MSE 250 Study Guide
Overview
Major classes of materials: definition & general properties
Atomic Bonding: 4 types; determining bond type
Atomic and Ionic Radii: trends in periodic table
Crystal Structures:
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metals: FCC, BCC, HCP
calculate atomic density
polymorphism
thermal expansion
Crystal Defects:
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vacancies (calculate vacancy concentration)
interstitials
solutes
dislocations: motion importance
grain boundaries (formation, structure, importance)
diffusion: mechanism, distance (equation), examples
Mechanical properties:
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stress, strain
moduli (Young’s modulus, Poisson’s ratio- be able to calculate)
stress-strain curve
deformation mechanisms
strengthening metals
hardness
ductility
resilience & toughness
fracture (equation for K1c); ductile vs. brittle; fracture control
fatigue (mechanism, effect of temperature, type of stress)
Alloys:
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phases, phase transitions;
completely soluble phase diagram
lever law
eutectic reaction
eutectoid reaction
peritectic reaction
peritectoid
Al-Cu alloys
steels
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martensitic reaction
metallic alloys
Ceramics:
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crystal structures: covalent (diamond); ionic (NaCl, CsCl); mixed ionic-covalent (silica)
crystal defects
glasses: Tg, volume vs. T, structure
mechanical properties: toughening, thermal shock
common ceramics
Polymers:
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structure
thermoplastic, thermoset
crosslinking
molecular weight (know how to calculate mass average, number average)
addition reaction - various steps; branching
condensation reaction
disorder/rotational freedom
tacticity
crystallinity: factors that affect it; effect on properties; lamellae; tie molecules
temperature effects
elastomers: vulcanization; why highly elastic?
Mechanical properties – effect of temperature on stress-strain curves;
elastic modulus vs. temperature
Strengthening of thermoplastics & thermosets
viscoelasticity - time effect
fracture: mechanisms
additives to polymers
Example questions
Calculate the density of Al, given its atomic radius and crystal structure.
Given the vacancy concentration, calculate Evf.
Why are vacancies important?
How do dislocations move, and what effect does their movement have?
How does diffusion occur in metals?
Estimate the time required for diffusion to occur, given a surface concentration and an interior
depth.
Given a stress-strain curve, determine Young’s modulus, the yield strength, the ultimate strength,
and the fracture strength.
Given a K1c value and the appropriate conditions, determine whether or not a part will fracture.
Given an S-N curve, determine if a part can survive a given number of cycles at a given stress.
How does temperature affect fatigue; creep?
Predict how long it will take a part to creep, given its Larsen-Miller parameter and the applied
stress.
How can one design a part to resist fatigue?
Why does a superalloy resist creep?
Given a complex phase diagram, draw a typical microstructures; determine if the reactions are
eutectic, peritectic, or other.
Use the lever law to predict amount of phases present, for different parts of various phase
diagrams.
Calculate the density of Si in the diamond structure.
What is the charge of a Cl vacancy in NaCl?
Draw the structure of a typical SiO2 glass, with and without Na impurities. What effect do the
impurities have?
Why are ceramics brittle?
What are 5 methods for toughening ceramics?
Why is thermal shock more of a problem for ceramics than metals?
Draw the structure of polyethylene.
Define a thermoplastic and a thermoset.
Explain how a typical epoxy is crosslinked.
Calculate the mass average and number average molecular weight of a sample.
Explain the steps in polymerizing ethylene.
How does the number of tie molecules affect toughness?
Explain how changes in temperature affect the mechanical properties of an amorphous polymer;
a cross-linked polymer; a semi-crystalline polymer.
1. The following stress-strain points are generated for a titanium alloy for aerospace
applications:
Calculate Young's modulus for this alloy
𝜎 = 𝐸𝜀 → 𝐸 =
𝜎
𝜀
300
= 107992.36
. 002778
600
𝐸=
= 107992.36
. 005556
𝐸=
𝐸=
900
= 90936.647
. 009897
Since the E value calculated at 900 is less than that of 300 and 600, we can infer that it is no
longer in the linear elastic range. The E value of the alloy is 107992.36 MPa.
2. A steel rod of radius 0.01 m and length 2. M is pulled on with a tensile force of 200,000 N,
and the bar stretches to a length of 2.08 m. The radius of the bar is reduced to 0.0099 m.
this test.
