticular material.The developed flow mode diagramclearly classifies the bulk solid materials into three groupsŽ.PC1,PC2and PC3.Materials in group PC1can betransported smoothly and gently from dilute-to fluidiseddense-phase.Materials in group PC2can be transported indilute-phase,unstable zone or slug-flow and materials ingroup PC3are conveyed in dilute-phase only.There is agood agreement achieved between the selected and ob-served flow modes for many test materials.2.Flow modes in pneumatic conveyingNumerous bulk solid materials with dramatically differ-Žent particle properties e.g.,particle size,size distribution,.shape,density,surface hardness are being transportedpneumatically in conventional systems.In general,threeflow modes are observed,which are described in detailbelow.2.1.Smooth transition from dilute-to fluidised dense-phaseŽThis flow mode usually is for fine powders e.g.,fly.ash,cement,pulverised coal.A typical set of pneumaticconveying characteristics is shown in Fig.1.When the air mass flow rate is decreased from high tolow and for a constant product mass flow rate,the pressuredrop also decreases and reaches a minimum value.Theregion to the right of this pressure minimum point usuallyis referred to as dilute-phase.As the air mass flow rate isdecreased further,the pressure drop increases usually ataFig.1.General form of pneumatic conveying characteristics for smoothw xtransition from dilute-to fluidised dense-phase3.Fig.2.General form of pneumatic conveying characteristics for dilute-w xphase,unstable-zone and slug-flow3.higher rate than in dilute-phase.This region generally is called fluidised dense-phase.The locus of pressure minimaŽ.is referred to as the pressure minimum curve PMC and often is used to define minimum conveying for dilute-phase.2.2.Dilute-phase,unstable-zone and slug-flowThis flow mode characteristic usually occurs for lightŽand free-flowing granular products e.g.,plastic pellets,.wheat,rice,muesli.Fig.2shows a typical set of pneu-matic conveying characteristics for this flow mode.In dilute-phase,the particles are distributed evenly overŽ. the entire cross section of the pipe see point1in Fig.2. When conveying takes place along a line at constant product mass flow rate in the direction of decreasing air mass flow rate,this line reaches a point of minimum pressure.At this stage,a layer of particles is being con-Ž. veyed along the bottom of the pipe see point2in Fig.2. With lower air mass flow rates,some particles become stationary along the bottom of pipeline and most of the material is transported in small clusters or dunes.The stationary particles may be picked by the moving clusters or dunes.With such information,it is possible to select minimum air flows for dilute-phase by selecting operating conditions say,to the right of minimum pressure.As the air mass flow rate is decreased further,the air velocity is not high enough to pick up all particles and some particles accumulate on the bottom of the pipeline and form long plugs.These long plugs are forced through the pipeline and produce high fluctuations in pressure and vibration.This region is referred to as the unstable zone Ž.see point3in Fig.2.If the air mass flow rate is reduced even further,it is found that the particles are conveyed gently and in the Ž.form of slugs see point4in Fig.2.Along the horizontal pipeline,the slug picks up the particles from the stationary layer in front of it and deposits the same quantity of particles behind it.Note that there is,generally,no inter-particle motion within the slug itself.()R.Pan r Powder Technology1041999157–163159Fig.3.General form of pneumatic conveying characteristics for dilute-w xphase only3.Therefore,from Fig.2,there are two boundaries sepa-rating the dilute-phase,unstable-zone and slug-flow re-gimes.2.3.Dilute-phase onlyThis flow mode usually occurs for heavy granularŽand r or crushed products e.g.,crushed coal,primary con-.centrate,zircon sand.Also,some light,fibrous and r orŽspongy materials e.g.,wood chips,grain dust,saw dust,.bagasse,pearlite are only able to be conveyed in dilute-phase.The reason is that,when these materials are packed together,the particles interlock easily and the material flowability changes dramatically.A typical set of pneu-matic conveying characteristics for this flow mode is shown in Fig.3.When the air mass flow rate is decreased from high to low and at a constant product mass flow rate,the pressure drop also decreases.Before reaching the pressure mini-mum point,the particles begin to saltate and build up quickly along the bottom of the pipeline.Blockage occurs as soon as the material completely fills a section of pipeline.2.4.SummaryFrom the above descriptions,it is obvious that there are great differences in conveying performance among the three flow modes.These differences can affect signifi-cantly the design,selection and operation of the pneumatic conveying system.Also,all the pneumatic conveying tests have demonstrated strongly that the flow modes in which the materials are conveyed are totally dependent on thew xmaterial properties1–3.Therefore,adequate considera-tion should be given to the selection of suitable flow modes for bulk solid materials during the design stage.3.Test resultsSome of the bulk solid materials which have been transported pneumatically in conventional systems are listed in Tables1–3,with their properties and flow modesachieved.The products listed in Tables1–3can be considered tocover a wide range of bulk solid materials encountered inindustry.For example,median particle diameter variesfrom11to4000m m,particle density from800to4742kgm y3and loose-poured bulk density from100to2778kgm y3.Note that the median particle diameter used here isdefined as the diameter at which the cumulative distribu-tion percentage under size is50%by mass or volumedepending on the measuring technique.The importance of material properties on pneumaticconveying performance,in particular,those propertieswhich involve particle r air interaction,has been appreci-ated by many researchers in a qualitative manner.Forexample,the permeability,air retention and de-aerationcharacteristics are used widely to determine the flow modes w xfor materials1,6,7.It is apparent that all the above characteristics of the Ž. material e.g.,permeability,air retention and de-aerationare a function of basic particle properties,such as particlesize,size distribution,density,shape and surface hardness.Also,the loose-poured bulk density of the product is afunction of such basic particle properties.Therefore,thereshould be a relationship between the loose-poured bulkdensity and the permeability,air retention and de-aerationcharacteristics of the material.Based solely on the loose-poured bulk density and themedian particle diameter,a diagram is produced,as shownTable1Test products in the flow mode of smooth transition from dilute-to fluidised dense-phaseMaterial r r d Investigators b py3y3Ž.Ž.Ž.kg m kg m m mFly ash1219763415.5AuthorFly ash2221795711.5Author Pulverised coal1160053841.3Author Pulverised coal2159054115Author Pulverised coal3159056320Author Pulverised coal4158056833Author Pulverised coal5141558846.3Author Pulverised coal6150040040Author Pulverised coal7153936825.8Authorw x Agricultural catalyst4660760270Ref.1w x Barytes4250159011Ref.1w x Cement3060107014Ref.1w xCoal155039384Ref.1w x Copper ore3950166055Ref.1w xFlour147051090Ref.1w xIron powder5710238064Ref.1w x Pulverised fuel ash244697925Ref.1w xPVC powder99061590Ref.1w x Sugar1580656157Ref.1w x Cement3160103022Ref.6w xCoal150061044Ref.6w xFuel ash245098020Ref.6()R.Pan r Powder Technology1041999157–163 160Table2Test products in the flow mode of dilute-phase,unstable-zone and slug-flowMaterial r r d Investigators b py3y3Ž.Ž.Ž.kg m kg m m mNarasin1745880325AuthoraWPP110396372980AuthoraBPP8344583760AuthoraWPP28654943120AuthoraWPP38875383684AuthoraWPP48955263747AuthoraWheat113567753788AuthoraWheat214167783502Author Duaralina1494688349Author Semolina1459736390AuthoraWheat314498113470AuthoraBarley135********Authorw x Agricultural catalyst4655767782Ref.1w x Magnesium sulphate23531010224Ref.1w xPoly pellets9125404000Ref.1w x Granulated sugar1580890458Ref.1w x Mustard seed11806801650Ref.6w xPoly powder990480825Ref.6w x Plastic pellets9145583850Ref.6w x Granulated sugar1590820720Ref.6a Equivalent volume diameter,WPP-White plastic pellets and BPP-Black plastic pellets.in Fig.4,which includes all the bulk solids materials listed in Tables1–3.Fig.4clearly indicates three groups marked PC1,PC2Žand PC3.Materials in group PC1 e.g.,fly ash,cement,.pulverised coal can be transported smoothly and gently from dilute-to fluidised dense-phase.Materials in group Ž.PC2 e.g.,plastic pellets,wheat,barley can be transported in dilute-phase,unstable zone or slug-flow and materials in Ž. group PC3 e.g.,primary concentrate,zircon sand are conveyedin dilute-phase only.Also from Tables1–3,as long as a product can be conveyed pneumatically,the product can be transported in dilute-phase.Therefore,the ultimate aim of this paper is to Table3Test products in the flow mode of dilute-phase onlyMaterial r r d Investigators b py3y3Ž.Ž.Ž.kg m kg m m mHigh silica flux26641519300Author Primary concentrate47422778142Authorw x Alumina3600104079Ref.1Ž.w xCoal as supplied1550870778Ref.1Ž.w xCoal degraded1550701146Ref.1w x Pearlite800100158Ref.1w x Potassium chloride198********Ref.1w x Potassium sulphate26251260131Ref.1w xSilica sand26301450174Ref.1w x Zircon sand46002600120Ref.1w xZircon sand46102600115Ref.6w xSlate dust28601280500Ref.6Ž.w xFuel ash grit2380400700Ref.6w x Coarse sand262015401020Ref.6Fig.4.Flow mode diagram of bulk solid materials in pneumatic convey-ing.find out whether or not the product can be conveyed in fluidised dense-phase or slug-flow.4.Determination of boundary4.1.Boundary between fine and coarse productsAs described in Section2,the flow mode of smooth transition from dilute-to fluidised dense-phase is for fineŽ. powders e.g.,fly ash,cement,pulverised coal,the flow mode of dilute-phase,unstable-zone and slug-flow for lightŽ. granular products e.g.,plastic pellets,wheat,rice,muesli and the flow mode of dilute-phase only for heavy granularŽand r or crushed products e.g.,crushed coal,primary con-.centrate,zircon sand and the products that are light, fibrous and spongy.Therefore,the difference between PC1Ž.and PC2or PC3see Fig.4can be described basically as the difference between fine and coarse products.When indicating the difference between products inw xgroups A and B,Geldart5,8uses the ratio of minimum bubbling to minimum fluidisation velocity.It has beenfound that products with u r u)1belong in group Amb mfand those with u r u-1in group B,where u ismb mf mb minimum bubbling velocity and u is minimum fluidisa-mftion velocity.Therefore,the boundary between products in groups A and B is defined byumb s11Ž. umfThen,comparing Fig.4with Geldart fluidisation classi-fication diagram,the similarity can be observed clearly Ži.e.,the difference between products in groups A and B is similar to that between fine and coarse products defined in .Ž.this paper.Therefore,Eq.1also can be tried to deter-mine the boundary between fine and coarse products shown in Fig.4.