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 fracture 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 controlling crack propagation behavior and, subsequently, the (effective) toughness of the composite. Here, we systematically investigate how dynamic brittle fracture navigates through a linear array of mesoscale inclusions. Using a variational phase-field (PF) approach, we compute the apparent crack speed and fracture energy dissipation rate to compare crack propagation (and the resulting toughening) under Mode-I loading for various configurations of inclusions. We identify an interplay between the size of inclusion and that of the -dominant zone in the presence of elastic heterogeneity: matching these two sizes gives rise to the best toughening outcome for a given area fraction of inclusions. We discuss mechanisms that rationalize this observation and the importance of the length scale parameter used in PF models in interpreting simulation results. Our work sheds physical insight into the interaction between size effects and material properties, thereby opening a venue for the rational design of functional (architected) composites for dynamic fracture applications.

中文翻译：

---

材料异质性对脆性固体裂纹扩展的细观尺寸效应：相场模拟的视角

脆性固体通常通过添加第二相材料来增韧。这种做法通常会导致复合材料在细观尺度上具有材料异质性：与断裂过程区域的尺度相比较大，但与应用的尺度相比较小。这种介观尺度异质性的特定配置（几何和机械）通常被认为对于控制裂纹扩展行为以及随后的复合材料的（有效）韧性非常重要。在这里，我们系统地研究动态脆性断裂如何穿过中尺度夹杂物的线性阵列。使用变分相场 (PF) 方法，我们计算表观裂纹速度和断裂能量耗散率，以比较各种夹杂物配置在 I 型载荷下的裂纹扩展（以及由此产生的增韧）。我们确定了在存在弹性异质性的情况下夹杂物的尺寸和主区域的尺寸之间的相互作用：对于给定的夹杂物面积分数，匹配这两种尺寸会产生最佳的增韧结果。我们讨论了使这一观察合理化的机制以及 PF 模型中使用的长度尺度参数在解释模拟结果方面的重要性。我们的工作对尺寸效应和材料性能之间的相互作用提供了物理洞察，从而为动态断裂应用的功能（架构）复合材料的合理设计开辟了场所。