Lecture 8 Deformation behavior for unsaturated soils

BY THE END OF THIS WORKSHOP, YOU WILL:1)Have a big-picture understanding of each MBE subject2)Be familiar with how key rules in each subject are tested3)Know how to problem-solve MBE questions in each subject•200 multiple choice questions•Across eight subjects•Subjects are mixed together• 1.8 minutes per questiono Tortso Real Propertyo Contractso Criminal Law and Procedureo Constitutional Lawo Evidenceo Civil ProcedureFOR EACH SUBJECT YOU WILL:1)Complete five questions in nine minutes or less2)Watch a short big-picture overview of the subject3)Watch a question-by-question analysis covering:•Most of the highly tested MBE rules•How to systematically approach MBE questions in all 8 subjectsDUTY BREACH CAUSATIONDAMAGES NEGLIGENCE Child duty of care Professional duty of care Emergency responder duty of careFollowing their conversation, the seller sent the buyer a contract, already signed by the seller, agreeing to sell 1,000 widgets to the buyer for a total contract price of $10,000.ASSOCIATIONS:1)Mirror image rule?2)UCC Battle of the Forms provisionSTEP 1:A woman playing tennis with a man became highly irritated because every time she prepared to serve, the man started talking loudly. Despite the woman’s repeated requests to stop, the man persisted in the behavior. The woman ran towards the man, swinging her racket to scare him and to get him to stop. However, as she swung the racket, she slipped and it flew out of her hand as she lost her balance. It flew through the air and struck the man in the head. The woman slipped because the owner of the tennis court had not cleaned the court properly after some maintenance work.A woman playing tennis with a man became highly irritated because every time she prepared to serve, the man started talking loudly. Despite the woman’s repeated requests to stop, the man persisted in the behavior. The woman ran towards the man, swinging her racket to scare him and to get him to stop. However, as she swung the racket, she slipped and it flew out of her hand as she lost her balance. It flew through the air and struck the man in the head. The woman slipped because the owner of the tennis court had not cleaned the court properly after some maintenance work.Assault?Negligence?Battery?A woman playing tennis with a man became highly irritated because every time she prepared to serve, the man started talking loudly. Despite the woman’s repeated requests to stop, the man persisted in the behavior. The woman ran towards the man, swinging her racket to scare him and to get him to stop. However, as she swung the racket, she slipped and it flew out of her hand as she lost her balance. It flew through the air and struck the man in the head. The woman slipped because the owner of the tennis court had not cleaned the court properly after some maintenance work.If the man sues the woman for negligence, which of the following would be her best defense?Battery?Assault?Negligence?STEP 1:A woman playing tennis with a man became highly irritated because every time she prepared to serve, the man started talking loudly. Despite the woman’s repeated requests to stop, the man persisted in the behavior. The woman ran towards the man, swinging her racket to scare him and to get him to stop. However, as she swung the racket, she slipped and it flew out of her hand as she lost her balance. It flew through the air and struck the man in the head. The woman slipped because the owner of the tennis court had not cleaned the court properly after some maintenance work.DistractorsSTEP 1:STEP 1: STEP 2:Which of the following standards shouldthe court use in determining the validity of the ordinance?Which of the following standards shouldthe court use in determining the validity of the ordinance?What is the basis for the suit?What does the ordinance say?What part of the constitution is being implicatedby the question?STEP 1: STEP 2:STEP 3:STEP 4:STEP 5:A woman playing tennis with a man became highly irritated because every time she prepared to serve, the man started talking loudly. Despite the woman’s repeated requests to stop, the man persisted in the behavior. The woman ran towards the man, swinging her racket to scare him and to get him to stop. However, as she swung the racket, she slipped and it flew out of her hand as she lost her balance. It flew through the air and struck the man in the head. The woman slipped because the owner of the tennis court had not cleaned the court properly after some maintenance work.If the man sues the woman for negligence, which of the following would be her best defense?A.The woman did not intend to make a harmful or offensive contact with the man.B.The owner’s failure to properly maintain the tennis court was the proximate cause of theman’s injuries.C.The woman did not place the man in reasonable apprehension of imminent contact.D.The woman could not reasonably foresee that the tennis court was slippery.。

2025年全国大学英语CET六级考试模拟试卷及解答参考一、写作（15分）Task 1: Writing (30 minutes)Part AWrite an email to your friend about a recent movie you watched. In your email, you should:1.Briefly introduce the movie and its main theme.2.Share your personal feelings about the movie.3.Recommend the movie to your friend, explaining why you think they would enjoy it.You should write about 100 words on the ANSWER SHEET 2.Do not sign your own name at the end of the letter. Use “Li Ming” in stead. Do not write the address.Example:Dear [Friend’s Name],I hope this email finds you well. I wanted to share with you a movie I recently watched that I thought you might find interesting.The movie I’m talking about is “Inception,” directed by Chris topher Nolan.It revolves around the concept of dream manipulation and the layers of reality. The story follows Dom Cobb, a skilled thief who specializes in extracting secrets from within the subconscious during the dream state.I was deeply impressed by t he movie’s intricate plot and the exceptional performances of the cast. The visual effects were breathtaking, and the soundtrack was perfectly matched to the action sequences. The movie made me think a lot about the nature of reality and the power of dreams.I highly recommend “Inception” to you. I believe it will be a captivating experience, especially if you enjoy films that challenge your perceptions and make you think.Looking forward to your thoughts on this movie.Best regards,Li MingAnalysis:This example follows the structure required for Part A of the writing task. It starts with a friendly greeting and a brief introduction to the subject of the email, which is the movie “Inception.”The writer then shares their personal feelings about the movie, highlighting the plot, the cast’s performances, the visual effects, and the soundtrack. This personal touch helps to engage the reader and provide a more authentic recommendation.Finally, the writer makes a clear recommendation, explaining that theybelieve the movie would be enjoyable for their friend based on itsthought-provoking nature and entertainment value. The email concludes with a friendly sign-off, maintaining a warm and inviting tone.二、听力理解-长对话（选择题，共8分）第一题听力原文：M: Hi, Lisa. How was your trip to Beijing last weekend?W: Oh, it was amazing! I’ve always wanted to visit the Forbidden City. The architecture was so impressive.M: I’m glad you enjoyed it. By the way, did you manage to visit the Great Wall?W: Yes, I did. It was a long journey, but it was worth it. The Wall was even more magnificent in person.M: Did you have any problems with transportation?W: Well, the subway system was very convenient, but some of the bus routes were confusing. I ended up getting lost a couple of times.M: That’s a common problem. It’s always a good idea to download a map or use a GPS app.W: Definitely. I also found the people in Beijing to be very friendly and helpful. They spoke English well, too.M: That’s great to hear. I’m thinking of visiting Beijing next month. Arethere any other places you would recommend?W: Oh, definitely! I would suggest visiting the Summer Palace and the Temple of Heaven. They are both beautiful and culturally significant.M: Thanks for the ti ps, Lisa. I can’t wait to see these places myself.W: You’re welcome. Have a great trip!选择题：1、Why did Lisa visit Beijing?A. To visit the Great Wall.B. To see her friends.C. To experience the local culture.D. To study Chinese history.2、How did Lisa feel about the Forbidden City?A. It was boring.B. It was too crowded.C. It was impressive.D. It was not as beautiful as she expected.3、What was the biggest challenge Lisa faced during her trip?A. Finding accommodation.B. Getting lost.C. Eating healthy food.D. Visiting all the tourist spots.4、What other places does Lisa recommend visiting in Beijing?A. The Summer Palace and the Temple of Heaven.B. The Great Wall and the Forbidden City.C. The National Museum and the CCTV Tower.D. The Wangfujing Street and the Silk Market.