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

GTBL042-07 GTBL042-Callister-v2 August 9, 2007 13:52

212 • Chapter 7 / Mechanical Properties

Support

= stress =

where M= maximum bending moment

Mc I 

= distance from center of specimen

to outer surface

c

I= moment of inertia of cross section

= applied load

Rectangular

Circular

F

Possible cross sections

Rectangular

Circular

F

R

d

b

2

L L

2

Mc

I

FL

4

d

2

bd^3

12

3 FL

2 bd^2

FL

4 R

R^4

4

FL

R^3

Figure 7.18 A three-point loading

scheme for measuring the

stress–strain behavior and flexural

strength of brittle ceramics,

including expressions for

computing stress for rectangular

and circular cross sections.

exists at the bottom specimen surface directly below the point of load application.

Since the tensile strengths of ceramics are about one-tenth of their compressive

strengths, and since fracture occurs on the tensile specimen face, the flexure test is a

reasonable substitute for the tensile test.

flexural strength The stress at fracture using this flexure test is known as theflexural strength,

modulus of rupture, fracture strength,or thebend strength,an important mechanical

parameter for brittle ceramics. For a rectangular cross section, the flexural strength

σfsis equal to

σfs=

3 FfL

2 bd^2

(7.20a)

Flexural strength for

a specimen having a

rectangular cross

section

whereFfis the load at fracture,Lis the distance between support points, and the

other parameters are as indicated in Figure 7.18. When the cross section is circular,

then

σfs=

FfL

πR^3

(7.20b)

Flexural strength for

a specimen having a

circular cross section

whereRis the specimen radius.

Characteristic flexural strength values for several ceramic materials are given

in Table 7.2. Furthermore,σfswill depend on specimen size; as explained in Section

9.6, with increasing specimen volume (that is, specimen volume exposed to a tensile

stress) there is an increase in the probability of the existence of a crack-producing

flaw and, consequently, a decrease in flexural strength. In addition, the magnitude

of flexural strength for a specific ceramic material will be greater than its fracture

strength measured from a tensile test. This phenomenon may be explained by dif-

ferences in specimen volume that are exposed to tensile stresses: the entirety of a

tensile specimen is under tensile stress, whereas only some volume fraction of a flex-

ural specimen is subjected to tensile stresses—those regions in the vicinity of the

specimen surface opposite to the point of load application (see Figure 7.18).