ex_mid_1_f08_sol (1) - ME 382 Fall 2008 Mid-term 1 Monday,...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ME 382 Fall 2008 Mid-term 1 Monday, October 6, 2008 This is a closed book exam; students are allowed to use an unmarked copy of the ME382 data book. Answer all questions. Show all calculations (on this exam) for full credit. There are a total of 9 pages to this exam. Use a ruler/ straight edge to read from graphs for full credit (marks will be deducted for excessive inaccuracy or sloppy graphs associated with not using a ruler where appropriate.) 50/0 édn S wry/fl Name: Section: Honor Pledge: Question 1 A circular, hollow cylinder is made of an aluminum alloy with a yield stress of 180 MPa. It is subjected to a torque T = 150 Nm and a compressive load P = 12.0 kN. The inner radius of the cylinder is R, = 5.0 mm and the outer radius is R2 = 10.0 mm. The elastic modulus is 70.0 GPa and the Poisson’s ratio is 0.330. (a) What are the normal strains in the hoop and the axial directions? 0’9 €rr69 T D MPK 6 7' {(9:12QO MP“ (61- ? wile? U5N111_————--‘"‘V:_________'————-~—-—’- T, n V Z Ru, “(Rf—R?) 1(009’00051} 5b,c\3 MPC. 3‘5 HDWEE O O -v6—1 _ ._ ( C .- fix ‘ F t Y Y" I _’ a ‘5 r M v 4 {EFKQQVS Ea: EL¢I”V1W*61X E “(De/q 5 l O ’ 6 _$D.Q3€(o _ ‘_ {mom} 31: "if [61; v(§(/* qéfl ' é”- : '10; 4'25“ (a (b) What is the maximum shear strain? \ / K , '1 Max Smear S‘T‘f‘am as r32; tswfiam a; awedfl: (fin-r \ TVCRLH'QflJ (c . o T T19 " 15-: °L_._._____———-——————-—(\SOD MMO‘ “my q 1 total Ml’a. J '5 Tl" (cathooos‘Qm (35‘ — E 1 “1066‘ -: 19,32. (39$ 10,33) '1 Eli-zxolqeé’r "’5 3-3:?5'3 ' 7.2331651 a‘gctgeliSé-‘E C _. Eva; = awe—H Ewe-Rir-Zl‘ie'B E. L e'L‘ #7 image-3 53:59 “M92 RE’ +0 (81,- 5931‘4‘629 'b/m" WW El%\-atl.)\iyi&\l\arz3li= awe—3 (c) What is the safety factor against yielding using the von Mises yield criterion? GE? “50.9.3 MP4. 6":0’930 3 =9 {\k r a) :915l0l.q MPa.’ Tugfwso C61 “+69 = “SD'C‘E’ —. 45% we. (d) What is the safety factor against yielding (under von Mises) if the load P is tensile instead of compressive? OR) m we“) W; 6.1,: ‘51; “fl I ’ I '- ’2. '2, Cf: 0,1,4’65 _ "‘2 v-56 3 2" (6L 5%)) +191 -_; R6, L '2. "S— Question 2 An alloy is made from two elements: Bidenium (Ed) and Palinium (Pn). Bidenium melts at 1200 °C and exhibits two allotropes: a body-centered—cubic phase (a) above 900 °C, and a face-centered—cubic phase ([3) below 900 °C. The atomic mass of Bidenium is 28 g/g-mole. Palinium melts at 800 °C, and forms a hexagonal—close-packed structure. The atomic mass of Palinium is 56 g/g-mole. Palinium and Bidenium have no solubility in each other. They do, however, form a compound dePny which has a melting temperature of 1500 °C. The unit cell of this compound has a face-centered cubic structure with a Palinium ion at each corner and a Bidenium ion in the middle of each face. There is no solubility of either Bd or Pn in the compound. An alloy consisting of 20 % by weight Pn exhibits a eutectic reaction at 700 °C. An alloy consisting of 20 % by weight Bd exhibits a eutectic reaction at 600 °C. Using this information answer the following questions: What is the chemical formula of the compound dePny? Pm; 8 a] Bol Q :3 Q. , Fajflngidc [S Pm r, W b) Draw the phase diagram for the alloy. The axis indicating the composition should be in weight percent of Pn. Label all fields in this phase diagram. Belg?