# materials science & engineering

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Practice Problem

A specimen of some metal having a rectangular cross section 10.4 mm x 13.3 mm is pulled in tension with a force of 8040  N, which produces only elastic deformation. Given that the elastic modulus of this metal is 79 GPa, calculate the resulting strain.

Problem 6.03

A specimen of aluminum having a rectangular cross section9.9 mm × 12.6 mm (0.3898 in. × 0.4961 in.) is pulled in tension with 35500 N (7981 lbf) force, producing only elastic deformation. The elastic modulus for aluminum is 69 GPa(or 10 × 106 psi). Calculate the resulting strain.

### Problem 6.08

A cylindrical rod of copper (E = 110 GPa, 16 × 106 psi) having a yield strength of 240 MPa (35,000 psi) is to be subjected to a load of 6660 N (1497 lbf). If the length of the rod is 380 mm (14.96 in.), what must be the diameter to allow an elongation of 0.54 mm (0.02126 in.)?

### Problem 6.19

A cylindrical specimen of some metal alloy 7.1 mm in diameter is stressed in tension. A force of 9980 N produces an elastic reduction in specimen diameter of 0.0039 mm. Calculate the elastic modulus (in GPa) of this material if its Poisson’s ratio is 0.34.

### Problem 6.37

A cylindrical metal specimen having an original diameter of 10.81 mm and gauge length of 51.2 mm is pulled in tension until fracture occurs. The diameter at the point of fracture is 7.79 mm, and the fractured gauge length is 66.6 mm. Calculate the ductility in terms of (a) percent reduction in area (percent RA), and (b) percent elongation (percent EL).

### Problem 6.54

(a) A 9.9-mm-diameter Brinell hardness indenter produced an indentation 2.3 mm in diameter in a steel alloy when a load of 1000 kg was used. Compute the HB of this material.
(b) What will be the diameter of an indentation to yield a hardness of 280 HB when a 500-kg load is used?

HW 4

Problem 4.04

Calculate the number of vacancies per cubic meter in some metal at 631°C. The energy for vacancy formation is 0.89 eV/atom, while the density and atomic weight for this metal are 4.89 g/cm3 (at 631°C) and 63.52 g/mol, respectively.

### Problem 4.05

Calculate the energy (in eV/atom) for vacancy formation in some metal, M, given that the equilibrium number of vacancies at 327oC is 4.49 × 1023 m-3. The density and atomic weight (at 327°C) for this metal are 19.3 g/cm3 and 40.50 g/mol, respectively.

### Problem 4.20

Calculate the number of atoms per cubic meter in aluminum. The density and atomic weight of aluminum are 2.70 g/cm3 and 26.98 g/mol respectively. The value of Avogadro’s number is 6.02 x 1023 atoms/mol.

Problem 3.09 (GO Tutorial)

Calculate the radius of a nickel atom in cm, given that Ni has an FCC crystal structure, a density of 8.90 g/cm3, and an atomic weight of 58.69 g/mol.

Problem 3.11

A hypothetical metal has the simple cubic crystal structure shown in Figure 3.3. If its atomic weight is 70.4 g/mol and the atomic radius is 0.144 nm, compute its density.

Problem 3.16

A hypothetical alloy has an atomic weight of 91.6 g/mol, a density of 9.60 g/cm3, and an atomic radius of 0.137 nm. Determine whether its crystal structure is FCC, BCC, or simple cubic. A simple cubic unit cell is shown in Figure 3.3.

Problem 3.19

Beryllium has an HCP unit cell for which the ratio of the lattice parameters c/a is 1.568. If the radius of the Be atom is 0.1143 nm, (a) determine the unit cell volume, and (b) calculate the theoretical density of Be, given that its atomic weight is 9.01 g/mol.

Determine the indices for the directions shown in the following cubic unit cell.

### Problem 3.47 (GO Multistep)

Determine the Miller indices for the planes shown in the following cubic unit cell.

#### Part 1

In this problem, you are asked to determine the Miller indices for the planes shown in this unit cell.

Start with plane B. Since the plane does not pass through the origin, use the coordinate system shown.

What are the intersections of this plane with the coordinate axes?

(a) What is the intercept of this plane with the x-axis?
(b) What is the intercept of this plane with the y-axis?
(c) What is the intercept of this plane with the z-axis?

MIME 1650

Extra credit assignment (Purely voluntary)

You are working as a Mechanical Engineer at United Technologies Research Center in Hartford, Connecticut. Your company is developing next generation of jet engines, which are light-weight and yet are more powerful than the currently used ones. This will cost a significant amount of fuel savings. At the core of the design are the blades that rotate at high speeds and deliver the required thrust for the aircraft. You are supposed to select materials for the construction of such blades. The possible strategies for such a job are:

1. Read up on jet engines with special emphasis on engine blades. How they work and what are the service conditions.
2. Identify these conditions and the relevant mechanical properties associated with those.
3. Determine which property is the most important, and the next most important etc… accordingly plan your strategy.
4. Read up on what are the materials currently being used and why?
5. Either do a little bit of research on why they are being used or suggest something that might perform even better.

Write 2-3 page report on your findings. One or two drawings/schematics would be nice. There is no hard and fast format as a long as the matter is logically presented.  Discussions/collaborations with one another are permitted, but must submit individual report. However, this boss will not act as a consultant and there will be no responses to e-mails regarding this matter. If the boss likes the report, there will be nice semester-end bonus added to the grade. The report is due at the time of the final exam.