Fig. 3: Out-of-plane 3D fracture structures in the theoretical model and in experiments, and the mirror-mist-hackle-macro-branching sequence of morphological transitions.
From: Quenched disorder and instability control dynamic fracture in three dimensions
a–e (left column) Uppermost out-of-plane crack structures — corresponding to the phase-field ϕ(x) = 1/2 iso-surface — inside the bulk (top view), for the five G values indicated (corresponding to the thick-boundary diamonds in Fig. 2), see text for extensive discussion. In each panel, the long axis is the propagation (x) direction and the perpendicular one in the crack front direction (z-axis). Both axes are expressed in units of ξ, and the basic length along z is twice that of along x, for visual clarity. The initial crack front is marked by the bright line in the left part of each panel. f, g (middle column) Tilted zoom-in 3D view of the regions marked by the rectangles in panels (b) and (e), respectively. See text for discussion. h, i (right column) Fracture surface morphologies (fractography) measured in 3D dynamic fracture experiments (the crack propagates from left to right) in glass, adapted with permission from Fig. 3b of ref. 28 (image concatenation appears in the original, see ref. 28, and the scale bar is the same for both panels). Panel (h) shows the mist region (the preceding mirror region is not shown, but is clearly observed in panel (a)), which is characterized by rather isolated, small-amplitude out-of-plane surface structures. Panel (h) bears qualitative similarities to panels (b) and (f). Panel (i) shows the hackle region, appearing at larger crack propagation distances in the same experiment, continuously emerging from the mist region that preceded it. The observed wider and elongated out-of-place surface structures bear clear similarities to panels (c) and (d). Similar fractographic morphologies are observed in numerous other experiments, e.g., see Fig. 4 in ref. 29, reporting on 3D fracture experiments in a glassy polymer (PMMA).
