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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 bodycentered 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" Nitv 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'FWugonMbowdé 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 : 8HXIOuCopprww/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 caseharden 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 steadystate 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 highpressure 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 ELLf5 jgwrg'l' law 3 :— —:D C14" CB
994 353
3,} brink C)4 {wLe 410M awhwwWengwam 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 facecentered cubic
crystal or a bodycentered cubic crystal? Why? (4 points) TM W agjlww) 0% Can beefﬂuvlfw M”? We 9““? WW?) so smlﬂa/ 44w mm aLa; (cm. A“: HWWM? Mhhﬁﬂmomweamlg. 0.52
0.3+. Question 7 Define and label the following on an engineering stressstrain curve
(9 points) (UToughness: 75% am Wow4W 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) FracturefRuptme 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 _ ‘ AOiﬂovoLlUH“ A An 3C?) 801—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 facecentered 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‘ﬂtIhs ...
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 Summer '08
 McKittrick

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