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**Microstructure and Properties**

MSE Fall, 2002 (1st mini-course) Prof. A. D. Rollett

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Course Content is the first of a pair of (mini-)courses that describe the relationship between materials microstructure and properties. deals mainly with single phase microstructures: the companion course, , deals with multi-phase microstructures. Technological materials (except Si-based) are multi-phase.

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Cheating Policy Students are referred to the University Policy About Cheating and Plagiarism (Organization Announcement No. 297, 6116/80). It shall be the policy in this course to discourage cheating to the extent possible, rather than to try to trap and to punish. On the other hand, in fairness to all concerned, cheating and plagiarism will be treated severely. Cheating includes but is not necessarily limited to: 1.Plagiarism, explained below. 2.Submission of work that is not the student's own for reports or quizzes. 3.Submission or use of falsified data. Plagiarism includes (but is not limited to) failure to indicate the source with quotation marks or footnotes, where appropriate, if any of the following are reproduced in the work submitted by a student: 1.A graph or table of data. 2. Specific language. 3.Exact wording taken from the work, published or unpublished, of another person."

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Jeopardy 1 1. A domain wall 4. Has low mobility because it is composed of dislocations. A1. What is the boundary between two regions whose magnetization lies in different directions? A4. Why is a low angle GB difficult to move? 5. Nabarro-Herring Creep 2. Discontinuous transformation A2. What type of transformation is recrystallization an example of? A5. What type of deformation is controlled by diffusion in the bulk? 3. Continuous transformation 6. Lamellar microstructure A3. What type of transformation is grain growth an example of? A6. What type of microstructure does a eutectoid reaction often give rise to?

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**Jeopardy 2 1. 4th rank tensor 4. Use the dot product.**

A1. What kind of property is anisotropic elasticity? A4. How can we determine the direction cosine between two vectors? 2. Temperature divided by melting point 5. Close packed direction A2. What does homologous temperature mean? A5. How can we identify the direction of slip in a crystal (Burgers vector)? 3. Tangling and storage of dislocations 6. Critical resolved shear stress A3. What causes work hardening? A6. What controls the onset of plastic flow (dislocation glide)?

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**Jeopardy 3 1. Magnetization is parallel to <100>**

4. The maximum flaw (crack) size is limited by the fiber size. A1. To what directions does magnetoxtalline anisotropy limit magnetization in domains in Fe? A4. Why does the strength of glass fibers increase as the diameter goes down? 2. Orowan bowing stress 5. A balance between energy required to create new crack surface and elastic energy released. A2. What do we call the stress required to force a dislocation past a set of hard obstacles? A5. What energies do we examine in order to derive the Griffith equation? 3. Small enough fibers (whiskers) can be dislocation free 6. E/2π A6. What is an estimate of the theoretical cohesive strength of a crystalline solid? A3. Why do very thin metal wires/whiskers exhibit very high strengths?

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**Jeopardy 4 1. Who is the funniest professor in MSE? 4. E100 and E111.**

Q1. I’m not going to say! Q4. In cubic materials, which pair of directions exhibit the largest and smallest modulus? 2. Controlled by diffusion along grain boundaries. 5. Cleavage fracture. Q5. What type of fracture leads to flat fracture surfaces, often crystallographic? Q2. What is the mechanism for Coble creep? 3. Size increases as the yield stress goes down. 6. Cup and cone. Q6. What is the term often used to describe ductile fracture in a tensile test? Q3. How does the plastic zone size depend on yield stress?

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**Jeopardy 5 1. Leak before break**

4. It works by dispersing a metastable second phase through the material that transforms in the vicinity of a crack tip. Q1. What is the design philosophy often applied to pressure vessels? Q4. How does transformation toughening work? 2. Which professor is the best tennis player in the dept? 5. Flat, crystallographic surfaces with “river lines.” Q5. What fracture morphology do you associate with brittle fracture (in metals)? Q2. Fruehan 3. Micro-cracking 6. Too large particles will transform on cooling, before any stress is applied to them. Q3. Which toughening mechanism in ceramics relies on a weak second phase? Q6. Why is there a critical size for particles for transformation toughening?

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**Jeopardy 6 1. Each phase experiences the same strain**

4. Upper bound in strength. Q1. What does isostress mean in estimating the modulus of a composite? Q4. What do we call the limit that specifies the maximum value of a property? Q2. What was originally housed in the clean room in Hamerschlag basement? 5. High modulus and simple lattice. Q5. What properties of non-metallic materials are associated with high thermal conductivity? 2. A coal-fired power plant 3. The modulus is the arithmetic mean of the component moduli. 6. Ductile-to-Brittle-Transition-Temperature. Q3. What average does the isostrain model lead to for composite modulus? Q6. What is the temperature at below which many materials become brittle?

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**Jeopardy 7 1. Diamond>AlN>SiC 4. Rule of Mixtures.**

Q1. Name three adamantine compounds that are excellent thermal conductors and their ranking? Q4. What rule can we apply as a first approximation to composite properties? 2. Where is the least politically correct inscription on a CMU building? 5. Reuss, Voigt Q5. What names are associated with the isostress and isostrain assumptions for composite modulus? Q2. On Margaret Morrison! 3. Hill average 6. K = C v l. Q3. Whose name is associated with the average of the isostress and isostrain models? Q6. What is the basic equation for thermal conductivity?

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**27-301 web site Go to neon.mems.cmu.edu Click on Faculty**

Click on Rollett Click on Educational Activities Click on (bottom of the list) Download powerpoint, word files of lecture notes*, lab manuals, homeworks etc. Blackboard will have on-line gradebook, quizzes. is the link for feedback on course outcomes (ABET). * lecture notes are only preliminary until the day of the lecture!

