Page 209 - Materials Science and Engineering An Introduction

6.6 Tensile Properties • 181

elastic–plastic transition, the point of yielding may be determined as the initial
departure from linearity of the stress–strain curve; this is sometimes called the
proportional limit proportional limit, as indicated by point P in Figure 6.10a, and represents the onset
of plastic deformation on a microscopic level. The position of this point P is difficult
to measure precisely. As a consequence, a convention has been established by which
a straight line is constructed parallel to the elastic portion of the stress–strain curve
at some specified strain offset, usually 0.002. The stress corresponding to the inter-
section of this line and the stress–strain curve as it bends over in the plastic region
8
yield strength is defined as the yield strength s y . This is demonstrated in Figure 6.10a. The units of
yield strength are MPa or psi. 9
For materials having a nonlinear elastic region (Figure 6.6), use of the strain offset
method is not possible, and the usual practice is to define the yield strength as the stress
required to produce some amount of strain (e.g., P = 0.005).
Some steels and other materials exhibit the tensile stress–strain behavior shown in
Figure 6.10b. The elastic–plastic transition is very well defined and occurs abruptly in
what is termed a yield point phenomenon. At the upper yield point, plastic deforma-
tion is initiated with an apparent decrease in engineering stress. Continued deforma-
tion fluctuates slightly about some constant stress value, termed the lower yield point;
stress subsequently rises with increasing strain. For metals that display this effect, the
yield strength is taken as the average stress that is associated with the lower yield point
10
because it is well defined and relatively insensitive to the testing procedure. Thus, it is
not necessary to employ the strain offset method for these materials.
The magnitude of the yield strength for a metal is a measure of its resistance to plas-
tic deformation. Yield strengths may range from 35 MPa (5000 psi) for a low-strength
aluminum to greater than 1400 MPa (200,000 psi) for high-strength steels.

Concept Check 6.1 Cite the primary differences between elastic, anelastic, and plastic
deformation behaviors.

[The answer may be found at www.wiley.com/college/callister (Student Companion Site).]

Tensile Strength
After yielding, the stress necessary to continue plastic deformation in metals increases
to a maximum, point M in Figure 6.11, and then decreases to the eventual fracture, point
tensile strength F. The tensile strength TS (MPa or psi) is the stress at the maximum on the engineering
stress–strain curve (Figure 6.11). This corresponds to the maximum stress that can be
sustained by a structure in tension; if this stress is applied and maintained, fracture will
result. All deformation to this point is uniform throughout the narrow region of the ten-
sile specimen. However, at this maximum stress, a small constriction or neck begins to
form at some point, and all subsequent deformation is confined at this neck, as indicated
by the schematic specimen insets in Figure 6.11. This phenomenon is termed necking,

8 Strength is used in lieu of stress because strength is a property of the metal, whereas stress is related to the magni-
tude of the applied load.
9 For customary U.S. units, the unit of kilopounds per square inch (ksi) is sometimes used for the sake of convenience, where
1 ksi = 1000 psi.
10 Note that to observe the yield point phenomenon, a “stiff” tensile-testing apparatus must be used; by “stiff,” it is
meant that there is very little elastic deformation of the machine during loading.