Abstract We develop a hierarchical model for the description of the stress state inside a cluster of degenerated graphite in spheroidal cast iron. The model is based on the following simplifying assumptions: at the microscale, the graphite particles are viewed as elliptical pores; at the mesoscale, clusters of graphite particles are modeled as elliptical inclusions made of an equivalent porous elastic material in plane strain. To calculate the equivalent elastic properties of the porous material, we adopt the Mori-Tanaka’s estimate. The accuracy of the model has been numerically verified by comparing the results of the model with FE simulations at three different levels: at the microscale, at the mesoscale, and coupling at the two scales. The model allows to study the effect of graphite microstructure on the average stress distribution inside the cluster.

中文翻译：

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开发适用于铸铁退化石墨的空隙簇分层模型

摘要 我们开发了一个层次模型来描述球墨铸铁中退化石墨簇内的应力状态。该模型基于以下简化假设：在微观尺度上，石墨颗粒被视为椭圆孔；在中尺度上，石墨颗粒簇被建模为椭圆形夹杂物，由平面应变中的等效多孔弹性材料制成。为了计算多孔材料的等效弹性特性，我们采用 Mori-Tanaka 的估计。通过在微观尺度、中尺度和两个尺度的耦合三个不同层次上将模型结果与有限元模拟结果进行比较，对模型的准确性进行了数值验证。