Page 380 - Mechanical Behavior of Materials

Section 8.7 Plastic Zone Size, and Plasticity Limitations on LEFM 381

Fracture toughness is generally more sensitive than other mechanical properties to anisotropy
and planes of weakness introduced by processing. For example, in forged, rolled, or extruded metal,
the crystal grains are elongated and/or flattened in certain directions, and fracture is easier where
the crack grows parallel to the planes of the flattened grains. Nonmetallic inclusions and voids
may also become elongated and/or flattened so that they also cause the fracture properties to vary
with direction. Thus, fracture toughness tests are often conducted for various specimen orientations
relative to the original piece of material. The six possible combinations of crack plane and direction
in a rectangular section of material are shown in Fig. 8.40. Fracture toughness data for three of these
possibilities are also given for some typical aluminum alloys.
Neutron radiation affects the pressure vessel steels used in nuclear reactors by introducing
large numbers of point defects (vacancies and interstitials) into the crystal structure of the material.
This causes increased yield strength, but decreased ductility, and the fracture toughness transition
temperature may increase substantially, as shown by test data in Fig. 8.41. As a result, there is a
large decrease in fracture toughness over a range of temperatures. Such radiation embrittlement
is obviously a major concern in nuclear power plants and is an important factor in determining
their service life.

8.6.4 Mixed-Mode Fracture

If a crack is not normal to the applied stress, or if there is a complex state of stress, a combination of
fracture Modes I, II, and III may exist. For example, a situation involving combined Modes I and II
is shown in Fig. 8.25. Such a situation is complex because the crack may change direction so that it
does not grow in its original plane, and also because the two fracture modes do not act independently,
but rather interact. Tests analogous to the K Ic test to determine K IIc or K IIIc are difficult to
conduct and are not standardized, so that toughness values for the other modes are generally
not known.
The situation is analogous to the need for a yield criterion for combined stresses. Several
combined-mode fracture criteria exist, but there is currently no general agreement on which is best.
Any successful theory must predict mixed-mode fracture data of the type shown in Fig. 8.42. These
particular data suggest that an elliptical curve could be used as an empirical fit, which is useful
where both K Ic and K IIc are known.

2 2
K I K II
+ = 1 (8.34)
K Ic K IIc

8.7 PLASTIC ZONE SIZE, AND PLASTICITY LIMITATIONS ON LEFM

Near the beginning of this chapter, it was noted that real materials cannot support the theoretically
infinite stresses at the tip of a sharp crack, so that upon loading, the crack tip becomes blunted
and a region of yielding, crazing, or microcracking forms. We will now pursue yielding at crack
tips in more detail. It is significant that the region of yielding, called the plastic zone, must not be
excessively large if the LEFM theory is to be applied.