Page 76 - Manufacturing Engineering and Technology - Kalpakjian, Serope : Schmid, Steven R.

Synthesis, Design and Projects 55

l.29. What is the significance of the fact that such metals as l.3 l. It has been noted that the more a metal has been cold
lead and tin have a recrystallization temperature that is about Worked, the less it strain hardens. Explain why.
room temperature? l.32. ls it possible to cold work a metal at temperatures
l.30. It was stated in this chapter that twinning usually above the boiling point of water? Explain.
occurs in hcp materials, but Fig. 1.5 b shows twinning in a rec- l.33. Comment on your observations regarding Fig. 1.13.
tangular array of atoms. Can you explain the discrepancy?

QUANTITATIVE PRGBLEMS

l.34. How many atoms are in a single repeating cell of an |]l.40. The unit cells shown in Figs. 1.2 through 1.4 can be
fcc crystal structure? How many in a repeating cell of an hcp represented by tennis balls arranged in various configurations
structure? in a box. In such an arrangement, the atomic packing factor
l.35. The atomic weight of copper is 63.55, meaning that (APF) is defined as the ratio of the sum of the volumes of the
6.023 >< 1023 atoms weigh 63.55 grams. The density of cop- atoms to the volume of the unit cell. Show that the APP is
per is 8970 kg/m3, and pure copper forms fcc crystals. 0.68 for the bcc structure and 0.74 for the fcc structure.
Estimate the diameter of a copper atom. u|.4l. Show that the lattice constant a in Fig. 1.3a is relat-
|}l.36. Plot the data given in Table 1.1 in terms of ed to the atomic radius by the formula a = 2\/2R, where R
grains/mmz vs. grains/mm3, and discuss your observations. is the radius of the atom as depicted by the tennis-ball model.
l.37. A strip of metal is reduced from 40 mm in thickness to |]l.42. Show that, for the fcc unit cell, the radius 1' of the
20 mm by cold working; a similar strip is reduced from largest hole is given by 1' = 0.414R. Determine the size of the
40 mm to 30 mm. Which one of these cold-worked strips will largest hole for the iron atoms in the fcc structure.
recrystallize at a lower temperature? Why? l.43. A technician determines that the grain size of a certain
|]l.38. A paper clip is made of wire that is 120 mm long etched specimen is 8. Upon further checking, it is found that
and 0.75 mm in diameter. If the ASTM grain size is 9, how the magnification used was 175><, instead of the 100>< that is
many grains are there in the paper clip? required by the ASTM standards. Determine the correct
|]l.39. How many grains are on the surface of the head of grain size.
a pin? Assume that the head of a pin is spherical with a 1-mm |.44. If the diameter of the aluminum atom is 0.5 nm, how
diameter and has an ASTM grain size of 2. many atoms are there in a grain of ASTM grain size 8?

SYNTHESIS, DESIGN AND PROIECTS

|.45. By stretching a thin strip of polished metal, as in a represent Figs. 1.5a and 1.6. If you repeat the same experi-
tension-testing machine, demonstrate and comment on what ment with more and more rubber bands around the same
happens to its reflectivity as the strip is being stretched. deck, what are you accomplishing as far as the behavior of
the deck is concerned?
I.46. Draw some analogies to mechanical fibering-for
example, layers of thin dough sprinkled with flour or melted l.50. Give examples in which anisotropy is scale dependent.
butter between each layer. For example, a Wire rope can contain annealed wires that are
isotropic on a microscopic scale, but the rope as a whole is
I.47. Draw some analogies to the phenomenon of hot
anisotropic.
shortness.
I.5 I. The movement of an edge dislocation was described in
l.48. Obtain a number of small balls made of plastic, wood,
Section 1.4.1 by means of an analogy involving a hump in a
marble, or metal, and arrange them with your hands or glue
carpet on the floor and how the whole carpet can eventually
them together to represent the crystal structures shown in
be moved by moving the hump forward. Recall that the en-
Figs. 1.2-1.4. Comment on your observations.
tanglement of dislocations was described in terms of two
I.49. Take a deck of playing cards, place a rubber band humps at different angles. Use a piece of cloth placed on a flat
around it, and then slip the cards against each other to table to demonstrate these phenomena.