Download Brittle Fracture of Ceramics

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Mechanical Properties of Ceramics
Ceramic materials are somewhat limited in applicability by their
mechanical properties, 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.
Brittle Fracture of Ceramics
At room temperature, both crystalline and noncrystalline ceramics almost
always fracture before any plastic deformation can occur in response to an
applied tensile load.
The brittle fracture process consists of the formation and propagation of
cracks through the cross section of material in a direction perpendicular to
the applied load.
The measure of a ceramic material’s ability to resist fracture when a crack
is present is specified in terms of fracture toughness. The plane strain
fracture toughness as discussed in Section 8.5 is defined according to the
expression:
For compressive stresses, there is no stress amplification associated with
any existent flaws. For this reason, brittle ceramics display much higher
strengths in compression than in tension (on the order of a factor of 10), and
they are generally utilized when load conditions are compressive.
Flexural Strength
The stress–strain behavior of brittle ceramics is not usually ascertained by a
tensile test as outlined in Section 6.2, 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; the three-point loading scheme is
illustrated in Figure 13.1.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 13.1 for rectangular and circular cross sections. The
maximum tensile stress (as determined using these stress expressions) 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.
The stress at fracture using this flexure test is known as the flexural
strength, modulus of rupture, fracture strength, or the bend strength, an
important mechanical parameter for brittle ceramics. For a rectangular cross
section, the flexural strength σfs is equal to
Mechanisms of Plastic Deformation
Although at room temperature most ceramic materials suffer fracture before
the onset of plastic deformation, a brief exploration into the possible
mechanisms is worthwhile. Plastic deformation is different for crystalline
and noncrystalline ceramics.
Crystalline Ceramics
For crystalline ceramics, plastic deformation occurs, as with metals, by the
motion of dislocations (Lec 8). One reason for the hardness and brittleness
of these materials is the difficulty of slip (or dislocation motion). For
crystalline ceramic materials for which the bonding is predominantly ionic,
there are very few slip systems (crystallographic planes and directions
within those planes) along which dislocations may move. This is a
consequence of the electrically charged nature of the ions.
For slip in some directions, ions of like charge are brought into close
proximity to one another; because of electrostatic repulsion, this mode of
slip is very restricted, to the extent that plastic deformation in ceramics is
rarely measurable at room temperature.
By way of contrast, in metals, since all atoms are electrically neutral,
considerably more slip systems are operable and, consequently, dislocation
motion is much more facile.
On the other hand, for ceramics in which the bonding is highly covalent,
slip is also difficult and they are brittle for the following reasons: (1) the
covalent bonds are relatively strong, (2) there are also limited numbers of
slip systems, and (3) dislocation structures are complex.
Noncrystalline Ceramics
Plastic deformation does not occur by dislocation motion for noncrystalline
ceramics because there is no regular atomic structure. Rather, these
materials deform by viscous flow, the same manner in which liquids
deform; the rate of deformation is proportional to the applied stress. In
response to an applied shear stress, atoms or ions slide past one another by
the breaking and reforming of interatomic bonds. However, there is no
prescribed manner or direction in which this occurs, as with dislocations.
Viscous flow on a macroscopic scale is demonstrated in Figure12.3
Viscosity is a measure of a noncrystalline material’s resistance to
deformation. For viscous flow in a liquid that originates from shear stresses
imposed by two flat and parallel plates, the viscosity η is the ratio of the
applied shear stress τ and the change in velocity dv with distance dy in a
direction perpendicular to and away from the plates, or
The units for viscosity are poises (P) and pascal-seconds (Pa-s); P=1 dynes/ cm2, and 1 Pa-s =1 N-s/m2. Conversion from one system of units to the
other is according to
Liquids have relatively low viscosities; for example, the viscosity of water
at room temperature is about Pa-s. On the other hand, glasses have 10
extremely large viscosities at ambient temperatures, which are accounted
for by strong interatomic bonding. As the temperature is raised, the
magnitude of the bonding is diminished, the sliding motion or flow of the
atoms or ions is facilitated, and subsequently there is an attendant decrease
in viscosity.