Student Name ………………………… Student Number …………………
DEPARTMENT OF MECHANICAL ENGINEERING
MECH 473 Ferrous and Non-Ferrous Materials
1 hour and 30 minutes Mid-term Test No.1 Thursday June 26, 2008
Total is 25 marks plus 1 bonus
(3) 1. Three new types of materials that are being developed by engineers include metamaterials, amorphous metals and carbon nanotubes. What property are engineers seeking to obtain from these materials that will make them so valuable and what is a possible application?
Metamaterials – optical properties having negative refractive index for use in optical communication devices, microscopes, and as camouflage or cloaking devices.
Amorphous metals – super high elastic modulus for super strong materials enabling the building of very tall building structures. Currently used to make the best golf club heads.
Carbon nanotubes – Properties being sought include high strength, electrical (ballistic electron transport), optical (emitters) and magnetic properties for use in numerous nanotechnology applications.
(2) 2. Calculate the theoretical density of Si in g/cm3- given the following data:
Avogradro’s number = 6.023 x 1023 atoms/mol
Atomic mass of Si = 28 g/mole
Lattice parameter, ao = 0.543 nm
Crystal structure is diamond cubic.
(8 atoms/unit cell) (28 g/mol)
Density of Si = ______= 2.32 g/cm3
(0.543 nm)3 (6.02 x 10 23 atoms/mol)
(2.5) 3. As a rule of thumb, at what temperature range should a material be used in order to neglect effects on its mechanical properties. What strengthening mechanisms are effective against creep? For materials designed for creep applications, what temperature range should they be used?
Temperature should be less than T/Tm = 0.3-0.4 (1/2)
Both solid solution hardening and precipitation hardening (age hardening) are effective against creep. (1)
Materials designed for creep resistance should be used at temperatures less than
T/Tm < 0.5 (1/2)
(2) 4. Sketch the following planes and directions within the hexagonal unit cell provided.
(2) 5. Sketch the following directions and planes within a cubic unit cell.
a) b) c) d)
(2) 6. For BCC materials, dislocations have habit planes and directions given by <111>{011}. What are the indices of the four slip directions of the form <111> that would lie on theslip plane? (2) If helpful, use the cubic unit cell provided.
(1) 7. Calculate the Burgers vector of the dislocation oriented in the [110] and lying on the of FCC aluminum given its lattice parameter, ao = 0.405 nm.
The Burgers vector is the shortest repeat distance (2r) in the [110] direction given by,
(1) 8. Could a dislocation having Burgers vector lying on the interact with another dislocation having lying on (111) to form a third dislocation? Prove your answer.
Therefore the interaction is possible because the third dislocation created is energetically favorable.
(1) 9. a) Atomic lattice vibrations called phonons conduct heat in which types of materials? b) How much faster/slower are they to electrons for the conduction of heat?
Phonons conduct heat in ceramics, semiconductors, and some plastics, i.e., any material that poorly conducts electrons, but not metals. (1/2)
Phonons are two orders of magnitude slower than electrons, i.e., 103 m/s for phonons versus 105 m/s for electrons.
(1) 10. Some metals do not suffer from ductile to brittle transitions when used at low temperatures. What crystal structure(s) do these materials have? Provide an example.
The FCC metals do not suffer from a brittle transition. Examples include stainless steel, aluminum, copper
(1) 11. All materials will suffer from fatigue if the applied stress is high enough. What is the crystal structure of the type of materials that have an endurance limit? What criteria do engineers use for design purposes for these types of materials?
The BCC materials have an endurance limit, which uses an endurance ratio of,
(I’ll accept hcp materials, e.g., titanium.)
(2.5) 12. State and describe the five (5) mechanisms that can be used to strengthen a material.
1) Strain hardening occurs by cold working a material to introduce dislocations, which act as barrier to the movement of other dislocations. (1/2)
2) Solid solution strengthening, which involves adding solutes, alloying addition or foreign atoms to the material, which block the movement of dislocations to increase its strength. (1/2)
3) Second phase strengthening involves adding an alloying addition to induce multiple phases such as the alpha and beta phases in brass. Dislocations are blocked at their phase boundaries increasing the materials strength. (1/2)
4) Dispersion strengthening (aging) involves the formation of precipitates within a grain, which block the movement of dislocations and increase its strength. (1/2)
5) Grain refinement strengthening involves reducing the size of the grains by rapidly cooling the material from a high temperature or by recrystallization during annealing after cold work. The grain boundaries block the movement of dislocations, which increases its strength. (1/2)
(2) 13. The critical flaw size corresponds to the transition between general yielding and fast fracture. If the fracture toughness of a high-strength steel can be increased by 50% (say from 100 to 150 MPa sqrt(m)) without changing its yield strength of 1250 MPa, by what percentage is its critical flaw size changed? Assume f = 1.
(2) 14. A material was measured to have a creep rate of 5 x 10 -1 at 1000 oC. The creep mechanism for this material is known to be by dislocation climb with an activation energy of 200 kJ/mol. Predict the creep rate at a service temperature of 600 oC, given the exponential gas constant to be 8.314 j/mol K).
Bonus – What are four material phenomena that plasma crystals grown in space can be useful to study?
Plasma crystals give insight in physical phenomena, which is otherwise unobservable on earth, such as (five given)
• Study the transition between solid – liquid – gas – plasma states of matter.
• Study the formation of defects
• Study the phase separation (different crystal structures formed by small and large atoms)
• Study the convection of fluids at interfaces
• Study the flow of heat through a crystal via phonons (lattice vibrations)