()R.Pan r Powder Technology 1041999157–163161Many theoretical and empirical correlations have been developed to predict the minimum fluidisation velocity,w x u 8,9.In the most of correlations,the minimum fluidis-mf ation velocity is predicted approximately byu s k d 2r y r 2Ž.Ž.mf p s f where k is determined by the experimental results of fluidisation and constant at ambient conditions.Different researchers usually have obtained different values of k from their own and literature data.It is clear that the minimum fluidisation velocity,u in mf Ž.Eq.2,is expressed in the terms of particle and air densities and cannot be used directly to locate the bound-ary between fine and coarse products shown in pared to the particle density,the air density can be neglected in most cases of pneumatic conveying.For example,assuming the particle density is 800kg m y 3and the total pipeline air pressure drop is 500kPa,r r r f s 100%-1%.Therefore,r br y r f r s 3Ž.Ž.s f s 1y ´Ž.Ž.Assuming v s k 1y ´and substituting Eq.3into Ž.Eq.2result in:u s v d 2r 4Ž.mf p bwhere v also is determined by the experimental results of fluidisation.However,usually the particle density,r has s been accepted widely as the key parameter in fluidisation.The loose-poured bulk density of the material,r is b always ignored and rarely recorded.Hence,although there are numerous data available in the literature,v still cannot be determined from the literature data.The following correlations have been recommended mostly for the prediction of minimum fluidisation velocity w x w x 8.These are:If d )100m m 9,p m'u s 1135.7q y 33.75Ž.Ž.mf r d f v r d 3r y r gŽ.f v s f Ar s2m d s 1.13d v pw x If d -100m m 10,p 0.9340.934 1.8r y r g d Ž.s f pu s6Ž.mf 20.0661111m r f The minimum fluidisation velocity then is calculated by Ž.Ž.using Eq.5or Eq.6for the products listed in Tables 1–3.The data relating the minimum fluidisation velocity to the loose-poured bulk density are produced and the least Ž.square method is used to determine v in Eq.4where v also is assumed constant at ambient conditions.To locate the boundary between the fine and coarse products accurately,the products around the boundary areŽ.used e.g.,30m m -d -500m m,see Fig.4.The mainp reason is that the products around the boundary have great influence on the boundary location and the products far from the boundary can be classified as fine or coarse products easily.The determined relationship between the minimum fluidisation velocity and the loose-poured bulk density is expressed as follows.u s 828.88d 2r 7Ž.mf p bŽ.Ž.y 2Note that in Eqs.5and 6,g s 9.81m s ,m s 1.8=10y 5Pa s and r s 1.2kg m y 3.f Ž.The comparison between the predictions by Eqs.7Ž.Ž.and 5or Eq.6for the employed materials is shown in Ž.Fig.5.Fig.5clearly shows that Eq.7has a reasonable accuracy.Also,a simple relationship between u and d has mb p w x been developed 5.That is:u s 100d 8Ž.mb pŽ.Ž.Ž.Substituting Eqs.7and 8into Eq.1,the following correlation to determine boundary between the fine and coarse products is obtained.d r s 0.12069Ž.p b Note that,for all the above equations,d is in m andp r in kg m y 3.b Ž.Eq.9then is plotted on Fig.4as line XY .Fig.4Ž.clearly demonstrates that Eq.9has good accuracy and reliability in determining the boundary between the fine and coarse products.The fine products defined here can be transported smoothly and gently from dilute-to fluidised dense-phase.The coarse products are conveyed in dilute-phase only or the flow mode of dilute-phase,unstable-zone and slug-flow,depending on their particle rbulk properties.4.2.Boundary between low-Õelocity slug-flow and dilute-phase onlyIn the conveying of dilute-phase only,the particles begin to saltate and build up quickly along the bottom ofŽ.Ž.Žparison of predicted u by Eq.5or Eqs.6and 7.mf()R.Pan r Powder Technology 1041999157–163162w x Fig.6.Air pressure and stresses acting on a horizontal particle slug 13.pipeline when the air velocity is not high enough to suspend them.Blockage occurs as soon as the material completely fills a section of pipeline.However,in slug-flow conveying,the pipeline is filled with the particles at one or more cross sections and the particles are transported along w x the pipeline in slugs 11.Therefore,selecting slug-flow or dilute-phase only for a bulk solid material depends on the relationship between the driving and resistance forces act-ing on a slug that is formed in the pipeline.If the driving force never exceeds the resistance force,the dilute-phase only has to be selected.Otherwise,the bulk solid material can be transported in slug-flow.The stresses and pressure acting on a particle slug w x element are shown in Fig.613.From Fig.6,it is clear that the driving force is pressure drop due to air flowing through the slug and the resistance force is the friction force between the slug and pipe wall.If the material obeys the Coulomb failure criterion,the friction stress for cohesionless material then is t s m s w w w w x 11.Stress s is the normal wall pressure acting perpendic-w ularly to the pipe wall.It is believed that the normal wall pressure is composed of two parts for horizontal slug-flow,one being caused by the pipe wall reacting against the axial compression stress s and the other being a direct x w x result of material weight 11.Also,the ratio of radial to axial stresses has been found to be a function of loose-poured bulk density and wall w x friction angle 12.Therefore,the friction force acting on the slug is directly related to and increases quickly with an w x increase in loose-poured bulk density 11–13.Hence,it is quite possible that due to the high friction force,the materials with high loose-poured bulk density are not able to be transported in slug-flow and the high air velocity is Žrequired to suspend the particles i.e.,dilute-phase only is .selected .However,other properties of the material,such as particle size,size distribution and permeability,also have great influences on the driving and resistance forces acting on the slug.For example,if the material has low perme-ability and does not allow air to flow easily through the Ž.slug,the pressure drop or driving force due to air flowing through the slug is low and the pressure at the back of the slug may climb up quickly due to more and more pres-surised air accumulating,which results in the increase of radial and axial stresses.Hence,it is difficult to determine an accurate value of loose-poured bulk density as the Žboundary between slug-flow and dilute-phase only i.e.,it is difficult to locate Boundary OO theoretically,see Fig..4.From Fig.4,it can be seen that there is a clear boundary between low-velocity slug-flow and dilute-phase only.When the loose-poured bulk density is over 1000kg m y 3,the bulk solid materials cannot be transported in slug-flow.Therefore,the following equation can be used to determine Boundary OO.r f 1000kg m y 310Ž.b Ž.Eq.10then is plotted on Fig.4as line OO.Although some products below Boundary OO cannot be conveyed in slug-flow,it still can be used generally and accurately to classify the bulk solid materials in terms of slug-flow and Ždilute-phase only.Two main exceptions i.e.,pearlite and .fuel ash grit,as circled in Fig.4are found to be due to particular product properties.As explained in Section 2.3,the main reason for pearlite is that the particles interlock easily and the material flowability changes dramatically when packed together.For fuel ash grit,the main reason is due to the wide particle size range affecting the permeabil-ity and slug-flow ability of the material.5.ConclusionsThe flow mode for a bulk solid material totally depends on material properties,in particular,those properties which Žinvolve particle r air interaction e.g.,permeability,air re-.tention and de-aeration .Usually,the particle r air interac-tion characteristics are a function of basic particle proper-ties,such as particle size,size distribution,density,shape and surface hardness.Loose-poured bulk density also is a function of these basic particle properties.Therefore,there should be a relationship between the loose-poured bulk density and the particle r air interaction characteristics.Hence,the loose-poured bulk density can be used directly to indicate the flow mode for a particular material in pneumatic conveying.The flow mode diagram shown in Fig.4is simple and characterised only by loose-poured bulk density and me-dian particle diameter.Based on such flow mode diagram,the bulk solid materials transported pneumatically in con-Žventional systems can be classified into three groups PC1,.ŽPC2and PC3.Materials in group PC1 e.g.,fly ash,.cement,pulverised coal can be transported smoothly and gently from dilute-to fluidised dense-phase.Materials in Ž.group PC2 e.g.,plastic pellets,wheat,barley can be transported in dilute-phase,unstable zone or slug-flow and Žmaterials in group PC3 e.g.,primary concentrate,zircon .sand are conveyed in dilute-phase only.()R.Pan r Powder Technology1041999157–163163Some exceptions can occur for bulk solids that displayŽunusual particle and bulk properties e.g.,light,spongy, interlocking characteristics and r or wide particle size .range.These bulk solid materials are transported in dilute-phase only.6.NomenclatureŽ.d Median particle diameter mpd Diameter of a sphere having the same volume vŽ.as the particle mŽy2.g Acceleration due to gravity m sŽ.k Constant in Eq.2Ž.l Length of single slug msŽy1.m Air mass flow rate kg sfŽy1.m Product mass flow rate kg ssŽ.p Interstitial air pressure Pa gŽy1.u Minimum bubbling velocity m smbŽy1.u Minimum fluidisation velocity m smfx Horizontal coordinateŽy3.r Loose-poured bulk density kg mbŽy3.r Air density kg mfŽy3.r Particle density kg msŽ.s Wall pressure PawŽ.s Axial stress in particle slug PaxŽ.t Shear stress at wall PawŽ.v Constant in Eq.4´Bulk voidage,´s1y r r y1b sŽ.m Air dynamic viscosity Pa s Referencesw x1M.G.Jones,The influence of bulk particulate properties on pneu-Ž.matic conveying performance,Thesis PhD,Thames Polytechnic, London,1988.w x2R.Pan,Scale-up procedure for the design of pneumatic conveyingŽ.systems,Thesis PhD,Department of Mechanical Engineering, University of Wollongong,Australia,1992.w x3R.Pan,B.Mi,P.W.Wypych,Pneumatic conveying characteristicsŽ.of fine and granular bulk solids,KONA12199477–85.w x4G.Dixon,The impact of powder properties on dense phase flow, Proc.Int.Conf.on Pneumatic Conveying,January1979,London, UK.w xŽ.5 D.Geldart,Types of gas fluidisation,Powder Technol.71973285–292.w x6N.J.Mainwaring, A.R.Reed,An appraisal of Dixon’s slugging diagram for assessing the dense phase potential of bulk materials, Pneumatech3,3rd Int.Conf.on Pneumatic Conveying Technology, 24–26March,1987,Jersey,UK.w x7M.G.Jones,ls,Product classification for pneumatic convey-Ž.Ž.ing,Powder Process.Handling221990117–122.w x8 D.Geldart,Gas Fluidisation Technology,Wiley,New York,1986. w xŽ.9 C.Y.Wen,Y.H.Yu,AIChE J.121966610.w x10J.Baeyens,D.Geldart,Fluidisation and Its Applications,Toulouse, 1973,p.263.w x11K.Konrad,D.Harrison,Prediction of the pressure drop for horizon-tal dense phase pneumatic conveying of particles,Pneumatransport 5,Fifth Int.Conf.on the Pneumatic Transport of Solids in Pipes, London,UK,April1980,pp.225–244.w x12 B.Mi,P.W.Wypych,Pressure drop prediction in low-velocityŽ.pneumatic conveying,Powder Technol.811994125–137.w x13R.Pan,P.W.Wypych,Pressure drop and slug velocity in low-veloc-Ž.ity pneumatic conveying of bulk solids,Powder Technol.941997 123–132.。

