Matsci Exam 3- HW Questions

Given a 80 % Sn (20.0 % Pb) composition, what is the weight percent of alpha (α) phase at 182 °C. a). 85.3 b). 49.6 c). 22.4 d). 77.6

22.4

If 100.0 MPa is applied along [001] in a FCC crystal, the resolved shear stress magnitude for the slip system (in MPa) is a). 244.9 b). 57.7 c). 70.7 d). 40.8

40.8

Given a 30 % Sn (70 % Pb) composition, what is the best estimate of the Sn content (wt%) of the liquid at 184˚C? (A)18.3 % (B) 30 % (C) 61.9 % (D) 97.8 %

61.9%

A plate of glass is subjected to a tensile stress of 40 MPa. If the fracture surface energy, γs , and Young's modulus, E, are 0.30 J/m² and 69 GPa respectively, what is the maximum length, a, of a surface flaw (in microns) that does not cause fracture. a). 16.48 b). 329.6 c). 25.875 d). 8.24

8.24

The stress-strain curves A-C below were obtained from different polymers in uniaxial tension at room temperature (25˚C). Rank them in order of lowest to highest chain mobility. a). A < C < B b). C < B < A c). A < B = C d). A < B < C

A < B < C

Given an 40 wt% Si (60 wt% Al) composition in the eqiulibrium phase diagram shown, which phases are present at 650˚C a). (Al) and Si b). (Al) only c). Si and liquid d). (Al) and liquid

Si and liquid

A polycrystalline copper sample is loaded past its yield point to 1.5% tensile strain, then the load is released. We call this sample the "pre-stretched sample." We now reload this pre-stretched sample to a 1.0% tensile strain. Which of the following statements is correct? a). The new yield strength of the pre-stretched sample is higher than that of the original sample. b). The yield strengths will be the same in both cases. c). The new yield strength of the pre-stretched sample is lower than that of the original sample. d). Copper is brittle and cannot be strained a second time.

The new yield strength of the pre-stretched sample is higher than that of the original sample

Austenite to pearlite transformation is an example of: a). eutectic reaction: liquid-solid 1 + solid 2 b). peritectic reaction: solid 1 + liquid -solid 2 c). eutectoid reaction: solid 1- solid 2 + solid 3 d). none of the above

eutectoid reaction: solid 1- solid 2 + solid 3

Intergranular

fracture cracks along grain boundaries

Strength of ceramics

greater strength in compression than in tension

Identify correct statement about nucleation rates during solidification of liquid metal a). heterogeneous nucleation rates are higher than homogeneous nucleation rates at all undercoolings b). homogeneous nucleation rates are higher than heterogeneous nucleation rates at all undercoolings c). heterogeneous nucleation rates peak at smaller undercoolings than homogeneous nucleation rates d). homogeneous nucleation rates peak at smaller undercoolings than heterogeneous nucleation rates

heterogeneous nucleation rates peak at smaller undercoolings than homogeneous nucleation rates

Solidification of a metal takes place by formation of cubic nuclei of edge length, d. Given that γ is the surface energy and ∆Gv is the volume free energy, the expression for the edge length of a critically sized cubic nucleus, d*, is: a). -6γ/∆Gv b). −γ/∆Gv c). -2γ/∆Gv d). -4γ/∆Gv

-4γ/∆Gv

How to strengthen Materials

-Grain size reduction : grain boundaries restrict dislocation motion -Solid solution strengthening: addition of another element -Cold work: causes dislocations to become more entangled with one another, making dislocation motion difficult

Yield Strength (Y.S.)

.2% offset of elastic region (area with linear slope)

In the Cu-Ag eutectic phase diagram shown below, use the Gibb's phase rule to determine how many degrees of freedom there are at point (X). a). 0 b). 1 c). 2 d). 3

0

A 25 wt.%Sn alloy slow cooled from 300 °C to 180 ºC results in a microstructure consisting of primary alpha and a eutectic microstructure. What is the weight fraction of the eutectic microstructure? a). 0.92 b). 0.62 c). 0.08 d). 0.15

0.15

In the phase diagram shown, the number of degrees of freedom at O is: a). 3 b). 1 c). 2 d). 4 e). 0

