Fig. 10: Facet-facet fracture interactions.
In order to isolate facet–facet interactions, we compare the predictions of stress intensity factors using model B, which includes a parent fracture and neighboring facets (Fig. 9), and model A, which only includes the parent fracture (Fig. 8a). This comparison is made as a function of the normalized fracture tip/front length s, for different parent fracture tilt angles ϕ and closeness between facets Λ. Panels a–c show the difference in the opening mode stress intensity factor, \({\Delta {K}_{{\rm{I}}}={K}_{{\rm{I}}}^{(B)}-{K}_{\text{I}}^{(A)}}\), for a range of distances between facets (from very close, Λ = 0.4, to far away, Λ = 1.6) and tilt angles ϕ = 10°, 20°, 40°. For small tilt angles (ϕ = 10°) and closely spaced facets (Λ = 0.4), the difference ΔKI is generally positive near the center of the facet (s ≈1/2) and negative near the edges (s ≈0 and s ≈1). This negative difference near the edges indicates stress shielding due to the proximity of adjacent fractures. As the tilt angle ϕ or the distance between facets Λ increases, the influence of neighboring facets on KI decreases. For less tilted and more distant facets, the edges of the fracture tips face each other, which can lead to stress amplification (compare panels Fig. 10a–c). Panels d–f and g–i show the influence of facet-facet interactions on the shear modes II and III (\({\Delta} {K}_{{\rm{II}}}={K}_{{\rm{II}}}^{(B)}-{K}_{\text{II}}^{(A)}\) and \(\Delta {K}_{{\rm{III}}}={K}_{{\rm{III}}}^{(B)}-{K}_{\text{III}}^{(A)}\), respectively). It is clear that close neighboring facets induce local shear. As expected, the influence of neighboring facets on the local shear modes decreases with increasing distance between facets, Λ, and with increasing inclination angle, ϕ (reducing shielding).
