In the past 100 years, precipitation strengthening has always been extremely important pathway to resist the deformation of material due to significantly improving matrix strength. The size deviation degree and the space distribution of precipitates have a great influence on the strength reported by recent experiments, however, this internal mechanism has been largely ignored and incompletely understood until to now in nickel-based superalloy. Herein, our work systematically clarifies the effect of size deviation degree on the complex interaction between precipitates and dislocations in a 3D space, to explore the enrichment of precipitation size and spatial distribution mediated strengthening mechanism. Especially, a new statistical approach using minimal spanning tree to describe the variation of the inter-precipitate spacing is proposed for accurately assessing contribution of the spatially randomly distributed precipitates to the strength. Importantly, the maximal precipitation strengthening occurs when the size variance is equal to the average size, due to high frequent interactions of dislocations with precipitations to cause the strong pinning and the distorted dislocation-line structure. The slight precipitate spatial enrichment corresponding to the optimal strength makes the precipitates tend to be evenly distributed on the slip plane, which results in more precipitates on the moving dislocation line, and then leads to a severely curved dislocation, arising the high dislocation line tension to inhibit its movement. A robustness test performed on nickel-based superalloys suggests our proposed method would be robust to accurately evaluate performance without experiment, and simultaneously gives optimal precipitate distributions. The current work provides a new strategy to adjust the distribution mode of precipitates to enhance mechanical properties of precipitate hardened alloys.

近100年来，由于基体强度显着提高，沉淀强化一直是抵抗材料变形的极其重要的途径。析出物的尺寸偏差程度和空间分布对最近的实验报道的强度有很大的影响，然而，到目前为止，这种内部机制在镍基高温合金中一直被忽视和不完全理解。在此，我们的工作系统地阐明了尺寸偏差程度对3D空间中析出物和位错之间复杂相互作用的影响，以探索析出物尺寸的富集和空间分布介导的强化机制。尤其，提出了一种使用最小生成树来描述沉淀间距变化的新统计方法，用于准确评估空间随机分布的沉淀对强度的贡献。重要的是，最大的沉淀强化发生在尺寸方差等于平均尺寸时，这是由于位错与沉淀的频繁相互作用导致强钉扎和扭曲的位错线结构。与最佳强度相对应的轻微析出物空间富集使析出物倾向于均匀分布在滑移面上，导致运动位错线上的析出物增多，进而导致位错弯曲严重，产生高位错线张力抑制其运动。对镍基高温合金进行的稳健性测试表明，我们提出的方法将是稳健的，无需实验即可准确评估性能，同时给出最佳的析出物分布。目前的工作提供了一种新的策略来调整析出物的分布模式，以提高析出物硬化合金的力学性能。