Archive of Applied Mechanics

, Volume 88, Issue 1–2, pp 65–81 | Cite as

Critical stresses estimation by crystal viscoplasticity modeling of rate-dependent anisotropy of Al-rich TiAl alloys at high temperature

  • Helal ChowdhuryEmail author
  • Konstantin Naumenko
  • Holm Altenbach
  • Manja Krüger


Determining critical stresses for different slip systems is one of the most important parts in crystal plasticity modeling of anisotropy. However, the task of finding individual critical resolved shear stress (CRSS) for every single slip system, if not impossible, is formidable and a delicate one especially if the microstructure is very complex. Slip family-based, mechanism-based and morphology-based (e.g., phase interface) slip systems classification and hence determining CRSS consistent with experimental measurements are often used in crystal plasticity. In this work, a novel approach to determining CRSS at high homologous temperature has been proposed by crystal plasticity modeling of rate-dependent anisotropy. Two-internal-variable-based phenomenological crystal viscoplasticity model is adopted for simulating isothermal, two-phase, single-crystal-like Al-rich lamellar Ti–61.8at.%Al binary alloy at high-temperature compression state (\(1050\,^\circ \hbox {C}\)) by employing finite strain and finite rotation framework. To the best of authors’ knowledge, this is the first micromechanical modeling attempt with long-period superstructures. Conventional approaches related to CRSS estimation are also compared with the proposed one. Our material parameters are based on calibrating three different sets of compressive stain rate-controlled plasticity data taken from the loading of two different lamellar directions. It is revealed that the proposed approach works fine for rate-dependent anisotropy modeling, while other conventional approaches highly under- or overestimate available anisotropic experimental behavior of this alloy.


Crystal viscoplasticity CRSS Al-rich TiAl alloy Rate-dependent anisotropy 



This work has been supported by DFG within the Ph.D. school GRK1554. We would like to gratefully acknowledge Prof. Albrecht Bertram (Magdeburg) for his suggestion regarding modeling approach and would like to thank our GRK fellow Mr. Philipp Thiem for his valuable comments from the material science perspectives. We also would like to express our special thanks of gratitude to Dr. Mokarram Hossain from Swansea University and to Mr. Mamun Al-Siraj from TU Darmstadt for their valuable comments after line-by-line proofreading.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Helal Chowdhury
    • 1
    Email author
  • Konstantin Naumenko
    • 2
  • Holm Altenbach
    • 2
  • Manja Krüger
    • 3
  1. 1.Graduate School for ‘Micro-Macro Interactions in Structured Media and Particle Systems’Otto-von-Guericke UniversityMagdeburgGermany
  2. 2.Institute of MechanicsOtto-von-Guericke UniversityMagdeburgGermany
  3. 3.Institute of Materials and Joining TechnologyOtto-von-Guericke UniversityMagdeburgGermany

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