答案：1、C2、C3、B4、A第二题Part Two: Listening ComprehensionSection C: Long ConversationsIn this section, you will hear one long conversation. At the end of the conversation, you will hear some questions. Both the conversation and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked A), B), C), and D).1.What is the main topic of the conversation?A) The importance of cultural exchange.B) The challenges of teaching English abroad.C) The experiences of a language teacher in China.D) The impact of language barriers on communication.2.Why does the speaker mention studying Chinese?A) To show his respect for Chinese culture.B) To express h is gratitude for the Chinese students’ hospitality.C) To emphasize the importance of language learning.D) To explain his reasons for choosing to teach English in China.3.According to the speaker, what is one of the difficulties he faced in teaching English?A) The students’ lack of motivation.B) The limited resources available.C) The cultural differences between Chinese and Western students.D) The high expectations from the school administration.4.How does the speaker plan to overcome the language barrier in his future work?A) By learning more Chinese.B) By using visual aids and non-verbal communication.C) By collaborating with local language experts.D) By relying on his previous teaching experience.Answers:1.C2.C3.C4.B三、听力理解-听力篇章（选择题，共7分）第一题Passage:A new study has found that the way we speak can affect our relationships and even our physical health. Researchers at the University of California, Los Angeles, have been investigating the connection between language and well-being for several years. They have discovered that positive language can lead to better health outcomes, while negative language can have the opposite effect.The study involved 300 participants who were monitored for a period of one year. The participants were asked to keep a daily diary of their interactions with others, including both positive and negative comments. The researchers found that those who used more positive language reported fewer physical symptoms and a greater sense of well-being.Dr. Emily Thompson, the l ead researcher, explained, “We were surprised to see the impact that language can have on our health. It’s not just about what we say, but also how we say it. A gentle tone and supportive language can make a significant difference.”Here are some examples of positive and negative language:Positive Language: “I appreciate your help with the project.”Negative Language: “You always mess up the project.”The researchers also looked at the effects of language on relationships. They found that couples who used more positive language were more likely toreport a satisfying relationship, while those who used negative language were more likely to experience relationship stress.Questions:1、What is the main focus of the study conducted by the University of California, Los Angeles?A) The impact of diet on physical health.B) The connection between language and well-being.C) The effects of exercise on mental health.D) The role of social media in relationships.2、Which of the following is a positive example of language from the passage?A) “You always mess up the project.”B) “I can’t believe you did that again.”C) “I appreciate your help with the project.”D) “This is a waste of time.”3、According to the study, what is the likely outcome for couples who use negative language in their relationships?A) They will have a more satisfying relationship.B) They will experience fewer physical symptoms.C) They will report a greater sense of well-being.D) They will likely experience relationship stress.Answers:1、B2、C3、D第二题Passage OneIn the United States, there is a long-standing debate over the best way to educate children. One of the most controversial issues is the debate between traditional public schools and charter schools.Traditional public schools are operated by government and are funded by tax dollars. They are subject to strict regulations and are required to follow a standardized curriculum. Teachers in traditional public schools are typically unionized and receive benefits and pensions.On the other hand, charter schools are publicly funded but operate independently of local school districts. They are free to set their own curriculum and teaching methods. Charter schools often have a longer school day and a more rigorous academic program. They are also subject to performance-based evaluations, which can lead to their closure if they do not meet certain standards.Proponents of charter schools argue that they provide more choices for parents and that they can offer a more personalized education for students. They also claim that charter schools are more accountable because they are subject to more direct oversight and can be closed if they fail to meet their goals.Opponents of charter schools argue that they take resources away fromtraditional public schools and that they do not provide a level playing field for all students. They also claim that charter schools can be more selective in their admissions process, which may lead to a lack of diversity in the student body.Questions:1、What is a key difference between traditional public schools and charter schools?A) Funding sourceB) CurriculumC) Teacher unionsD) Academic rigor2、According to the passage, what is a potential advantage of charter schools?A) They are subject to fewer regulations.B) They offer more choices for parents.C) They are more likely to receive government funding.D) They typically have a shorter school day.3、What is a common concern expressed by opponents of charter schools?A) They are less accountable for their performance.B) They may lead to a lack of diversity in the student body.C) They are more expensive for local taxpayers.D) They do not follow a standardized curriculum.Answers:1、B) Curriculum2、B) They offer more choices for parents.3、B) They may lead to a lack of diversity in the student body.四、听力理解-新闻报道（选择题，共20分）第一题News ReportA: Good morning, everyone. Welcome to today’s news broadcast. Here is the latest news.News Anchor: This morning, the World Health Organization (WHO) announced that the number of confirmed cases of a new strain of the H1N1 flu virus has reached 10,000 worldwide. The WHO has declared the outbreak a public health emergency of international concern. Health officials are urging countries to take immediate measures to contain the spread of the virus.Q1: What is the main topic of the news report?A) The announcement of a new strain of the H1N1 flu virus.B) The declaration of a public health emergency.C) The measures taken to contain the spread of the virus.D) The number of confirmed cases of the new strain.Answer: BQ2: According to the news report, who declared the outbreak a public health emergency?A) The World Health Organization (WHO)B) The Centers for Disease Control and Prevention (CDC)C) The European Union (EU)D) The United Nations (UN)Answer: AQ3: What is the main purpose of the health officials’ urging?A) To increase awareness about the flu virus.B) To encourage people to get vaccinated.C) To take immediate measures to contain the spread of the virus.D) To provide financial assistance to affected countries.Answer: C第二题News Report 1:[Background music fades in]Narrator: “This morning’s top news includes a major announcement from the Ministry of Education regarding the upcoming changes to the College English Test Band Six (CET-6). Here’s our correspondent, Li Hua, with more details.”Li Hua: “Good morning, everyone. The Ministry of Education has just announced that starting from next year, the CET-6 will undergo significant modifications. The most notable change is the inclusion of a new speaking section, which will be mandatory for all test-takers. This decision comes in response to the increasing demand for English proficiency in various fields. Let’s goto the Education Depar tment for more information.”[Background music fades out]Questions:1、What is the main topic of this news report?A) The cancellation of the CET-6 exam.B) The addition of a new speaking section to the CET-6.C) The difficulty level of the CET-6 increasing.D) The results of the CET-6 exam.2、Why has the Ministry of Education decided to include a new speaking section in the CET-6?A) To reduce the number of test-takers.B) To make the exam more difficult.C) To meet the demand for English proficiency.D) To replace the written test with an oral test.3、What will be the impact of this change on students preparing for the CET-6?A) They will need to focus more on writing skills.B) They will have to learn a new type of test format.C) They will no longer need to take the exam.D) They will be able to choose between written and oral tests.Answers:1、B2、C3、B第三题You will hear a news report. For each question, choose the best answer from the four choices given.Listen to the news report and answer the following questions:1、A) The number of tourists visiting the city has doubled.B) The city’s tourism revenue has increased significantly.C) The new airport has attracted many international tourists.D) The city’s infrastructure is not ready for the influx of tou rists.2、A) The government plans to invest heavily in transportation.B) Local businesses are benefiting from the tourism boom.C) The city is experiencing traffic congestion and overcrowding.D) The city is working on expanding its hotel capacity.3、A) Th e city’s mayor has expressed concern about the impact on local culture.B) The tourism industry is collaborating with local communities to preserve traditions.C) There are concerns about the negative environmental effects of tourism.D) The city is implementing strict regulations to control tourist behavior.Answers:1.B) The city’s tourism revenue has increased significantly.2.C) The city is experiencing traffic congestion and overcrowding.3.B) The tourism industry is collaborating with local communities to preserve traditions.五、阅读理解-词汇理解（填空题，共5分）第一题Read the following passage and then complete the sentences by choosing the most suitable words or phrases from the list below. Each word or phrase may be used once, more than once, or not at all.Passage:In the past few decades, the internet has revolutionized the way we communicate and access information. With just a few clicks, we can now connect with people from all over the world, share our thoughts and experiences, and even conduct business transactions. This rapid advancement in technology has not only brought convenience to our lives but has also raised several challenges and concerns.1、_________ (1) the internet has made it easier for us to stay connected with friends and family, it has also led to a decrease in face-to-face interactions.2、The increasing reliance on digital devices has raised concerns about the impact on our physical and mental health.3、Despite the many benefits, there are also significant_________(2) associated with the internet, such as privacy breaches and cybersecuritythreats.4、To mitigate these risks, it is crucial for individuals and organizations to adopt robust security measures.5、In the future, we need to strike a balance between embracing technological advancements and maintaining a healthy lifestyle.List of Words and Phrases:a) convenienceb) challengesc) privacy breachesd) physicale) significantf) mentalg) privacyh) embracei) reliancej) face-to-face1、_________ (1)2、_________ (2)第二题Reading PassagesPassage OneMany people believe that a person’s personality is established at birthand remains unchanged throughout life. This view is supported by the idea that personality is determined by genetic factors. However, recent studies have shown that personality can be influenced by a variety of environmental factors as well.The word “personality” can be defined as the unique set of characteristics that distinguish one individual from another. It includes traits such as extroversion, neuroticism, and agreeableness. These traits are often measured using psychological tests.According to the passage, what is the