Mat Sci Exam 3 LMS HW Questions

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: -2γ/∆Gv −γ/∆Gv -4γ/∆Gv -6γ/∆Gv

-4γ/∆Gv

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).

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?

0.15

In the phase diagram shown, the number of degrees of freedom at O is:

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?

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.

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.

1.6%

A TTT diagram for the iron-carbon system at the eutectoid composition is shown. The final microstructure for path 1 is,

100% martensite

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.

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?

127

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.

16.48

Given a 80 % Sn (20.0 % Pb) composition, what is the weight percent of alpha (α) phase at 182 °C.

22.4

Of microstructures (3), (4), (6) & (7) shown, which has the highest ductility?

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

40.8

The Avrami curves for the recrystallization as a function of temperature are shown. At which temperature is the nucleation time the longest?

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.

5.66

A TTT diagram for the iron-carbon system at the eutectoid composition is shown. The final microstructure for path 3 is,

50% pearlite and 50% bainite

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:

61.70 g Alpha, 38.30 g Liquid

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?

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.

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.

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?

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:

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

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.

8.24

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 .

900.9 °C

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 < B < C

Given the tensile fracture profiles shown, rank the materials from lowest to highest ductility

A < C < B

Given the Pb-Sn phase diagram, the compositions of the phases of 30 wt.% Sn alloy at equilibrium at 184 C are:

Alpha - 18.3% Sn ; Liquid - 61.9% Sn

For pure copper undergoing solidification in a graphite crucible which of the following is true: Copper nuclei forming heterogeneously on the crucible surface have the same critical size nuclei r* as nuclei forming in the bulk of the melt The rate of heterogeneous nucleation is always lower than the rate of homogeneous nucleation at all undercoolings The activation energy ΔG* for heterogeneous nucleation is larger than homogeneous. 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. Larger K+ ions replace Na+ ions at the surface causing a compressive stress and closing cracks. quick cooling of the glass which results in a compression at the surface and tension in the bulk Decreasing the grain size to reduce dislocation mobility Etching in acid which removes small surface flaws and blunts larger cracks

Decreasing the grain size to reduce dislocation mobility

In lab we tested chemically strengthened glass. The principle behind this strengthening mechanism is,

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

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

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

For the TTT curves shown, which of the following is TRUE? (Assume the sample is just above the Eutectoid temperature prior to cooling) 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. 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. 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.

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.

Given an 40 wt% Si (60 wt% Al) composition in the eqiulibrium phase diagram shown, which phases are present at 650˚C.

Si and liquid

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

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

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?

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

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

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

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

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

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

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

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

high temperature annealing

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: reheat to 600°C and hold for 1 hour; quench to room temperature. reheat to 200°C and hold for 1 hour; quench to room temperature. reheat to 450°C and hold for 1 hour; quench to room temperature. reheat to 550°C and hold for 1 hour; quench to room temperature.

reheat to 200°C and hold for 1 hour; quench to room temperature.

Which of the following is the preferred slip system in a FCC metal? slip plane:{100}; slip direction: <111> slip plane:{111}; slip direction: <100> slip plane:{110}; slip direction: <111> slip plane:{111}; slip direction: <110>

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

Adding 1% by weight magnesium to pure aluminum (which is within its solubility limit) strengthens the metal by enabling dislocation motion. weakens the metal by enabling dislocation motion. weakens the metal by inhibiting dislocation motion. strengthens the metal by inhibiting dislocation motion.

strengthens the metal by inhibiting dislocation motion.