ES-260 Practice Final Exam Fall Name: St. No. Problems 1 to 3 were not appropriate for the current course coverage.

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1 ES-260 Practice Final Exam Fall 2014 Name: St. No. Circle correct answers All Questions worth 4 pts each. The True and False section at the end are bonus questions worth 1 point for a correct and -1 point for an incorrect answer. Only mark those bonus answers you are sure of because it can hurt you if you guess and guess wrong!!!! Problems 1 to 3 were not appropriate for the current course coverage. 4. Which of the following is NOT a hardening or strengthening mechanism in metals: (a) (b) (c) (d) (e) Grain Size Reduction Solid Solution Cold Working Coherent Phase Precipitation High Temperature Soak with Furnace Cool Answer : E

2 5. The most common slip system for single crystal silicon (diamond cubic) is <110> directions on {111} planes. A silicon crystal is subjected to a tensile stress of 15 MPa. The active slip plane is the (111) plane and the angle between the normal to the slip plane and the tensile axis is 35 o. If the angle between the tensile axis and the slip direction is 65 o and the critical resolved shear stress is 5 MPa, will the sample yield? (a) (b) YES NO 6. Compute the electrical conductivity of a 7 mm diameter cylindrical silicon specimen 55.1 mm long in which a current of 0.25 A passes in the axial direction. A voltage of 24 volts is measured across two probes that are separated by 44.5 mm. The electrical conductivity is (a) 2.2 (W*m) -1 (b) 12 (W*m) -1 Answer : A (c) (W*m) -1 (d) 0.08 (W*m) Answer : B (e) none of the above 7. A structural component in the form of a wide plate is to be fabricated from a steel alloy that has a plane strain facture toughness of 100 MPa*m 1/2 and a yield strength of 200 MPa. The flaw size resolution limit of the flaw detection apparatus is 2.0 mm. If the design stress is one half of the yield strength and the value of Y is 1.0, will a critical flaw for this plate be detected? A. YES B. NO Answer : B 8. Determine the maximum elastic shear strain that could possibly be observed in an incompressible (constant volume) metal rod subjected to an applied tensile stress of 100 MPa. Young's modulus, E, of this alloy is 300 GPa. Remember that τ = σcos( λ) cosϕ ( ). (a) γ = (b) γ = (c) ε = (d) none of the above Answer : A

3 9. Calculate the drift velocity of the free electrons in copper and with this velocity calculate the length of time a typical free electron would take to move along the entire length of a 1 meter long spool of wire under a voltage gradient of 0.5 V/m? It is known that the electron mobility in copper, m 2 μ e = Vsec (a) t = 0.28s (b) t = 3.57s (c) t = 14.29s Answer : C (d) t = 0.07s (e) none of the above 10. The outer surface of a steel gear is to be hardened by carburization. A diffusion heat treatment at 600 C (873 K) for 10 minutes increases the carbon concentration to 0.75 wt% at a position 0.1 mm below the surface. Estimate the diffusion time required to achieve this same concentration at a depth of 1.0 mm below the surface of the gear. Assume that the surface concentation is constant. (a) t = 75min (b) t = 600min (c) t = 100min (d) t = 1000min Answer : D (e) none of the above

4 Use this Hafnium-Vanadium phase diagram for questions Upon cooling from 2000 C, at what temperature does the first solid begin to form in 25 wt % Hf, Hf-V alloy? (a) 1520 C (b) 1850 C (c) 1450 C (d) 1190 C (e) none of the above Answer : B 12. For a 25 wt % V, Hf-V alloy, what is (are) the composition of the phase(s) in equilibrium at 1100 C? (a) (b) (c) (d) (e) 25 wt% V 37 wt % V and 96 wt % V 1 wt % V and 36 wt % V 65 wt % V none of the above Answer : C 13. For a Hf-V alloy, what is the overall composition of the ahf - HfV 2 eutectoid mixture? (a) 66 wt% V (b) (c) (d) (e) 18 wt % V 34 wt % V 82 wt % V none of the above Answer : E

5 14. When the b phase decomposes on cooling it decomposes in (a) (b) (c) (d) (e) a peritectic reaction a eutectic reaction a peritectoid reaction a eutectoid reaction a nonequilibrium reaction Answer : D 15. When the b phase decomposes into a and HfV 2, the mass fraction a is (a) 0.18 (b) (c) (d) 0.82 (e) none of the above Answer : D 16. Which statement is true? (a) (b) (c) (d) Vanadium is polymorphic Vanadium and Hafnium are polymorphic Hafnium is polymorphic Neither Vanadium nor Hafnium are polymorphic Answer : C