main idea about personality?A. Personality is solely determined by genetic factors.B. Personality remains unchanged throughout life.C. Personality is influenced by both genetic and environmental factors.D. Personality is determined by a combination of psychological tests.Vocabulary Understanding1、The unique set of characteristics that distinguish one individual from another is referred to as ________.A. personalityB. genetic factorsC. environmental factorsD. psychological tests2、The view that personality is established at birth and remains unchanged throughout life is ________.A. supportedB. challengedC. irrelevantD. misunderstood3、According to the passage, traits such as extroversion, neuroticism, and agreeableness are part of ________.A. genetic factorsB. environmental factorsC. personalityD. psychological tests4、The passage suggests that personality can be influenced by ________.A. genetic factorsB. environmental factorsC. both genetic and environmental factorsD. neither genetic nor environmental factors5、The word “personality” is best defined as ________.A. the unique set of characteristics that distinguish one individual from anotherB. the genetic factors that determine personalityC. the environmental factors that influence personalityD. the psychological tests used to measure personalityAnswers:1、A2、A3、C4、C5、A六、阅读理解-长篇阅读（选择题，共10分）First QuestionPassage:In the digital age, technology has transformed almost every aspect of our lives, including education. One significant impact technology has had on learning is through online platforms that offer a wide variety of courses and educational materials to anyone with internet access. This democratization of knowledge means that individuals no longer need to rely solely on traditional educational institutions for learning. However, while online learning provides unprecedented access to information, it also poses challenges such as ensuring the quality of the content and maintaining student engagement without the structure of a classroom setting. As educators continue to adapt to these changes, it’s clear that technology will play an increasingly important role in s haping the future of education.1、According to the passage, what is one major advantage of online learning?A) It guarantees higher academic achievements.B) It makes educational resources more accessible.C) It eliminates the need for traditional learning methods entirely.D) It ensures that all students remain engaged with the material.2、What challenge does online learning present according to the text?A) It makes it difficult to assess the quality of educational content.B) It increases the reliance on traditional educational institutions.C) It decreases the amount of available educational material.D) It simplifies the process of student engagement.3、The term “democratization of knowledge” in this context refers to:A) The ability of people to vote on educational policies.B) The equal distribution of printed books among citizens.C) The process by which governments control online information.D) The widespread availability of educational resources via the internet.4、How do educators respond to the changes brought about by technology in education?A) By rejecting technological advancements in favor of conventional methods.B) By adapting their teaching practices to incorporate new technologies.C) By insisting that online learning should replace traditional classrooms.D) By ignoring the potential benefits of online learning platforms.5、Based on the passage, which statement best reflects the future outlook for education?A) Traditional educational institutions will become obsolete.B) Technology will have a diminishing role in the education sector.C) Online learning will complement but not completely replace traditional education.D) Students will no longer require any form of structured learning environment.Answers:1.B2.A3.D4.B5.CThis is a fictional example designed for illustrative purposes. In actual CET exams, the passages and questions would vary widely in topic and complexity.第二题Reading PassagesPassage OneGlobal warming is one of the most pressing environmental issues facing the world today. It refers to the long-term increase in Earth’s average surface temperature, primarily due to human activities, particularly the emission of greenhouse gases. The consequences of global warming are far-reaching, affecting ecosystems, weather patterns, sea levels, and human health.The Intergovernmental Panel on Climate Change (IPCC) has warned that if global warming continues at its current rate, we can expect more extreme weather events, such as hurricanes, droughts, and floods. Additionally, rising sealevels could displace millions of people, leading to social and economic instability.Several measures have been proposed to mitigate the effects of global warming. These include reducing greenhouse gas emissions, transitioning to renewable energy sources, and implementing sustainable agricultural practices. However, despite the urgency of the situation, progress has been slow, and many countries have failed to meet their commitments under the Paris Agreement.Questions:1、What is the primary cause of global warming according to the passage?A、Natural climate changesB、Human activitiesC、Ecosystem changesD、Increased carbon dioxide levels in the atmosphere2、Which of the following is NOT mentioned as a consequence of global warming?A、Extreme weather eventsB、Rising sea levelsC、Improved crop yieldsD、Increased global biodiversity3、What is the IPCC’s main concern regarding the current rate of global warming?A、It is causing a decrease in Earth’s average surface temperatu re.B、It is leading to more extreme weather events.C、It is causing the Earth’s magnetic field to weaken.D、It is causing the ozone layer to thin.4、What are some of the proposed measures to mitigate the effects of global warming?A、Reducing greenhouse gas emissions, transitioning to renewable energy sources, and implementing sustainable agricultural practices.B、Building more coal-fired power plants and expanding deforestation.C、Increasing the use of fossil fuels and reducing the number of trees.D、Ignoring the issue and hoping it will resolve itself.5、Why has progress in addressing global warming been slow, according to the passage?A、Because it is a complex issue that requires international cooperation.B、Because people are not concerned about the consequences of global warming.C、Because scientists do not have enough information about the issue.D、Because the Paris Agreement has not been effective.Answers:1、B2、C3、B4、A5、A七、阅读理解-仔细阅读（选择题，共20分）First QuestionPassage:In the age of rapid technological advancement, the role of universities has shifted beyond traditional academic pursuits to include fostering innovation and entrepreneurship among students. One such initiative taken by many institutions is the integration of technology incubators on campus. These incubators serve as platforms where students can turn their innovative ideas into tangible products, thereby bridging the gap between theory and practice. Moreover, universities are increasingly collaborating with industry leaders to provide practical training opportunities that prepare students for the challenges of the modern workforce. Critics argue, however, that this shift might come at the cost of undermining the foundational academic disciplines that have historically formed the core of higher education.Questions:1、What is one key purpose of integrating technology incubators in universities according to the passage?A) To reduce the cost of university education.B) To bridge the gap between theory and practice.C) To compete with other universities.D) To focus solely on theoretical knowledge.Answer: B) To bridge the gap between theory and practice.2、According to the text, how are universities preparing students for the modern workforce?A) By isolating them from industry professionals.B) By providing practical training through collaboration with industry leaders.C) By discouraging entrepreneurship.D) By focusing only on historical academic disciplines.Answer: B) By providing practical training through collaboration with industry leaders.3、What concern do critics raise about the new initiatives in universities?A) They believe it will enhance foundational academic disciplines.B) They fear it could undermine the core of higher education.C) They think it will make universities less competitive.D) They are worried about the overemphasis on practical skills.Answer: B) They fear it could undermine the core of higher education.4、Which of the following best describes the role of universities in the current era as depicted in the passage?A) Institutions that strictly adhere to traditional teaching methods.B) Centers that foster innovation and entrepreneurship among students.C) Organizations that discourage partnerships with industries.D) Places that prevent students from engaging with real-world challenges.Answer: B) Centers that foster innovation and entrepreneurship among students.5、How does the passage suggest that technology incubators benefit students?A) By ensuring they only focus on theoretical studies.B) By giving them a platform to turn ideas into products.C) By limiting their exposure to practical experiences.D) By encouraging them to avoid modern workforce challenges.Answer: B) By giving them a platform to turn ideas into products.This set of questions aims to test comprehension skills including inference, detail recognition, and understanding the main idea of the given passage. Remember, this is a mock example and should be used for illustrative purposes only.Second QuestionReading Passage:The Future of Renewable Energy SourcesIn recent years, there has been a growing interest in renewable energy sources due to their potential to reduce dependency on fossil fuels and mitigate the effects of climate change. Solar power, wind energy, and hydropower have all seen significant advancements in technology and cost-efficiency. However, challenges remain in terms of storage and distribution of these energy sources. For solar energy to become a viable primary energy source worldwide, it must overcome the limitations posed by weather conditions and geographical location. Wind energy faces similar challenges, particularly in areas with low wind speeds. Hydropower, while more consistent than both solar and wind energies, is limited。