∆𝑙 = 2.08 − 2 = .08 𝑚 (𝑖𝑡 𝑖𝑠 𝑔𝑒𝑡𝑡𝑖𝑛𝑔 𝑙𝑎𝑟𝑔𝑒𝑟)
. 08
= .04
2
200,000
𝜎=
= 6.37 𝑥 108 𝑃𝑎
𝜋 ∗. 012
𝜀=
𝐸=
𝜎 6.37 𝑥 108
=
= 15.9 𝐺𝑃𝑎
𝜀
. 04
3.
a.)Determine the rate of diffusion of Cu in Al at 300K, using D = Do exp (-ED/RT),
where Do = 0.15 cm2/sec, and ED = 125 kJ/mole.
𝐸𝑑
125000 𝐽
𝐷 = 𝐷𝑜 𝑒 −𝑅𝑇 = .15 𝑒 −8.314∗300𝐾 = 2.54 𝑥 10−23
note: 125kJ=125000J
b.) Determine the temperature at which the diffusivity D of Cu in Al is twice the diffusivity at
500K.
𝐸𝑑
𝐸𝑑
2𝐷𝑜 𝑒 −𝑅∗500 = 𝐷𝑜 𝑒 −𝑅𝑇
ln(2) −
ln(2) −
Ed
𝐸𝑑
=
𝑅 ∗ 500 𝑅𝑇
125000𝐽/𝑚𝑜𝑙
125000𝐽/𝑚𝑜𝑙
=−
8.314 ∗ 500
8.314 ∗ 𝑇
T=512 K
c) Using your result for D of Cu in Al at 500K, estimate the distance that a Cu impurity would
diffuse in Al at 500 K after 1 hour.
𝐸𝑑
𝐷𝑜 𝑒 −𝑅𝑇 = .15 𝑒 −
125000 𝐽/𝑚𝑜𝑙
8.314∗500𝐾
= 1.31 𝑥 10−14
𝑥 = √𝐷 ∗ 𝑡 = √1.31 𝑥 10−14 ∗ 3600𝑠 = 6.86 𝑥 10−6 𝑐𝑚
note: 3600s=1hr
4. An aluminum wire (1 inch in diameter, 1000 m long) is used to pull a cable car up a mountain.
If the weight of the unloaded cable car is 1 ton, and if there are 6 people in the car, and each
weighs an average of 150 pounds. E = 10 x 106 psi
a) calculate the stress (in pounds per sq. inch),
𝑡𝑜𝑡𝑎𝑙 𝑓𝑜𝑟𝑐𝑒, 𝐹 = 1 𝑡𝑜𝑛 + 6 ∗ 150𝑙𝑏𝑠 = 2000 + 900 = 2900 𝑙𝑏𝑠
𝜎=
𝐹
2900
=
= 3.69 𝑥 103 𝑝𝑠𝑖
𝐴 𝜋 ∗. 52
b) calculate the strain of the wire when it begins to lift the cable car,
𝜎 = 𝐸𝜀 → ε =
σ 3.69 𝑥 103 𝑝𝑠𝑖
=
= 3.69 𝑥 10−4
E
10 𝑥 106 𝑝𝑠𝑖
c) calculate the change in length of the cable.
𝜀=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑙𝑒𝑛𝑔𝑡ℎ
→ ∆𝑙 = 𝜀 ∗ 𝑙𝑜 = 3.69 𝑥 10−4 ∗ 1000𝑚 = .369𝑚
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
d) determine the change in the diameter of the wire (Poisson's ratio is 0.31
for Al) - be sure to indicate the proper sign (positive for increase, negative for decrease)
𝑣=−
𝜀𝑙𝑎𝑡
→ 𝜀𝑙𝑎𝑡 = −𝑣 ∗ 𝜀𝑙𝑜𝑛𝑔 = −.31 ∗ 3.69 𝑥 10−4 = −1.1439 𝑥 104
𝜀𝑙𝑜𝑛𝑔
5. An external crack of length .5 cm is found on an aircraft wing made of aluminum. During the
flight, the largest applied stress will be 250 MPa. Is it safe to fly? Aluminum has a KIC value of
20 MPam1/2. Let y=1.
1
𝐾𝐼 = 𝑦 ∗ 𝜎 ∗ √𝜋 ∗ 𝑎 = 1 ∗ 250 ∗ √𝜋 ∗ .005𝑚 = 31.32𝑀𝑃𝑎2
Since the calculated KI value is greater than the critical value, it is not safe to fly because the
crack will grow.