Brittle solids are often toughened by adding a second-phase material. This practice often results in composites with material heterogeneities on the meso scale: large compared to the scale of the process zone but small compared to that of the application. The specific configuration (both geometrical and mechanical) of this mesoscale heterogeneity is generally recognized as important in determining crack propagation and, subsequently, the (effective) toughness of the composite. Here, we systematically investigate how dynamic crack propagation is affected by mesoscale heterogeneities taking the form of an array of inclusions. Using a variational phase-field approach, we compute the apparent crack speed and fracture energy dissipation rate to compare crack propagation under Mode-I loading across different configurations of these inclusions. If fixing the volume fraction of inclusions, matching the inclusion size to the K-dominance zone size gives rise to the best toughening outcome. Conversely, if varying the volume fraction of inclusions, a lower volume fraction configuration can lead to a better toughening outcome if and only if the inclusion size approaches from above the size of the K-dominance zone. Since the size of the K-dominance zone can be estimated \textit{a priori} given an understanding of the application scenario and material availability, we can, in principle, exploit this estimation to design a material's mesoscale heterogeneity that optimally balances the tradeoff between strength and toughness. This paves the way for realizing functional (meta-)materials against crack propagation in extreme environments.

翻译：脆性固体常通过添加第二相材料实现增韧。这种工艺往往在介观尺度上形成具有材料非均匀性的复合材料：该尺度远大于过程区尺度，但远小于应用尺度。这种介观非均匀性的具体构型（包括几何构型和力学构型）通常被认为对裂纹扩展及后续复合材料的（有效）韧性起决定性作用。本文系统研究了以夹杂物阵列形式存在的介观非均匀性对动态裂纹扩展的影响机制。采用变分相场方法，计算了表观裂纹扩展速度与断裂能耗散率，以比较I型加载条件下不同夹杂物构型中的裂纹扩展行为。当固定夹杂物体积分数时，将夹杂物尺寸匹配至K主导区尺寸可获得最佳增韧效果。反之，改变夹杂物体积分数时，仅在夹杂物尺寸从上方趋近K主导区尺寸的条件下，较低体积分数构型才能产生更优的增韧效果。由于在理解应用场景和材料可得性的前提下可先验估计K主导区尺寸，理论上可利用该估计值设计材料的介观非均匀性，从而在强度与韧性之间实现最优权衡。这为开发极端环境下抗裂纹扩展的功能（超）材料开辟了新途径。