Materials Science and Engineering A 494(2008)173–178Contents lists available at ScienceDirectMaterials Science and EngineeringAj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /m s eaHot deformation behavior and microstructure evolution of twin-roll-cast Mg–2.9Al–0.9Zn alloy:A study with processing mapW.P.Peng ∗,P.J.Li,P.Zeng,L.P.LeiKey Laboratory for Advanced Manufacturing by Materials Processing Technology,Tsinghua University,Beijing 100084,PR Chinaa r t i c l e i n f o Article history:Received 3March 2008Received in revised form 4April 2008Accepted 8April 2008Keywords:AZ31alloy Twin-roll-cast Processing mapDynamic recrystallization Grain boundary slidinga b s t r a c tThe hot deformation behavior and microstructure evolution of twin-roll-cast of Mg–2.9Al–0.9Zn–0.4Mn (AZ31)alloy has been studied using the processing map.The tensile tests were conducted in the temper-ature range of 150–400◦C and the strain rate range of 0.0004–4s −1to establish the processing map.The different efficiency domains and flow instability region corresponding to various microstructural char-acteristics have been identified as follows:(i)the continuous dynamic recrystallization (CDRX)domain in the range of 200–280◦C/≤0.004s −1with fine grains which provides a potential for warm deformation such as deep drawing;(ii)the discontinuous dynamic recrystallization (DDRX)domain around 400◦C at high strain rate (0.4s −1and above)with excellent elongation which can be utilized for forging,extru-sion and rolling;(iii)the grain boundary sliding (GBS)domain at slow strain rate (below 0.004s −1)above 350◦C appears abundant of cavities,which result in fracture and reduce the ductility of the adopted mate-rial;and (iv)the flow instability region which locates at the upper left of the processing map shows the metallographic feature of flow localization.©2008Elsevier B.V.All rights reserved.1.IntroductionMagnesium alloys have been increasingly used in the auto-motive,aerospace and electronic industries because of their low density and high specific strength.Sheet components from Mg alloys are especially attractive.However,magnesium alloys exhibit low formability due to their hexagonal close-packed crystal (HCP)structure with only two independent operative basal slip systems at room temperature.They are more workable at elevated tem-peratures because of the activation of non-basal slip systems such as prismatic and pyramid.As a result,the fabrication of magne-sium sheets is a difficult process consisting of numerous sequential steps of cold or warm rolling passes,so the reduction of manu-facturing costs and the improvement of formability are desired.Recently,continuous strip casting and direct rolling method have received attention as an integrated producing process [1–3].Good mechanical properties and fine microstructures were obtained by controlling the twin-roll-cast process.Due to the low stacking fault energy (SFE),dynamic recrys-tallization (DRX)plays an important role in the hot deformation of Mg alloys.There are several possible ways in which dynamic recrystallization may take place in Mg alloys [4,5].The formation∗Corresponding author.Tel.:+861062773639;fax:+861062788074.E-mail address:pengweiping99@ (W.P.Peng).of new grains may occur by conventional DRX (nucleation and growth,DDRX),by continuous dynamic recrystallization (CDRX),by subgrain rotation recrystallization (RRX),or via twin–twin and dislocation slip–twin interactions.Despite several previous publi-cations concerning DRX and other deformation mechanisms such as twinning,dynamic recover (DRV),and gain boundary slide (GBS)in magnesium alloys [6–8],there is few systematic study of twin-roll-cast AZ31alloy with the hot deformation behavior,microstructure evolution and deformation mechanism.The aim of the present investigation is to study the hot deforma-tion behavior and microstructure evolution of twin-roll-cast AZ31alloy using the processing map.The processing map was developed on the basis of dynamic materials modeling (DMM)[9],with the complementary relationship between the rate of visco-plastic heat generation induced by deformation and the rate of energy dissipa-tion associated with microstructural mechanisms occurring during the deformation process.A non-dimensional efficiency index Áwas used to represent the power dissipation through microstructural mechanisms and is given as Á=2m m +1(1)where m is the strain rate sensitivity of flow stress.The contour plot of the iso-efficiency Ávalues on the temperature–strain rate field constitutes the processing map.The dissipation characteristics vary for different microstructural mechanism,each domain on the map corresponds with a single dominant mechanism operating under0921-5093/$–see front matter ©2008Elsevier B.V.All rights reserved.doi:10.1016/j.msea.2008.04.029174W.P.Peng et al./Materials Science and Engineering A 494(2008)173–178Fig.1.The annealed microstructure of the twin-roll-cast AZ31alloy:(a)optical micrograph.(b)OIM map measured by EBSD.(c)Inverse stereographic triangle showing the orientation of the ND.(d)Histogram showing the angle between the c -axis and the ND.those conditions of the domain.In addition to the Ácontours,the instability criterion given by the equation=∂ln[m/m +1]∂ln ˙ε+m <0(2)was applied to delineate the temperature–strain rate regimes offlow instability on the processing map.A detailed description of the development of the model,as well as the significance of Ávalue in the interpretation of the domains,was given by Prasad and Sasidhara [10].2.ExperimentalThe chemical composition (wt.%)of the alloy adopted in this investigation was as follows:Al,2.92;Zn,0.85;Mn,0.35;Si,0.025;Fe,0.006;Ni,0.0007;Be,0.002;and balance Mg.The addition of silicon improves the flowability of molten melt while the beryl-lium prevents it from oxidation.The sheets were obtained by the twin-roll-cast technique at a casting speed of 6m/min with 4mm in thickness.They were then rolled into 0.8mm via the short rolling process.Finally,the sheets were annealed at 300◦C for 2h to obtain uniform fine microstructure.Fig.1(a)shows the annealed opti-cal micrograph of the twin-roll-cast AZ31alloy sheets.Note that the microstructure is a kind of equiaxial recrystallized grain with an average size about 16␮m.Fig.1(b)shows the orientation map (OIM)measured by electron backscatter diffraction (EBSD).Fig.1(c)shows an inverse stereographic triangle depicting the orientation of the ND of a large amount of grains in the as-received material.A concentration of poles near the {0001}direction indicates a basaltexture.Fig.1(d)shows the histogram of the angle between the c -axis and the ND.This representation gives an idea of the spread of the {0001}fiber texture which means the basal texture is not that much strong.The tensile specimens with a gage length of 28mm were cut from the sheets parallel to the rolling direction.The uniaxial ten-sile tests were conducted at the temperature and strain rate range of 150–400◦C and 0.0004–4s −1,respectively.The specimens were first heated up to the deformation temperature and held isother-mally for 3min prior to the stretch,and then elongated to fracture using a Gleeble-1500D thermal simulator testing machine.The deformed specimens were air cooled and then sectioned parallel to the deformation direction,grinded,polished,and etched for the metallographic examination.In all metallographices the tensile axis are horizontal.3.Results and discussion 3.1.Flow stress curvesThe typical true stress–true strain curves obtained at the higher and lower strain rate of hot working range of AZ31alloy are shown in Fig.2where (a)and (b)correspond to 4and 0.0004s −1,respec-tively.At the lower temperature (150◦C),the flow curve exhibited severe strain hardening and failure occurred near the peak in all the adopted strain rates.At the intermediate temperatures (200and 250◦C),the material exhibited strain hardening followed by a steady decline toward a plateau.The strains for the onset of steady-state flow increased as the temperature decreased and the strain rate increased,where at higher strain rates (4s −1)wereW.P.Peng et al./Materials Science and Engineering A 494(2008)173–178175Fig.2.True stress–true strain curves obtained for AZ31alloy at (a)4s −1and (b)0.0004s −1for various temperatures.about 25%and at lower strain rates (0.0004s −1)were below 5%.At the higher temperatures (300◦C and above),the flow curves were somewhat different.At the higher strain rates strain hardening was restricted to smaller critical strains followed by flow softening lead-ing to a steady-state flow with a peak stress presented (Fig.2(a)).Meanwhile,at the lower strain rates,the initial strain hardening component was reduced and the material exhibited only steady-state flow behavior (Fig.2(b)).3.2.Processing mapThe processing map obtained at a strain of 0.3(steady-state flow)is shown in Fig.3.The processing maps at larger strains are essentially similar,so these are not shown here.The three distinct domains are shown in darker color in Fig.3:Domain I with a peak efficiency of about 42.9%at 250◦C/0.0004s −1;Domain II with a peak efficiency of about 38.7%at 400◦C/4s −1;and Domain III with a peak efficiency of about 57.8%at 400◦C/0.0004s −1.It should be noticed that the peak efficiency may be higher than 38.7%in Domain II since the contours did not meet the peakvalue.Fig.3.The efficiency domains and the flow instability regions plotted along with the processing map of AZ31alloy.In Fig.3,the thick lines represent the boundary for the region that has the negative value of (Eq.