A coupled phase field model derives dislocation nucleation from a single energy functional, yielding grain-size-dependent thresholds and showing that dissipationless shielding provides no toughening.
A discrete dislocation analysis of mode I crack growth
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A phase field model of coupled crack and dislocations: emission, blunting, and the necessity of dissipative toughening
A coupled phase field model derives dislocation nucleation from a single energy functional, yielding grain-size-dependent thresholds and showing that dissipationless shielding provides no toughening.