AI 中文总结
本研究构建了裂纹与位错耦合的相场模型，揭示位错发射可屏蔽裂纹但需引入位错运动阈值阻力这类耗散项才能实现增韧的机制。
AI 中文摘要
我们提出了一种含宏观裂纹的单晶相场模型，其中裂纹和几何必需位错源自单一能量泛函。仅通过能量最小化即可决定位错形核，该形核通过沿滑移弦评估的闭式积分准则实现。此准则可产生点式强度条件无法得到的尺寸效应：即与晶粒尺寸相关的屈服应力。当滑移被抑制时，模型重现格里菲斯断裂；当断裂被抑制时，由完全非光滑求解器测得的形核载荷与闭式形核准则的吻合度达4%。耦合计算产生两阶段响应：在远低于解理的载荷下，从缺口尖端发射的位错带会钝化并屏蔽尖端，提高起始载荷；一旦裂纹扩展，位错带便会愈合；一组由同号位错组成的紧凑团簇随尖端移动，其抵消的配对壁则被钉扎在晶界处，且耗散的断裂阻力等于弹性阻力。在纯能量的无耗散极限下，位错发射可屏蔽裂纹但无法使其增韧；增韧需要耗散，后续将通过位错运动的阈值阻力引入该耗散项。
英文摘要
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.
Comments35 pages, 5 figures