(2))and would exhibit flow instability,which was represented as the lighter color regions.The region at the upper left part of the processing map was associated with low temperature and high strain rate.4.DiscussionIn a number of previous studies,constitutive equations were for-mulated for conventionally hot worked magnesium alloys [11,12].They included a power law relationship at low stresses,an exponen-tial relationship at high stresses,and a hyperbolic sine relationship for an extensive stresses range.All the three constitutive equations are related to the Zener–Hollomon parameter which is defined as Z =˙εexp QHWRT(3)The Zener–Hollomon parameter (Z)combines the control variable of strain rate and temperature through an Arrhenius function with activation energy Q HW .The Zener–Hollomon parameter is plotted in Fig.4as a function of flow stress at a true strain of 0.3.The value of Q is 135kJ/mol associated to the lattice diffusion activation energy.As indicated in the double logarithmic plot,all the data falls onto the threesuc-Fig.4.The influence of the Zener–Hollomon parameter,Z ,on the steady-state stress for the twin-roll-cast AZ31alloy.176W.P.Peng et al./Materials Science and Engineering A 494(2008)173–178Fig.5.The variations of tensile elongation and efficiency as a function of temperature at strain rate (a)4s −1and (b)0.0004s −1.cessive lines.The slope,namely the so-called stress exponent n ,is about 3.8,6.4and 11.6in the lower stress region,intermediate stress region and higher stress region,respectively.As reported in previous studies [7,12,13],AZ31alloy at the lower stress region,where n is close to 3.8,coincides with the value of GBS.The value of n changes from 3.8to 6.4,which occurs at stresses of about 30MPa,the rate controlling process of deformation should be DRX and/or slip deformation by c +a dislocation movement.While at higher stress,the n value reaches 11.6,which responds to the twinning and slip deformation by a dislocation movement.Identified by the different n values,the corresponding regions on the processing map are discussed in the following sections.4.1.Domains I and II (DRX)Domain I in Fig.3occurred in the temperature range of 200–280◦C and strain rate of 0.0004–0.004s −1while the Domain II occurred above 350◦C and the strain rate ranges from 0.4to 4s −1.The relative strain–stress plots are shown in Fig.2.Nor-mally,the dynamic recrystallization process is classified aseitherFig.6.Typical microstructures in the high efficiency domains:(a)Domain I (CDRV),(b)Domain II (DDRX)and (c)Domain III (GBS +cavity).W.P.Peng et al./Materials Science and Engineering A494(2008)173–178177continuous or discontinuous.Continuous recrystallization(CDRX) is considered as an extension of the recovery process.This type of recrystallization can be accompanied by gradual softening in theflow curve,leading to a plateau inflow curves.Discontinu-ous recrystallization(DDRX)involves the nucleation of new grains, followed by growth,which typically causes a significant softening peak in theflow curve.As shown in Fig.2,Domains I and II could correspond to CDRX and DDRX,respectively.The tensile ductility and efficiency variations as a function of temperature are plotted for the present material in Fig.5.In the temperature range close to Domain I,as shown in Fig.5(b),the efficiency exhibits a peak value at250◦C and decreases at either side,while the fracture ductility is monotonic raising from200to 300◦C.The peak efficiency at250◦C reaches42.9%with ductility of57.2%,while at300◦C,30.5%efficiency associated with68.1% ductility.Nonetheless,the good ductility in Domain I provides a potential for warm deformation such as sheet metal deep drawing. The good correlation between efficiency and ductility of Domain II is shown in Fig.5(a).At the temperature range of300–400◦C, ductility increases from51.3%to64.6%,which is in good agreement with the efficiency raising from26.4%to38.7%.Fig.6(a)and(b) shows the microstructure of Domains I and II,respectively.These features,extremefine grains(a)and equiaxed grains with the grain boundaries wavy in nature(b),are in well agreement with the recrystallized grain feature.Since the extremelyfine grains were obtained at Domain I,it could be used for the last rolling process at this deformation condition to achievefine grains.Many studies [7,14,15]also supported that Domain I is an optimal condition for sheet metal forming especially for deep drawing.The different characteristics between efficiency and ductility in Domains I and II are due to the different DRX mechanism in the two domains.There is evidence that progressive lattice rota-tion may occur at grain boundaries in magnesium alloys[4,6,7], and that this may eventually lead to the formation of new grains. The mechanism is based on local shearing near grain boundaries, which occurs because of the lack of thefive independent slip systems required for homogeneous plasticity.Dynamic recovery of the geometrically necessary dislocations then occurs,result-ing in the formation of new subgrains or grains.The rotational recrystallization(RRX)can be used to explain the dynamic recrys-tallization mechanism in Domain I.At intermediate temperatures (200–300◦C),the controlling mechanism of plastic deformation is cross-slip of a dislocation on non-basal planes.This cross-slip is predominantly activated near original grain boundaries where the stresses are highly concentrated.The cross-slip of a dislocation by the Friedel–Escaig mechanism leads to a transition from a primary screw orientation to an edge orientation.This edge dislocation lies in a non-basal plane,which is characterized by a high value of the stacking fault energy.Therefore,this dislocation can readily climb. Dislocation rearrangements by cross-slip and climb generate a low-angle boundary network in the vicinity of the original boundaries. Continuous absorption of dislocations in the low-angle boundaries results in CDRX[5].Yi et al.[16]studied the formation of DRX in this temperature range by the EBSD measurements and found that new recrystallized grains have similar orientations as the original grains.This is why the ductility in Domain I is not higher than that in Domain II,though the former grain size isfiner than the latter.In Domain II,where at higher deformation temperatures,non-basal slip is easier,the operation of c+a slip promotes the formation of high-angle boundaries.Deformation becomes more homogeneous,and the dynamic recrystallization changes into the discontinuous process.The dramatic changes of mechanical behav-ior with increasing deformation temperature originate from the high activity of c+a slip systems and DRX.4.2.Domain III(GBS+cavity)Domain III in Fig.3occurs above350◦C in the strain rate range from0.0004to0.004s−1.Theflow curves are similar to those of Domain I,where the stress exhibits only a steady-stateflow.How-ever,stress value is extremely low,less ually,when deformed at low strain rate and high temperature,the basic mech-anisms involved are the grain boundary triple junctions mitigating the formation of wedge cracks.The stress exponent(3.8)is in sup-port of GBS with high temperature and low strain rate.This is in good agreement with the results published for Mg alloys[17], where the dominant deformation mechanism was reported to be GBS accommodated by slip controlled by grain boundary diffu-sion.The corresponding efficiency and ductility are presented in Fig.5.The highest ductility is78.8%at350◦C with an efficiency of41.5%,while at400◦C,the ductility decreased to72.3%as the efficiency increased to57.8%.The result could be ascribed to the cavity behavior in the domain.It was found that the onset of cavity is300◦C/0.0004s−1and more cavities were found at higher tem-perature with larger strain.The microstructure obtained in this condition is shown in Fig.6(c)where cavities are found at the grain boundaries.Some cavities are evident at the grain boundaries or triple points.The grains still remain nearly equiaxed through-out the straining until fracture.In AZ31alloy,the second phase with low melt temperature Mg17Al12at the grain boundary pro-motes the cracking process.The occurrence of grain boundary cracking has its influence on the tensile ductility obtained at a strain rate of0.0004s−1.The cracking process is very efficient in converting the energy into free surface energy and,hence, the cracking domain is characterized by high efficiencies.The high efficiency at400◦C along with the low tensile ductility indicates that the domain represents the gain boundary crack-ing process.In another study on the development of cavitation during deformation,Lee and Huang[18]have reported grain bound-ary cavitation during GBS infine grained the AZ31alloy after a large strain even at400◦C.The similar result was reported at as-cast Mg–2Zn–1Mn[19]and Mg–3Al[20]by Prasad and coworkers.4.3.Flow instability regionThe instability region is shown in Fig.3,which occurs at lower temperatures with higher strain rates and occupies the upper left part of the processing map.Generally,instability associated with this deformation condition is due to a localizedflow.At tempera-tures below200◦C,the dominant slip mode in magnesium alloys is the basal mode,which could contribute only two independent slip systems to deformation.Therefore,to fulfill the von Mises criterion,non-basal slip systems and twinning should be active. Nonetheless,theflow localization generated with the lack of slip system.The occurrence of twinning highly depends on the grain size and the deformation temperature and the strain rate(Z parame-ter)[12,21].It dominates the deformation at high Z but this gives way to slip dominatedflow when Z is lower,that is,tempera-ture increases and strain rate decreases.Meanwhile,fine grains retard the twinning generation.From the microstructure exam-ination,only under the deformation conditions of150◦C/4s−1, 150◦C/0.4s−1,and200◦C/4s−1where Z is higher than3×1015, the twinning presents,which coincides with the results by Beer et al.With the lowered Z value,the structure develops subgrains and serrations at the grain boundaries(GB)mantle before subgrain boundary occurs at the grain core.The microstruc-178W.P.Peng et al./Materials Science and Engineering A 494(2008)173–178Fig.7.Typical microstructures of the specimens deformed at 150◦C/0.0004s −1corresponding to the flow instability region.ture manifestation of instability in this alloy is shown in Fig.7,which corresponds with the specimen deformed at 150◦C/0.004s −1.The grains are visibly elongated and the GB are slightly to strongly irregular.Serrations develop in the GB of AZ31alloys as a result of local migrations to absorb dislocation walls.5.ConclusionsProcessing map for twin-roll-cast AZ31alloy has been obtained at the hot working temperature range of 150–400◦C and the strain rate range from 0.0004to 4s −1.The domains of the processing map are interpreted in terms of the associated microstructural mecha-nisms and the conclusions are as follows:(1)The domain occurring around 250◦C at the strain raterange 0.0004–0.004s −1was interpreted to represent CDRX,which provides a better workability for warm deformation.(2)DDRX domain was identified with the optimum deformationconditions above 400◦C/0.4s −1.The high ductility ascribes to the operation of c +a dislocation and DRX.