A lower bound curve can be constructed to corre­spond to a lower limiting fracture probability, which normally is set to 5% or 2%, taking into account the uncertainty ofthe T0 determination. The uncertainty of determining T0 depends on the number of speci­mens used to establish T0. The uncertainty (A T0) is defined from a normal distribution with two vari­ables, the test temperature, and the number of speci­mens used for the T0 determination, as follows:

AT0 = — Z [19]

r

where b= 18-20 °C, depending on the value of T — T0, r is the number of valid test data used to determine T0, and Z is the confidence level (e. g., Z85% = 1.44).

The median KJc is used to determine the value of and the uncertainty of T0 according to ASTM E1921. When Kjc(med) is equal to or greater than 83 MPa Vm, b = 18 °C. Alternatively, b = 20 can be used for all values of Kjc(med) not less than the mini­mum of 58 MPa Vm.

KJc(0.02) = 24.1 + 290 exp{°.°19(T — T0(margin))}

[23]

Kfc(0.05) = 252 + 366 exp{0.019(T — T0(margin)) }

[24]

When the dataset consists of several test tempera­tures, the median KJc is obtained from the basic rela­tionship (eqn [18]) as follows:

Jmd) = — E f30 + 70 exp[0.019(T,- — T0)]} [25]

r i=1

where r is the number of valid test data.

The 2% lower bound curve is sometimes used as a criterion to determine if the material should be analyzed by taking into account possible material inhomogeneity. This further analysis can be done using the SINTAP procedure (discussed in Section 4.14.2.5), which ensures that a conservative lower bound definition is obtained regardless of possible low fracture toughness values.16,17 If there are values below the 2% curve, the data preferably should be analyzed using the not yet standardized multimodal procedure.17 An example of the 2% curve and the effect of the basic SINTAP analysis are shown in Figure 10.

4.14.2.1.3 Limits of applicability

The applied cleavage fracture model strictly applies only to the transition region of the material, although the model also includes a term to take into account the conditional probability of crack propagation. This term is needed because in and near the lower shelf, the fracture event is mainly controlled by crack
propagation and therefore cannot be correctly described by only the crack initiation term. The situation is complicated by the fact that the lower shelf is not always close to the assumed, theoretically estimated, constant value of 20 MPa Vm (although it usually is). It is also assumed (Section 4.14.1.3.2) that the crack initiators are randomly distributed and that no global interaction exists between the crack initiators. The material is also assumed to be macro — scopically homogeneous. The method applies for transgranular, cleavage fracture events, although it may be used, with caution, for intergranular-type fracture especially when the fracture event is pre­dominantly stress controlled (as is typical in the lower transition area). Figure 11 shows scanning electron microscope views of both transgranular cleavage and intergranular fracture mode surfaces. The scope of applicability and the limitations of the method are also discussed in Sections 4.14.2.5 and 4.14.3.1 and the application to structures in Section 4.14.3.2.