Midterm_GENG2190_W2023_solutions

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Page 1 of 10 UNIVERSITY OF WINDSOR FACULTY OF ENGINEERING Department of Mechanical, Automotive and Materials Engineering Engineering Materials Fundamentals GENG2190-1/2, Winter 2023 – Dr. J. Magliaro Midterm Examination (this examination is the property of Dr. J. Magliaro) Date: Tuesday February 28 th , 2023 Examination Time : 6:30pm to 8:20pm – 110 minutes Please note that: 1) This examination has a MC and T/F section, Part I, followed by two (2) multipart problems, Part IIa and IIb. Turn off and remove all cell phones, other communication devices and any other articles from your possession/test location during the Examination Time . This is an individual examination, you are expected to be working alone during the entire period of the Examination Time and Time for solution submission . 2) This examination is closed book/notes. Do not ask the Instructor or GAs any questions during the exam as no further information will be provided. Please also note the information contained on the la st page of this exam under the heading “Useful Equations”. You are free to use any calculator during the exam provided it is not accessed through a laptop, cellphone or comparable communication device. 3) Make and state any assumptions you feel necessary in your solution. This statement is often overlooked by many undergraduate engineering students. Your exam will also be evaluated based upon your assumptions and the clarity/professionalism utilized in writing your solutions. 4) This examination is worth 35 % of your final grade . Individual question grading is provided on this sheet and above each major section of the exam. NAME STUDENT ID Part I [15 marks] Part IIa [15 marks] Part IIb [15 pts] Total [45 pts]

Page 2 of 10 Part Ia: Multiple choice [1 mark each] 1. Plastic deformation by slip is associated with which type of motion: a) Grain rotation b) Shear (relative sliding) c) Axial (tension/compression) d) Bending 2. Ductile material failure occurs by three primary mechanisms, listed in order as: a) Void nucleation > Void growth > Void coalescence b) Void growth > Void nucleation > Void coalescence c) Void coalescence > Void growth > Void nucleation d) Void nucleation > Void growth > Crack propagation 3. The correct units for stress are as follows: a) N/m 3 b) MN∙m -2 c) kJ/m 2 d) Pa∙m 4. The correct ordering for classes of materials, from least to most stiff, is as follows: a) Polymers < Metals < Ceramics < Composites b) Ceramics < Metals < Composites < Polymers c) Metals < Composites < Ceramics < Polymers d) Polymers < Composites < Metals < Ceramics 5. Identify/select the least ductile material: a) Material A: %RA = 32 % b) Material B: %RA = 24 % c) Material C: %RA = 62 % d) Material D: %RA = 11 % 6. Calculate the cell edge length, a , of sodium assuming a BCC crystal structure, atomic mass of 23.0 g/mol and density of 0.97 g/cm 3 . a) 4.29 ∙10 -4 μm b) 4.29 ∙10 3 pm c) 4.29 ∙10 -12 m d) 4.29 ∙10 -10 mm

Page 3 of 10 7. Further to the previous question, estimate the atomic radius of sodium. a) 1.86 ∙10 -10 mm b) 1.86 ∙10 -2 nm c) 186 pm d) 1.86 ∙10 -12 m 8. Which of the following is an example of a ceramic material: a) Crude oil b) Lithium c) Quartz d) Concrete 9. In the above image, points A, B and C (in this stated order) coincide with the phenomena of: a) Yielding, fracture and necking b) Fracture, necking and yielding c) Necking, yielding and fracture d) Yielding, fracture and necking 10. A 3 mm-diameter steel cable ( E = 207 GPa, α = 9. 0∙10 -6 o C -1 ) has a length of 500 mm and is suspending a fixture above the floor with 1.5 mm of clearance at room temperature. What is the minimum increase in temperature, ΔT , required for the fixture to touch the floor? a) 1100.0 o C b) 333.3 o C c) 33.3 o C d) 167.6 o C

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Page 4 of 10 11. Which of the following engineering applications does not generally rely on ceramics: a) Semiconductors b) Buildings and infrastructure c) Vehicle frames d) Lenses and optics 12. Which of the following is not a strengthening mechanism for metals: a) Plastic deformation (cold work hardening) b) Grain refinement via heat treatment c) Solid solution alloying d) Annealing 13. Which statement about grain boundaries is incorrect: a) A greater frequency of grain boundaries impedes dislocations within a crystal b) Diffusion occurs more readily at grain boundaries c) Defects such as impurities are found in greater concentrations at grain boundaries d) Grain boundaries are a planar-type defect 14. The correct stacking sequence for the FCC crystal structure is as follows: a) ABABAB… b) ABCABC… c) AAAAAA…. d) ABCABABC… 15. Which of the following crystal defects is shown in the above image? a) Twinning b) Grain elongation c) Edge dislocations d) Stacking faults