1

Austenite with a carbon concentration of 0.01 wt% is cooled slowly from 1000°C to 700°C. What is the sequence of microstructures during the cooling process? a). 1-5-2-4 b). 1-2-7 c). 1-3 d). 1-8-6

1-5-2-4

Concrete can take up to ~26 MPa of compressive stress. The density of concrete is about 2.2 g/cm³. What is the height limit (in the unit of km) of a vertical concrete pillar to avoid exceeding the maximum compressive stress due to its own weight? For the acceleration of gravity use g=9.8 m/s². a). 1.57 b) 1.33 c). 1.45 d). 1.21

1.21

Given a 3 wt% Si (97.0 wt% Al) composition in the eqiulibrium phase diagram shown, what is the best estimate of the Si content (wt%) in α at 558°C. a). 1.6% b). 3.0% c). 100% d). 12.6%

1.6%

Recrystallization temp

1/3-1/2 of original temperature

A TTT diagram for the iron-carbon system at the eutectoid composition is shown. The final microstructure for path 1 is, a). 100% martensite b). 100% austenite c). 50% martensite and 50% austenite d). 90% martensite and 10% austenite

100% martensite

The final microstructure for path 4 is (A)100% martensite (B) 100% pearlite (C) 50% pearlite, 50 % martensite (D)50% bainite, 50% martensite

100% pearlite

A metal plate with a 0.8 mm deep surface crack is loaded in tension along the z axis. What is the maximum allowable stress (in MPa) that will NOT cause fracture? You may assume that the shape factor is 1. a). 34.7 b). 2.8 c). 87.2 d). 1097.1

1097.1

In the figure shown, a tensile stress, σ, is applied to a single crystal BCC specimen 45° from the normal to the slip plane and 60° from the slip direction. The critical resolved shear stress, τCRSS, for the material is 45.0 MPa. What is the minimal tensile stress (MPa) to be applied to this cylindrical specimen to initiate plastic slip for this slip system? a). 127 b). 153 c). 45 d). 16

127

Given a 30 % Sn (70 % Pb) composition, what is the weight percent of b phase at 182C? (A)14.7 % (B) 45.2 % (C) 54.8 % (D) 85.3 %

14.7%

A plate of glass is subjected to a tensile stress of 40 MPa. If the fracture surface energy, γs , and Young's modulus, E, are 0.30 J/m² and 69 GPa respectively, what is the maximum length of an interior crack (in microns) that does not cause fracture. a). 659.2 b). 16.48 c). 51.75 d). 8.24

16.48

The Avrami curves for the recrystallization as a function of temperature are shown. At which temperature is the nucleation time the longest? a). 135°C b). The nucleation time cannot be compared from this figure c). The nucleation time is the same at all temperatures d). 43°C

43°C

A high strength steel has a yield strength of 1500 MPa and a KIC of 100 MPa*m1/2. Calculate the size of a surface crack in the unit of mm that will lead to catastrophic failure of this material at an applied stress that is 50% of the yield strength. For this geometry, Y = 1. a). 5.66 b). 5.14 c). 4.72 d). 4.92

5.66

The final microstructure for path 2 is (A) 100% martensite (B) 50% bainite, 50% martensite (C) 50% pearlite, 50% martensite (D) 50% pearlite and 50% bainite

50% bainite, 50% martensite

A TTT diagram for the iron-carbon system at the eutectoid composition is shown. The final microstructure for path 3 is, a). 50% pearlite, 50% martensite b). 50% pearlite and 50% bainite c). 100% martensite d). 50% bainite, 50% martensite

50% pearlite and 50% bainite

A tensile stress, s, is applied to a single crystal fcc specimen 35° from the normal to the (111) plane and 60° from the [11I0] slip direction as shown. Calculate the minimal tensile stress to be applied to this cylindrical specimen to initiate plastic slip. The critical resolved shear stress for the material is 20.7 MPa. (A)50.5 MPa (B) 8.47 MPa (C) 50.5 GPa (D)8.47 GPa

50.5 MPa

Given the Pb-Sn phase diagram, the amounts of the phases at equilibrium at 184 C for a 100 g sample of an alloy with 35 wt.% Sn are: a). 78.99 g Alpha, 21.01 g Liquid b). 38.30 g Alpha, 61.70 g Liquid c). 61.70 g Alpha, 38.30 g Liquid d). 18.3 g Alpha, 61.9 g Liquid

