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

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

7.10 Flexural Strength • 211

where the unloading began. There will also be an elastic strain recovery associated

with fracture.

7.9 COMPRESSIVE, SHEAR, AND TORSIONAL

DEFORMATION

Of course, metals may experience plastic deformation under the influence of applied

compressive, shear, and torsional loads. The resulting stress–strain behavior into the

plastic region will be similar to the tensile counterpart (Figure 7.10a: yielding and the

associated curvature). However, for compression, there will be no maximum, since

necking does not occur; furthermore, the mode of fracture will be different from that

for tension.

Concept Check 7.2

Make a schematic plot showing the tensile engineering stress–strain behavior for a

typical metal alloy to the point of fracture. Now superimpose on this plot a schematic

compressive engineering stress–strain curve for the same alloy. Explain any differ-

ences between the two curves.

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

Mechanical Behavior—Ceramics

Ceramic materials are somewhat limited in applicability by their mechanical proper-

ties, which in many respects are inferior to those of metals. The principal drawback

is a disposition to catastrophic fracture in a brittle manner with very little energy

absorption. In this section we explore the salient mechanical characteristics of these

materials and how these properties are measured.

7.10 FLEXURAL STRENGTH

The stress–strain behavior of brittle ceramics is not usually ascertained by a tensile

test as outlined in Section 7.2, for three reasons. First, it is difficult to prepare and

test specimens having the required geometry. Second, it is difficult to grip brittle

materials without fracturing them; and third, ceramics fail after only about 0.1%

strain, which necessitates that tensile specimens be perfectly aligned to avoid the

presence of bending stresses, which are not easily calculated. Therefore, a more

suitable transverse bending test is most frequently employed, in which a rod specimen

having either a circular or rectangular cross section is bent until fracture using a three-

or four-point loading technique;^11 the three-point loading scheme is illustrated in

Figure 7.18. At the point of loading, the top surface of the specimen is placed in a

state of compression, while the bottom surface is in tension. Stress is computed from

the specimen thickness, the bending moment, and the moment of inertia of the cross

section; these parameters are noted in Figure 7.18 for rectangular and circular cross

sections. The maximum tensile stress (as determined using these stress expressions)

(^11) ASTM Standard C 1161, “Standard Test Method for Flexural Strength of Advanced
Ceramics at Ambient Temperature.”