, Volume 51, Issue 2, pp 429–441 | Cite as

Neighborhood influences on stress and strain partitioning in dual-phase microstructures

An investigation on synthetic polycrystals with a robust spectral-based numerical method
  • Martin DiehlEmail author
  • Pratheek Shanthraj
  • Philip Eisenlohr
  • Franz Roters
Computational Micromechanics of Materials


The mechanical response of multiphase metallic materials is governed by the strain and stress partitioning behavior among their phases, crystals, and subgrains. Despite knowledge about the existence of these complex and long-ranging interactions, the experimental characterization of such materials is often limited to surface observations of microstructure evolution and strain partitioning, i.e. ignoring the influence of the underlying features. Hence, for the interpretation of the observed surface behavior it is imperative to understand how it might be influenced by the subsurface microstructure. In the present study, we therefore systematically change the subsurface microstructure of synthetic dual-phase polycrystals and investigate the altered response of a 2D region of interest. The series of high-resolution crystal plasticity simulations are conducted with a fast and efficient spectral-based iterative scheme for calculating the mechanical response of complex crystalline materials. To overcome the slow convergence of the conventional spectral-based solver when dealing with heterogeneous materials of large contrast in stiffness (or strength), direct and mixed variational conditions for mechanical equilibrium and strain compatibility have been formulated such that they can be combined with a general class of non-linear solution methods. The different solution techniques have been implemented into DAMASK, the Düsseldorf Advanced Material Simulation Kit, and the ones showing the best performance are used in this study. The results show that the subsurface microstructure has a dominant influence on the observed stress and strain partitioning. Additionally, it can be seen that the zone of influence increases with increasing heterogeneity of the microstructure.


Crystal plasticity Dual-phase steel Spectral method Voronoi tessellation Stress and strain partitioning 



This research was carried out under Project Number M 41.2.10410 in the framework of the Research Program of the Materials innovation institute (M2i) (


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Martin Diehl
    • 1
    Email author
  • Pratheek Shanthraj
    • 1
    • 2
  • Philip Eisenlohr
    • 3
  • Franz Roters
    • 1
  1. 1.Microstructure Physics and Alloy DesignMax-Planck-Institut für Eisenforschung GmbHDüsseldorfGermany
  2. 2.Aachen Institute for Advanced Study in Computational Engineering ScienceRWTH Aachen UniversityAachenGermany
  3. 3.Chemical Engineering and Materials ScienceMichigan State UniversityEast LansingUSA

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