(3)Grain boundary sliding is responsible for the high efficiencydomain (57%)occurring below 0.004s −1and spreading over 350–400◦C.The grain boundary cavities associated with the domain reduce the ductility of the material.(4)The flow instability region occurring at the low temperaturerange under high deformation rates (>0.4s −1)is associ-ated with flow localization and serrations at the grain boundaries.AcknowledgementThe work presented in this paper has been fully supported by Natural Science Foundation of China (Project Ref.No.50675115).References[1]D.Liang,C.B.Cowley,JOM TMS 55–56(2004)26–28.[2]T.Minoa,M.Asakawa,D.Lee,et al.,J.Mater.Process.Technol.177(2006)534–538.[3]S.X.Song,J.A.Horton,N.J.Kim,T.G.Nieh,Scripta Mater.56(2007)393–395.[4]S.E.Ion,F.J.Humphreys,S.H.White,Acta Mater.30(1982)1909–1919.[5]F.J.Humphrey,M.Hatherly,Recrystallization and Related Annealing Phenom-ena,Pergamon Press,Oxford,1995.[6]A.Galiyev,R.O.Kaybishev,G.Gottstein,Acta Mater.49(2001)1199–1207.[7]J.C.Tan,M.J.Tan,Mater.Sci.Eng.A 339(2003)81–89.[8]M.T.Perez-Prado,J.A.del-Valle,J.M.Contreras,et al.,Scripta Mater.50(2004)661–665.[9]Y.V.R.K.Prasad,H.L.Gegel,S.M.Doraivelu,et al.,Metall.Trans.15A (1984)1883–1892.[10]Y.V.R.K.Prasad,S.Sasidhara,Hot Working Guide:A Compendium on ProcessingMaps,ASM International,Metals Park,OH,1997.[11]A.M.Galiyev,R.O.Kaibyshev,Phys.Met.Metallogr.81(1996)451–457.[12]A.G.Beer,M.R.Barnett,Mater.Sci.Eng.A 423(2006)292–299.[13]L.Helis,K.Okayasu,H.Fukutomi,Mater.Sci.Eng.A 430(2006)98–103.[14]E.Doege,K.Droder,J.Mater.Process.Technol.115(2001)14–19.[15]S.Yoshihara,H.Nishimur,H.Yamamoto,K.Manabe,J.Mater.Process.Technol.142(2003)609–613.[16]S.B.Yi,S.Zaefferer,H.G.Brokmeier,Mater.Sci.Eng.A 424(2006)275–281.[17]H.Watanabe,T.Mukai,M.Mabuchi,K.Higashi,Acta Mater.49(2001)2027–2037.[18]C.J.Lee,J.C.Huang,Acta Mater.52(2004)3111–3122.[19]O.Sivakesavam,Y.V.R.K.Prasad,Mater.Sci.Eng.A 362(2003)118–124.[20]N.Srinivasan,Y.V.R.K.Prasad,1.P.Rama-Rao,Mater.Sci.Eng.A 476(2008)146–156.[21]M.R.Barnett,Z.Keshavarz, A.G.Beer, D.Atwell,Acta Mater.52(2004)5093–5103.。

Formalizing Behavior of Geographic Feature TypesbyRobert D. Rugg, Max J. Egenhofer, and Werner KuhnNational Center for Geographic Information and AnalysisReport 95-7Copyright© National Center for Geographic Information and AnalysisJune 1995AbstractThis paper addresses the problem of formalizing the natural-language definitions of spatial features. While the Spatial Data Transfer Standard (SDTS) supports the structural aspects of the definition of spatial features, it falls short of providing means to convey explicitly their behavior. An approach using functional algebra is developed using the example of the SDTS standard entity types “dam,” “watercourse,” and “lake,” together with the operations expressed in the natural-language definitions of these features. Formal algebraic specifications go beyond the SDTS approach, by providing precise mathematical representations of the behavior of geographic features and the interactions among related feature types. Functional specifications also help in refining the selection of attributes needed to characterize the behavior of a given feature type. An implication of the functional approach is to provide precise mathematical signatures of feature types as an alternative to natural-language definitions. Mathematical specifications are unambiguous across cultures and languages and provide a strict basis for assessing the interoperability of objects in feature-based GISs.AcknowledgmentsThis work was partially supported by the National Science Foundation (NSF) for National Center for Geographic Information and Analysis (NCGIA) under grant number SBE-8810917. Bob Rugg's work was supported under the visiting scholars program of the National Center for Geographic Information and Analysis (NCGIA) at the University of Maine and by a sabbatical leave from the Department of Urban Studies and Planning, Virginia Commonwealth University. Max Egenhofer’s research is further supported by NSF grant IRI-9309230, and grants from Intergraph Corporation, Space Imaging Inc., Environmental Systems Research Institute, and the Scientific and Environmental Affairs Division of the North Atlantic Treaty Organization.1.IntroductionRecently, it has been suggested that even an extended entity-relationship model, i.e., one that provides for specified relationships between types of geographic features1, would be insufficient for data exchange in which the meanings associated with feature types are intended to be well defined and preserved. This is because the meaning conveyed in the definition of an entity type includes dynamic concepts that involve how the entity in question will function in a given situation. Operations in this sense are poorly modeled, and only indirectly observed, in a system based on the static concepts of entity, attribute, and relationship. Frank and Kuhn (1995) note:Some data definition languages (e.g., EXPRESS [ISO, 1992]) allow tospecify data types, but lack formal semantics. They describe static datatypes with attributes and relationships, omitting the specification ofoperations. However, a specification language based on types must have amethod to associate data types with operations. Otherwise the concept oftype remains vacuous.An example is using a road (a data type) for vehicular traffic (an operation). During the winter season, in Maine, people cross frozen lakes and rivers, in cars and snowmobiles, as if they were roads. The same operation would be impossible in the summer time, and hazardous at other times of year. Is the frozen lake a “road?” If we specify the operations that are the critical properties of a road, for instance that it handles vehicular traffic, we have a more robust understanding of this type of feature than if we are content to classify things by static attributes like size, shape, and composition, or by static relationships such as the road crossing above the river on a bridge.Frank (1994), Frank and Kuhn (1995), Kuhn and Frank (1991), Mark (1993), and others have proposed using functional algebra as a technique for modeling spatial data. Frank and Kuhn (1995) assert that functional language data type specifications for “open GIS”serve to describe differences in semantics of geographic information systems (GIS) operations. Kuhn (1994) proposed that this technique can be applied directly to the problem of defining feature types for spatial data transfers. For example, he pointed out that the SDTS definition for DAM, “a barrier constructed across a watercourse to control the flow or raise the level of water” (SDTS: 9) includes phrases that describe how a dam functions. This natural-language definition suggests operations of the entity type DAM, namely changeFlow (of water) and changeLevel (of water). Thus, he was able to replicate the SDTS definition precisely, using a functional specification language.Kuhn also showed that by examining the operations suggested in the definitions, the German term “Damm” is closer in meaning to the SDTS entity type EMBANKMENT than it is to the SDTS DAM. Although it appears that the German “Talsperre” is a close synonym of DAM, it is entirely possible that there is no precise German equivalent of an entity type that was originally defined in English. Thus, in order for the full meaning of the definition of DAM to be preserved in a transfer, particularly an international transfer, the model used for defining entity types must include operations as well as attributes and relationships. An entity-attribute-relationship model can be used to record the knowledge1We use the term feature in the SDTS sense: the combination of a real world entity type and its representation as an object in a database. When we use the term entity type, we mean specifically the classification of real world phenomena as presented in Part 2 of SDTS.that the DAM has a certain HEIGHT and DISCHARGE, that the WATERCOURSE has a depth and a FORCE_OF_FLOW, and that the DAM has a relationship of CONTROL_OVER_WATER_LEVEL to the WATERCOURSE. However, even knowing all this, we still do not know, other than from the natural-language definition, that the basic purpose of a DAM, i.e., its behavior, is to control the flow and raise the level of water.Spatial data transfer and data sharing within the emerging Global Information Infrastructure will require much tighter control over the semantics of the data being shared. We need methods that will enable producers of data to specify the full meaning of what they are providing and that will enable data users to understand exactly what information they are receiving. Otherwise, we will never have information highways, but only continue to have bit-string highways (Zemankova, 1995).In the following sections, we will extend Kuhn's example by providing a more exhaustive definition of the entity type “dam,” first using the current types, definitions, attributes, and capability to model relationships found in SDTS, and then using functional algebra to specify the behavior of the dam.2.The Entity Type DAM in SDTSPart 2 of SDTS is based on a “Conceptual Model” of spatial features (SDTS: 2) consisting of entity types, entity instances, attributes, and attribute values. It is assumed that all natural phenomena can be described by applying these concepts.The concept of relationships between entity types is not expressly included in the SDTS model, although it is possible to represent such relationships as attributes of one entity for which the attribute value is the related entity. Part 2 of SDTS also includes a large number of included terms, for approximately 1,200 entity types with definitions that overlap those of one of the 200 standard entity types defined in the standard. Often, an included term is a subcategory of a standard term. For example, pond is an included term under the standard term lake. Standard attributes are defined in SDTS to help distinguish the nuances of meaning between a standard term and an included term. For example, size is an attribute and so a pond can be encoded into SDTS as a small lake.There is no logical reason why all the necessary information about real world features cannot be represented within the framework devised for SDTS. However, critics have argued, among other things, that•relationships among entity types should be an explicit part of the SDTS model;•natural-language definitions are too vague and unreliable to be consistently used and understood by diverse individuals, particularly if theindividuals are in different organizations, live