Page 62 - Mechanical Behavior of Materials

Problems and Questions 63

MOFFATT,W.G., G. W. PEARSALL,and J. WULFF. 1964. The Structure and Properties of Materials, Vol. I:
Structure, John Wiley, New York.
SHACKELFORD, J. F. 2009. Introduction to Materials Science for Engineers, 7th ed., Prentice Hall, Upper
Saddle River, NJ.

PROBLEMS AND QUESTIONS

Section 2.4
2.1 Table 2.2(b) gives a value of E = 160 GPa for a fiber of linear polyethylene, in which the
polymer chains are aligned with the fiber axis. Why is this value so much higher than
the typical E = 3 GPa mentioned for polymers—in fact almost as high as the value for iron
and steel?
2.2 Consider Fig. 2.16, and assume that it is possible to make accurate measurements of the elastic
modulus E for high stresses in both tension and compression. Describe the expected variation
of E with stress.
2.3 Consider Fig. 2.16 and two atoms that are initially an infinite distance apart, x =∞,atwhich
point the potential energy of the system is U = 0. If they are brought together to x = x 1 ,the
potential energy is related to the total force P by

dU
= P

dx
x=x 1
Given this, qualitatively sketch the variation of U with x. What happens at x = x e ? What is the
significance of x = x e in terms of the potential energy?
2.4 Using Table 2.2, compare the strengths of Al 2 O 3 whiskers versus Al 2 O 3 fibers, and also
compare the two diameters of tungsten wire with each other. Can you explain the large
differences observed?
2.5 Consult Callister (2010) or Shackelford (2009) in the References, or another materials science
or chemistry text, and study the crystal structure of carbon in the form of graphite. How
does the structure differ from that of diamond? Why is graphite in bulk form usually soft
and weak? And how could a whisker of such a material have the high strength and elastic
modulus indicated in Table 2.2(a)?

Section 2.5
2.6 Explain why slip in a crystal is easiest in close-packed planes, and within these planes, in
close-packed directions.
2.7 Explain why polycrystalline metals with an HCP crystal structure are generally more brittle
than polycrystalline BCC metals.
2.8 With a proper sequence of thermal processing, aluminum alloyed with 4% copper can be
caused to contain a large number of very small particles of the hard intermetallic compound
CuAl 2 . How would you expect the yield strength of such a processed alloy to differ from that
for pure aluminum? Answer the same question for the percent elongation? Why?
2.9 Cold working a metal by rolling it to a lesser thickness or hammering it introduces a large
number of dislocations into the crystal structure. Would you expect the yield strength to be