Exam2_solution - /MSE 201 Exam#2 Spring 2009 Circle your...

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Unformatted text preview: /MSE 201 Exam #2 Spring, 2009 Circle your section: Name (print) SIOIH+1 OA/ Sec. 1 WW (Yingling) Sec. 2 Tu/Th (Irving) I have neither given nor received unauthorized aid on this test. X (signature) No notes, books, or information stored in calculator memories may be used. Cheating will be punished severely. All of your work must be written on these pages and turned in. To receive full or partial credit on numerical problems, you must show your calculations in step-by—step fashion. Units must be shown when applicable and all plots must have labeled axes. Be sure that you read and answer all parts of each question. Multiple choice questions (3 points each): Carefully circle or write only one answer. 1. In steady-state diffusion, there is: a. a constant concentration gradient b. a constant driving force c. a constant diffusion flux .all of the above 2. Assuming steady—state diffusion, calculate the diffusion flux of carbon at 600 °C through a 2- cm 01- iron sheet if the concentration gradient 1s -0. 75 kg/m4. The activation energy is 0 83 eV/atom, andDo=6,'2x10 7m2/s ’ QJ = _” m a 5.2:05X1011:kg/(m s) ® = (Bodega/J 75F ) /0 A b. 2.57x10 kg/(m: s) = - _ ~11 K/7 7.":54X1012kg/(ms) x7 Z32 V 7S—Y'/0 gmoj‘ .3 77x1010 kg/(m s) 3. When solving for non-steady state diffusion, the concentration at x = 00 is: a. CS b. CX @c. d. not defined 4. Hardness is a measure of a material’s ability to: a. recover elastic strain @resist local plastic deformation c. resist corrosion d. resist elastic deformation 5. If a tensile stress of 50 MPa is applied to a material with E = 5 GPa and 0'y= 1 GPa, what is the strain? .001 (OM/9“ 0 0 / b. 0.001 5 = fall a ' c. 0.1 ¥,/ 6. Metal strengthening during cold work is a result of @an increase in dislocation density " . a decrease in a number of slip systems c. an increase in the grain size (1. segregation of impurity atoms at dislocations 7. Annealing at a temperature above the recrystallization temperature for an at least an hour will: a. have no effect on the properties gained by cold working everse the effects gained by cold work c. increase the effects gained by cold work d. none of the above 8. Which of the following is not a method for strengthening or hardening a material? a. grain size reduction b. alloying 0. cold working .annealing 9. In a ductile metal, necking typically begins to appear when: a. The yield strength is reached b. The material fractures The tensile strength is reached d. The material is strained to 0.002 10. Slip systems are: a. combination of different types of dislocations .combination of close packed planes and close packed directions c. combinati'On of crystal structure and microstructure d. combination of slip planes and strain fields 11. (BONUS — 6 points) A single crystal of a metal that has the FCC crystal structure is oriented such that a tensile stress is applied in the [100] direction. The critical resolved shear stress for this material is 0.5 MPa. Which slip direction is the most favorably oriented for the slip to occur on the (1 11) plane: a. [10-2] b. [111] .[1—10] c. [041] 12. Case hardening of a steel (Fe-C alloy) gear with initial concentration of 0.10 wt% C is accomplished by raising the composition 8 mm below the surface to at least 0.30 wt% C through a process called carburizing. An engineer has proposed elevating the surface concentration to 1.10 wt% c for 307.787 hours at 950 °c. NOte that 13(950 °C) = 1.6><10'11 mZ/s. IF POINT IS ‘CLOSE TO TABULATED VALUE YOU CAN USE VALUE FROM TABLE AND AVOID LINEAR INTERPOLATION. (a) (6p0ints) What is the final concentration at x = 8 mm? :7 Mfg) 2: 0.57a07 \ 4/, (b) (3 points) Based on your answer above, was the engineer successful in case hardening the device? Why? /l/0, 0.2770264 <a3 W173 ”LE4 [5 W amouwr‘ raga/wed 7L° accomfilli‘z‘ 71¢"! Wp/m’kf 13. (6 points) The diffusion coefficients for self diffusion are D(500 0C) = 2.4x10'12 mZ/s and D(900°C) = 1.7><10"° mZ/s. Calculate the activation energy in eV/atom. § IIII-I-II-I-I — III-Il-l-I-ll g Ill-IBE-Ii!-I 3 III-E-II-Ilfl- ‘ g I-IV‘I-I-II-“I Stress at which 3: I-n-I-I-II-l- dislocat:(1)1:ebegin to / 000 MPa 3; § III-I-I-I-EEE g~llllllllll s g Ill-I-II-II-Il °° Ill-II-I-I-I-I g I'll-I-I-IIIII or (a 0221/ 6 «148° III-IIIIIIII- Strain above which 3 III-I-I-I-I-I- deformation is' 0. 00? v "I........... , permanent . 9 III-I-I-IIIIII 1* ’0: ‘0 Sm What ‘5 . F‘ VIII-I-I-I-I-I change In length ' o _------------ when a stress of 250 o 0.004 0.008 0.0m. 0.016 0.020 0,024 MPa is applied? 7: m 4'”; Strain 20.007 27 A{ 3010/0“, Tensile strength {MPa} Yield strength (MPa) 15. A tensile load of 90,000,000 N is applied to single crystal cylinder of Al with radius of 18 cm. A slip system with a critical resolved shear stress of 450 MPa is aligned such that its surface normal and slip direction are both 45° from the applied tensile load. (a) (8 points) Calculate the resolved shear stress. ,z 90AM We», 75; Z722 449% WA ’ ~ “Hf/“4% 27mg 6” [77‘2‘ (/72 MPL (b) (4 points) Will slip occur? Why? /V0 T/L ZVVZ/qpa 4 V379 ”Nye 16. (15 points) An engineer is asked to design a material with a tensile strength of at least 300 MPa and a yield strength of at least 120 MPa while maintaining a ductility of 40 %EL. The proposed solution was a Cu-Ni alloy with composition of 25 wt% Ni. Using the graphs below, answer the following questions: so 60 400 '2 so .C 50 w w V‘ c» 40 300 g g 40 i9 39 30 200 3° (1 10 20 30 40 50 20 o 10 20 30 40 50 Nickel content (wt%) Nickel content (wt‘Y ) 180 25 (a) What is the yield strength of this alloy? 160 / 3 O M fk 140 20 E . . . z b What IS the tensfle stren h of thls allo ? a y 120 5 3 r0 MA 100 15 E )— (c) What is the ductility of this alloy? 80 10 b .. " 60 p A E L b 3 7/ o 0 10 20 30 40 so Nickel content (wt%) PROBLEM 17 continued ((1) Was the engineer successful? Why or why not? aria 142,; M4 M ’90- ”07L W 3 6;: >(éom/7o 7‘5>3er7< flail. 4 90/» (e) A second engineer annealed the material at the recrystallization temperature for an hour.’ Does the annealed material meet the requirements? Why or why not? No. KeefySWM‘A'vv flat/”34:1 Vtu (490% Co/p/ war/(”Mam AQLUL M7L A/(oy/ 0:7 17. (12 points) Draw the modes of fracture for the following types of materials pulled in tension. Ductile . Brittle Moderatel Ductile \/ W A m Constants and Equations for Exam #2 ...
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