These models assume that the scatter band of the fracture toughness values can be modeled using Weibull statistics.
It has been shown theoretically (21) that so long as no stable crack extension occurs during the loading, and the constraint in the specimen does not change, which means that the triaxiality of the stress and strain field at the crack tip does not change during the loading event, the scatter band follows the Weibull distribution.
Other, more practical books show the scatter band that exists in reality because of chemical, processing and procedural variations and measurement errors.
Figure 8 shows a typical scatter band between the tensile properties of test bars cut from standard ASTM keel blocks and the hardness of the same broken test bar shoulder.
The virgin, bottle flake, and recycled powder define a relatively narrow scatter band
, with no significant differences between the materials.