Page 375 - Mechanical Behavior of Materials

376 Chapter 8 Fracture of Cracked Members

Polymers that are useful as engineering materials typically have K Ic values in the range 1 to
√
5MPa m. Although these are low values, most polymers are used at low stresses due to their low
ultimate strengths, so that under typical usage the likelihood of fracture is roughly similar to that for
metals. Modifying a low-ductility polymer with ductile particles such as rubber increases its fracture
toughness. The addition of short chopped fibers or other stiff reinforcement may decrease toughness
if crack growth paths are available that do not intersect the reinforcement. Conversely, long fibers,
and especially continuous ones, in a polymer matrix composite may obstruct crack growth to the
point that the toughness is in the range of that for metals.
√
Ceramics have low values of fracture toughness, also in the range 1 to 5 MPa m, as might
be expected from their low ductility. This range of K Ic values is similar to that for polymers,
but it is quite low in view of the fact that ceramics are high-strength materials. Indeed, their
strengths in tension are usually limited by the inherent flaws in the material, as discussed near
the beginning of this chapter. Recent efforts in materials development have led to modifications
to ceramics that increase toughness somewhat. For example, alumina (Al 2 O 3 ) toughened with a
√
second phase of 15% zirconia (ZrO 2 ) has K Ic ≈ 10 MPa m. This occurs because high stress
causes a phase transformation (crystal structure change) in the zirconia, which increases its
volume by several percent. Thus, when the crack tip encounters a zirconia grain, the increase
in volume is sufficient to cause a local compressive stress that retards further extension of the
crack.
Fracture toughness exhibits more statistical variation than other materials properties, such as
yield strength. Coefficients of variation are often 10% and may reach 20%. Taking 15% as a typical
value, about one out of ten values from a large sample are expected to be 19% below the mean,
one out of a hundred 35% below, and one out of a thousand 46% below. Safety factors used in
design need to reflect this rather large uncertainty. (See Appendix B near the end of this book for
additional discussion of statistical variation and also for some sample statistical data on fracture
toughness.)

8.6.2 Effects of Temperature and Loading Rate
Fracture toughness generally increases with temperature; illustrative test data for a low-alloy steel
and a ceramic are shown in Figs. 8.33 and 8.34. An especially abrupt change in toughness over
a relatively small temperature range occurs in metals with a BCC crystal structure, notably in
steels with ferritic–pearlitic and martensitic structures. The temperature region where the rapid
transition occurs varies considerably for different steels, as illustrated in Fig. 8.35. There is
usually a lower shelf of approximately constant K Ic below the transition region, and an upper
shelf above it, corresponding to a higher approximately constant K Ic . (Only one set of data
in Fig. 8.35 covers a sufficient range to exhibit an upper shelf.) Such temperature-transition
behavior is similar to that observed in Charpy or other notch-impact tests, as discussed in
Chapter 4.
The distinct temperature-transition behavior in BCC metals is difficult to explain merely on
the basis of the increase in ductility associated with the temperature range involved. It is, in fact,
due to a shift in the physical mechanism of fracture. Below the temperature transition, the fracture
mechanism is identified as cleavage, and above it, as dimpled rupture. Microphotographs of fracture
surfaces exhibiting these mechanisms are shown in Fig. 8.36. Cleavage is fracture with little plastic