61.70 g Alpha, 38.30 g Liquid

Given the Pb-Sn phase diagram, the compositions of the phases of 30 wt.% Sn alloy at equilibrium at 184 C are: a). Alpha - 61.9% Sn ; Liquid - 97.8% Sn b). Alpha - 18.3% Sn ; Liquid - 61.9% Sn c). Alpha - 61.9% Sn ; Liquid - 18.3% Sn d). Alpha - 18.3% Sn ; Liquid - 97.8% Sn

Alpha - 18.3% Sn ; Liquid - 61.9% Sn

Given the tensile fracture profiles shown, rank the materials from highest to lowest ductility a). A > C > B b). A > B > C c). B > C > A d). C > B > A A-Rectangular straight break B- Point Triangular break C- Oval, teethed break

B > C > A

For pure copper undergoing solidification in a graphite crucible which of the following is true: a). The rate of heterogeneous nucleation is always lower than the rate of homogeneous nucleation at all undercoolings b). The activation energy ΔG* for heterogeneous nucleation is larger than homogeneous. c). Copper nuclei forming heterogeneously on the crucible surface have the same critical size nuclei r* as nuclei forming in the bulk of the melt d). The rate of heterogeneous nucleation is always greater than the rate of homogeneous nucleation at all undercoolings

Copper nuclei forming heterogeneously on the crucible surface have the same critical size nuclei r* as nuclei forming in the bulk of the melt

Which of the following cannot be used to strengthen glass. a). Larger K+ ions replace Na+ ions at the surface causing a compressive stress and closing cracks. b). Decreasing the grain size to reduce dislocation mobility c). Quick cooling of the glass which results in a compression at the surface and tension in the bulk d). Etching in acid which removes small surface flaws and blunts larger cracks

Decreasing the grain size to reduce dislocation mobility

What causes slips?

Greater resolved shear stress than critical resolved shear stress

In lab we tested chemically strengthened glass. The principle behind this strengthening mechanism is a). Larger K+ ions replace Na+ ions at the surface causing compressive stress and closing cracks. b). The ion exchange process increases the surface energy of the cracks, thus increasing the fracture toughness. c). Replace all Na+ ions with larger K+ ions throughout the entire volume of the glass. d). Smaller Na+ ions replace K+ ions at the surface causing compressive stress and closing cracks.

Larger K+ ions replace Na+ ions at the surface causing compressive stress and closing cracks.

Which sequence represents the correct order of yield strengths for different steel microstructures (highest to lowest)? (A) Tempered Martensite > Martensite > Coarse Pearlite > Fine Pearlite (B) Martensite > Bainite > Coarse Pearlite > Spheroidite (C) Coarse Pearlite > Fine Pearlite > Tempered Martensite > Martensite (D) Martensite > Spheroidite > Fine Pearlite > Bainite

Martensite > Bainite > Coarse Pearlite > Spheroidite

For martensite, which of the following statements is false? The Fe-C phase diagram can be found on Page 7 (A) Martensite forms when austenite is rapidly cooled to room temperature. (B) Martensite is a non-equilibrium phase that does not appear in phase diagram. (C) Martensite can have a carbon concentration higher than 6.7wt%. (D) Martensitic transformation occurs almost instantaneously, as it does not require diffusion.

Martensite can have a carbon concentration higher than 6.7wt%

Which microstructure (1 to 5) has the greatest ductility and which one has the highest tensile strength? (A)Microstructure 3 (greatest ductility) and Microstructure 3 (highest tensile strength) (B) Microstructure 2 (greatest ductility) and Microstructure 3 (highest tensile strength) (C)Microstructure 3 (greatest ductility) and Microstructure 2 (highest tensile strength) (D)Microstructure 5 (greatest ductility) and Microstructure 3 (highest tensile strength)

Microstructure 3 (greatest ductility) and Microstructure 2 (highest tensile strength) 3- solid orange 2- orange and purple stripes with purple lines separating regions

