The effect of ductile tearing on the measured J-integral is addressed in ASTM E 1921 by limiting the amount of ductile crack growth prior to brittle fracture to avoid inaccuracies from excessive plastic deformation. In some standards, specific formulas for correcting the effect of excessive ductile crack growth have also been presented. It is possible to correct in this way for small crack growth relative to the exces­sive plastic deformation that occurs, but the statistical effect associated with the probability of cleavage fracture initiation cannot be corrected.

Ductile tearing preceding brittle fracture affects the measured fracture toughness by increasing the
volume ahead of the crack tip where brittle fracture initiation can occur, which increases the cumulative probability of failure. This statistical crack growth effect is comparable to the statistical size effect, which also is due to the increased volume of material under stress, increasing the probability of brittle fracture initiation as the crack length increases. In addition to increasing the volume of potential cleavage initiators, ductile tearing also tends to change the crack tip stress distribution. On the other hand, a small amount of ductile tearing can be regarded as beneficial since it can increase the stress triaxiality at the crack tip. This triaxiality effect is of minor importance when compared to the statistical effect that is dis­cussed next.

The statistical effect is due to the preceding ductile crack growth and is dependent on the amount of the crack growth.18,21 A simplified expression for the fracture probability (Pf) at stress intensity (Kj), considering a small amount of ductile tearing (Da < 1 mm), is given in the form1 ,22:

2O2Da
KI2(2m + 1)

[28]

where m and O are material-dependent constants, B is specimen thickness, B0 and K0 are scale factors, and Kmin = 20 MPa Vm. The value of O has been esti­mated to be 5500 MPa for medium strength struc­tural steels (ffy = 300—550 MPa). Equation [28] can be simplified by setting (2 m + 1) = 1 when O becomes ^4700 MPa. Parameter m is defined from the ductile — tearing power law function of the form:

f (Da)=J1mmDam [29]

where J1 mm is the value of J-integral at 1 mm crack growth and Da is crack growth.

By substituting the expression for failure pro­bability (eqn [13]) into eqn [28], one can derive a more practical formula giving a corrected value for Kj (Kj eff) due to ductile crack growth as follows:

2O2Da 1/4 r n

Kjeff = Kmin + (Kj — Kmin) 1 + ,7 [30]

Equations [29] and [30] can be used to take into account the increased fracture probability due to small amounts of ductile tearing, in addition to a possible standard correction for plastic deformation. Consideration of the statistical ductile-tearing effect may become relevant for high-strength steels with a
low-strain hardening capacity or for steels exhibiting low ductile-tearing resistance.

An example of analyses corrected for ductile crack growth is shown in Figure 17. The material is a ther­mally embrittled pressure vessel steel (A508 Cl. 3), which therefore has a high T0 (+69 °C). In this case, the correction lowers the fracture toughness in the upper transition region, but has a negligible effect on the value of T0 and the behavior near the lower shelf.