International Journal of Fracture

, Volume 216, Issue 1, pp 41–57 | Cite as

Multiscale crystal-plasticity phase field and extended finite element methods for fatigue crack initiation and propagation modeling

  • Alireza Sadeghirad
  • Kasra Momeni
  • Yanzhou Ji
  • Xiang Ren
  • Long-Qing Chen
  • Jim LuaEmail author
Original Paper


This paper presents a physics-based prediction of crack initiation at the microstructure level using the phase field (PF) model without finite element discretization, coupled with an efficient and accurate modeling of crack propagation at macro-scale based on extended finite element method (XFEM). Although the macro-scale model assumes linear elastic material behavior, at micro-scale the behavior of plastically deforming heterogeneous polycrystals is taken into account by coupling the PF model and a crystal plasticity model in the fast Fourier transform computational framework. A sequential coupling has been established for the multiscale modeling where the macro-scale finite element (FE) model determines the hot spots at each cyclic loading increment and passes the associated stress/strain values to the unit-cell phase-field model for accurate physics-based microstructure characterization and prediction of plasticity induced crack initiation. The PF model predicts the number of cycles for the crack initiation and the phenomenological crack growth models are employed to propagate the initiated crack by the appropriate length to be inserted in the FE mesh. Finally, the XFEM solution module is activated to perform mesh independent crack propagation from its initial crack size to the final size for the total life prediction. The effectiveness of the proposed multiscale method is demonstrated through numerical examples.


Phase field model Crystal plasticity Fast Fourier transform Extended finite element method Multiscale modeling Fatigue crack initiation and propagation 



The authors gratefully acknowledge the support from NAVAIR under contract N68335-16-C-0197. In addition, Dr. K. Momeni would like to acknowledge the funding from LEQSF(2015-18)-LaSPACE and LONI supercomputing resources. The authors are also grateful to Prof. David McDowell, Prof. Mark Horstemeyer, Dr. Yibin Anna Xue, and Dr. Justin Hughes for helpful comments on the short crack growth model. The EBSD data was also provided in courtesy by Dr. Stefan Zaefferer and Hasso Weiland.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Alireza Sadeghirad
    • 1
  • Kasra Momeni
    • 2
    • 3
  • Yanzhou Ji
    • 2
  • Xiang Ren
    • 1
  • Long-Qing Chen
    • 2
  • Jim Lua
    • 1
    Email author
  1. 1.Global Engineering and Materials, Inc.PrincetonUSA
  2. 2.Department of Materials Science and EngineeringThe Pennsylvania State UniversityUniversity ParkUSA
  3. 3.Department of Mechanical EngineeringLouisiana Tech UniversityRustonUSA

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