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Difficulty
According to the central idea in the note, what is the order of the four linked factors in materials science?
Solution
The chain is
So processing affects structure, structure affects properties, and properties affect performance.
Which bonding type is associated with delocalized electrons, electrical conductivity, and ductility?
Solution
That is metallic bonding.
The delocalized electrons explain why metals conduct electricity and why they can deform plastically without immediately fracturing.
How many atoms are in one face-centered cubic (FCC) unit cell?
Solution
An FCC unit cell contains
atoms.
What point defect is created when an atom is missing from its normal lattice site?
Solution
That defect is a vacancy.
It is one of the common point defects listed in the note.
What do Miller indices describe in a crystal?
Solution
Miller indices describe crystallographic planes and directions.
They are used to identify things like slip systems, cleavage planes, and anisotropy.
A tensile specimen carries a force of $12$ kN over an original area of $30$ mm$^2$.
What is the engineering stress?
Solution
Use
so
Since $1\ \text{N/mm}^2 = 1\ \text{MPa}$,
Which heat treatment is used to increase hardness by rapid cooling?
Solution
That treatment is quenching.
Rapid cooling can suppress diffusion and produce a harder microstructure.
Which material class is typically low density, low modulus, viscoelastic, and strongly dependent on temperature and strain rate?
Solution
That class is polymers.
The note lists them as low density, low stiffness, and strongly affected by temperature and strain rate.
Which characterization method is best for identifying crystal structure and phase identity by lattice spacing?
Solution
The best method is X-ray diffraction (XRD).
The note says XRD is used for crystal structure and phase identification.
Before screening candidate materials, what is the first thing you should define in the selection workflow?
Solution
You should first define the function of the part.
From there, you can identify the loading, environment, temperature, lifetime, and other constraints.
Difficulty
An FCC metal has atomic radius $r = 0.125$ nm.
What is the unit-cell edge length?
Solution
For FCC,
so
Thus,
Material A has a grain size of $16\ \mu\text{m}$ and material B has a grain size of $4\ \mu\text{m}$.
According to the Hall-Petch relation, which material should have the higher yield strength, and how do the Hall-Petch terms compare?
Solution
The Hall-Petch term is proportional to $d^{-1/2}$.
For material A:
For material B:
So material B has the larger Hall-Petch term, by a factor of $2$.
Therefore, material B should have the higher yield strength.
At a temperature in a two-phase $\alpha+\beta$ region, suppose
Find the mass fractions of $\alpha$ and $\beta$.
Solution
Use the lever rule:
and
Substitute the values:
So the two phases are present in equal amounts.
Using
what happens to diffusivity when temperature increases and $D_0$ and $Q$ stay fixed?
Solution
As $T$ increases, the quantity $-Q/RT$ becomes less negative, so the exponential term gets larger.
Therefore, diffusivity increases with temperature, and it usually increases rapidly because of the exponential dependence.
On a tensile test curve, what does the ultimate tensile strength mark?
Solution
The ultimate tensile strength is the maximum engineering stress reached on the curve.
After that point, necking usually begins.
Put the precipitation-hardening steps in order, and state why quenching is used.
Solution
The usual sequence is:
Solution heat treat
Quench
Age
Quenching is used to retain a supersaturated solid solution so that fine precipitates can form during aging.
A specimen stretches from $50$ mm to $55$ mm.
What is the true strain?
Solution
Use
so
That is the exact true strain.
A crystal structure has 4 atoms per unit cell, a coordination number of 12, and a packing factor of 0.74.
Which common crystal structure is it?
Solution
Those values match face-centered cubic (FCC).
The note lists FCC as having 4 atoms per unit cell, coordination number 12, and packing factor 0.74.
Difficulty
You need a panel for a drone wing skin that is light, stiff, and reinforced in a preferred direction.
Which material class from the note is the best fit?
Solution
The best fit is a composite, especially a fiber-reinforced polymer.
Composites are used for high specific stiffness, directional reinforcement, and tailored performance.
An alloy is in an $\alpha+\beta$ region with
Which phase is more abundant, and by how much?
Solution
Use the lever rule:
So $\alpha$ is more abundant, with a mass fraction of $0.6$ versus $0.4$ for $\beta$.
A component has stress $\sigma = 120$ MPa, crack size $a = 5$ mm, and geometry factor $Y = 1$.
If the fracture toughness is $K_{IC} = 16$ MPa$\sqrt{\text{m}}$, is the component safe by the crack-growth criterion in the note?
Solution
Use
with $a = 5$ mm $= 0.005$ m:
Since
the component is safe by this criterion.
A steel part is too brittle after quenching.
Which heat treatment should follow to reduce brittleness while keeping useful hardness?
Solution
The next step should be tempering.
The note says tempering reduces brittleness after a quench while helping keep useful hardness.
A designer strengthens an aluminum alloy by solution heat treating, quenching, and then aging it so that fine precipitates form.
What strengthening mechanism is being used?
Solution
That is precipitation hardening.
The fine precipitates impede dislocation motion and raise strength.
Difficulty
A metal is made finer-grained and then cold-worked.
What happens to yield strength and ductility, and why?
Solution
The yield strength increases and the ductility decreases.
Fine grains strengthen the metal by impeding dislocation motion, and cold work increases dislocation density, which makes further slip harder.
A part must keep its shape at high temperature, resist wear, and act as an electrical insulator.
Which material class is the best fit, and what tradeoff should you expect?
Solution
The best fit is a ceramic.
The main tradeoff is that ceramics are typically brittle and have low ductility.
A rapid quench changes a steel microstructure to martensite.
Explain how the processing change leads to the property change.
Solution
Rapid quenching suppresses diffusion, so the steel transforms into a metastable martensitic structure instead of a diffusion-controlled equilibrium structure.
That new structure is much harder, but also more brittle.
So the processing change leads to a structure change, which then changes properties.
A steel gear needs high hardness, but it must not fail in a brittle way.
Based on the note, what heat-treatment sequence best balances those requirements?
Solution
The best sequence is to quench, then temper.
Quenching raises hardness, and tempering reduces brittleness and improves toughness enough to make the part more reliable in service.