ENGR 2180: Engineering Materials, Fall 05

Assignment 2 Solutions to assignments must be computer generated and printed hard copies.

Include names of all the group members on your report (Group of maximum 3 of your choice).

Similarity or plagiarism across groups will be assigned zero points to all groups involved. No replacement/alternate assignments will be made.

Show all works for full credit for that problem.

Present data and information in a tabular or graphical form as appropriate.

Identify your answers clearly for quantitative questions. Use Level 2 CES EduPack to answer the EduPack-based questions - include all the graphs in your report. Identify materials on the graphs by using the label function available in EduPack. Late submissions will not be accepted.

1. The wire of a hoist has a cross sectional area of 80 mm2. The hoist is used to lift a crate weighing 500 kg. What is the stress in the cable? The free length of the cable is 3 m. How much will it extend if it is made of magnesium (modulus 45 GPa)? How much will it extend if it is made of polypropylene, PP (modulus 1.6 GPa)? (Assume purely elastic deformations).

2. A catapult has two rubber bands, each rubber band has a rectangular cross-section with a width 9 mm and thickness of 3 mm. The unstretched length of the rubber band is 200 mm. When the catapult is used, its arms are stretched to three times their original length before release. Assume the elastic modulus of rubber is 10-3 GPa and that it remains constant when the rubber band is stretched. How much elastic energy is stored in the catapult just before its release? The operating equation is given as follows:

Where, U is the elastic energy stored in each rubber band, E is the elastic modulus, A is the area of cross section of the rubber band, x is the amount of stretch of the rubber band, and L is the unstretched length of the rubber band3. Show that APF value of CPH structure is 0.74. Show all works. (20 points)4. Using 3D modeling software (Solidworks, Inventor, etc), create single unit cell of BCC and FCC structure when atomic radius is 1 mm (I know this is big but it will make your life easier). Then investigate the interstitial space of each structure regarding to shape, size and number. Present your works with pictures. (20 points)

5. A volume fraction f = 0.2 of silicon carbide (SiC) particles is combined with an aluminum matrix to make a metal matrix composite. The modulus and density of the two materials are listed below. The modulus of particle-reinforced composites lies very close to the lower bound, equation (4.22) given in the textbook. (a) Calculate the density and approximate modulus of the composite. Is the specific modulus (E/) of the composite material greater than that of unreinforced aluminum?

(b) How much larger is the specific modulus if the same volume fraction of SiC in the form of continuous fibers is used instead? For continuous fibers the modulus lies very close to the upper bound, equation (4.21) given in the textbook.

Aluminum:

Density: 2.70 Mg/m3, Modulus: 70 GPa

Silicon Carbide Density: 3.60 Mg/m3, Modulus: 230 GPa

6. Determine the crystallographic direction and plane that would have the maximum LD and PD (there are multiple, so pick one), and show the values when atomic radius is 0.145 nm and crystal structure BCC

7. Market need: My cell phone charging cable is made of polyethylene and breaks easy.Investigate for new materials with Need Statement and Selection Strategy. (20 points)