International Journal of Fracture

, Volume 207, Issue 1, pp 1–26 | Cite as

Multi-scale analysis of the early damage mechanics of ferritized ductile iron

  • D. O. Fernandino
  • A. P. Cisilino
  • S. Toro
  • P. J. Sanchez
Original Paper


A multi-scale analysis of the linear elastic and the early damage stages of ferritic ductile iron is introduced in this work. The methodology combines numerical and experimental analyses in the macro and micro scales. Experiments in the micro-scale are used for the characterization of the material micro constituents and the assessment of the micro-scale damage mechanisms; experiments in the macro-scale provide the data to calibrate and validate the models. The 2D multi-scale problem is modeled using the pre-critical regime of the Failure-Oriented Multi-Scale Variational Formulation, which is implemented via a FE\(^{2}\) approach. Finite element analysis in the micro-scale is customized to account for plastic deformation and matrix-nodule debonding. The multi-scale model is found effective for capturing the sequence and extent of the damage mechanisms in the micro-scale and to estimate, via inverse analyses, parameters of the matrix-nodule debonding law. Results allow to develop new insights for the better understanding of the ductile iron damage mechanics and to draw conclusions related to the modeling aspects of the multi-scale simulation.


Ductile iron Fracture mechanisms Mechanical testing Multi-scale damage Finite elements 

List of symbols

Experimentally-measured macro-scale quantities

\(\sigma ^{EXP}\)


\(\varepsilon ^{EXP}\)


\(\varepsilon _p^{EXP}\)

Plastic strain

\(\sigma _s^{EXP} ,\varepsilon _s^{EXP}\)

Stress and strain at the MND process start

\(\sigma _e^{EXP} ,\varepsilon _e^{EXP} \)

Stress and strain at the MND process end

\(E_0^{EXP} \)

Young’s modulus of the undamaged material

\(E^{\prime EXP} \)

Young’s modulus as function of plastic strain

\(\sigma _{0.2}^{EXP} ,\varepsilon _{0.2}^{EXP} \)

Offset yield stress and strain

\(\beta ^{EXP}\)

Slope of the stress–strain curve in the elasto-plastic regime

Homogenized (effective) macro-scale quantities

\(\sigma ^{HOM}\)


\(\varepsilon ^{HOM}\)


\(\varepsilon _p^{HOM} \)

Plastic strain

\(\sigma _s^{HOM} ,\varepsilon _s^{HOM}\)

Stress and strain at the MND process start

\(\sigma _e^{HOM} ,\varepsilon _e^{HOM}\)

Stress and strain at the MND process end

\(E_0^{HOM} \)

Young’s modulus of the undamaged material

\(E^{\prime HOM} \)

Young’s modulus as functions of plastic strain

\(\sigma _{0.2}^{HOM} ,\varepsilon _{0.2}^{HOM} \)

Offset yield stress and strain

\(\beta ^{HOM}\)

Slope of the stress–strain curve in the elasto-plastic regime

Micro-scale quantities are denoted with sub-indexes \(\left( \cdot \right) _{\upmu ,\mathrm{i}}\), where \(\hbox {i}\) indicates the micro-constituent phase, either the nodules (Nod), MNI, LTF or FTF

\({\varvec{\sigma }} _{\mu ,i}\)

Micro-scale stress

\({\varvec{\varepsilon }} _{\mu ,i}\)

Micro-scale strain

\(E_{\mu ,i} ,\nu _{\mu ,i}\)

Elastic modulus and Poisson’s ratio

\(\sigma _{\mu ,i}^y ,H_{\mu ,i}\)

Yield stress and hardening modulus



Ductile iron


Ferritic ductile iron


First to freeze zone


Last to freeze zone


Representative volume element


Matrix-nodule interface


Matrix-nodule decohesion



This research has been supported by grants awarded by CONICET (PIP 2013-2105 631), ANPYCT (PICT 2011-0159), the National University of Mar del Plata (ING 399-14) and the European Research Council under the European Union Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement No. 320815 (ERC Advanced Grant Project “Advanced tools for computational design of engineering materials” COMP-DES-MAT). The authors wish to express their gratitude to Prof. Alfredo Huespe (CIMEC-UNL-CONICET) for his valuable comments on the manuscript and for his assistance with the numerical simulations. The authors also acknowledge MEGAFUND S.A. for providing the material for the experimental analyses.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • D. O. Fernandino
    • 1
  • A. P. Cisilino
    • 1
  • S. Toro
    • 2
    • 3
  • P. J. Sanchez
    • 2
    • 3
  1. 1.INTEMAUniversidad Nacional de Mar del Plata-CONICETMar del PlataArgentina
  2. 2.CIMEC-UNL-CONICETSanta FeArgentina
  3. 3.GIMNI-UTN-FRSFSanta FeArgentina

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