chapter_4

4Material Behavior—Linear Elastic Solids The previous two chapters establish elasticityﬁeld equations related to the kinematics ofsmall deformation theory and the equilibrium of the associated internal stressﬁeld.Basedon these physical concepts,three strain-displacement relations(2.2.5),six compatibilityequations(2.6.2),and three equilibrium equations(3.6.5)were developed for the generalthree-dimensional case.Because moment equilibrium simply results in symmetry of the stresstensor,it is not normally included as a separateﬁeld equation set.Also,recall that thecompatibility equations actually represent only three independent relations,and these equa-tions are needed only to ensure that a given strainﬁeld will produce single-valued continuousdisplacements.Because the displacements are included in the general problem formulation,thesolution automatically gives continuous displacements,and the compatibility equations are notformally needed for the general system.Thus,excluding the compatibility relations,it is foundthat we have now developed nineﬁeld equations.The unknowns in these equations include3displacement components,6components of strain,and6stress components,yielding a total of15unknowns.Thus,the9equations are not sufﬁcient to solve for the15unknowns,andadditionalﬁeld equations are needed.This result should not be surprising since up to this pointin our development we have not considered the material response.We now wish to completeour general formulation by specializing to a particular material model that provides reasonablecharacterization of materials under small deformations.The model we will use is that of alinear elastic material,a name that categorizes the entire theory.This chapter presents thebasics of the elastic model specializing the formulation for isotropic materials.Related theoryfor anisotropic media is developed in Chapter11.Thermoelastic relations are also brieﬂypresented for later use in Chapter12.4.1Material CharacterizationRelations that characterize the physical properties of materials are called constitutive equa-tions.Because of the endless variety of materials and loadings,the study and development ofconstitutive equations is perhaps one of the most interesting and challengingﬁelds in mechan-ics.Although continuum mechanics theory has established some principles for systematicdevelopment of constitutive equations(Malvern1969),many constitutive laws have beendeveloped through empirical relations based on experimental evidence.Our interest here is69limited to a special class of solid materials with loadings resulting from mechanical or thermaleffects.The mechanical behavior of solids is normally deﬁned by constitutive stress-strainmonly,these relations express the stress as a function of the strain,strain rate,strain history,temperature,and material properties.We choose a rather simple material modelcalled the elastic solid that does not include rate or history effects.The model may bedescribed as a deformable continuum that recovers its original conﬁguration when the loadingscausing the deformation are removed.Furthermore,we restrict the constitutive stress-strainlaw to be linear,thus leading to a linear elastic solid.Although these assumptions greatlysimplify the model,linear elasticity predictions have shown good agreement with experimentaldata and have provided useful methods to conduct stress analysis.Many structural materialsincluding metals,plastics,ceramics,wood,rock,concrete,and so forth exhibit linear elasticbehavior under small deformations.As mentioned,experimental testing is commonly employed in order to characterize the mechanical behavior of real materials.One such technique is the simple tension test in which aspecially prepared cylindrical orﬂat stock sample is loaded axially in a testing machine.Strainis determined by the change in length between prescribed reference marks on the sample and isusually measured by a clip gage.Load data collected from a load cell is divided by the cross-sectional area in the test section to calculate the stress.Axial stress-strain data is recorded andplotted using standard experimental techniques.Typical qualitative data for three types ofstructural metals(mild steel,aluminum,cast iron)are shown in Figure4-1.It is observed thateach material exhibits an initial stress-strain response for small deformation that is approxi-mately linear.This is followed by a change to nonlinear behavior that can lead to largedeformation,ﬁnally ending with sample failure.For each material the initial linear response ends at a point normally referred to as the proportional limit.Another observation in this initial region is that if the loading is removed,the sample returns to its original shape and the strain disappears.This characteristic is theprimary descriptor of elastic behavior.However,at some point on the stress-strain curveunloading does not bring the sample back to zero strain and some permanent plastic deform-ation results.The point at which this nonelastic behavior begins is called the elastic limit.Although some materials exhibit different elastic and proportional limits,many timesthese values are taken to be approximately the same.Another demarcation on the stress-straincurve is referred to as the yield point,deﬁned by the location where large plastic deformationbegins.s70FOUNDATIONS AND ELEMENTARY APPLICATIONSBecause mild steel and aluminum are ductile materials,their stress-strain response indicates extensive plastic deformation,and during this period the sample dimensions will be changing.In particular the sample’s cross-sectional area undergoes signiﬁcant reduction,and the stress calculation using division by the original area will now be in error.This accounts for the reduction in the stress at large strain.If we were to calculate the load divided by the true area,the true stress would continue to increase until failure.On the other hand,cast iron is known to be a brittle material,and thus its stress-strain response does not show large plastic deformation.For this material,very little nonelastic or nonlinear behavior is observed.It is therefore concluded from this and many other studies that a large variety of real materials exhibits linear elastic behavior under small deformations.This would lead to a linear constitutive model for the one-dimensional axial loading case given by the relation s ¼E e ,where E is the slope of the uniaxial stress-strain curve.We now use this simple concept to develop the general three-dimensional forms of the linear elastic constitutive model.4.2Linear Elastic Materials—Hooke’s LawBased on observations from the previous section,in order to construct a general three-dimensional constitutive law for linear elastic materials,we assume that each stress component is linearly related to each strain components x ¼C 11e x þC 12e y þC 13e z þ2C 14e xy þ2C 15e yz þ2C 16e zxs y ¼C 21e x þC 22e y þC 23e z þ2C 24e xy þ2C 25e yz þ2C 26e zxs z ¼C 31e x þC 32e y þC 33e z þ2C 34e xy þ2C 35e yz þ2C 36e zxt xy ¼C 41e x þC 42e y þC 43e z þ2C 44e xy þ2C 45e yz þ2C 46e zxt yz ¼C 51e x þC 52e y þC 53e z þ2C 54e xy þ2C 55e yz þ2C 56e zxt zx ¼C 61e x þC 62e y þC 63e z þ2C 64e xy þ2C 65e yz þ2C 66e zx (4:2:1)where the coefﬁcients C ij are material parameters and the factors of 2arise because of the symmetry of the strain.Note that this relation could also be expressed by writing the strains as a linear function of the stress components.These relations can be cast into a matrix format ass x s y s z t xy t yz t zx 2666666437777775¼C 11C 12ÁÁÁC 16C 21ÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁÁC 61ÁÁÁÁC 662666666437777775e x e y e z 2e xy 2e yz 2e zx 2666666437777775(4:2:2)Relations (4.2.1)can also be expressed in standard tensor notation by writings ij ¼C ijkl e kl (4:2:3)where C ijkl is a fourth-order elasticity tensor whose components include all the material parameters necessary to characterize the material.Based on the symmetry of the stress and strain tensors,the elasticity tensor must have the following properties (see Exercise 4-1):Material Behavior—Linear Elastic Solids 71C ijkl¼C jikl(4:2:4)C ijkl¼C ijlkIn general,the fourth-order tensor C ijkl has81components.However,relations(4.2.4)reduce the number of independent components to36,and this provides the required matchwith form(4.2.1)or(4.2.2).Later in Chapter6we introduce the concept of strain energy,andthis leads to a further reduction to21independent elastic components.The components of C ijklor equivalently C ij are called elastic moduli and have units of stress(force/area).In order tocontinue further,we must address the issues of material homogeneity and isotropy.If the material is homogenous,the elastic behavior does not vary spatially,and thus all elastic moduli are constant.For this case,the elasticity formulation is straightforward,leading to thedevelopment of many analytical solutions to problems of engineering interest.A homogenousassumption is an appropriate model for most structural applications,and thus we primarilychoose this particular case for subsequent formulation and problem solution.However,there area couple of important nonhomogeneous applications that warrant further discussion.Studies in geomechanics have found that the material behavior of soil and rock commonly depends on distance below the earth’s surface.In order to simulate particular geomechanicsproblems,researchers have used nonhomogeneous elastic models applied to semi-inﬁnitedomains.Typical applications have involved modeling the response of a semi-inﬁnite soilmass under surface or subsurface loadings with variation in elastic moduli with depth(see thereview by Poulos and Davis1974).Another more recent application involves the behavior offunctionally graded materials(FGM)(see Erdogan1995and Parameswaran and Shukla1999,2002).FGMs are a new class of engineered materials developed with spatially varyingproperties to suit particular applications.The graded composition of such materials is com-monly established and controlled using powder metallurgy,chemical vapor deposition,orcentrifugal casting.Typical analytical studies of these materials have assumed linear,exponen-tial,and power-law variation in elastic moduli of the formC ij(x)¼C o ij(1þax)C ij(x)¼C o ij e ax(4:2:5)C ij(x)¼C o ij x awhere C o ij and a are prescribed constants and x is the spatial coordinate.Further investigation offormulation results for such spatially varying moduli are included in Exercises5-6and7-12insubsequent chapters.Similar to homogeneity,another fundamental material property is isotropy.This property has to do with differences in material moduli with respect to orientation.For example,manymaterials including crystalline minerals,wood,andﬁber-reinforced composites have differentelastic moduli in different directions.Materials such as these are said to be anisotropic.Notethat for most real anisotropic materials there exist particular directions where the properties arethe same.These directions indicate material symmetries.However,for many engineeringmaterials(most structural metals and many plastics),the orientation of crystalline and grainmicrostructure is distributed randomly so that macroscopic elastic properties are found to beessentially the same in all directions.Such materials with complete symmetry are calledisotropic.As expected,an anisotropic model complicates the formulation and solution ofproblems.We therefore postpone development of such solutions until Chapter11and continueour current development under the assumption of isotropic material behavior.72FOUNDATIONS AND ELEMENTARY APPLICATIONSThe tensorial form(4.2.3)provides a convenient way to establish the desired isotropic stress-strain relations.If we assume isotropic behavior,the elasticity tensor must be the same under all rotations of the coordinate ing the basic transformation properties from relation(1:5:1)5,the fourth-order elasticity tensor must satisfyC ijkl¼Q im Q jn Q kp Q lq C mnpqIt can be shown(Chandrasekharaiah and Debnath1994)that the most general form that satisﬁes this isotropy condition is given byC ijkl¼ad ij d klþbd ik d jlþgd il d jk(4:2:6)where a,b,and g are arbitrary constants.Veriﬁcation of the isotropy property of form (4.2.6)is left as ing the general form(4.2.6)in stress-strain relation(4.2.3) givess ij¼l e kk d ijþ2m e ij(4:2:7)where we have relabeled particular constants using l and m.The elastic constant l is called Lame´’s constant,and m is referred to as the shear modulus or modulus of rigidity.Some texts use the notation G for the shear modulus.Equation(4.2.7)can be written out in individual scalar equations ass x¼l(e xþe yþe z)þ2m e xs y¼l(e xþe yþe z)þ2m e ys z¼l(e xþe yþe z)þ2m e zt xy¼2m e xyt yz¼2m e yzt zx¼2m e zx(4:2:8)Relations(4.2.7)or(4.2.8)are called the generalized Hooke’s law for linear isotropic elastic solids.They are named after Robert