The prediction of precipitated graphite nodules size and distribution in a large industrial casting is critical to understand the mechanical behavior of cast iron components used in heavy vehicles. An accurate prediction of the graphite nodules requires a validated and integrated macro-micro modeling framework, which forms the motivation behind the present study. Classical theories in the literature (Lesoult et al. in Acta Mater 46:983–995, 1998) proposed two stages of graphite growth: in (i) liquid stage, after encapsulation by the austenite grain, and in (ii) solid stage, surrounded by only austenite phase. In this work, a new stage of graphite growth was proposed, where a graphite nodule was in direct contact with the liquid metal, existing in the presence of an austenite grain separated from the nodule. The resulting three-stage graphite growth in a microscopic control volume was formulated using a volume-averaged micro-model. This was made to evolve with the help of a macroscopic temperature field obtained from finite-element-based numerical simulation and thus creating a comprehensive modeling framework. Further, for the first time, a diffusion-based deforming-grid micro-model was developed to obtain the exact nature of a single graphite nodule growth based on the position of individual phases in the microscopic control volume. The model predictions were validated with experimental results from the step-casting experiments in the present study, as well as with the observations of single nodule growth from in situ synchrotron X-ray tomography (Bjerre et al. in Model Simul Mater Sci Eng 26:085012, 2018; Azeem et al. in Acta Mater 155:393–401, 2018). The proposed models captured, faithfully, the experimental patterns of graphite growth evolution, number density of the nodules, and the size distribution as a function of cooling rate. This integrated multi-scale modeling approach is envisaged to be effective for determining exact graphite growth behavior of a single nodule and volume-averaged graphite growth in a large casting.

中文翻译：

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工业铸铁石墨生长机理的多尺度综合模型

大型工业铸件中沉淀石墨球尺寸和分布的预测对于了解重型车辆中使用的铸铁部件的机械性能至关重要。石墨结核的准确预测需要经过验证和集成的宏观微观建模框架，这构成了本研究背后的动机。文献中的经典理论（Lesoult et al. in Acta Mater 46:983–995, 1998）提出了石墨生长的两个阶段：（i）液态阶段，在被奥氏体晶粒包裹后，以及（ii）固态阶段，仅被奥氏体相包围。在这项工作中，提出了石墨生长的新阶段，其中石墨球与液态金属直接接触，存在与球团分离的奥氏体晶粒。在微观控制体积中产生的三阶段石墨生长使用体积平均微观模型制定。这是在从基于有限元的数值模拟中获得的宏观温度场的帮助下发展起来的，从而创建了一个全面的建模框架。此外，首次开发了基于扩散的变形网格微观模型，以根据微观控制体积中各个相的位置来获得单个石墨节生长的确切性质。模型预测得到了本研究中逐步铸造实验的实验结果以及原位同步加速器 X 射线断层扫描观察到的单个结核生长的验证（Bjerre 等人在 Model Simul Mater Sci Eng 26 中： 085012，2018 年；Azeem 等人在 Acta Mater 155:393–401，2018）。所提出的模型忠实地捕捉到了石墨生长演化的实验模式、结核的数量密度以及作为冷却速率函数的尺寸分布。这种集成的多尺度建模方法被认为可以有效地确定单个球状体的精确石墨生长行为和大型铸件中的体积平均石墨生长。