in different cultures, or,worse, speak different natural languages; and•even if the meaning of a definition is clearly understood, the information about a particular slice of real world entities provided for a particularapplication may be of limited or no use in other applications.We will return to these criticisms at the conclusion of this paper. First, we review how a standard entity is recorded in SDTS, using an extended version of Kuhn's example.In SDTS, a DAM is a standard entity type. The water controlled by the DAM, in SDTS, flows through a WATERCOURSE. A related term is RESERVOIR, the standing body of inland water backed up behind a dam. In SDTS, RESERVOIR is an included term under the standard term LAKE, the definition for which should read “any standing body of inland water.” These are defined in SDTS as follows:DAM A barrier constructed across a watercourse tocontrol the flow or raise the level of water.WATERCOURSE A way or course through which water may or doesflow.LAKE Any standard [sic] body of inland water.Several SDTS standard attributes may be used to further describe the DAM, WATERCOURSE, and (or) LAKE and the relationships among them. For example, each can have a NAME and a WIDTH. The DAM has a HEIGHT and DISCHARGE and is characterized by CONTROL_OVER_WATER_LEVEL of the WATERCOURSE. It may be intended for FLOOD_CONTROL, HYDROELECTRIC_POWER, or other purposes. It is usually MANMADE and may be EXISTING or PROPOSED. The WATERCOURSE has a DIRECTION_OF_FLOW, WETTED_PERIMETER, CROSS_SECTIONAL_AREA, FORM_RATIO, and FORCE_OF_FLOW. It may be INTERMITTENT or PERENNIAL and may be RECREATIONAL. It is related to the DAM as a FEATURE_PRESENT. The reservoir LAKE has an AREA, a VOLUME, a SALINITY, and a SEASONAL_DEPTH and is MANMADE. It may be EXISTING or PROPOSED and may be RECREATIONAL, intended for WATER_SUPPLY or IRRIGATION, and subject to use RESTRICTIONS. It is related to the DAM and the WATERCOURSE each as a FEATURE_CONNECTED (Table 1). An instance of each entity type would be coded in SDTS as a tuple with each field containing an attribute value (Table 2).Each of the entity types and attributes in SDTS has a standard definition. However, there is no standard linkage between entities and attributes. In the above examples, the attributes listed for each entity type are available to be used, but are not required. As a result, any two encoders of SDTS entity and attribute information will likely arrive at different attribute schemas for any given entity type. Even more importantly, attributes that are crucial for modeling the behavior or operation of a particular entity type may be omitted from the data transfer. Finally, even this relatively simple example shows that the relationships among various entity types are a critical part of the information to be conveyed. A dam cannot exist without a corresponding watercourse, nor a reservoir without both. Once a dam is included, we also need an attribute of the watercourse that indicates how its level is affected by the dam. The previously proposed attribute “depth”could serve this purpose.A more important limitation of the current SDTS model is that the operations of (or affecting) entity types are not specified. If the Orono Town Dam were to be used in a hydrologic model of the Stillwater River, for example, the model and certain properties of the dam would have to be transferred outside SDTS as part of a “private agreement”between the data producer and the user. On the other hand, if the data were only being used as part of an inventory of the locations of and dimensions of existing dams, the SDTS description might be entirely sufficient.SDTS Entity Type SDTS Attribute Relates to Entity TypeD AM N AMEW IDTHH EIGHTD ISCHARGEC ONTROL_OVER_W ATER_LEVEL W ATERCOURSEF LOOD_CONTROLH YDROELECTRIC_P OWERM ANMADE/A RTIFICALLY_I MPROVED/N ATURALE XISTING/P ROPOSEDW ATERCOURSE N AMEW IDTHdepth*D IRECTION_OF_FLOWW ETTED_PERIMETERC ROSS_SECTIONAL_AREAF ORM_RATIOF ORCE_OF_FLOWI NTERMITTENT/P ERENNIALR ECREATIONALF EATURE_PRESENT D AML AKE N AMEW IDTHA REAV OLUMEdepth*S ALINITYS EASONAL_DEPTHM ANMADE/A RTIFICALLY_I MPROVED/N ATURALE XISTING/P ROPOSEDR ECREATIONALW ATER_SUPPLYI RRIGATIONR ESTRICTIONSF EATURE_CONNECTED D AMF EATURE_CONNECTED W ATERCOURSE* Note: the attribute DEPTH was among several entries in The American Cartographer proposed standard that were removed in the final editing of SDTS. Therefore, it must currently be defined by the user.Table 1:Selected Entity Types and Attributes.Field ValueE NTITY_T YPE D AMN AME Orono Town DamW IDTH200 metersH EIGHT10 metersD ISCHARGE100 cubic meters per second C ONTROL_OVER_WATER_LEVEL<foreign identifier>*F LOOD_CONTROL trueH YDROELECTRIC_POWER trueM ANMADE/A RTIFICALLY_IMPROVED/N ATURAL MANMADEE XISTING/P ROPOSED existing* points to the entry for Stillwater River in the table of watercoursesTable 2:An Instance of the Entity Type DAM.3.Functional Algebras for Entity Type DefinitionsFunctional algebras, also called universal algebras, algebraic specifications, and functional [programming] languages, are a formal method of specifying the behavior of abstract data types. They are “… based on the evaluation of expressions, suitably generalized to allow complex data structures to be specified. The description 'functional' arises from their use of side-effect-free functions as the main program structuring and abstraction device.” (Bailey, 1990).A specification using functional algebra consists of three main kinds of expressions: abstract data types, functions, and axioms. Abstract data types are specified by sort identifiers, functions are specified by operation identifiers, and axioms, or equations, specify the behavior of the operations on the sorts. The combination of sort and operation identifiers constitutes the signature of the data type.Functions are of two basic types: constructor functions and observer functions. Constructors add new instances or modify the current state of a sort. In terms of the SDTS model, we would say that constructor functions create or change entity instances. Observers return information about the sort without adding to it or changing its state. They return attribute values of entity instances. Axioms specify the results for each observer function of the operation of each constructor function.Using Gofer (Jones, 1993) syntax, abstract data types can be specified using data statements. Functions are defined by the :: symbol and axioms as equalities using thesymbol =. An example of a Gofer language specification is Kuhn's “glas spec.” The sort identifier introduces the abstract data type Glas with two possible states: it is a new glas or it has been filled:data Glas = NewMug (Int) | Fill (Glas, Int)The new glas is of type integer where the value is the size of the glas. The filled glas is of type (glas, integer) where the value of the integer is the amount of water added to the glas.The operation on the glas is to take a drink. The observer functions include noting the size of the glas, the level of beer remaining, and whether the glas is empty or full. Note that the constructor function “drink” is an operation that affects the glas itself, whereas the observer functions simply return data values.drink :: (Glas, Int) -> Glassize :: Glas -> Intlevel :: Glas -> Intempty :: Glas -> Boolfull :: Glas -> BoolThe operation “drink” includes an argument of type integer which is the amount of water consumed in the drink. The resulting “glas” has that much less remaining to be consumed. The observer “size” keeps track of the maximum capacity of the glas expressed as an integer. The observer “level” keeps track of the amount of beer in the glas, another integer quantity. The Boolean operators “empty” and “full” are either true or false for a given state of the glas.The axioms for the glas are as follows. Note that there are two axioms for each of the operations “drink,” “size,” and “level,” one for each of the two types of glas. The values of the observers “empty” and “full” are derived from values of the other observers “level”and “size.”drink (NewMug (i), j)= NewMug (i)drink (Fill (m,i), j)| full (Fill (m,i))=Fill (NewMug (size (m)), size (m) - j) | i>j= Fill (m, i-j)| otherwise= drink (m, j-1)size (NewMug (i))= isize (Fill (m,i))= size (m)level (NewMug (i))= 0level (Fill (m,i))| (level (m) + i) > size (m) = size (m)| otherwise= level (m) + iempty (m)= level (m) == 0full (m)= level (m) == size (m)The first axiom indicates that there is nothing to drink from a new glas. The second shows that there are three possible outcomes of drinking from a filled glas. If the glas starts out full, its level is lowered by the amount of the drink. If the glas is not full and the amount of the drink is less than what remains in the glas, the level is again lowered by the amount of the drink. If the amount to be drunk is at least as much as the amount remaining in the glas, the result is that the amount to be drunk is lowered by one unit (until the amount to be drunk equals the amount remaining). The size of the new glas is given (3rd axiom) and does not change when the glas is filled (4th axiom). The level of the new glas is zero (5th axiom). The sixth axiom shows that the level of the glas increases by the amount it is filled, unless the amount of beer added is beyond its capacity, in which case the glas is simply filled up. The glas is empty if its level is zero (7th axiom) and full if it is filled to capacity (8th axiom).The glas example can serve as an analogy for the reservoir created when a new dam is constructed. The following section presents a more detailed specification of a dam and its associated reservoir along a watercourse.4. A Definition of Dam using Functional AlgebraFor the purpose of this example, the abstract data types correspond to entity types in SDTS. Because functional algebra requires that we specify operations, the critical first step in arriving at a specification is to be clear about precisely which operations are involved. In the example of a dam, we can take the natural-language definition from SDTS and picture a series of operations as illustrated below. First, while the dam is only proposed, we have a single entity, the watercourse, with attributes of depth2 and flow. Cross-sectional views of this pre-dam situation are illustrated in Figure 1.2To simplify the metrics of the problem, we assume that the gradient of the watercourse and its cross-sectional area, taken