Hooke who in1678ﬁrst proposed that the deformation of an elastic structure is proportional to the applied force.Notice the signiﬁcant simplicity of the isotropic form when compared to the general stress-strain law originally given by(4.2.1).It should be noted that only two independent elastic constants are needed to describe the behavior of isotropic materials.As shown in Chapter11,additional numbers of elastic moduli are needed in the corresponding relations for anisotropic materials.Stress-strain relations(4.2.7)or(4.2.8)may be inverted to express the strain in terms of the stress.In order to do this it is convenient to use the index notation form(4.2.7)and set the two free indices the same(contraction process)to gets kk¼(3lþ2m)e kk(4:2:9) This relation can be solved for e kk and substituted back into(4.2.7)to gete ij¼12ms ijÀl3lþ2ms kk d ijMaterial Behavior—Linear Elastic Solids73which is more commonly written ase ij¼1þnEs ijÀnEs kk d ij(4:2:10)where E¼m(3lþ2m)=(lþm)and is called the modulus of elasticity or Young’s modulus,and n¼l=[2(lþm)]is referred to as Poisson’s ratio.The index notation relation(4.2.10)may be written out in component(scalar)form giving the six equationse x¼1Es xÀn(s yþs z)ÂÃe y¼1Es yÀn(s zþs x)ÂÃe z¼1Es zÀn(s xþs y)ÂÃe xy¼1þnEt xy¼12mt xye yz¼1þnt yz¼1t yze zx¼1þnEt zx¼12mt zx(4:2:11)Constitutive form(4.2.10)or(4.2.11)again illustrates that only two elastic constants areneeded to formulate Hooke’s law for isotropic materials.By using any of the isotropic formsof Hooke’s law,it can be shown that the principal axes of stress coincide with the principalaxes of strain(see Exercise4-4).This result also holds for some but not all anisotropicmaterials.4.3Physical Meaning of Elastic ModuliFor the isotropic case,the previously deﬁned elastic moduli have simple physical meaning.These can be determined through investigation of particular states of stress commonly used inlaboratory materials testing as shown in Figure4-2.4.3.1Simple TensionConsider the simple tension test as discussed previously with a sample subjected to tensionin the x direction(see Figure4-2).The state of stress is closely represented by the one-dimensionalﬁelds ij¼s00 000 000 2435Using this in relations(4.2.10)gives a corresponding strainﬁeld 74FOUNDATIONS AND ELEMENTARY APPLICATIONSe ij ¼sE 000Àn E s 000Àn Es 2666437775Therefore,E ¼s =e x and is simply the slope of the stress-strain curve,while n ¼Àe y =e x ¼Àe z =e x is the ratio of the transverse strain to the axial strain.Standard measure-ment systems can easily collect axial stress and transverse and axial strain data,and thus through this one type of test both elastic constants can be determined for materials of interest.4.3.2Pure ShearIf a thin-walled cylinder is subjected to torsional loading (as shown in Figure 4-2),the state of stress on the surface of the cylindrical sample is given bys ij ¼0t 0t 000002435Again,by using Hooke’s law,the corresponding strain ﬁeld becomese ij ¼0t =2m 0t =2m000002435and thus the shear modulus is given by m ¼t =2e xy ¼t =g xy ,and this modulus is simply the slope of the shear stress-shear straincurve.(Simple Tension)(Pure Shear)(Hydrostatic Compression)FIGURE 4-2Special characterization states of stress.Material Behavior—Linear Elastic Solids 754.3.3Hydrostatic Compression(or Tension)Theﬁnal example is associated with the uniform compression(or tension)loading of a cubical specimen,as shown in Figure4-2.This type of test would be realizable if the sample was placed in a high-pressure compression chamber.The state of stress for this case is given bys ij¼Àp000Àp000Àp2435¼Àp d ijThis is an isotropic state of stress and the strains follow from Hooke’s lawe ij¼À1À2nEp000À1À2nEp000À1À2nEp 266664377775The dilatation that represents the change in material volume(see Exercise2-11)is thus givenby W¼e kk¼À3(1À2n)p=E,which can be written asp¼Àk W(4:3:1) where k¼E=[3(1À2n)]is called the bulk modulus of elasticity.This additional elasticconstant represents the ratio of pressure to the dilatation,which could be referred to as thevolumetric stiffness of the material.Notice that as Poisson’s ratio approaches0.5,the bulkmodulus becomes unbounded and the material does not undergo any volumetric deformationand hence is incompressible.Our discussion of elastic moduli for isotropic materials has led to the deﬁnition ofﬁve constants l,m,E,n,and k.However,keep in mind that only two of these are needed tocharacterize the material.Although we have developed a few relationships between variousmoduli,many other such relations can also be found.In fact,it can be shown that allﬁve elasticconstants are interrelated,and if any two are given,the remaining three can be determined byusing simple formulae.Results of these relations are conveniently summarized in Table4-1.This table should be marked for future reference,because it will prove to be useful forcalculations throughout the text.Typical nominal values of elastic constants for particular engineering materials are given in Table4-2.These moduli represent average values,and some variation will occur for speciﬁcmaterials.Further information and restrictions on elastic moduli require strain energy con-cepts,which are developed in Chapter6.Before concluding this section,we wish to discuss the forms of Hooke’s law in curvilinear coordinates.Previous chapters have mentioned that cylindrical and spherical coordinates(seeFigures1-4and1-5)are used in many applications for problem solution.Figures3-9and3-10deﬁned the stress components in each curvilinear system.In regards to theseﬁgures,it followsthat the orthogonal curvilinear coordinate directions can be obtained from a base Cartesiansystem through a simple rotation of the coordinate frame.For isotropic materials,the elasticitytensor C ijkl is the same in all coordinate frames,and thus the structure of Hooke’s law remainsthe same in any orthogonal curvilinear system.Therefore,form(4.2.8)can be expressed incylindrical and spherical coordinates as76FOUNDATIONS AND ELEMENTARY APPLICATIONSs r ¼l (e r þe y þe z )þ2m e rs R ¼l (e R þe f þe y )þ2m e R s y ¼l (e r þe y þe z )þ2m e ys f ¼l (e R þe f þe y )þ2m e f s z ¼l (e r þe y þe z )þ2m e zs y ¼l (e R þe f þe y )þ2m e y t r y ¼2m e r yt R f ¼2m e R f t y z ¼2m e y zt fy ¼2m e fy t zr ¼2m e zr t y R ¼2m e y R (4:3:2)The complete set of elasticity ﬁeld equations in each of these coordinate systems is given in Appendix A.4.4Thermoelastic Constitutive RelationsIt is well known that a temperature change in an unrestrained elastic solid produces deform-ation.Thus,a general strain ﬁeld results from both mechanical and thermal effects.Within the context of linear small deformation theory,the total strain can be decomposed into the sum of mechanical and thermal components asTABLE 4-1Relations Among Elastic ConstantsE nk m l E ,n E nE E E n E,k E 3k ÀE6k k 3kE 9k ÀE 3k (3k ÀE )9k ÀE E ,m E E À2mm E m m (E À2m )E ,l E 2lE þl þRE þ3l þR 6E À3l þR 4l n ,k 3k (1À2n )n k 3k (1À2n )2(1þn )3k n 1þn n ,m 2m (1þn )n2m (1þn )m 2mn n ,l l (1þn )(1À2n )n nl (1þn )3n l (1À2n )2n l k ,m 9k m 3k À2mk m k À2m k ,l 9k (k Àl )3k Àl l3k Àl k 32(k Àl )l m ,lm (3l þ2m )l þm l2(l þm )3l þ2m 3m l R ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃE 2þ9l 2þ2E l p Material Behavior—Linear Elastic Solids 77e ij ¼e (M )ij þe (T )ij (4:4:1)If T o is taken as the reference temperature and T as an arbitrary temperature,the thermal strains in an unrestrained solid can be written in the linear constitutive forme (T )ij ¼a ij (T ÀT o )(4:4:2)where a ij is the coefﬁcient of thermal expansion tensor .Notice that it is the temperature difference that creates thermal strain.If the material is taken as isotropic,then a ij must be an isotropic second-order tensor,and (4.4.2)simpliﬁes toe (T )ij ¼a (T ÀT o )d ij (4:4:3)where a is a material constant called the coefﬁcient of thermal expansion .Table 4-2provides typical values of this constant for some common materials.Notice that for isotropic materials,no shear strains are created by temperature change.By using (4.4.1),this result can be combined with the mechanical relation (4.2.10)to givee ij ¼1þn s ij Àn s kk d ij þa (T ÀT o )d ij (4:4:4)The corresponding results for the stress in terms of strain can be written ass ij ¼C ijkl e kl Àb ij (T ÀT o )(4:4:5)where b ij is a second-order tensor containing thermoelastic moduli.This result is sometimes referred to as the Duhamel-Neumann thermoelastic constitutive law .The isotropic case can be found by simply inverting relation (4.4.4)to gets ij ¼l e kk d ij þ2m e ij À(3l þ2m )a (T ÀT o )d ij (4:4:6)Thermoelastic solutions are developed in Chapter 12,and the current study will now continue under the assumption of isothermal conditions.Having developed the necessary six constitutive relations,the elasticity ﬁeld equation system is now complete with 15equations (strain-displacement,equilibrium,Hooke’s law)for 15unknowns (displacements,strains,stresses).Obviously,further simpliﬁcation is neces-TABLE 4-2Typical Values of Elastic Moduli for Common Engineering MaterialsE (GPa )nm (GPa )l (GPa )k (GPa )a (10À6=8C )Aluminum 68.90.3425.754.671.825.5Concrete 27.60.2011.57.715.311Copper 89.60.3433.47193.318Glass 68.90.2527.627.645.98.8Nylon 28.30.4010.1 4.0447.2102Rubber 0.00190.4990:654Â10À30.3260.326200Steel 2070.2980.211116413.578FOUNDATIONS AND ELEMENTARY APPLICATIONSsary in order to solve speciﬁc problems of engineering interest,and these processes are thesubject of the next chapter.ReferencesChandrasekharaiah DS,and Debnath L:Continuum Mechanics,Academic Press,Boston,1994.Erdogan F:Fracture mechanics of functionally graded materials,Composites Engng,vol5,pp.753-770,1995.Malvern LE:Introduction to the Mechanics of a Continuous Medium,Prentice Hall,Englewood Cliffs,NJ,1969.Parameswaran V,and Shukla A:Crack-tip stressﬁelds for dynamic fracture in functionally gradientmaterials,Mech.of Materials,vol31,pp.579-596,1999.Parameswaran V,and Shukla A:Asymptotic stressﬁelds for stationary cracks along the gradient infunctionally graded materials,J.Appl.Mech.,vol69,pp.240-243,2002.Poulos HG,and Davis EH:Elastic Solutions for Soil and Rock Mechanics,John Wiley,New York,1974. Exercises4-1.Explicitly justify the symmetry relations(4.2.4).Note that theﬁrst relation follows directly from the symmetry of the stress,while the second condition requires a simple(C ijklþC ijlk)e lk to arrive at the required conclusion.expansion into the form s ij¼124-2.Substituting the general isotropic fourth-order form(4.2.6)into(4.2.3),explicitly develop the stress-strain relation(4.2.7).4-3.Following the steps outlined in the text,invert the form of Hooke’s law given by(4.2.7)and develop form(4.2.10).Explicitly show that E¼m(3lþ2m)=(lþm)and n¼l=[2(lþm)].ing the results of Exercise4-3,show that m¼E=[2(1þn)]and l¼E n=[(1þn)(1À2n)].4-5.For isotropic materials show that the principal axes of strain coincide with the principal axes of stress.Further,show that the principal stresses can be expressed in terms of theprincipal strains as s i¼2m e iþl e kk.4-6.A rosette strain gage(see Exercise2-7)is mounted on the surface of a stress-free elastic solid at point O as shown in the followingﬁgure.The three gage readings give surfaceextensional strains e a¼300Â10À6,e b¼400Â10À6,e c¼100Â10À6.Assumingthat the material is steel with nominal properties given by Table4-2,determine all stresscomponents at O for the given coordinate system.Material Behavior—Linear Elastic Solids794-7.The displacements in an elastic material are given byu ¼ÀM (1Àn 2)EI xy ,v ¼M (1þn )n 2EI y 2þM (1Àn 2)2EI (x 2Àl 42),w ¼0where M ,E ,I ,and l are constant parameters.Determine the corresponding strain and stress ﬁelds and show that this problem represents the pure bending of a rectangular beam in the x,y plane.4-8.If the elastic constants E ,k ,and m are required to be positive,show that Poisson’s ratiomust satisfy the inequality À1<n <12.For most real materials it has been found that0<n <12.Show that this more restrictive inequality in this problem implies that l >0.4-9.Under the condition that E is positive and bounded,determine the elastic moduli l ,m ,and k for the special cases of Poisson’s ratio:v ¼0,14,12.4-10.Show that Hooke’s law for an isotropic material may be expressed in terms of sphericaland deviatoric tensors by the two relations~sij ¼3k ~e ij ,^s ij ¼2m ^e ij 4-11.A sample is subjected to a test under plane stress conditions (speciﬁed bys z ¼t zx ¼t zy ¼0)using a special loading frame that maintains an in-plane loading constraint s x ¼2s y .Determine the slope of the stress-strain response s x vs.e x for this sample.4-12.A rectangular steel plate (thickness 4mm)is subjected to a uniform biaxial stress ﬁeld asshown in the following ﬁgure.Assuming all ﬁelds are uniform,determine changes in the dimensions of the plate under thisloading.20 MPa30 MPa80FOUNDATIONS AND ELEMENTARY APPLICATIONS。

