mt_sol_A - T ' H ' E Materials Science and Engineering 564...

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Unformatted text preview: T ' H ' E Materials Science and Engineering 564 SIN—E fi'iza‘frgirr?5:755? , r r UNIVERSITY Midterm Exam A February 13, 2008 Instructions: /< E ’ Enter your course code here: You have approximately 50 minutes to complete this exam. Answer all questions. Write your answers in the spaces provided. Show starting governing equations and calculations in your work in order to receive paitial credit. You may use your single—sided sheet of personal notes and a calculator. The point values for each question are given below. Good luck! TOTAL: / 100 1/6 MSE 564 Midterm WI2008 Anderson-A 1. Computing Change in Volume (10 points) A cube With undeformed edge length equal to 1cm is deformed with a uniform strain state: 0.05 0.06 0.02 [eij]= 0.06 0.02 0.04 0.02 0.04 —0.03 What is the change in volume due to the uniform strain state? i:f0M (—QCW‘QI 9mm“ %N~es (fig/’3'} Eu '1’ €1,231” €33 50 AV: QoDLt' V0 T." O'OLFC‘MB \YLW ’ MY _‘ 2. Deformation in a Single Crystal of Copper {12 points) Table 1.3 of Hertzberg provides the elastic constants for a crystal of copper: 011 = 16.84 x 1010 Pa 0,2 = 12.14 x1010 Pa C44 = 7.54 X 1010 Pa sll = 1.50 x 104113.1-l 312 = 063 x 10*11 Pa‘1 S44 2 1.33 x 10‘11 Pa" A tensile stress 033 = 2 MPa is applied along the [001] direction. Determine the elastic strain state in the crystal. ink-QM +3) et- ‘: ' (react/1M3 miscri‘voFiL/‘e/lag'ific deity/Mathew. I; W‘suw‘ ouQ/j=’+040 (5' : " r M C ‘3 ZMPa 13 mast-eat, Wm Qt“ 1‘ 3&6}, go ": 1; 5 1: ~ l -—u -1 -v— “I $13 3 C 0.103 10 “Pa 3 (mPab=-Lze was £44514 53 '3‘ I/ 1 i “g o Gz=@c*3 = (emu-16%”) £20098) = “"74" '6 e :52“ o“ ' 5 ’53 3 90,434,363 1! O page 2/ 6pages total MSE 564 Midterm WI2008 Anderson—A Computing strain (13 points) In the figure below, the angle BOA is changed to B’OA’ due to deformation. Determine numerical values of as many components of strain as possible based on information in the figure. Leave blank any entries that cannot be determined. You may assume small strain theory. Note the axis labels in the figure. l l 20- 1 l ‘ l, I l l 1 l E _ l 10“ 1 5 V l I l l l w fl w w a w ,. 3A, 0— o F, AHLW y 0 10 26 Answer. ‘/.M,...«-» *\.\ Jr“ “if g a“ ~- = O r l O .07. « ex aw i“ ~— OVWj MC; { 043005 \.’\\£D\Q~ec§) $13 cm\y £9), {3:3er.113 camel. Q—{Q Cw AQQVMQQQL Ar t: 63*) t 3—93 7* Mfl'uj : 2' O : 0J0 3 T: L: ‘11.; z ‘ D‘lg MSE 564 Midterm W/2008 Anderson-A 4. Computing yield strength and onset of necking (10 points) a. Based on the information in the table below, what material is expected to have the smallest strain rior to neckin? Metal Stacking fault Strain—hardening Slip energy (ml/ml) exponent 11 character Stainless Steel < 10 ~0.45 Planar Cu ~90 ~03 Planar/ wavy ~0.15 Wav b. Provide a physical explanation in words to explain why this is the case. Do not use equations to explain. f:§5t1ég . a; ,, 3c: 3 e. ,3 36'? t” cLuQfiem. _ i” 3 J {as re,» ...._e§ses._ ,,M~e.a re; My ,, mesa/Lacs... «eyewvs. +2- < 5. Estimating true strain to failure (10 points) A bar with an initial circular cross sectional of radius r = 6 mm is strained in tension until it fractures at a neck. The cross section of the neck is also circular, but with a radius of 2 mm and the cross section outside the neck is circular, with a radius of 5 mm. Estimate the true strain to failure in the necked region. " ‘le We; we. w 'f,1«;éi:slfamhm tens, ,, _ mflWnMA-z ‘ N, “mummy NEW.“ .1 11"” t f Agwmm‘i AV” 0/ {’97 x in it 3 +5 \ Q \ A ' WWW—y.— 6‘“ W" figs: nil—E". : ,QAA TCQMMBL +3 I“ ETEM’QL "W szm)?’ “(t :- 2.2. Answer: Z page 4/ 6pages total MSE 564 Midterm WI2008 Anderson—A 6. Strengthening mechanisms (12 points) a. The table below lists solution strengthening as one type of strengthening mechanism for metals at room temperature. Complete the left column by adding two additional types of strengthening in metals at room temperature. b. The right column indicates that solution strengthening depends on the square root of solute concentration. In a similar manner, list the functional dependence of our additional mechanisms on a relevant microstructural/material parameter. Strenthening mechanism De endence solution strengthening (solute concentration)“2 ,- i“ la 3; mv‘ ‘ 12qu work (em shat-«Q kvwegfl {dmmcofim $®A9$jg3 d7.” .642. max/"re Czlr’ 5 => 7k. _ cyfl 2A bouwd sch/9M $4.3M" C r ' $‘%&\) Ml W du‘b' ‘ , \ 04% t w QJ/j 3 1 “‘5 O3 ,5 It vi Alsa- reo» S, cm a 7. Single Crystal Yield (12 points) A BCC crystal yields when the resolved shear stress acting on a {l 10}/<l l l> type slip system reaches 2 MPa. What magnitude of tension along a <100> type direction is needed to yield the crystal? T t szi 1 5 <Ho7<iu7 6‘7 ‘ 1 ['70] aftoo‘] (HQ C 0:] fl i] < Va T3511. . fleet!) g-H Qty, ll -~a «v.3. E ,3 5‘11 T 1 (it W5 5“: \jr-Qlé c—H : f: TCRSS 2' \fio- Answer: q (\A 17$ page 5 / 6pages total 8. MSE 564 Midterm W/2008 Anderson-A Miscellaneous T rue/False Questions (21 points) a. b. C. f. O a. Circle TRUE or FALSE as appropriate for each statement below. During primar slip, the tensile axis rotates toward the slip plane normal. f FALSE TRUE Eva) If the dominant deformation mechanism in a polycrystal is grain boundary (Coble creep, the creep rate is likely to halve if the stress is halved. m3 FALSE Solution strengthening of BCC iron using substitutional atoms (such as chromium) is more effective than one based on interstitial carbon. TRUE {EALSE 3 Whether or not an upper and lower yield point is observed in low carbon steels depends on te test temperature and strain rate. TRUE ' Ceramic materias are brittle at room temperature because they contain no dislocation . TRUE Polycrystliine etals generally do not exhibit an easy glide regime (regime l). i EUE )FALSE Texture development during rolling or drawing is generally not dependent on stacking fault energy. TRUE 2% ALSE“) W END OF EXAM page 6 / 6pages total ...
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This note was uploaded on 07/17/2008 for the course MSE 564 taught by Professor Anderson during the Winter '08 term at Ohio State.

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mt_sol_A - T ' H ' E Materials Science and Engineering 564...

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