# Assignments

Either:
Write a ten-page term paper on a topic agreed upon with Prof. Eagar,
Or
Solve a problem set consisting of ten open-ended problems found below.
(Note: The problem set may be done in teams.)
Problems
1. A 12 mm diameter steel bolt joining two plates, each of 2 cm thickness, is tensioned to one-half of its yield strength of 900 MPa. The depth of the threads is one millimeter.
• What force is holding the two plates together due to tension in the bolt?
• How much has the bolt extended due to this tension?
2. Estimate the maximum shear load that can be applied to a riveted joint between two one millimeter thick aluminum sheets. The aluminum sheet has a yield strength of 100 MPa and a tensile strength of 225 MPa. The rivets are 2.5 mm in diameter, on 5 mm centers. Their strength is 175 MPa yield and 250 MPa tensile.
• Assume that the sheets are held together with one row of rivets.
• Assume that a double row of rivetS holds the sheets together.
3. Two steel plates are to be joined together using either bolting or welding. The joint can be made with either six bolts or with 500 grams of weld metal. No procedure qualification is needed to produce the bolted joint. but the welded joint will require qualification of a test weld at a cost of \$I,000. The probability of passing this qualification is 80% on the first attempt, 98% on the second attempt and 100% on the third attempt. The total cost of depositing weld metal is \$8.00 per kilogram. The cost of a bolt, the bolt hole and assembly is \$6.00 per bolt. How many units of production are needed to make the welded joint less expensive than the bolted joint?

4. An adhesive with a viscosity of 20 gm/cm/sec is applied between two disks of 2 cm diameter, using a force of 10 newtons. How long does it take to form a joint of 0.01 mm thickness? If the adhesive hardens to a viscosity of 108 gm/cm/sec, how long will the joint last under a tensile load of 500 newtons?

5. Estimate the force required to quickly separate two Johansson blocks which are 5 cm square, if the joint is 0.005 mm thick. The surface energy of water is 0.080 J/m2 and the viscosity is 1 gm/cm/sec. If the thickness of the lower block is 2 cm, how long will the joint last if the lower block is suspended by attachment to the upper block? The density of steel is 7.8 gm/cm3.

6. The world's largest diffusion bonding furnace can join plates 2.5 m by 3.5 m with a force of 10,000 metric tons. If the initial area of asperity contact is only ten percent of the apparent area of the plate and the flow strength of the material being bonded is 70 MPa at the bonding temperature. have the asperities deformed plastically at the start of the process?

7. The initial thickness of a transient liquid phase diffusion bond is 0.1 mm. The diffusivity of the diffusing species in the base metal is 10-10 cm2/sec. Estimate the time necessary to complete the bond. Compare this time with the time required to complete a joint which is initially 0.01 mm thick. [Note that the relationship in Equation 5 for heat diffusivity can be applied to mass diffusivity as well.]

8. In wave soldering of printed circuit boards, the board is floated over a bath of flowing solder. All of the heat is supplied to the board by the molten solder. If the speed of soldering is controlled by the wetting time of freshly cleaned copper and the length of the solder bath is 3 cm, what is the maximum velocity at which the boards can be passed over the bath to provide fully soldered joints? If the electronic components on the board must not be heated to a depth greater than 0.5 mm beneath their surface, what is the slowest rate of travel of the board over the molten solder bath? You may assume a thermal diffusivity of the ceramic or plastic component housing of 0.02 cm2/sec.

9. A laser beam with a source intensity of 106 watts/cm2 strikes a large piece of steel with an absorption efficiency of forty percent.
• Estimate how long it will take to melt the surface of the steel if the heat necessary to raise iron from room temperature to the molten state is 10.2 joules/mm3.
• How long would it take for an arc of 104 watts/cm2 to melt the surface? The thermal diffusivity of steel is 0.1 cm2/sec.
• Compare these times with the time to melt an aluminum surface. The thermal diffusivity of aluminum is 0.7 cm2/sec and the heat content from room temperature to the molten state is 2.87 joules/mm3.
10. The time of a resistance spot weld is measured in cycles of 60 Hz electric current.
• Estimate the depth to which a copper electrode is heated by conduction from the steel sheet in a 12 cycle weld. The thermal diffusivity of copper is 0.9 cm2/sec.
• The electrode has internal water cooling. The distance from the electrode-sheet interface to the water cooling channel is 7 mm. In a robotic welding application, welds of 12 cycle duration are made at a rate of 40 welds per minute. Is the water effective in cooling the end of the electrode during this process?