A two-scale model of degenerated graphite in cast iron

A two-scale model for clusters of degenerated graphite in gray cast iron is presented. The novelty of the model is that, at the mesoscale, a single cluster is described as a spheroidal inclusion made of porous materials. At the microscale, the porous material contains a random distribution of randomly oriented spheroidal voids modeling the graphite precipitates. To calculate the stress state inside and at the outer surface of the cluster, two different approaches are presented. In the first approach, the effective elastic properties of the porous material at the microscale are obtained using Pan and Weng homogenization scheme, based on Eshelby's equivalent principle and the Mori-Tanaka's estimate; at the mesoscale, the stress distributions inside and at the outer surface of the cluster are calculated using Eshelby's solution applied to an inclusion made of equivalent porous material. The second approach is based on a finite element analysis of a cluster embedding 216 randomly oriented and randomly distributed spheroidal voids. A comparison between the numerical results obtained with the two approaches indicates good agreement in terms of average (elastic and stress distribution) properties. The equivalent elastic properties (Young's modulus) calculated at the microscale in the two approaches are also compared with some experimental results available in the scientific literature.