Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

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.)