Mechanical4-5

M a t e r i a l s a n d M e c h a n i c a l E n g i n e e r i n gSections1. Introduction、2. Atomic Bonds、3. Material Properties、4. Selection of MaterialsObjectivesAfter learning this chapter, you should be able to do the following :Understand how material properties are used to qualify materials for engineering design. ..Understand how traditional and composite materials are used in engineering design.1.IntroductionMaterial science encompasses the study of the structure and properties of any material, as well as using this body of knowledge to create new types of materials, and to tailor the properties of a material for specific uses.Materials are the foundation and fabric of manufactured products.Mechanical design is dependent on and limited by materials.New materials and processes enable other new technologies to be commercially successful..Properties of materials are usually the deciding factor in choosing which materials should be used for a particular application. .Material properties depend on the material microstructure, which in turn results from its composition and processing.2. Atomic BondsMetallic BondsIn a metal, the outer electrons are shared among all the atoms in the solid.Each atom gives up its outer electrons and becomes slightly positively charged. The negatively charged electrons hold the metal atoms together. .Since the electrons are free to move, they lead to good thermal and electrical conductivity.Ionic BondsAtoms like to have a filled outer shell of electrons. Sometimes, by transferring electrons from one atom to another, electron shells are filled.The donor atom will take a positive charge, and the acceptor will have a negative charge. The charged atoms or ions will be attracted to each other, and form bonds.Covalent BondsSome atoms like to share electrons to complete their outer shells. Each pair of shared atoms is called a covalent bond. Hydrogen BondsHydrogen bonds are common in covalently bonded molecules which contain hydrogen, such as water (H2O).NotesThere are two types of bonds:1.Primary bonds ( Metallic Bonds, Covalent Bonds, Ionic Bonds )2.Secondary bonds (Hydrogen Bonds, etc.)Primary bonds are the strongest bonds which hold atoms together. Secondary bonds are much weaker than primary bonds. They often provide a "weak link" for deformation or fracture.3. Material PropertiesThe principal properties of materials which are of importance to the engineer in selecting materials can be broadly divided into :Mechanical Properties ( concerned mainly with strength )Physical Properties ( such as melting temperature,density, etc )3.1 Tensile TestThe mechanical properties used in engineering are determined by performing a tensile test. .Typical test machines may test the specimen in different ways including tension and compression.Stress-Strain CurveIn a static tensile test, the stress-strain curve is produced.Characteristics of the curve include a linear region and a region of rapid elongation known as the plastic region.The point at which the linear region ends is called the proportional limit.The slope of the curve in the linear region is called the Young’s modulus.The proportional limit defines the point where a small increase in the stress yields a large deformation. This phenomenon is called yielding.Most engineering designs tend to avoid the plastic region. If the goal of a design is to design within the linear region, then all stresses in the structure or component must be below the yield stress.A material that can undergo large plastic deformation before fracture is called a ductile material. A material that exhibits little or no plastic deformation at failure is called a brittle material.3.2 Young’s ModulusYoung's modulus measures the resistance of a material to elastic (recoverable) deformation under load. .A stiff material has a high Young's modulus and changes its shape only slightly under elastic loads. A flexible material has a low Young's modulus and changes its shape considerably. .A stiff material requires high loads to elastically deform it - not to be confused with a strong material, which requires high loads to permanently deform (or break) it.Measurement (Tensile Test)3.3 StrengthThe strength of a material is its resistance to failure by permanent deformation (usually by yielding). .A strong material requires high loads to permanently deform (or break) it - not to be confused with a stiff material, which requires high loads to elastically deform it.Measurement (Tensile Test)3.4 Toughness （韧性）Toughness is the resistance of a material to being broken in two, by a crack running across it - this is called "fracture" and absorbs energy. .A tough material requires a lot of energy to break it, usually because the fracture process causes a lot of plastic deformation. .A brittle material may be strong but once a crack has started the material fractures easily because little energy is absorbed (e.g. glass).Measurement(Compact Tension Test)3.5 Elongation （延展性）Measurement(Tensile Test)3.6 DensityDensity is a measure of how heavy an object is for a given size, i.e. the mass of material per unitvolume. .The weight of a product is a very common factor in design. In transport applications, lightweight design is very important - for example, to reduce the environmental impact of cars, or to increase the payload of aircraft.3.7 Max. Service TemperatureThe strength of a material tends to fall quickly when a certain temperature is reached. This temperature limits the maximum operating temperature for which the material is useful.3.8 ResistivityResistivity is a measure of the resistance to electrical conduction for a given size of material.Resistivity is affected by temperature - for most materials the resistivity increases with temperature. An exception is semiconductors (e.g. silicon) in which the resistivity decreases with temperature.Measurement: The resistivity can be calculated quite easily be measuring the resistance of a piece of wire of constant cross-section and known length.4. Selection of MaterialsThe main criteria to influence the selection of materials for any particular engineering product can be summarized as the following: Property requirements、Processing requirements、Economic requirementsUltimately our final choice will involve a compromise. There is rarely, if ever, an ideal solution.4.1 Mild SteelSteels are the most important engineering materials, and cover a wide range of alloys based on iron andcarbon. .Mild steel contains 0.1-0.2 %C. They are cheap, strong steels used for construction, transport and packaging. .All steels have a high density and a high Young's modulus. The strength of mild steel is improved by cold working. It is inherently very tough. .Mild steel rusts easily, and must be protected by painting, galvanizing or other coatings.Design strengths:•High strength-to-weight ratio •High stiffness-to-weight ratio •Good strength with high toughness•Very cheap •Easy to shape •Easy to weld •Easy to recycleDesign weaknesses:•High density •Poor electrical and thermal conductivity4.2 Alloy SteelAlloy steels are mostly fairly cheap, covering a range of carbon contents (0.1-1.0%). The high carbon content steels respond well to heat treatment to give very high strength and good toughness for gears, drive shafts, pressure vessels,tools. .Alloy steels containing other elements as well as carbon are classified into low alloy and high alloy, depending on the amount of additional alloying elements. Heat-treated high alloy steels give very high strengths, but are more expensive. .Alloy carbon steels rust easily, and must be protected by painting or other coatings.Design strengths:•High strength with good toughness •High stiffness •Mostly very cheap •Quite easy to shape•Easy to weld •Easy to recycleDesign weaknesses:•High density •Poor electrical and thermal conductivity4.3 Stainless SteelStainless steels are more expensive steels containing typically 25% of Chromium and Nickel, which gives excellent corrosion resistance and also high strength and toughness (used for chemical plant and surgical instruments).Design strengths:•High strength with good toughness •High stiffness •Mostly very cheap •Quite easy to shape•Quite easy to weld •Easy to recycleDesign weaknesses:•High density •Poor electrical and thermal conductivity4.4 Aluminum AlloyAluminum is a lightweight, reasonably cheap metal widely used for packaging and transport. It has only been widely available and used for the last 60 years. .Raw aluminum has low strength and high ductility (ideal for foil). Strength is increased by alloying and heat treatment. Some alloys are cast, others are used for wrought products. .Aluminum is quite reactive, but protects itself very effectively with a thin oxide layer to resist corrosion.Design strengths:•High strength-to-weight ratio •High stiffness-to-weight ratio•High electrical and thermal conductivity •Easy to shape •Easy to recycleDesign weaknesses:•Difficult to arc weld4.5 Titanium AlloysTitanium alloys are quite low density, stiff, strong alloys and are expensive. They are used most in sports products (e.g. golf clubs and bicycles) and in aircraft (e.g. engine fan blades). .Pure titanium has moderate strength, but the standard titanium alloy contains 6% aluminum and 4% vanadium, which gives the high strength needed in a jet engine. .Titanium is a reactive metal when hot, but has good corrosion resistance at room temperature.Design strengths:•High strength, even at high temperatures •High stiffness •Corrosion resistant, even resistant to salt waterDesign weaknesses:•High cost •Chemically very reactive when hot •Quite difficult to shape - usually cast4.6 SiliconSilicon is doped with very low levels of other elements to give it the particular "semiconducting" electrical properties needed for transistors and microchips. .To supply the huge demand for computer chips, processes have developed so that it can be produced as very large high purity crystals. .Silicon is the base material used for the manufacture of computer chips, and is therefore one of the most important materials.Design strengths:•Semiconducting propertiesTypical products:•Transistors •Computer chips4.7 DiamondDiamond is covalently bonded pure carbon, and has the highest Young's modulus and hardness of allmaterials. .Diamond is naturally occurring but can also be manufactured. It is increasingly used for its very high hardness in cutting tools.Design strengths:•Excellent corrosion resistance •Low density •High electrical resistance. •High hardnessDesign weaknesses:•Low tensile strength •Low toughness •Difficult to shape4.8 CompositeComposites are formed from two or more types of materials. Examples include polymer/ceramics and metal/ceramics composites. .Composites are used because overall properties of the composites are superior to those of the individual components. .For example: polymer/ceramics composites have a greater modulus than the polymer component, but are not as brittle as ceramics.There are two types of composites: Fiber Reinforced Composites Particle Reinforced Composites4.9 Example 1 (Automobile)The new Lincoln LS represents a current example of the use of light weight materials on a high volume production vehicle Aluminum, plastics and magnesium are selected to achieve weight reduction. (Totally more than 20% of vehicle weight) The Ford P2000, is a good example of what the mix might be for vehicles by the end of the next two decadesThe P2000 meets the goal of 50% weight reduction in the body and chassis. To do this light weight materials are used in every application where feasible.4.10 Example 2 (Aircraft)Structural materials mass distribution on the Boeing 747 and 777 :Aluminum alloys constitute by far the biggest proportion of structural mass of most modern aircraft, with steels, titanium alloys and structural composites all accounting for approximately 10%.A new series of aluminum alloys have recently been developed which contain the element lithium. These alloys are lighter and stiffer than existing alloys, and are now finding use on the latest aircraft designs.NotesTitanium has a density approximately twice that of aluminum, but when alloyed with other elements, can exhibit very high mechanical properties.The reason titanium alloys are not used more extensively on airframes is due to cost. Titanium alloys cost up to 10 times more than aluminum alloysStructural composite materials are finding increasing use on modern aircraft (especially military aircraft) because of their very attractive low density and high mechanical properties.。

