“…To provide focus, recall that the bridging mechanism of ductile-phase toughening, DC ss , scales with the diameter, 2R, and the area fraction, f, of this phase intercepted by the crack: [11][12][13][14] DC ss = fRv, where r o is the yield strength of the ductile phase and v is a work of rupture parameter governed by the plastic stretch, u c fi v = 2.5 u c /R. [11][12][13][14] Note that, to maximize the contribution to this toughening mechanism, the ductile phase should percolate through the joint, so that the area fraction term, f, participates fully.…”