Development of a hierarchical model for voids clusters suitable for cast iron degenerated graphite

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.