GTBL042-07 GTBL042-Callister-v2 August 6, 2007 12:43
7.3 Stress–Strain Behavior • 195
0
Weakly
bonded
Strongly
bonded
Separation r
Force
F
dF
dr r 0
Figure 7.7 Force
versus interatomic
separation for
weakly and strongly
bonded atoms. The
magnitude of the
modulus of elasticity
is proportional to the
slope of each curve at
the equilibrium
interatomic
separationr 0.
for all but some of the rubber materials; this effect is shown for several metals in
Figure 7.8.
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
virtually the same for both tensile and compressive situations; it follows that the
modulus of elasticity is the same from both tension and compression tests. Shear
stress and strain are proportional to each other through the expression
τ=Gγ (7.7)
Relationship
between shear stress
and shear strain for
elastic deformation
whereGis theshear modulus,the slope of the linear elastic region of the shear stress–
strain curve. Table 7.1 also gives the shear moduli for a number of the common metals.
Temperature (°F)
Temperature (°C)
–200 0 200 400 600 800
70
60
50
40
30
20
10
400
300
200
100
0 0
Modulus of elasticity (10
6 psi)
Modulus of elasticity (GPa)
Aluminum
Steel
Tungsten
–400 0 400 800 1200 1600
Figure 7.8 Plot of
modulus of elasticity
versus temperature
for tungsten, steel,
and aluminum.
(Adapted from K. M.
Ralls, T. H. Courtney,
and J. Wulff,
Introduction to
Materials Science and
Engineering.
Copyright©c1976 by
John Wiley & Sons,
New York.
Reprinted by
permission of John
Wiley & Sons, Inc.)