Microstructures at 725˚C for cooling paths A and B? (A)Microstructure 2 for A and Microstructure 4 for B (B) Microstructure 3 for A and Microstructure 1 for B (C)Microstructure 3 for A and Microstructure 4 for B (D)Microstructure 1 for A and Microstructure 3 for B (E) Microstructure 4 for A and Microstructure 3 for B

Microstructure 3 for A and Microstructure 4 for B 3- Solid orange 4- Red and purple stripe with orange lines seperating regions

The initial flat portion of the S-shaped Avrami curve (shown) for any phase transformation corresponds to (A) Tempering (B) Nucleation (C) Annealing (D) Growth

Nucleation

For the TTT curves shown, which of the following is TRUE? (Assume the sample is just above the Eutectoid temperature prior to cooling) a). Quenching to and holding at 650°C favors the formation of a large number of nuclei which grow slowly, relative to doing so at 350°C. b). Quenching to and holding at 650°C favors the formation of a small number of nuclei which grow rapidly, relative to doing so at 350°C. c). Quenching to and holding at 350°C favors the formation of a large number of nuclei which grow rapidly, relative to doing so at 650°C. d). Quenching to and holding at 350°C favors the formation of a small number of nuclei which grow slowly, relative to doing so at 650°C. .

Quenching to and holding at 650°C favors the formation of a small number of nuclei which grow rapidly, relative to doing so at 350°C.

Importance of increased dislocations

Results in stronger material: - dislocations interact with each other more if there are more of them -More dislocations harder it is for them to move, which creates stronger material

Given a 30 % Sn (70 % Pb) composition, what is its most likely microstructure at 200˚C? (A) Blue and white stripes (B) Solid blue with red sprinkles (C) Solid Red with orange dots (D) Blue ad white stripes with blue dots

Solid red with orange dots

For a two-component system, three phases are in equilibrium under 1 atm pressure. Which of the following statement is true, (A)The composition of each of the three phases can be varied independently of the others. (B)The composition of only two of the phases can be varied independently. (C)The composition of only one of the phases can be varied independently. (D)The composition of each of the three phases is fixed.

The composition of each of the three phases is fixed.

The stress-strain curves A-C below were obtained from different polymers in uniaxial tension at room temperature (25˚C). Which of the following is true a). The relative order of elastic moduli are A ~ B < C b). The elastic moduli of A and B are almost identical with a value of ~3 GPa c). The elastic moduli of A and B are almost identical with a value of ~300 MPa d). A and B have elastic moduli of ~62 MPa and ~35 MPa, respectively.

The elastic moduli of A and B are almost identical with a value of ~300 MPa

Which of the following statements is TRUE? a). Toughness is directly proportional to the yield stress. b). Toughness can be obtained from the area under the elastic portion of the stress strain curve. c). Toughness can be obtained from the area under the interatomic energy versus distance curve. d). Toughness can be obtained from the area under the entire stress strain curve.

Toughness can be obtained from the area under the entire stress strain curve

BCC slip system

[110] <111>

FCC slip system

[111] <110>

Given a 30 % Sn (70 % Pb) composition in wt%, which phases are present at 200˚C (A)a only (B) b only (C) a and liquid (D) b and liquid (E) a and b

a and liquid

A small undercooling of a metal below its melting point will typically lead to (A) a high nucleation rate with few nuclei. (B) a high nucleation rate with many nuclei. (C) a low nucleation rate with few nuclei. (D) a low nucleation rate with many nuclei.

a low nucleation rate with few nuclei.

Resilience (Ur)

area under elastic region (linear slop area)

In steel, it is least likely to find carbon (A) near dislocations (B) at interstitial sites (C) as substitutional atoms (D) at grain boundaries

as substitutional atoms

Steel pipes can be protected from corrosion by: a). contacting with a Zn electrode b). connecting with the positive terminal of a battery c). applying thin coating of NaCl d). increasing the carbon content of the surface

contacting with a Zn electrode

heating a tugsten wire with 100 nm-grains and 4000 MPa yield strength increases the grain size 1.6 um. As a result you would expect the yield strength of this wire to: a). increase to 16000 MPa B). decrease to 1400 MPa c). remain the same d). increase to 8000 MPa