译林版高中英语选必四Unit4 Grammar and usage 教案

《英语》（选择性必修·第四册）Unit 4Never too old to learnGrammar and usageI. Learning objectivesBy the end of the lesson, students will be able to:1. analyse complicated sentences;2. understand the basic rules of simple, compound sentence, complex and compound-complexsentence;3. practice application of complicated sentences.II. Key competence focusAnalysis and practice of complicated sentencesIII. Predicted area of difficultyAnalysis of complicated sentences.IV. Teaching proceduresT greets the class.T: Class begins, boys and girls! Good morning/afternoon!Step 1 Revising the core words and phrases learnt last period.Fill in the blanks with proper forms of the (given) words.1. Our class ________ (compose) of 20 boys and 15 girls, most of whom are excellent at writing.1. is composed2. An ________ (educate) guess is a guess which is based on a certain amount of knowledge andis therefore likely to be correct.2. educated3. He’s too ________ (bind) up in his work to have much time for his children.3. bound4. We must find a way ________ (resolve) these problems before it’s too late.4. to resolve5. He walked on the opposite side of the street ________ (refresh) his memory of the building.5. to refresh6. Listening with an open mind to ________ (criticize) and accepting useful advice are the key toprogress and improvement.6. criticism7. You are a very ________ (inquire) mind person and your paper will achieve very good scores.7. inquiring8. If installed, the instrument ________ (register) every change of direction or height.8. will register9. I’ve personally never subscribed ________ the view that either sex is superior to the other.9. to10. In the world of fashion it sometimes seems that the only constant is ________ (cease) change.10. ceaseless【设计意图：上一节课核心词汇较多，有必要复习一下这些内容。

译林版高中英语学案选择性必修第四册精品课件UNIT 3 Section A

criterion
shave
refreshed
mode
delay
duration
rude
justify
relevant
infer
firm
genuine
seize
corporate
temporary
labour force
earn a living
public servant
comfort zone
重点短语 put sth on the line detective work
语
gain the upper hand prior to
言
put one’s best foot forward
能
1.助动词do/does/did强调谓语动词
力重点句式 2.when it comes to... 当谈到……
Para.4
D.Our work helps us make a living and make a life for
ourselves and for others.
Para.5
E.Through the work we do,our goals can be attained and our
dreams achieved.
consequently,it can give us a great sense of achievement and satisfaction.
定语从句,修饰something [尝试翻译] 无论我们的兴趣在哪里,无论我们的职业选择是什么,工作都能让我们有机会从事我们喜欢的事情,从而给我们极大的成就感和满足感。
Activity 4 思考分享提升思维 1.What career do you want to pursue? The answer is open. 2.In the future,if you are keen to “live to work”,what preparations should you start making now? The answer is open.

译林版高中英语学案选择性必修第四册精品课件 UNIT 4 Section A

目录索引
Part 1 Reading comprehension Part 2 Language points
素养导航·明目标
blank
composition
educator
refresh objective
criticize
语必 subscribe comprehension cease
言背 assumption occupation
qualify
能单 competence lamp
random
力词 essay
paragraph
sneeze
polish
drawer
presentation
librarian
forehead extension
bound
resolve
inquire
register
self-worth reasoning
第三步深读课文融会提能
Activity 6 课文语篇填空
Acquiring knowledge helps me 1. better (well)understand the
world.However,as I journey through my life,I gradually realize that more
accepting new ideas 6. blindly (blind).
Besides,a lifelong learner means taking full advantage of 7.___w_h_a_t_ev_e_r_____
resources you can find for lifelong learning.Finally,you must be fully aware

学术英语人文社科类Unit4精编版课件

Text A
Suggested answers
Language building-up
Task 1 Specialized vocabulary
1 Translate the following sociological terms from English into Chinese or vice versa.
1 social division
社会分工
2 social being
社会人
3 intellectual life 4 human emotion
精神生活人类情感
5 social class
社会阶级
6 人类的社会生活
human social life
Unit 4
The Study of Society and People
Text A
Unit 4
Suggested answers
The Study of Society and
Critical reading and thinking
People
Task 1 The tree diagram below shows how the authors
develop the text about the study of sociology. Fill in the
7 全球的社会进程
global social process
8 婚姻幸福
marital happiness
9 公共场所
public places
10 和他人交往
socialize with others
11 社会环境
social context
12 行为模式

高教社大学英语教材四

高教社大学英语教材四As an AI language model, I'm unable to write a 1000-word article exactly based on the given title. However, I can provide you with a sample article on the topic of "High Education Press University English Textbook Four." Please note that this content is for illustrative purposes only and may not accurately reflect the specific requirements of the given title.Sample Article:The High Education Press University English Textbook Four is an essential resource for English learners at the university level. Designed to enhance language proficiency and cultivate comprehensive language skills, this textbook caters to the academic needs of students pursuing higher education. In this article, we will delve into the key features of the textbook and explore its impact on English language learning.1. Introduction: The Importance of High-Quality English TextbooksIn today's globalized world, English has become the lingua franca of international communication. Proficiency in English is a crucial asset for students aiming to excel in their academic and professional endeavors. High-quality English textbooks, such as the High Education Press University English Textbook Four, play a pivotal role in equipping learners with the necessary language skills.2. Comprehensive Language Skills DevelopmentThe High Education Press University English Textbook Four adopts a holistic approach to language learning, focusing on the development of fouressential language skills: listening, speaking, reading, and writing. The textbook provides a wide range of interactive exercises, audiovisual materials, and real-life scenarios to engage learners and foster active participation.3. Task-Based Learning ApproachOne notable aspect of the textbook is its task-based learning approach. By integrating real-world tasks and communicative activities, learners are encouraged to apply their language knowledge in practical situations. This approach enhances learners' language fluency and promotes critical thinking and problem-solving skills.4. Authentic Study Materials and Linguistic DiversityTo reflect the multicultural nature of the English language, the High Education Press University English Textbook Four incorporates a variety of authentic study materials. From articles and interviews to multimedia resources, learners are exposed to diverse linguistic contexts, enabling them to develop cultural awareness and intercultural communication competence.5. Language Proficiency AssessmentThe textbook includes regular assessments to evaluate learners' progress and level of language proficiency. These assessments encompass listening comprehension, oral presentation, reading comprehension, and writing skills. By providing feedback and guidance, the textbook aids learners in identifying their strengths and areas for improvement.6. Supplementary Online ResourcesIn keeping up with the digital age, the High Education Press University English Textbook Four offers supplementary online resources. These resources enhance students' access to additional learning materials, videos, and interactive exercises, fostering autonomous learning and self-paced progress.7. Integration of Academic ContentRecognizing the importance of subject-specific language skills, the textbook seamlessly integrates academic content across various disciplines. By incorporating discipline-specific vocabulary, research papers, and case studies, the textbook prepares learners for academic success and empowers them to confidently engage in disciplinary discourse.8. Teacher Support and Pedagogical GuidanceThe High Education Press University English Textbook Four provides comprehensive teacher support, including a teacher's guide, lesson plans, and additional resources. The textbook ensures consistency and continuity in the teaching and learning process, supporting teachers in implementing effective classroom strategies.In conclusion, the High Education Press University English Textbook Four serves as an indispensable tool for university-level English learners. By combining effective pedagogical approaches, authentic study materials, and comprehensive language skill development, this textbook equips students with the language proficiency required for academic and professional success.。

