Table 4 In this paper, we distinguish between two types of dislocation sources which operate along the crack front: First, there are intrinsic sources operating at the crack front but inside the grains. Second, we suggest the intersection points of grain boundaries with the crack front are preferred dislocation nucleation sites.

From: Elucidating the dual role of grain boundaries as dislocation sources and obstacles and its impact on toughness and brittle-to-ductile transition

Comparison of the distances of the sources

Relevant measure for \(\lambda \)

Example, material/microstructure

mean distance of the intrinsic sources along the crack front << mean distance of the intersection points of grain boundaries with the crack front

\(\lambda \) = the mean distance of the intrinsic sources

• Materials with narrow intrinsic source distances

  

• Coarse-grained materials and single crystals

mean distance of the intersection points of grain boundaries with the crack front << mean distance of the intrinsic sources along the crack front

\(\lambda \) = the mean distance of the intersection points of grain boundaries with the crack front

• Materials with broad intrinsic source distances

  

• Fine-grained materials