“ {s 53 2: Ammo/o Pm (3i '2 X); 5‘ 5 c) An alloy of 90 % Pn is cooled from 1000 °C. Sketch how you expect the temperature to vary with time. / o l K C\ /\ [000 A Coolie? Ema l5 wflUS-s N7W [V '7 " fix" £5713”! D (“€2.31 r QinQCw-i—J“ 600 1, W «X (6%" r {a 50% :{ d) l m3 of Bidenium is cooled from just above 900 °C. Calculate the new volume of the sample just below 900 °C. Assume that the ionic radius of Bidenium does not change during the phase transition. ghouls, 30am 5 C C‘ N 0/1; C“ I 2 Mam /U (fi- Oc; 437/06 573 '9‘” B€ic§w '50? if. ( . C if“ a ‘ ‘1': :1 53“ L; l» J V O V ' i 1’: 5’“ if.” V ‘5'“) MK ' ( k? ,9 {1" {K I z i '3 ‘ ~ ‘\ rm ‘V w ' (l y P I in \i I 5" if ~ 2’- / b t 9&8 :c c "3;; W J 4 ix “filmy/(2 4 x my. I, Q; l m“ 5:} (p 4 caeS—fgm 5 6 “if? m H“: F c” Question 3 A material has a simple cubic crystal structure. A plot of the potential energy of an atom against separation, is given below, along with a plot of the force between the two atoms at 0 K. You may assume that the vibrational energy of these atoms is given by kT, where k is Boltzman's constant, and T is the absolute temperature. 410£1 210'21 o 3 > 9 (D C m -210fl 410'?1 -610m 1 2 3 4 5 Separation (10-10 m) [— 410'11 3 10'11 2 10'11 E -11 g 1 10 0 LI. 0 -1 10‘11 -2 10'11 1 2 3 4 5 separation (10'10 m) a) What is the lattice parameter of this material at absolute zero FYO’VVV "U-AJL (Luna/7,37 W LAWK “f’”""ej‘QMA C . —I '30 (Rb 41M {M‘gfi Miflafl) LA 2 X 10 m A’t W FOA‘Nx/ t F 3. 42,1 b) Estimate the melting temperature of this material Film” "MA-L «antiwar; M, 1 42k “MAL 19a u a j , Em : d§.5x10'“3‘ 2: 23» .I Emj’kT’M 1'? -5.S>(Io' T 1" *1-38XID' 3K x7” “T 398,5K c) Calculate the thermal strain at 150 K. —2.3 Emm at» leak, E19, : kT : 4.32m”; xt‘a’o '3" 3-2.07 x 10"“ 3' Co"! V €4.15 0%» (LA::’V:"“fl “NANA “6'4” ’2’” '3'? K *" awfvfif‘fi :3 I l ‘ U ‘r. 3%,?JfiJW’mi/xhww 7 11150 :- _(’5_:Hé j. 1 ‘ q > x '0 m: Z-:)LXIO m 2.. . -w TVA/yuan}, flMWflm 2 Q 2': ( 2 fi "'“ 2 0)"?i’: m d) What is the theoretical strength of the material at O K ’H C’V QC 6 «WK-"t me c Shox {0 N MAE 3F / f 2_ 4:22, Men: 'Yb : (2x10 Ll m 2. Fiw 1 30ng fi. ,750 MFA j 1 kng {2 x H; m 9) Estimate the modulus of the material at 0 K F) E= 0"“ 15M? : LAP) d6“ :4! Afl/fln hr Vzvo . “A” - 0 ,JF .. 2 x. t w 1' “714- Jt“ ,f “MG F'frwv 1A? gvfr dz” Y’YD fi.%%“§wg ‘E: wazfl106’7‘h Z x 1 0'1!) ” a [15 80“ Wk the. #pr LGLA ,1. Maxi/(7&4) 6% A” W gnaw :1 .. n w 0 3, Ti“ LA 1M $6371. A?» WNW m 757C441: Vii/M23}: “Le LU GAA. A6 an" J 1 ...
View Full Document

Page1 / 9

ex_mid_1_f08_sol (1) - ME 382 Fall 2008 Mid-term 1 Monday,...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online