decrease to 1400 MPa

At 1 atm pressure which is true for the 2 phase region of the Cu-Ni isomorphous phase diagram a). degrees of freedom -2, vary temp and overall Ni composition b). degrees of freedom-2, vary temp but not overall Ni composition c). degrees of freedom-1, composition of two phases is fixed by choice of temp d). degrees of freedom-1, vary temp but not overall Ni composition

degrees of freedom-1, composition of two phases is fixed by choice of temp

Ionic crystals are brittle because a). A large number of disolcations prevents their movement b). the potential energy distance curve has low curvature c). dislocations are hard to create and hard to move due to charge neutrality considerations. d). it is difficult for dislocations to glide across directional bonds.

dislocations are hard to create and hard to move due to charge neutrality considerations.

Transgranular

fracture cracks across (or through) grains

Relationship between strength and ductility

increase in strength causes decrease in ductility. Increase in ductility causes decrease in strength.

Annealing cold-worked Cu at 600 would: a). increase its yield strength b). increase its elastic modulus c). decrease its ductility d). increase its ductility

increase its ductility

The thermodynamic driving force for forming a solid particle with a radius of 10 nm from a supercooled liquid at T (T < Tmelt) (A)decreases as T decreases. (B) is precisely zero at T = Tmelt. (C) increases as T decreases. (D) is independent of T.

increases as T decreases.

Rectangle to Rectangle break

material under stress was brittle (brittle fracture)

Triangle to Triangle break

material under stress was very soft

Tensile Strength (T.S.)

max of entire curve

Typically one would expect to observe a cup and cone fracture surface upon failure of : a). NaCl b). highly crosslinked epoxy c). mild steel d). single crystal Si

mild steel

In a Ni-3 at % Cu alloy single crystal, the slightly larger Cu atoms compared to Ni are most likely to be a). at the surface b). near an edge dislocation in the region containing the extra half plane c). near an edge dislocation in the region below the extra half plane d). at interstitial sites

near an edge dislocation in the region below the extra half plane

Edge dislocation

parallel to applied stress

Screw dislocation

perpendicular to applied stress

Which of the following is the preferred slip system in a BCC metal? a). slip plane:{100}; slip direction: <111> b). slip plane:{110}; slip direction: <111> c). slip plane:{111}; slip direction: <110> d). slip plane:{111}; slip direction: <100>

slip plane:{110}; slip direction: <111>

Young's modulus (E)

slope in linear elastic region

Failure Strain (Ef)

strain at failure after unloading

Decreasing the grain size to reduce dislocation mobility) a). strengthens the metal by inhibiting dislocation motion. b). weakens the metal by inhibiting dislocation motion. c). strengthens the metal by enabling dislocation motion. d). weakens the metal by enabling dislocation motion.

strengthens the metal by inhibiting dislocation motion.

Toughness (W)

total area under stress strain curve

Given a 30 % Sn (70 % Pb) composition, what is the best estimate of the weight percent liquid at 184˚C? (A)14.7 % (B) 26.8 % (C) 73.2 % (D) 85.3 %

26.8%

A high strength steel has a yield strength of 1600 MPa and a K1C of 100 MPa•(m)1/2. Calculate the size of a surface crack that will lead to catastrophic brittle failure of this material at an applied stress of one fifth of its yield strength. For this geometry, Y = 1. (A)0.00124 mm (B) 0.031 mm (C) 0.099 mm (D)1.24 mm (E) 31 mm

31mm

If solid copper (melting point of 1085°C) homogeneously nucleates at 849°C, calculate the critical radius. For copper, the latent heat of fusion is 1.77 × 108 J/m3 and the surface free energy is 0.600 J/m2 (A)6.78 nm (B) 19.5 nm (C) 31.2 nm (D)39.0 nm

39.0 nm

Of microstructures (3), (4), (6) & (7) shown, which has the highest ductility? a). (7) b). (4) c). (3) d). (6)

4

Given a 85.0 wt % Sn (15.0 wt % Pb) composition in the equilibrium phase diagram shown, what is the best estimate of the weight percent β at 184˚C? a). 64.3% b). 35.7% c). 85.3% d). 73.2%

