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

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

204 • Chapter 7 / Mechanical Properties

Percent reduction in area %RA is defined as

%RA=

(

A 0 −Af

A 0

)

× 100 (7.12)

Ductility, as percent

reduction in area

whereA 0 is the original cross-sectional area andAfis the cross-sectional area at

the point of fracture (refer to footnote 10 on page 203). Percent reduction in area

values are independent of bothl 0 andA 0. Furthermore, for a given material the

magnitudes of %EL and %RA will, in general, be different. Most metals possess at

least a moderate degree of ductility at room temperature; however, some become

brittle as the temperature is lowered (Section 9.8).

A knowledge of the ductility of materials is important for at least two reasons.

First, it indicates to a designer the degree to which a structure will deform plasti-

cally before fracture. Second, it specifies the degree of allowable deformation during

fabrication operations. We sometimes refer to relatively ductile materials as being

“forgiving,” in the sense that they may experience local deformation without fracture

should there be an error in the magnitude of the design stress calculation.

Brittle materials areapproximatelyconsidered to be those having a fracture

strain of less than about 5%.

Thus, several important mechanical properties of metals may be determined from

tensile stress–strain tests. Table 7.2 presents some typical room-temperature values

of yield strength, tensile strength, and ductility for several of the common metals

(and also for a number of polymers and ceramics). These properties are sensitive

to any prior deformation, the presence of impurities, and/or any heat treatment to

which the metal has been subjected. The modulus of elasticity is one mechanical

parameter that is insensitive to these treatments. As with modulus of elasticity, the

magnitudes of both yield and tensile strengths decline with increasing temperature;

just the reverse holds for ductility—it usually increases with temperature. Figure 7.14

shows how the stress–strain behavior of iron varies with temperature.

Resilience

resilience Resilienceis the capacity of a material to absorb energy when it is deformed elastically

and then, upon unloading, to have this energy recovered. The associated property is

themodulus of resilience,Ur, which is the strain energy per unit volume required to

stress a material from an unloaded state up to the point of yielding.

Computationally, the modulus of resilience for a specimen subjected to a uniaxial

tension test is just the area under the engineering stress–strain curve taken to yielding

(Figure 7.15), or

Definition of

modulus of resilience

Ur=

∫y

0

σd (7.13a)

Assuming a linear elastic region,

Modulus of resilience

for linear elastic

behavior

Ur=

1

2

σyy (7.13b)

in whichyis the strain at yielding.