together, result in a constant value for the attribute "depth" over the segments where the dam will be built. We can then use this attribute to operationalize the variable "water level" in the definition of dam.Fig. 1. WATERCOURSEThe situation can also be represented algebraically (Specification 1), with an abstract data type WATERCOURSE, whose only functions are to observe the depth and flow of the stream.Specification 1:data Watercourse = Stream (Int,Int)streamDepth :: Watercourse -> IntstreamFlow :: Watercourse -> IntstreamDepth (Stream(u,v)) = ustreamFlow (Stream(u,v)) = v4.1Constructing a DamThe first phrase in the definition of DAM is, “a barrier constructed across…” So, we have an operation “construct the dam.” As a result of this operation, several changes occur in the objects shown in Figure 1. Of course, there is a new DAM where there was none before. The WATERCOURSE is now split into two parts that will behave differently, an upstream part and a downstream part. Also, a portion of the valley through which the WATERCOURSE flows is about to be flooded. This RESERVOIR area will become a new LAKE. Figure 2 illustrates the situation after the DAM has been built, but before the LAKE is filled.Fig. 2. New DAMThe algebraic specification now involves the entity types DAM and LAKE in addition to WATERCOURSE. The operations include constructing a dam and creating a new lake. We then observe that the new dam is (as yet) open, its height is zero, and its discharge is zero. The new lake is empty and its depth is also zero. The maximum height of the dam is set at the time of construction (Specification 2)Specification 2:data Dam = ConstructDam (Int) | Operate (Dam,Int,Int) dataWatercourse=Upstream(Int,Int)|Downstream(Watercourse,Int.Int) data Lake = NewLake (Int) | Fill (Lake, Int)maxHeight :: Dam -> IntdamHeight :: Dam -> IntdamOpen :: Dam -> BoolstreamDepth :: Watercourse -> IntstreamFlow :: Watercourse -> IntlakeDepth :: Lake -> IntlakeEmpty :: Lake -> BoolmaxHeight (ConstructDam (k)) = kdamHeight (ConstructDam (k)) = 0damOpen (ConstructDam (k)) = TruestreamDepth (Upstream(u,v)) = ustreamDepth (Downstream(w,u,v)) = streamDepth (Upstream (u,v)) streamFlow (Upstream(u,v)) = vstreamFlow (Downstream(w,u,v)) = streamFlow (Upstream (u,v)) lakeDepth (NewLake(m)) = 0lakeEmpty (NewLake(m)) = True4.2Raising a DamThe next operation is to raise the height of the dam and begin to fill the reservoir. This is illustrated in Figure 3.Fig. 3. Raise DAMWe add the operation of raising the dam, which results in the dam being closed and stopping the flow of water downstream. We add a condition to the operation of raising the dam that prevents the dam from being raised higher than its maximum possible height (or lower than zero). The mutual interdependence of the entity types is reflected in more complex operations and equations (Specification 3).Specification 3:data Dam = ConstructDam (Int) | Operate (Dam,Int,Int)data Watercourse= Upstream(Int,Int)|Downstream(Watercourse,Int,Int) data Lake = NewLake (Int) | Fill (Lake, Int)damRaise :: (Dam,Int) -> DammaxHeight :: Dam -> IntdamHeight :: Dam -> Intdischarge :: Dam -> IntdamOpen :: (Dam,Watercourse,Lake) -> BooldamClose :: (Dam,Watercourse,Lake) -> BoolstreamDepth :: (Dam,Watercourse,Lake) -> IntstreamFlow :: (Dam,Watercourse,Lake) -> IntlakeDepth :: (Dam,Watercourse,Lake) -> IntlakeEmpty :: (Dam,Watercourse,Lake) -> BoolmaxHeight (ConstructDam(k)) = kmaxHeight (Operate (d,i,j)) = maxHeight (d)damHeight (ConstructDam(k)) = 0damHeight (Operate (d,i,j)) = idischarge (ConstructDam(k)) = 0discharge (Operate (d,i,j)) = jstreamDepth (d,Upstream(u,v),l) = ustreamDepth (d,Downstream(w,u,v),l)| damClose (d,w,l) == True = 0| damOpen (d,w,l) == True = streamDepth (d,w,l)+ lakeDepth(d,w,l) - damHeight (d)| otherwise = streamDepth (d,Upstream(u,v),l) streamFlow (d,Upstream(u,v),l) = vstreamFlow (d,Downstream(w,u,v),l)| damClose (d,w,l) == True = 0| damOpen (d,w,l) == True = streamFlow (d,w,l)+ discharge (d)| otherwise = streamFlow(d,Upstream(u,v),l)damOpen (ConstructDam (k),w,l) = TruedamOpen (Operate(d,k),w,l) = damHeight (d) < lakeDepth (d,w,l) lakeEmpty (ConstructDam(d),w,l) = TruelakeDepth (ConstructDam(d),w,l) = 0damRaise (ConstructDam (d),h) = error“Cannot raise height of a dam under construction”damRaise (Operate (d,i,j),h)| (h>i) && (h < maxHeight(d)) = Operate (d,h,j)| otherwise = error “Illegal new height for dam”damClose (d,w,l) = damHeight (d) > lakeDepth(d,w,l)4.3Reservoir is FullThe above state of affairs continues until the reservoir fills to the level of the dam, as illustrated in Figure 4.Fig. 4. LAKE FullWe add an observer function to indicate when the lake is full (Specification 4).Specification 4:lakeFull :: (Dam,Watercourse,Lake) -> BoollakeFull (d,w,l) = lakeDepth (d,w,l) == damHeight (d)When this occurs, the dam is neither “open” (discharging extra water into the downstream segment of the watercourse) nor “closed” (preventing any water from flowing downstream). The downstream segment of the watercourse returns to its normal upstream depth.4.4Lowering a Dam (discharging)An operation that has different consequences is illustrated in Figure 5: lowering the dam.Fig. 5. Lower DAMWhen this happens, there is a period of time when the height of the reservoir exceeds that of the dam. The downstream flow is increased relative to the upstream flow by the additional amount of discharge from the dam. The dam-lowering operation and its effects are shown in Specification 5.Specification 5:discharge :: (Dam, Watercourse, Lake) -> Intdischarge (ConstructDam (k),w,l) = 0discharge (Operate (d,i,j),w,l)| damOpen (d,w,l) = (( lakeDepth (d,w,l) - damHeight (d)) /streamDepth (d,w,l)) * streamFlow (d,w,l)damLower :: (Dam,Int) -> DamdamLower (ConstructDam (k),h) = error “Cannot lower a new dam”damLower (Operate (d,i,j),h)| (h<i) && (h >= 0) = Operate (d,h,j)| otherwise = error “Illegal new height for dam”As shown in Figure 6, eventually the level of the reservoir falls to the height of the dam and the system is again in equilibrium (as observed by the functions “dam not open”,“dam not closed”, and “lake full”).Fig. 6. LAKE FULLThis condition was specified earlier. The only difference is that there are new values of the observations for the height of the dam and the depth of the lake. A complete specification, including all the operations described above, is appended.5.Conclusions5.1SummaryThe natural-language definition for DAM expresses operations that can be formalized in terms of algebraic specifications for the operations (construct, raise, lower, open, close) and their effects (discharge, stream depth, stream flow, lake depth, lake empty, lake full). Such specifications are precise and capable of being expressed in any number of natural languages without ambiguity.Functional algebra offers a formal method for refining the work begun in an informal fashion with the development of Part 2 of SDTS. The SDTS model of entity types and attributes is rigorously supported in algebraic specifications in the form of abstract data types and observer functions. The example of the dam shows that relationships among entity types can also be precisely modeled using functional algebra. In order to expressthe operation of a dam and its effects, one must include the related entity types WATERCOURSE and LAKE as arguments to some of the functions of the dam. Functional algebra goes beyond current entity-attribute-relationship models by specifying the operations of entity types. Without this methodology, the behavior of such phenomena as roads, dams, and watercourses can only be described through a natural-language definition, or modeled through a specific computer program that accompanies the data.5.2DiscussionAttributes are specified in terms of observer functions that are needed to describe the operations of entity types and (or) the effects of these operations on other entity types. The standard attributes defined in SDTS were obtained informally through an analogous process: by determining which attributes were necessary to distinguish one standard entity type from another, or to capture the nuance of meaning between a standard entity type and an “included term.” Functional specifications offer the possibility of refining the selection of attributes to include only those that are essential to understanding the operations of entity types.Functional specifications also offer an advantage for transfer of data across applications.A given view of an entity type can be specified as a series of operations. For example, the effects of raising the dam may be of interest to a hydrologist and also to an ecologist, whereas its mere existence may be sufficient for the purposes of an airplane navigator. Functional specifications cannot solve the problem that data collected for one purpose may not meet other requirements, but at least they can help to clarify whether a problem exists and why.Perhaps the most significant contribution that functional algebra can make in the area of exchange standards is to identify functionally equivalent entity types. If the signature of a given entity type in one system matches, or is mathematically equivalent, to that of an entity type in another system, these entity types are not only synonyms—in the sense of natural language—but also they are, strictly speaking, interoperable. Thus, algebraic specifications of entity types can be useful in overcoming cultural and linguistic barriers to spatial data exchange.Algebraic specifications also present some difficulties. Although fairly easy to use for experienced programmers familiar with the method, they are not intuitively obvious to the beginner. There are, for example, three possible kinds of statements that can be used to specify abstract data types: a type statement, a data statement, or a class statement. The arguments to functions appearing on the right hand side of an axiom must be also appear on the left hand side, which in turn imposes a rigorous control over data type specifications and the form of functional specifications. We were unable to find reference materials written at a sufficiently high level to set forth the full power of functional programming languages to specify complex geographic entity types and their behaviors. The examples presented here only succeeded after many hours of trial and error. Better reference materials are needed before this approach can be widely accepted as a basis for feature definitions.。