Micromechanical Polycrystalline Damage–Plasticity Modeling for Metal Forming Processes

  • Benoit Panicaud
  • Léa Le Joncour
  • Neila Hfaiedh
  • Khemais Saanouni
Living reference work entry

Abstract

This chapter deals with the presentation of micromechanical modeling of the elastoplastic material behavior exhibiting ductile damage together with microstructural evolution in terms of grain rotation and phase transformation, under large inelastic strains. A description of the main experimental methods is proposed and multiscale measurements are discussed. For the mesoscopic scale, diffraction techniques are presented as well as microscopy’s results for a specific material. For the macroscopic scale, techniques of tensile test coupled with digital image correlation are described. This allows the damage measurement at different scales. Micromechanical modeling aspects based on the thermodynamics of irreversible processes with state variables defined at different scales are discussed. A non-exhaustive review of several possible models is given. These models depend on the hypothesis for the energy or strain equivalence and on the smallest scale considered. Two particular models are then detailed with their associated constitutive equations and the corresponding numerical aspects. Application is made to two different materials to test the ability of the model to be used for metal forming simulations.

Keywords

Fatigue Nickel Anisotropy Chromium Ferrite 

Abbreviations and Notations

CDM

Continuous damage mechanics

CRSS

Critical resolved shear stress

DIC

Digital image correlation

DSS

Duplex stainless steel(s)

EBSD

Electron backscatter diffraction

FEA

Finite element analysis

ODF

(Crystalline) orientation distribution function

RVE

Representative volume element

SEM

Scanning electron microscopy

X

Zero-rank tensor = scalar variable

XRD

X-ray diffraction

\( \overrightarrow{X} \)

One-rank tensor = vector variable

\( \underset{\bar{\mkern6mu}}{X} \)

Second-rank tensor

\( \underset{\bar{\mkern6mu}}{\underset{\bar{\mkern6mu}}{X}} \)

Fourth-rank tensor

\( \underset{\bar{\mkern6mu}}{X}\cdot \underset{\bar{\mkern6mu}}{Y} \)

Contraction between the second-rank tensors \( \underset{\bar{\mkern6mu}}{X} \) and \( \underset{\bar{\mkern6mu}}{Y} \)

\( \underset{\bar{\mkern6mu}}{X}:\underset{\bar{\mkern6mu}}{Y} \)

Double contraction between the second-rank tensors \( \underset{\bar{\mkern6mu}}{X} \) and \( \underset{\bar{\mkern6mu}}{Y} \)

\( \underset{\bar{\mkern6mu}}{X}\otimes \underset{\bar{\mkern6mu}}{Y} \)

Tensorial product between the second-rank tensors \( \underset{\bar{\mkern6mu}}{X} \) and \( \underset{\bar{\mkern6mu}}{Y} \)

〈〈X〉〉

Macaulay brackets which means the positive part of a scalar X

\( {\left(\underset{\bar{\mkern6mu}}{X}\right)}^T\ \mathrm{or}\ {\left(\underset{\bar{\mkern6mu}}{\underset{\bar{\mkern6mu}}{X}}\right)}^T \)

Transpose of X (second-rank or fourth-rank tensor)

\( \left\Vert \underset{\bar{\mkern6mu}}{X}\right\Vert =\sqrt{\underset{\bar{\mkern6mu}}{X}:\underset{\bar{\mkern6mu}}{X}/3} \)

Euclidean norm of a second-rank tensor \( \underset{\bar{\mkern6mu}}{X} \)

\( \left\Vert \overrightarrow{X}\right\Vert =\sqrt{\overrightarrow{X}\cdot \overrightarrow{X}} \)

Euclidean norm of a vector \( \overrightarrow{X} \)

x

Average of the quantity x

Capital letters are for macroscopic or part quantities, whereas minuscule letters are for mesoscopic or microscopic ones.

Notes

Acknowledgments

Authors would like to thank gratefully the different people that are indirectly participants of this work through their collaboration to the theoretical, numerical, and experimental aspects: Manuel François, Arjen Roos, Andrzej Baczmanski, and Chedly Braham. We would also thank Emmanuelle Rouhaud for the time that she generously spent to correct this entire chapter. All these collaborations have allowed progressing on this particular domain and making the present authors as efficient as possible.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Benoit Panicaud
    • 1
  • Léa Le Joncour
    • 1
  • Neila Hfaiedh
    • 1
  • Khemais Saanouni
    • 1
  1. 1.ICD/LASMIS, STMR UMR-CNRS 6279University of Technology of TroyesTroyes CedexFrance

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