Page 5 of 10 Part Ia: True/False choice [0.5 marks each] Indicate whether the provided statements are true (T) or False (F) in the provided spaces. 1. Cartridge brass is a Cu-Zn alloy which is generally produced through interdiffusion. 2. Wood, nacre (“mother of pearl”, the material seashells are comprised of), peanut shells and corn husks are all examples of natural composites. 3. FCC metals tend to be more ductile than BCC and HCP metals because they possess more slip planes and close-packed directions. 4. Carbon atoms are normally present as substitutional atoms in steel alloys. 5. Work (strain) hardening is the tendency for a given material to experience an increase in strength, post-yield, from the yield stress up to the tensile stress. 6. Interstitial atoms, vacancies and substitutional impurities are all examples of point defects. 7. Materials generally form with monocrystalline structures. 8. FCC and HCP crystal structures have the same atomic packing factor (APF) and coordination number (CN). 9. Polymers are exclusively a synthetic material (i.e., there are no examples of naturally occurring polymeric materials). 10. The Hall- Petch effect refers to the tendency for a given material’s yield strength to decrease as the grain size decreases.

Page 6 of 10 Part IIa: Question #1 [15 marks] A guy-wire supporting a power line must withstand 250 kN tensile loads during extreme weather and cannot experience more than a 6 mm change in its tensioned (initial) 6 m length due to thermal expansion and/or contraction from seasonal temperature changes, which vary from -15 o C to 35 o C. Three candidate alloys are being considered as the base material for this wire, summarized in the table below. Material Elastic modulus, E [GPa] Yield strength, σ Y [MPa] Thermal exp. coeff. [ o C -1 ] s o [MPa] k d [ MPa√m ] 316L steel 210 580 9.0 ∙ 10 -6 164.0 1.91 Ti-6Al-4V 114 880 8.5 ∙ 10 -6 675.5 0.23 7075 Al 72 500 2.3 ∙ 10 -5 108.3 16.10 Conduct the following analyses: a) Which material is the stiffest compared to the others, which material is strongest and which material is least resistant thermal expansion/contraction? Briefly (no more than one sentence) justify your answers. b) Determine which of the candidate materials, if any, will not exceed the maximum allowable change in length due to thermal expansion/contraction. c) Calculate the minimum allowable diameter(s) for the guy-wire if it were fabricated from the remaining, acceptable material(s). d) Estimate the average grain size(s) for each of the remaining, acceptable material(s). BONUS: If the guy wire is to be fabricated from all of the remaining materials but its diameter cannot exceed 20 mm, calculate the minimum allowable grain size (if necessary) after heat treatment for the affected material(s).

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Page 7 of 10 This page is intentionally left blank for your solutions to Part IIa (if needed).

Page 8 of 10 Part IIb: Question #2 [15 marks] Unknown material A is diffused into unknown material B, in two independent experiments and the data below this text is extrapolated. Process Diffusivity [m 2 /s] Temperature [K] Experiment A 6.22 ∙ 10 -20 473 Experiment B 2.60 ∙ 10 -17 573 Conduct the following analyses: a) If 1500 minutes were required to complete the diffusion process described in Experiment A, how many hours would be required for experiment B? b) Determine the diffusion constants, D o and Q d , for the unknown material pair. c) Identify the unknown material pair using the newly determined constants and the provided table. d) Given r = 0.143 nm, A = 27.0 g/mol and the number of atoms per cell (from part (c)) estimate the structural density of the host metal.

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Page 10 of 10 Useful Equations: Important constants N A = 6.02×10 23 atoms/mol k = 1.381×10 -23 kg∙m 2 /s 2 ∙K T [ o C] = T [K] – 273.15 R = 8.314 J/kg∙K 1 m = 10 3 mm = 10 6 μm = 10 9 nm Mechanics of Materials 𝜎 = ? 𝐴 𝜀 = ∆? ? ? 𝜎 ? = ?𝜀 ? 𝜈 = − 𝜀 ? 𝜀 ? = − 𝜀 ? 𝜀 ? 𝜀 ? = 𝜀 ?? + 𝜀 ?? %?𝐴 = 𝐴 ? − 𝐴 ? 𝐴 ? ∆? = ? ? 𝛼∆𝑇 %?? = 𝐴 ? − 𝐴 ? 𝐴 ? Atomic Properties of Materials ? ? = 4 3 ?? 3 ? 𝑐 = 𝑎 3 4? = √3 𝑎 ??? 4? = √2 𝑎 𝐹?? 2? = 𝑎 ?? 𝐴 ? = 4?? 2 ? = ? 𝑖 + ? ? 2 + ? 𝑐 8 ? = 𝑛𝐴 ? 𝑐 ? ? 𝐴?? = ? 𝑎???? ? 𝑐 Crystal Imperfections ? 𝑣 = ?? − ? 𝑣 ?? ln ? 𝑣 = ln ? − ? 𝑣 ?𝑇 ? 𝑣 = ?? − ? 𝑣 ?? Strengthening Mechanisms, Heat Treatment and Diffusion 1 ? 0.5 = ?? − ? ?? 𝐽 = ? 𝐴? 𝐽 ? = −? 𝜕? 𝜕𝑥 ? = ? ? ? − ? 𝑑 ?? ? 𝑌 = ? ? + 𝑘 √? 𝑧 = 𝑥 2√?? ? 1 ? 1 = ? 2 ? 2