Page 204 - Materials Science and Engineering An Introduction

176 • Chapter 6 / Mechanical Properties of Metals

Figure 6.7 Force versus interatomic
separation for weakly and strongly bonded
atoms. The magnitude of the modulus of
elasticity is proportional to the slope of each Strongly
curve at the equilibrium interatomic bonded
separation r 0 . dF
dr r 0
Force F 0 Separation r

Weakly
bonded

Furthermore, with increasing temperature, the modulus of elasticity decreases, as is
shown for several metals in Figure 6.8.
As would be expected, the imposition of compressive, shear, or torsional stresses
also evokes elastic behavior. The stress–strain characteristics at low stress levels are vir-
tually the same for both tensile and compressive situations, to include the magnitude of
the modulus of elasticity. Shear stress and strain are proportional to each other through
the expression
Relationship
between shear stress (6.7)
and shear strain for t = Gg
elastic deformation
where G is the shear modulus, the slope of the linear elastic region of the shear
stress–strain curve. Table 6.1 also gives the shear moduli for a number of common
metals.

Temperature (°F)
–400 0 400 800 1200 1600
70

Figure 6.8 Plot of modulus of elasticity 400 60
versus temperature for tungsten, steel, and Tungsten
aluminum. 50
(Adapted from K. M. Ralls, T. H. Courtney, and
J. Wulff, Introduction to Materials Science and 300
Engineering. Copyright © 1976 by John Wiley & 40
Sons, New York. Reprinted by permission of Modulus of elasticity (GPa) Modulus of elasticity (10 6 psi)
John Wiley & Sons, Inc.) 200 Steel 30

100 20
Aluminum
10
0 0
–200 0 200 400 600 800
Temperature (°C)