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

GTBL042-07 GTBL042-Callister-v2 August 6, 2007 12:43

7.2 Concepts of Stress and Strain • 189

T

T

F

F

F

F

F

F

F

A 0

A 0

A 0

(a) (b)

(c) (d)





l l 0 l 0 l

Figure 7.1 (a)

Schematic

illustration of how a

tensile load produces

an elongation and

positive linear strain.

Dashed lines

represent the shape

before deformation;

solid lines, after

deformation. (b)

Schematic

illustration of how a

compressive load

produces contraction

and a negative linear

strain. (c) Schematic

representation of

shear strainγ, where

γ=tanθ.

(d) Schematic

representation of

torsional

deformation (i.e.,

angle of twistφ)

produced by an

applied torqueT.

the specimen size. For example, it will require twice the load to produce the same

elongation if the cross-sectional area of the specimen is doubled. To minimize these

geometrical factors, load and elongation are normalized to the respective parameters

engineering stress ofengineering stressandengineering strain.Engineering stressσis defined by the

engineering strain relationship

σ=

F

A 0

(7.1)

Definition of

engineering stress

(for tension and

compression)

in whichFis the instantaneous load applied perpendicular to the specimen cross

section, in units of newtons (N) or pounds force (lbf), and A 0 is the original

2"

Gauge length

Reduced section

2 "

"Diameter

"

1

4

3

4

(^38) Radius
0.505" Diameter
Figure 7.2 A
standard tensile
specimen with
circular cross
section.