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Homework, Test Review Mid-course Test/ Q1. What is the rule for determining the slip direction in a close-packed material?Close packed directions have the smallest Burgers vector and therefore correspond to the direction of slip. Mid-course Test/ Q4. For a steel with 0.8% carbon (by weight), sketch the microstructures that you would expect to observe based on the following thermal histories.(a)Slow cooled (normalized)(b)Quenched from 1030K (into water)(c)Quenched from 1030K (as in part b), then tempered (annealed) at 820K.(d)Quenched from 1030K (as in part b), then tempered at 970K.

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**Homework, Test Review, contd.**

Mid-course Test/ Q8. [10 points] A specimen of Al and a specimen of Fe are deformed to the same stress at room temperature. The shear modulus of Al is ~ 27GPa, and the shear modulus of Fe is ~80 GPa. Assume that the Taylor factor is the same in both materials. The Burgers vector of Al is nm and the Burgers vector in iron is nm. Assume that any other constants are unity.(a) What is the ratio of their dislocation contents (densities)? Express your answer as (Al):(Fe) = x:y(b) Based on your answer to (a), what is the ratio of the stored energies in the two specimens? Express your answer as E(Al):E(Fe) = x:y.Answer: (a) the ratio of dislocation densities is given by (Al):(Fe) = (GFebFe/GAlbAl)2 = {(80x0.249)/(27x0.283)}2 = {2.607}2 = 6.80(b) The ratio of stored energies is given by the ratio of shear moduli; E(Al):E(Fe) = GAlbAl2Al: GFebFe2Fe = (GAlbAl2/GFebFe2) x (GFebFe/GAlbAl)2 = GFe/GAl= 80/27 = 2.96.

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Homework 4 Review, contd. HWK4/ Q1e. The orientation of several grains has been characterized in a polycrystal: their orientations with respect to the tensile axis are [259], [001], [011] and [111]. Calculate their Schmid factors and calculate their average in order to estimate the yield stress of the polycrystal. Answer: the average Schmid factor = ( )/4= Therefore the polycrystal should yield at 190/0.405 = 469 MPa. HWK4/ Q2a. The expected answer was that the Orowan stress would become larger than the Hall-Petch stress. This suggests that generating/nucleating dislocations inside each grain will eventually become more difficult than propagating them from one grain to the next. HWK4/ Q2b. The expected answer was that you would find out that the creep rate is far too large for the high strength at small grain size to be useful!

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Homework 3 Review HWK 3/ Q4. The “Goss” orientation, {110}//ND, <001>//RD, was chosen so as to place a soft direction in the rolling plane which itself is a low index plane. This simplifies the domain structure considerably. It also is representative of a technologically significant material, i.e. transformer steel. HWK 3/ B:Q1. The difficulty here is (a) to associate matrices with symmetry operations and (b) to do the matrix arithmetic correctly. Much better to use a Math package. Training in Mathematica needed? B2. [10 points] (a) The thermal conductivity of a material has been measured ….. (b) Comment on how you might design such an experiment. Hint: a sketch would be useful. The key here is to realize that you must impose the thermal gradient in one direction and simultaneously measure the heat flow in different direction!

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Labs Lab 1 = Investigation of recrystallization with measurement of grain size (comparison of area versus line intercept methods). Purpose of the lab: illustration of basic method of influencing microstructure development, microstructure quantification. Lab 2 = Investigation of mechanical properties as a function of microstructure, as illustrated by different heat treatments of two steels. Purpose of the lab: learn about how strongly microstructure affects properties in a classical (and useful) system. Also to learn how to quantify (mechanical) properties.

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301 Lab 2 Grading The grading will be according the following: - 35% presentation skills (facing the audience, speaking clearly, explaining each slide…) - 20% technical content of presentation (correctness of introduction, procedures, results, discussion) - 20% answering questions from audience and instructor - 25% quality of the slides set (as the written documentation of the Lab report): this part of the grade is common to all members the group if a single submission is made by the group.

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**Test, Exams, Grading Policy**

Homeworks: 1 per week 100 points Quizzes: 1 per week 20 points Exams: two: see weighting below Grading Policy A > 85% B > 75% C > 65% D > 55% The instructor will request an Oral exam in borderline cases. Weighting (%): Homeworks 15 Quizzes 5 Lab 30 Exams 50 Notes: the distribution between the two exams is to be determined. The quizzes are mainly there to encourage students to stay on top of the material. The 30% weighting for the Lab (or Project) reflects the number of units assigned to the Lab part of the class.

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Calendar: 301 See the 301 Calendar posted on the website

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Exam Rules Mid-course test on Friday 27th; Final exam on Oct. 18th (AM). Topics for 27th: microstructure; grain growth; recrystallization; stereology; relating microstructure to phase diagrams; examples of microstructures in steel as a function of thermal history; magnetism (especially soft ferromagnetic materials); domains and domain walls; grain size (Hall-Petch, N-H creep); dislocations, plastic yield (Orowan bowing stress); critical resolved shear stress; Taylor equation; creep (Nabarro-Herring, Coble); Griffith equation. No books; no lecture notes; no computers One “cheat sheet” with notes (both sides if you like); hand in the the cheat sheet with the exam paper/book. Calculator OK

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**Mid-course evaluations**

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**301 Final Exam Rules Exam on Friday Oct. 18th.**

Topics for final: all topics discussed in class. A few topics were for information and do not need to be understood in detail (effect of symmetry on 4th rank elastic tensor properties; anything in the handouts that was not discussed in class). No books; no lecture notes; no computers One “cheat sheet” with notes (both sides if you like); hand in the the cheat sheet with the exam paper/book. Calculator OK

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**301 Final Exam: topics You may safely neglect the following topics:**

[to be posted]

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