A coupled phase-field crystal-plasticity model yields Hall-Petch crack nucleation and inverse Hall-Petch crack propagation, explaining a non-monotonic grain-size toughness trend.
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Grain-size dependence of plastic-brittle transgranular fracture
A coupled phase-field crystal-plasticity model yields Hall-Petch crack nucleation and inverse Hall-Petch crack propagation, explaining a non-monotonic grain-size toughness trend.