2026/08/05 by Khanh Chau Le, Thi My Kieu Tran
Physics and Astronomy · Computer Science · Mathematics · #cond-mat.mtrl-sci #cs.NA #math-ph #math.MP #math.NA #physics.class-ph
35 pages, 5 figures
arxiv created 2026/08/05 · arxiv updated 2026/08/06
We propose a phase field model of a macrocracked single crystal in which the crack and the geometrically necessary dislocations descend from a single energy functional. Energy minimization alone then decides dislocation nucleation, through an integral criterion evaluated in closed form along slip chords. The criterion yields a size effect inaccessible to point-wise strength conditions: a grain-size-dependent yield stress. With slip suppressed the model reproduces Griffith fracture; with fracture suppressed, the nucleation load measured by the full non-smooth solver agrees with the closed-form nucleation criterion to four percent. The coupled computations produce a two-stage response: at loads an order of magnitude below cleavage, dislocation bands emitted from the notch tip blunt and shield it, raising the initiation load; once the crack grows, the bands heal; a compact cluster of like-signed dislocations travels with the tip, its canceling partner walls pinned at the grain boundary, and the dissipated fracture resistance equals the elastic one. In the purely energetic, dissipationless limit, emission shields the crack but does not toughen it; toughening requires dissipation, incorporated in the sequel through the threshold resistance to dislocation motion.