### Characterization of Nodular Cast-Iron Using Multi-Scale Constitutive Modeling

#### Abstract

The constitutive properties of cast-iron materials depend on the graphite morphology and the characteristics of the metallic matrix. Specifically, in the nodular cast-iron, these properties are affected by the spheroidicity of the graphite and the volume fractions of the ferritic phase and pearlitic microconstituent.

The constitutive properties of such materials are usually presented by means of an analytical formula in terms of micro-structural characteristics. In the derivation of an analytical expression, the formulation of hypotheses are needed to define the behavior, shape and distribution of the elements in the micro-structure. Then, the analytical formulation to predict the constitutive behavior of the nodular cast-iron is restricted to the micro-structures that satisfy such hypotheses. In the present work, we use a computational constitutive multi-scale model to predict the Young’s modulus of the pearlitic nodular cast-iron. In order to define an adequate Representative Volume Element, we use a set of micrographics images, obtained from an optical device. Each image is enhanced and segmented to obtain the volume fraction of each phase and the boundary of each object in the micrography. With this information, a finite element mesh is constructed for each image. Finally, the numerical results are compared with an analytical expression. Some conclusions are presented at the end of the work.

The constitutive properties of such materials are usually presented by means of an analytical formula in terms of micro-structural characteristics. In the derivation of an analytical expression, the formulation of hypotheses are needed to define the behavior, shape and distribution of the elements in the micro-structure. Then, the analytical formulation to predict the constitutive behavior of the nodular cast-iron is restricted to the micro-structures that satisfy such hypotheses. In the present work, we use a computational constitutive multi-scale model to predict the Young’s modulus of the pearlitic nodular cast-iron. In order to define an adequate Representative Volume Element, we use a set of micrographics images, obtained from an optical device. Each image is enhanced and segmented to obtain the volume fraction of each phase and the boundary of each object in the micrography. With this information, a finite element mesh is constructed for each image. Finally, the numerical results are compared with an analytical expression. Some conclusions are presented at the end of the work.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**