64.3%

Figure shown is a stress vs. strain curve for a FCC metal specimen. The figure on the right is magnified to show the low strain behavior. Estimate the yield stress (σYS) in MPa using the 0.2% offset method. a). 75 b). 68 c). 55 d). 60

68

For a single crystal FCC metal, under uniaxial tension test along its [124] direction, the yield point is 150 MPa. The slip system is . Calculate the critically resolved shear stress of this particular metal, in units of MPa. a). 73 b). 80 c). 150 d). 66 e). 309.0

73

Figure shown is a stress vs. strain curve for a cylindrical FCC metal. The figure on the right is magnified to show the low strain behavior. Estimate the elastic modulus (E) in GPa? a). 60 b). 0.103 c). 75 d). 7.5

75

Given the Cu-Ag eutectic phase diagram shown, if you slowly cool a 27 wt.% Ag alloy from 1200 ºC to 778 ºC , we get: a). 70.16% Alpha and 29.84% Liquid, wherein Alpha has a composition of 92.1 wt.% Cu. b). 77.07% Alpha and 22.93% Liquid, wherein Alpha has a composition of 7.9 wt.% Ag. c). 70.16% Alpha and 29.84% Liquid, wherein Liquid has a composition of 71.9 wt.% Ag. d). 77.07% Alpha and 22.93% Beta, wherein Beta has a composition of 8.8 wt.% Cu.

77.07% Alpha and 22.93% Beta, wherein Beta has a composition of 8.8 wt.% Cu.

If copper (melting point of 1085°C) homogeneously nucleates with a critical radius of 50 nm, what temperature was it cooled to? For copper (63.55 g/mol), the latent heat of fusion is -1.77 × 108 J/m3 and the surface free energy is 0.600 J/m2 a). 1000.5°C b). 914.5°C c). 900.9 °C d). 937.9 °C

900.9 °C

The microstructures for cooling paths C and D at 725˚C are, (A)Microstructure 5 for C and Microstructure 5 for D (B) Microstructure 3 for C and Microstructure 4 for D (C) Microstructure 4 for C and Microstructure 3 for D (D)Microstructure 2 for C and Microstructure 5 for D (E) Microstructure 5 for C and Microstructure 2 for D

Microstructure 5 for C and Microstructure 2 for D 5-Blue and white stripes 2- orange and purple stripes with purple lines separating regions

For a supercooled liquid of a metal, which of the following is TRUE? a). The solidification rate is independent of supercooling. b). Growth rate of solid nuclei monotonically increases with increasing supercooling. c). Nucleation rate of the solid nuclei monotonically decreases with increasing supercooling. d). The overall solidification rate monotonically decreases with increasing supercooling. Near the melting temperature, the overall solidification rate is nearly zero.

Near the melting temperature, the overall solidification rate is nearly zero.

According to the tensile test graph shown, which of the following statements is TRUE? a). The yield strength is ~ 60 MPa and the ultimate tensile strength is ~ 170 MPa. b). The ultimate tensile strength is ~ 170 MPa and the Young's modulus is ~60 GPa. c). The ultimate tensile strength is ~ 170 MPa and the Young's modulus cannot be estimated. d). The fracture strength is ~ 150 MPa and the ultimate tensile strength is ~ 150 MPa.

The ultimate tensile strength is ~ 170 MPa and the Young's modulus is ~60 GPa.

Which of the following is not a method for strengthening metals: a). high temperature annealing b). grain size reduction c). solid solution hardening d). cold working

high temperature annealing

Compared with martensite, tempered martensite has, (A)higher tensile strength. (B) higher yield strength. (C) Both (A) and (B) (D)higher ductility

higher ductility

You wish to harden an aluminum alloy containing 5 wt.% copper by creating a large number of small CuAl2 precipitates within an Al matrix. You first heat the sample to 550°C, hold it for several hours, and then quench to room temperature. The highest strength (largest number of nuclei) is obtained by: a). reheat to 450°C and hold for 1 hour; quench to room temperature. b). reheat to 600°C and hold for 1 hour; quench to room temperature. c). reheat to 200°C and hold for 1 hour; quench to room temperature. d). reheat to 550°C and hold for 1 hour; quench to room temperature.

reheat to 200 C and hold for one hour, quench till room temp

Ridged Break

typical break for majority of ductile metals