An Integrated Multi-scale Model for Graphite Growth Mechanism in Industrial Cast Iron

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.