Page 124 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C003.fm Page 104 Monday, May 23, 2005 5:42 PM

104 Fracture Mechanics: Fundamentals and Applications

FIGURE 3.1 Crack-tip-opening displacement (CTOD).
An initially sharp crack blunts with plastic deforma-
tion, resulting in a finite displacement (d ) at the crack
tip.

Substituting Equation (3.2) into Equation (3.1) gives
K
2
4
I
δ = y = 2u πσ E (3.3)
YS
where δ is the CTOD. Alternatively, CTOD can be related to the energy release rate by applying
Equation (2.54):

δ = 4 G (3.4)
πσ YS

Thus, in the limit of small-scale yielding, CTOD is related to G and K . Wells postulated that CTOD
I
is an appropriate crack-tip-characterizing parameter when LEFM is no longer valid. This assumption
was shown to be correct several years later when a unique relationship between CTOD and the J
integral was established (Section 3.3).
The strip-yield model provides an alternate means for analyzing CTOD [3]. Recall Section
2.8.2, where the plastic zone was modeled by yield magnitude closure stresses. The size of the
strip-yield zone was defined by the requirement of finite stresses at the crack tip. The CTOD can
be defined as the crack-opening displacement at the end of the strip-yield zone, as Figure 3.3
illustrates. According to this definition, CTOD in a through crack in an infinite plate subject to a
remote tensile stress (Figure 2.3) is given by [3]

δ = 8 σ a lnsec   πσ   (3.5)
YS
πE  2 σ 
YS

FIGURE 3.2 Estimation of CTOD from the displace-
ment of the effective crack in the Irwin plastic zone
correction.