GTBL042-09 GTBL042-Callister-v3 October 4, 2007 11:53
2nd Revised Pages308 • Chapter 9 / Failurestage of propagation is flat and smooth, and appropriately termed themirrorregion
(Figure 9.14). For glass fractures, this mirror region is extremely flat and highly
reflective; on the other hand, for polycrystalline ceramics, the flat mirror surfaces
are rougher and have a granular texture. The outer perimeter of the mirror region is
roughly circular, with the crack origin at its center.
Upon reaching its critical velocity, the crack begins to branch—that is, the crack
surface changes propagation direction. At this time there is a roughening of the crack
interface on a microscopic scale, and the formation of two more surface features—
mistandhackle; these are also noted in Figures 9.14 and 9.15. The mist is a faint
annular region just outside the mirror; it is often not discernible for polycrystalline
ceramic pieces. And beyond the mist is the hackle, which has an even rougher texture.
The hackle is composed of a set of striations or lines that radiate away from the crack
source in the direction of crack propagation; furthermore, they intersect near the
crack initiation site, and may be used to pinpoint its location.
Qualitative information regarding the magnitude of the fracture-producing stress
is available from measurement of the mirror radius (rmin Figure 9.14). This radius is
a function of the acceleration rate of a newly formed crack—that is, the greater this
acceleration rate, the sooner the crack reaches its critical velocity, and the smaller the
mirror radius. Furthermore, the acceleration rate increases with stress level. Thus,
as fracture stress level increases, the mirror radius decreases; experimentally it has
been observed thatσf∝1
rm^0.^5(9.14)
Hereσfis the stress level at which fracture occurred.
Elastic (sonic) waves are generated also during a fracture event, and the locus
of intersections of these waves with a propagating crack front gives rise to another
type of surface feature known as aWallner line. Wallner lines are arc shaped, and
they provide information regarding stress distributions and directions of crack prop-
agation.9.7 FRACTURE OF POLYMERS
The fracture strengths of polymeric materials are low relative to those of metals
and ceramics. As a general rule, the mode of fracture in thermosetting polymers
(heavily crosslinked networks) is brittle. In simple terms, during the fracture process,
cracks form at regions where there is a localized stress concentration (i.e., scratches,
notches, and sharp flaws). As with metals (Section 9.5), the stress is amplified at the
tips of these cracks leading to crack propagation and fracture. Covalent bonds in the
network or crosslinked structure are severed during fracture.
For thermoplastic polymers, both ductile and brittle modes are possible, and
many of these materials are capable of experiencing a ductile-to-brittle transition.
Factors that favor brittle fracture are a reduction in temperature, an increase in
strain rate, the presence of a sharp notch, increased specimen thickness, and any
modification of the polymer structure that raises the glass transition temperature
(Tg) (see Section 11.17). Glassy thermoplastics are brittle below their glass transition
temperatures. However, as the temperature is raised, they become ductile in the
vicinity of theirTgs and experience plastic yielding prior to fracture. This behavior
is demonstrated by the stress–strain characteristics of poly(methyl methacrylate) in
Figure 7.24. At 4◦C, PMMA is totally brittle, whereas at 60◦C it becomes extremely
ductile.