Segmentation of a three-dimensional crack front under mode I+III: closed-form predictions tested by a Born-weight dual boundary element–peridynamics coupling

A planar crack front driven in mixed mode I+III leaves its plane beyond a thresholdmixity and breaks into an echelon of tilted facets, the lance marks and factory roofs offractography. Their spacing is set by a material length that a scale-free elastic theoryleaves open, and this paper supplies it. A collar factor, the characteristic function of thereach of the front along its own length, is obtained in closed form and by lattice sums, anda selection rule turns it into a facet spacing of one to three horizons, and below 1.6 fora bond-based collar; the lattice sums place it within 2.4 to 3.1 per cent of its continuumvalue at three points per horizon. A second closed form gives the share of the fractureenergy carried by bonds that fail in tension under mixity. The Born-weight dual boundaryelement method carries the description to three dimensions, delivering the intensity factorsalong the front as primary unknowns and loading a peridynamic collar that resolves theseparation. The onset and growth rate of the linear-stability analysis, and the facet tilt ofthe tension criterion, are each tested there on a front free to leave its plane.