材料作文英语大学

材料作文英语大学Introduction:Material-based composition is an essential skill for university students as it tests their ability to understand, analyze, and synthesize information from a given text, image, or scenario. This type of essay is not only a common assessment tool in English courses but also a valuable skill for academic and professional writing.Understanding the Task:When presented with a material-based composition, students are expected to read or view the material carefully, identify the main ideas, and then construct an essay that responds to the prompt. The essay should demonstrate a clear understanding of the material and present a well-organized argument or analysis.Key Components of Material-Based Composition:1. Thorough Reading: Begin by reading the material multiple times to ensure a comprehensive understanding of its content and nuances.2. Identifying the Prompt: The prompt is the question or statement that guides your response. It is crucial to address the prompt directly in your essay.3. Note-Taking: Jot down key points, themes, or arguments from the material. This will help you organize your thoughtsand identify the main ideas you want to discuss.4. Planning Your Response: Create an outline for your essay. This should include an introduction, body paragraphs that explore different aspects of the material, and a conclusion.5. Writing the Introduction: Start your essay with an introduction that provides background information on the material and states your thesis. The thesis should be a clear, concise statement of your argument or analysis.6. Developing Body Paragraphs: Each paragraph should focus on one main idea related to the prompt. Use evidence from the material to support your points and analyze how itcontributes to your overall argument.7. Concluding Your Essay: The conclusion should summarizeyour main points and restate your thesis. It's also an opportunity to suggest implications or areas for further exploration.Strategies for Effective Writing:- Use a variety of sentence structures to maintain interest and demonstrate your language proficiency.- Employ proper citation and referencing styles to acknowledge the source material.- Edit and proofread your work to eliminate errors and ensure clarity.Common Pitfalls to Avoid:- Straying from the prompt: Ensure that every part of youressay is relevant to the question or statement provided.- Overgeneralizing: Support your arguments with specific examples from the material.- Failing to cite sources: Proper citation is crucial to avoid plagiarism and to give credit to the original authors.Conclusion:Mastering material-based composition is a critical aspect of academic writing in university. By understanding the task, planning your response, and employing effective writing strategies, you can produce well-structured and persuasive essays that demonstrate your comprehension and analytical skills. Remember to proofread your work to polish your final submission.。

四下英语第四单元课文

四下英语第四单元课文The fourth unit of the English textbook presents a fascinating exploration of various aspects of the language and its usage. As a comprehensive guide to mastering the nuances of English, this unit delves into the intricacies of grammar, vocabulary, and communication skills. Through a well-structured curriculum, students are provided with the tools necessary to enhance their proficiency in the English language, empowering them to engage in meaningful discourse and effectively express their thoughts and ideas.One of the key highlights of this unit is the in-depth examination of grammatical structures. Students are introduced to the fundamental rules and conventions that govern the English language, enabling them to construct coherent and grammatically correct sentences. From the proper use of verb tenses to the intricate web of subject-verb agreement, this unit offers a systematic approach to understanding the foundational elements of English grammar. By mastering these core concepts, students develop a stronger command of the language, which in turn enhances their ability to communicate with clarity and precision.Alongside the grammatical focus, the fourth unit also emphasizes the importance of vocabulary expansion. Through engaging exercises and thought-provoking discussions, students delve into the rich tapestry of English vocabulary, exploring the nuances of word choice, synonyms, and contextual appropriateness. This comprehensive approach to vocabulary development equips students with the linguistic versatility necessary to express themselves effectively in a variety of settings, from formal academic writing to informal conversations.Moreover, the fourth unit places a strong emphasis on the development of communication skills. Students are challenged to engage in interactive activities that hone their listening, speaking, and presentation abilities. From participating in group discussions to delivering oral presentations, learners are given the opportunity to put their newfound knowledge into practice, fostering their confidence and fluency in the English language.One of the standout features of this unit is its integration of authentic materials and real-world examples. By incorporating excerpts from literature, news articles, and other relevant sources, the curriculum provides students with a deeper understanding of how the English language is used in various contexts. This exposure to diverse and engaging content not only enhances theircomprehension but also inspires them to explore the language further, cultivating a genuine appreciation for its richness and complexity.Furthermore, the fourth unit encourages critical thinking and problem-solving skills. Through carefully crafted exercises and case studies, students are challenged to analyze language use, identify common errors, and develop strategies for effective communication. This approach not only strengthens their linguistic abilities but also fosters the development of essential life skills, such as logical reasoning, attention to detail, and the ability to adapt to different communication scenarios.In conclusion, the fourth unit of the English textbook presents a comprehensive and dynamic learning experience. By delving into the intricacies of grammar, vocabulary, and communication skills, students are empowered to enhance their proficiency in the English language and engage in meaningful discourse. The integration of authentic materials, real-world examples, and interactive activities further enriches the learning process, making it a valuable resource for students seeking to expand their linguistic horizons and become confident, effective communicators in the English-speaking world.。

高中英语必修4必备知识点总结

高中英语必修4必备知识点总结High School English Compulsory 4: Essential Knowledge Points Summary。

High School English Compulsory 4 is an important subject for students in China. It covers a wide range of topics and skills, including reading, writing, listening, and speaking. In this article, we will summarize the essential knowledge points that students need to know in order to excel in this subject.1. Reading Comprehension。

Reading comprehension is a crucial skill for high school students. In the compulsory 4 curriculum, students are expected to read and understand a variety of texts, including essays, articles, and literary works. They should be able to identify the main idea of a text, understand the author's purpose, and analyze the text's structure and organization.In addition, students should be able to recognize and understand different types of literary devices, such as similes, metaphors, and symbolism. They should also be able to analyze the characters, plot, and themes of a literary work.2. Writing Skills。

新视野大学英语第四册第一单元Section A课件

Listen to a short passage on logic, and fill in the missing information. Logic was further extended by AlFarabi who categorized it into two separate groups (idea and proof ). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication ( 时间与意义 ). In the East, logic was developed by Hindus, Buddhists and Jains (耆那教徒).
Doing the right thing is not the problem. Knowing what the right thing is, that’s the challenge. — Lyndon B. Johnson (36th US president)
It is one thing to be clever and another to be wise. — George R. R. Martin (American author)
Listen to a short passage on logic, and fill in the missing information.
Logic is often divided into three parts: inductive reasoning, abductive reasoning, and deductive reasoning.

Material4_4综合英语专四阅读训练

Material4_4综合英语专四阅读训练Material 4-4Text AIt has always been difficult for the philosopher or scientists to fit time into his view of the universe. Prior to Einsteinian physics, there was no truly adequate formulation of the relationship of time to the other forces in the universe, even though some empirical equations included time qualities. However, even the Einsteinian formulation is not pefhaps totally adequate to the job of fitting time into the proper relationship with the other dimensions, as they are called, of space. The primary problem arises in relation to things that might be going faster than the speed of light,or have other strange properties.Examination of the Lorentz-Fitsgerald formulas yields the interesting speculation that if something did actually exceed the speed of light it would have its mass expressed as an imaginary number and would seem to be going backwards in time. The barrier to exceeding the speed of light is the apparent need to have an infinite quantity of mass moved at exactly the speed of light. If this situation could be leaped over in a large quantum jump—which seems highly unlikely for masses that are large in normal circumstances—then the other side may be achievable.The idea of going backward in time is derived from the existence of a time vector that is negative, although just what this might mean to our senses in the unlikely circumstance of our experiencing this state cannot be conjectured. There have been, in fact, some observations of particle chambers which have led some scientists to speculate that a particle called the tachyonmay exist with the trans-light properties we have just discussed.The difficulties of imagining and coping with these potential implications of our mathematical models points out the importance of studying alternative methods of notation for advanced physics. Professor Zuckerkandl, in his book Sound and Symbol, hypothesized that it might be better to express the relationships found in quantum mechanics through the use of a notation derived from musical notations. To oversimplify greatly, he argues that music has always given time a special relationship to other factors or parameters or dimensions. Therefore, it might be a more useful language in which to express the relationships in physics where time again has a special role to play, and cannot be treated as just another dimension.The point of this, or any other alternative to the current methods of describing basic physical processes, is that time does not appear—either by common experience or sophisticated scientific understanding—to be the same sort of dimension or parameter as physical dimensions, as is deserving of completely special treatment, in a system of notation designed to accomplish that goal.One approach would be to consider time to be a field effect governed by the application of energy to mass—that is to say, by the interaction of different forms of energy, if you wish to keep in mind the equivalence of mass and energy. The movement of any normal sort of mass is bound to produce a field effect that we call positive time. An imaginary mass would produce a negative time field effect. This is not at variance with Einstein's theories, since the "faster" a given mass moves the more energy was applied toit and the greater would be the field effect. The time effectspredicted by Einstein and confirmed by experience are, it seems, consonant with this concept.1. The passage supports the inference that .A. Einstein's theory of relativity is wrongB. the Lorentz-Fitzgerald formulas contradict Einstein's theoriesC. time travel is clearly possibleD. it is impossible to travel at precisely the speed of light2. The tone of-the passage is .A. critical but hopefulB. hopeful but suspiciousC. suspicious but speculativeD. speculative but hopeful3. Which of the following can be best described as the central idea of the passage?A. Anomalies in theoretical physics notation permit intriguing hypotheses and indicatethe need for refined notation of the time dimension.B. New observations require the development of new theories and new methods of describing the new theories.C. Einsteinian physics can be much improved in its treatment of tachyons.D. Time requires a more imaginative approach than tachyons.4. According to the author, it is too soon to .A. call Beethoven a physicistB. adopt proposals such as Zuckerkandl'sC. plan for time travelD. study particle chambers for tachyon traces5. It can be inferred that the author sees Zuckerkandl as believing that mathematics is a( n)A. necessary evilB. languageC. musical notationD. great hindrance to full understanding of physicsText DIt sounds clichéd and somewhat sappy, but it does bear repeating that children are our most vulnerable citizens. In fact, it was the impending birth of our first son in 1988 that played heavily into our decision to start E Magazine. We were at a local breakfast place on our way to work, reading New York Times stories about that year's "Greenhouse Summer," describing what we all now know to be one of the effects of global warming. It was our first realization, as new parents-to-be, that we really were going to leave a terrible legacy for future generations if we didn't do something about mounting environmental problems.Sentimental or not, 1 often think about how crucial it is to consider our youngest when weighing important issues. If you've read this page often you've heard me go on about the 35 ,000 children globally who die every day (one every three seconds) from air- and water-borne diseases and water and food shortages—and about the horrible and related economic inequalities that only worsen each day around the world, largely due to neglect.Despite these frightful conditions, I often hear people and news pundits dismiss the plight of the poor and destitute as simply the result of their own lack of ambition and therefore not worthy of our attention. Not worthy of welfare or higher minimum wages thatmight help them rise up and out of a vicious cycle. Not worthy of the financial aid that might enable their crippledeconomies to better serve their needs. Or not worthy of coming to America, where opportunities might be greater. Instead, many seek to close our borders and force them to deal with their own problems.But how often do we consider the plight of the children of the people with whom we choose not to sympathize? Can they be blamed for the circumstances that cause them to live in such abject poverty, to have no safe food or potable water? Bringing it home to issues we struggle with day-to-day in the U. S. , did our children create the conditions that resulted in the toxic fumes, chemicals and mercury pollution in the environment that cause their asthma, childhood cancer and autism? When we propose cutting $100million from food subsidy programs for the poor, do we stop to think about the children of these low-income families who will go hungry? And when we allow our medical-industrial complex to effectively deny affordable healthcare to millions of our citizens, do we consider that children are many among those who may have to go without needed treatments?It's "easy to be hard," proclaimed a 1967 song from the musical, Hair (later popularized by the pop group Three Dog Night). Not so easy, though, when one considers the youngest victims.6. The author argues that children are the most vulnerable because .A. they will suffer from the effects of worsening environmentB. they are more sensitive to the changing climate than adultsC. they are far more likely to develop various diseases than adultsD. they know nothing about the harmful effects of globalwarming7. The word "legacy" in Paragraph 2 most probably refers to .A. heritageB. traditionC. inheritanceD. environment8. It can be inferred that E Magazine is devoted to the issue of .A. economic inequalitiesB. economic environmentC. environmental protectionD. effects of global warming9. The author believes that the life of poor people may be improved if .A. they are more ambitious and aggressiveB. they can deal with their problems boldlyC. they are not neglected by the rich peopleD. they are given more aid and opportunities10. The author suggests that the children of the poor people should .A. enjoy free medical-care programsB. be taken into sufficient considerationC. have ample safe food and potable waterD. live in an environment without pollution。

