Self-consistent one-particle 3D unit cell model for simulation of the effect of graphite aspect ratio on Young’s modulus of cast-iron

The graphite phase of ferritic cast-iron was assumed to consist of randomly oriented, rotationally symmetric, ellipsoidal inclusions of same dimensions. Accordingly, a self-consistent one-particle 3D unit cell model was developed to simulate the effect of graphite aspect ratio on cast-iron elastic constants. The cube shaped unit cell is made up of an inner rotational ellipsoid of graphite surrounded by α Fe–2.5%Si matrix in a concentric outer ellipsoid of the same aspect ratio as the inner graphite ellipsoid in order to model the desired graphite content. The remainder of the unit cell is filled up by the cast-iron compound, the elastic behaviour of which is determined self-consistently. In order to obtain elastic properties, the unit cell was subjected to uniaxial loading. Calculations of stress and strain distributions, in dependence on the orientation of the graphite ellipsoid, were carried out by the finite element method using 3D elements. Finally, updated values of Young’s modulus and Poisson’s ratio were derived by employing Hooke’s law. This procedure was repeated, using the updated elastic constants as new input, to get a self-consistent convergent solution. The results are compared with finite element calculations using a conventional one-particle 3D unit cell model with multiphase elements, and an analytical solution given in the literature. Comparison with experimental data shows the relatively wide range of validity and the superiority of the self-consistent method.