6 For questions 17 to 19 use the aluminum-copper phase diagram below. A B C D 17. Alloys A, B, C and D have differing microstructures on cooling. Which of the alloys will permit formation of Guinier-Preston zones, q'', and q' to permit precipitation hardening? (a) A (b) B (c) C (d) D Answer : A 18. What is mass fraction proeutectic phase in alloy B? (a) 0.70 (b) 0.52 (c) 0.30 (d) 0.48 Answer : D 19. Alloys A, B, C and D have differing microstructures on cooling. On cooling, which of the alloys underwent a peritectic reaction to form a single phase? (a) A (b) B (c) C (d) D Answer : D

7 20. Steady-state creep data taken for a stainless steel at a stress level of 70 MPa are given as follows: ε s = Kσ n exp -Q kt ( ) - 1 ε s hr T( K) If it is known that the value of the stress exponent n for this alloy is 7.0, compute the steady state creep rate at 1250 K and a stress level of 50 MPa (a) 0.02 hr -1 (b) hr -1 (c) hr -1 (d) 2.5 hr -1 Answer : B 21. The correct Miller indices for plane B are: (a) (1/2 1/3 0) (b) (3 2 0) (c) (1/3 1/2 0) (d) (2 3 0) (e) none of the above 22. The second X-ray diffraction peak for W (BCC) occurs at 2Q = 58 o. If the x-ray wavelength of nm, what is the lattice parameter for W? (a) 0.175nm Answer : D (b) 0.5 nm (c) nm Answer : C (d) 0.48 (e) none of the above

8 23. A tensile test specimen of a viscoelastic polymer was suddenly pulled in tension to a measured strain of 0.5; the stress necessary to maintain this constant strain was measured as a function of time. Determine the relaxation time, τ, if the initial stress level was 10 MPa which decreased to 0.5 MPa after 30 s. (a) (b) (c) (d) 5 s 10 s 20 s 50 s Answer : B (e) none of the above 24. For a eutectoid steel, cooling regime (a) will result in a microstructure consisting of (a) 50% martensite - 50% bainite (b) 50% tempered martensite - 50% bainite (c) 100% tempered martensite (d) 50% martensite - 50% tempered martensite (e) none of the above Answer : B 25. For a eutectoid steel, cooling regime (b) will result in a microstructure consisting of pearlite, martensite and bainite, True or False? (a) true (b) false Answer : B

9 Bonus Questions (up to 12 points either way + or -) True or False Circle T or F. CAREFUL WRONG ANSWERS count against RIGHT ANSWERS. Hot working of metals can only be achieved above the glass transition temperature. T F Resilience is elastically recoverable energy. T F Metrology is the study of size. T F It takes three active slip systems (slip plane - slip direction pairs) to completely deform an internal grain of metal. T F Nanoscale materials have at least two dimensions between 1 and 20 nm. T F Tensile strength of a polymer increases with its number average molecular weight. T F Modulus and strength of a ceramic material increases as its porosity increases. T F In a binary system, an invariant reaction always involves three phases. T F The modulus of elasticity of elastomers increases with increase in temperature. T F The yield strength of Cu decreases as its grain size increases. T F Cold working or strain hardening increases the density of vacancies and line defects. T F As the hardness of an alloy increases the yield and tensile strengths increase. T F

10 n := m - 3 q := C μ n := 0.14 μ p := m 2 voltsec m 2 voltsec ( ) σ := nq μ n + μ p σ := σ = ( Ωm) σ = σ := σ = 400

11 τ := 15cos( 35deg) cos( 65deg) τ = E I ρ I := 0.25 l = A E := 24 l := A := π l I σ := A E σ = MPam = 100MPa πa c m π a c := 1m π a c = m E := 300GPa G := E 2( ) τ := τ50mpa γ := G γ =

12 E J := nq μ l v := 0.14 m2 Vs 0.5 V m v - 1 = m - 1 s x 1 t1 = x 2 t min = min

13 C o := 7 C α := 1 C γ := F α := F α = 0.824

14 = 0.481

15 10-5 = K70 7 exp -Q K70 7 -Q = exp -Q ln( 250) = Q := = K70 7 exp K := e := exp e = d := nm 2sin 58 deg 2 d = m a := d 2 a = 0.226nm a := d 11 a = m

16 .5 = 10exp -30s τ s