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Abaqus/CAE 中的材料属性和装配件第四讲L1.2概述•定义并分配材料属性•材料评估•材料库•什么是装配件?•定位部件实例•阵列•布尔操作•装配件集和表面•显示组Introduction to Abaqus/CAE示•练习定义并分配材料属性L1.4定义并分配材料属性•材料属性•广泛的材料库包含几乎所有的Abaqus材料模型。

•用户以Abaqus求解器所需的格式输入材料数据•数据可直接输入，可从文件中读取，也可从材料库中导入。

Introduction to Abaqus/CAEL1.5定义并分配材料属性•截面属性•包括附加尺寸，或为变形体分配材料属性的单元类型信息型信息。

•参考材料定义。

Introduction to Abaqus/CAEL1.6•为区域分配截面属性•变形体的每个区域必须引用包含材料定义的截面属性。

定义并分配材料属性Part region 1:left fender Part region 2:right fenderPart region 3:hingeShell section 1Solid section 1Introduction to Abaqus/CAE车架模型可能的部件、截面和材料Material 1:steelL1.7定义并分配材料属性•对于被赋予截面属性的部件，Abaqus/CAE 提供了一个视觉上的反馈Section assigned to top half Section assigned to topand bottom halfIntroduction to Abaqus/CAEL1.8定义并分配材料属性•壳/薄膜的视觉反馈•可通过此功能来检查壳/薄膜厚度的定义•Offsets 可以定义壳的参考面(由节点定义)和中面之间的关系(默认两者是一致的）•Offset 对于薄膜不可用Introduction to Abaqus/CAE*此功能亦适用于Visualization 模块*Part Display Options dialog box Edit Section Assignment dialog boxL1.9定义并分配材料属性•梁的视觉上的反馈•梁的建模是基于线特征；其横截面尺寸认为是截面属性。

Introduction to Abaqus/CAEL1.10定义并分配材料属性•可以通过观察梁的外形改变梁截面属性的定义•很容易检测建模误差**该特征在后处理中也有效Introduction to Abaqus/CAE材料评估L1.12材料评估•超弹性材料的曲线拟合能力，可以允许用户对实验数据比较不同超弹性模型的拟合结果。

Introduction to Abaqus/CAE材料库L1.14材料库•方便材料定义，材料库可以保存Abaqus中有效的材料模型•可以为金属（弹性和塑性）、橡胶（超材料库只在Property 模块中激活弹性）等创建材料库•材料库能够在Abaqus/CAE创建，也可以从第三方插件类似Granta Design 和Matereality导入数据•材料库中的材料可以添加到任何的Abaqus/CAE模型•材料库可以在不同的用户之间共享点击这里添加选中的材料到当前模型Introduction to Abaqus/CAE什么是装配件?L1.16什么是装配件?•装配件中包含有限元模型中所有的几何体。

•每个Abaqus/CAE模型包含一个装配件。

•即使用户已经创建一些部件，在没有创建部件实例之前，装配件是空的。

•装配件不直接包含部件；它包含的是部件的“实例”。

•为方便起见，实例可以被显示或隐藏。

•下面的观点解释了部件，部件实例和装配件之间的关系。

Introduction to Abaqus/CAEL1.17什么是装配件?•部件•用户在部件模块创建部件。

•每个部件是独立的几何实体，每个部件是独的几何实体它的修改或操作独立于其它部件。

•每个部件只存在于它自己的坐标系中，与其它部件无关。

•每个部件都要引用参考截面属性。

例子: 模拟泵支架的三个部件Introduction to Abaqus/CAEL1.18什么是装配件?•部件实例和装配件•用户在组装模块创建部件实例。

•实例与它的原始部件保持相关性。

•用户可以将一个部件多次实例化，并将同一部件的多个实例进行组装。

•部件的每个实例与在属性模块中分配给部件的截面属性相关。

•用户可以在全局坐标系中定位部件实例，形成装配件。

•用户可以在部件模块中修改原始的部件。

回到组装模块之后，Abaqus/CAE将自动的更新每个部件的实例。

Introduction to Abaqus/CAEL1.19什么是装配件?•依赖和不依赖的部件实例•你可以创建依赖或不依赖的部件实例.•不依赖的实例是部件的一个有效的拷贝不依赖的实例是部件的个有效的拷贝并能被修改.•依赖的部件共享原始部件的几何以及网格同时不能被修改.•缺省的创建依赖的部件实例.•依赖和不依赖的部件实例的含义将在分网一节详细讨论.Introduction to Abaqus/CAEL1.20什么是装配件?•例子：婴儿四轮车的装配件车身的一个实例轴的两个实例轴支座的四个实例把手的一个实例轮子的四个实例Introduction to Abaqus/CAE当部件定义变化时，轮子的实例自动更新定位部件实例•在组装模块中，定位是主要的任务。

两种一般的方法：•绝对定位•相对定位•绝对定位不是装配件的特征：•平移•旋转•用另外的部件替换已有部件Introduction to Abaqus/CAEL1.23定位部件实例•利用定位约束进行相对定位•相对定位约束：•在两个几何部件实例之间定义几何关系。

•在装配件中，定义部件实例必须遵从的规则。

比如，一个表面必须与另一个表面平行。

•是装配件的特征。

对于相对定位约束，可以进行编辑、隐藏、删除等操作。

•在一些情况下，可能会与已有的定位约束冲突。

比如，让一个表面同时平行于另外两个表面。

Introduction to Abaqus/CAEL1.24定位部件实例•表面平行约束（只限三维部件实例）边平行约束同表面平行约束类似，并且二维和三维部件实例都可以使用。

•Abaqus/CAE将旋转可移动的部件，直到两个选定的表面平行，并且箭头指向相同的方向。

Introduction to Abaqus/CAEL1.25定位部件实例•面到面约束（只对三维部件实例有效）边到边约束同面到面约束类似，并且选定的表面二维和三维部件实例都可以使用。

•Abaqus/CAE旋转可移动部件实例，直到两个选定的表面平行，并且箭头指向相同的方向。

另外，被移动部件实例的平移距离应满足指定的间距。

固定的部件实例可移动的部件实例Introduction to Abaqus/CAE平面视图平面视图L1.26定位部件实例•共轴约束（只对三维部件实例有效）•Abaqus/CAE旋转并平移可移动部件实例直到两选定的表面旋转轴旋转轴可移动部件实例，直到两个选定的面共轴，并且箭头指向相同的方向。

固定部件实例可移动部件实例Introduction to Abaqus/CAEL1.27定位部件实例•重合点约束•将可移动部件实例中选定的点与固定部件实例中选定的点重合。

•平行坐标系约束•将可移动部件实例中选定的基准坐标系与固定部件实例中选定的基准坐标系平行。

Introduction to Abaqus/CAE阵列L1.30阵列•被选中的部件实例可以采用线性或圆周的阵列来进行多次拷贝.Introduction to Abaqus/CAE布尔操作L1.32布尔操作–利用部件布尔工具，用户可以通过合并或切削部件实例创建新的部件。

–合并操作还可以被应用与孤立网格。

–在这种情况下应用节点等价。

Introduction to Abaqus/CAE装配件集和表面L1.35装配件集和表面•装配件集利用一个或多个部件实例定义区域，这些区域可以用来定义：•载荷和边界条件•在分析过程中生成输出•装配件表面利用一个或多个部件实例定义区域，这些表面可以用来定义：•接触•分布载荷•当一定的几何组具有多个使用目的时，装配件集合表面定义将非常有用。

•注意：一般情况下，集或表面比直接利用鼠标选择几何体定义载荷、边界条件和场会更方便。

此外，定义集还可以为结果的可视化处理提供标识。

Introduction to Abaqus/CAEL1.36装配件集和表面•组集和表面可以在部件级或装配级定义•部件级组集出现在特征树中t t Part-level set的part 目录下的set 目录里•实例部件的组集出现在特征树中的Assembly 目录下•部件级组集在与Assembly 相关的模块中也有效•在与Assembly 相关的模块中部件级组集只有“只读”接口A blIntroduction to Abaqus/CAE只读接口Assembly-level setL1.37装配件集和表面•不同的组集和表面可以合并•举例，可以将不同实例的上表面合并为一个表面Introduction to Abaqus/CAE显示组•在Abaqus/CAE的每个模块中显示组都是可用的。

•显示组即可以包含几何实体，又可以包含有限元实体，比如又可以包含有限元实体比如单元、节点和表面。

•显示组可以基于前面保存的显示组。

Introduction to Abaqus/CAEL1.40显示组•创建显示组的多种方法工具栏(1)主菜单栏Select attributefrom list in工具栏( 2)selectionstoolbarIntroduction to Abaqus/CAE习题4a: 分配材料属性和定义装配件绞模型—L1.42习题4a: 分配材料属性和定义装配件—绞模型•习题任务1.为可变形的绞部件创建材料定义。

22.通过引用材料定义创建截面定义。

3.为绞部件分配截面定义。

4.在装配件模块中，利用绝对定位约束和相对定位约束的组合定位部件实例。

Introduction to Abaqus/CAE习题4b: 分配材料属性和定义装配件卡箍和挡—片模型L1.44习题4b: 分配材料属性和定义装配件—卡箍和挡片模型•习题任务1.为可变形的卡箍部件创建材料定义。

2.通过引用材料定义创建截面定义。

3.为卡箍部件分配截面定义。

4.在装配件模块中定位部件实例。

Introduction to Abaqus/CAE。