Page 270 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C005.fm Page 250 Monday, May 23, 2005 5:47 PM

250 Fracture Mechanics: Fundamentals and Applications

FIGURE 5.31 Intergranular fracture in a steel ammonia tank. Photograph courtesy of W.L. Bradley.

environmental cracking mechanisms are discussed in detail in Chapter 11. Figure 5.31 shows an
intergranular fracture surface in a steel weld that was in contact with an ammonia environment.
Intergranular corrosion involves the preferential attack of the grain boundaries, as opposed to
general corrosion, where the material is dissolved relatively uniformly across the surface. Inter-
granular attack is different from environmental assisted cracking, in that an applied stress is not
necessary for grain boundary corrosion.
At high temperatures, grain boundaries are weak relative to the matrix, and a significant portion
of creep deformation is accommodated by grain-boundary sliding. In such cases void nucleation
and growth (at second-phase particles) is concentrated at the crack boundaries, and cracks form as
grain boundary cavities grow and coalesce. Grain-boundary cavitation is the dominant mechanism
of creep crack growth in metals [51], and it can be characterized with time-dependent parameters
*
such as the C integral (see Chapter 4).
.
APPENDIX 5: STATISTICAL MODELING OF CLEAVAGE FRACTURE

When one assumes that fracture occurs by a weakest link mechanism under J-controlled conditions,
it is possible to derive a closed-form expression for the fracture-toughness distribution. When
weakest link initiation is necessary but not sufficient for cleavage fracture, the problem becomes
somewhat more complicated, but it is still possible to describe the cleavage process mathematically.

A5.1 WEAKEST LINK FRACTURE

As discussed in Section 5.2, the weakest link model for cleavage assumes that failure occurs
when at least one critical fracture-triggering particle is sampled by the crack tip. Equation
4
(5.22) describes the failure probability in this case. Since cleavage is stress controlled, the

4 It turns out that Equation (5.22) is valid even when the Poisson assumption is not applicable [40]; the quantity ρ is not
the microcrack density in such cases but ρ is uniquely related to microcrack density. Thus, the derivation of the fracture-
toughness distribution presented in this section does not hinge on the Poisson assumption.