Page 257 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C005.fm Page 237 Monday, May 23, 2005 5:47 PM

Fracture Mechanisms in Metals 237

FIGURE 5.21 Initiation of cleavage at a microcrack that forms in a second-phase particle ahead of a mac-
roscopic crack.

slip planes by means of dislocation interaction. A far more common mechanism for microcrack
formation in steels, however, involves inclusions and second-phase particles [1, 25, 26].
Figure 5.21 illustrates the mechanism of cleavage nucleation in ferritic steels. The macroscopic
crack provides a local stress and strain concentration. A second-phase particle, such as a carbide or
inclusion, cracks because of the plastic strain in the surrounding matrix. At this point the microcrack
can be treated as a Griffith crack (Section 2.3). If the stress ahead of the macroscopic crack is sufficient,
the microcrack propagates into the ferrite matrix, causing failure by cleavage. For example, if the
particle is spherical and it produces a penny-shaped crack, the fracture stress is given by

E
 πγ  / 12
σ =  p  (5.17)
f
2
 (1 − ν C 
)
o
where γ is the plastic work required to create a unit area of fracture surface in the ferrite and C is
o
p
the particle diameter. It is assumed that γ >> γ , where γ is the surface energy (c.f. Equation (2.21)).
p
s
s
Note that the stress ahead of the macrocrack is treated as a remote stress in this case.
Consider the hypothetical material described earlier, where σ = 400 MPa and E = 210,000 MPa.
YS
2
Knott [1] has estimated γ = 14 J/m for ferrite. Setting σ = 3 σ and solving for critical particle
f
p
YS
diameter yields C = 7.05 µm. Thus the Griffith criterion can be satisfied with relatively small
o
particles.
The nature of the microstructural feature that nucleates cleavage depends on the alloy and heat
treatment. In mild steels, cleavage usually initiates at grain boundary carbides [1, 25, 26]. In
quenched and tempered alloy steels, the critical feature is usually either a spherical carbide or an
inclusion [1, 27]. Various models have been developed to explain the relationship between cleavage
fracture stress and microstructure; most of these models resulted in expressions similar to Equation (5.18).
Smith [26] proposed a model for cleavage fracture that considers stress concentration due to a
dislocation pile-up at a grain boundary carbide. The resulting failure criterion is as follows:
 τ 2 C  2 4 Eγ
C o 2 f k σ + 2 1 + i o  = p (5.18)

y
  2 π k y   π ( ν 1− 2 )