Mae20 midterm_SAMPLE EXAM_solutions

Mae20 midterm_SAMPLE EXAM_solutions - 1 sou(77 0N5 Summer...

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Unformatted text preview: 1 sou/(77 0N5 Summer, 2008 SAMPLE EXAM MAE 20, Elements of Materials Science Mid —-term Exam 1. One page of notesfformula sheet allowed 2. The number of points is indicated next to the question Question 1 Define the term: atomic packing fi'actio'n. Show that the atomic packing Gk fi'action for a body-centered cubic (bee) crystal is 0.68 (or 68%) (10 points) V303) C. :Tf __ 1 ‘ c #APPUoC) fig, mafia/96% Question 2 (a) Determine the indices for the directions shown in the following cubic unit cell (8 points): “1" Nit-v 2 (b) Determine the Miller indices for the planes shown in the following unit cell (8 points): .. ----u-+y Question 3 Give a reason why covalently bonded materials are generally less dense than ionically or metallicaily bonded materials? (6 points) Cowl-(Mtg MAM Mahmw MM “with amt», Wale me wat- otmadt W ilt'FWugonMbo-wdé fidfiwmmmt— Question 4 Calculate the number of octahedral interstitial sites that uniquely belong to a face centered cubic unit cell? What are their 00- -ordinates? (7 points) 1 WM nuke} we Men ——1 19_ mm 011th manganese]; m; =3 Question 5 Calculate the concentration of vacancies in copper at room temperature (25 °C). What temperature will be needed to heat treat copper such that the concentration of vacancies produced will be 1000 times more than the equilibrium concentration of vacancies at room temperature? Assume that the activation energy is 20 Kcal/mole (8 points) and the lattice parameter for fee Copper to be 0.3615 nm. NM 04 Coffer mun/W : Arm/QM : 8-HXIOuCopprww/3 (93615 "Hoom’? 3’ [M “v”— W ”M 1%) (842119201) 61f)[:_________ “Now/M l ‘13? (a: 2ng lQ157L IO Vacaan,/Mg WW; 1.86M; /W= 7(3‘7‘2’ ma 2‘1)??? Ewing] ‘lsfi‘T elT ~13 3?5K I Questionfi (a) The objective is to case-harden a steel sheet to be used in a gear. The sheet of steel is 1.5 mm thick and has nitrogen atmospheres on both sides at 1200 0C, and is permitted to achieve a steady-state diffiJsion condition. The diffusion coefficient for nitrogen in steel at this temperature is 6 10 lln1$11r"sec,and the diffusion flux IS 1.2 10'? kg/m -sec. The concentration of nitrogen in the steel at the high-pressure surface IS 4 kg/m3. Determine how far into the sheet, from this high—pressure side, the concentration is 2 kgfm3? Assume a linear concentration profile. (8 points) Ust‘g ELL-f5 jgwrg'l' law 3 :— -—:D C14" CB 994- 353 3,} brink C)4 {wLe 410M awhwwWengw-am 9+Lg/m3,m Semi?) $Eh (KB) % IE): ‘XA + D [CA —-C5] {H— m JP»? (risk) ...._ locr. :Fcc (b) Is the value of the diffusion coefficient (D) of Carbon larger in a face-centered cubic crystal or a body-centered cubic crystal? Why? (4 points) TM W agjlww) 0% Can beeffluvlfw M”? We 9““? WW?) so s-mlfla/ 44w mm aLa; (cm. A“: HWWM? Mhhfiflmomweamlg. 0.52 0.3+. Question 7 Define and label the following on an engineering stress-strain curve (9 points) (UToughness: 75% am Wow-4W awe- 9" ”3"" “£5 }/ (AWE bl“ «£35m 9,4,7? Wm Raf/I‘M (2) Elastic limit 1% W} ohm»: 71h rye/@1549 [am MM W 0/? Mun/HQ wwwd— mm, 9W muffle W -W67/fl‘4 [Hvoluw [am {a worm pix 1140: W) (3) FracturefRuptm-e stress: : éoaol a)“ EFL—“lg Ongmafi Carma—$901M 6131420.. Stress C 5) Question 8 Prove the following two relations between the engineering stress (5), engineering strain (e), and true stress (0') and true strain (3). Assume that the volume of the material is constant. (8 pointS) 5’: jig and 61-“ 1—111 : l _[ (a)c=s(l+e) AD é [10 :6“: Fii:i.A‘° : fl _ ‘ AOiflovoLl-UH“ A An 3C?) 80-1—8) AL: Ania (b)8=ln(1+e) €= METJgJ—i LCHQ) Question 9 How many slip systems are there in a single crystal of the face-centered cubic (fcc) system. Draw one possible slip system. Indicate clearly the slip plane and the slip direcion.( oin . ., {A t :13 t5) ‘2 31‘? angle-«n 1H»? %H13<HO> :12 Question 10 Draw an approximate stress distribution near an elliptical holelcrack of longitudinal length 2 microns and a transverse length of 4 microns. What is the stress concentration factor? (6 points) 91505“ [MW in Aficfiy 6 Question 11 (a) What is the difference between a material failure by (a) fatigue, and (b) creep (6 (b) Suggest two ways to prevent fatigue failure (4 points) ae- ‘ (at) UM Wwimmfilw Wale/ml, ’7 W (W e Case mm . LC) flimwie flW “W/MW' @‘gkotwfigb‘fi (a) j‘fltI-hs ...
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