Predicting crack propagation with peridynamics: a comparative study

Abstract

The fidelity of the peridynamic theory in predicting fracture is investigated through a comparative study. Peridynamic predictions for fracture propagation paths and speeds are compared against various experimental observations. Furthermore, these predictions are compared to the previous predictions from extended finite elements (XFEM) and the cohesive zone model (CZM). Three different fracture experiments are modeled using peridynamics: two experimental benchmark dynamic fracture problems and one experimental crack growth study involving the impact of a matrix plate with a stiff embedded inclusion. In all cases, it is found that the peridynamic simulations capture fracture paths, including branching and microbranching that are in agreement with experimental observations. Crack speeds computed from the peridynamic simulation are on the same order as those of XFEM and CZM simulations. It is concluded that the peridynamic theory is a suitable analysis method for dynamic fracture problems involving multiple cracks with complex branching patterns.

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Abbreviations

XFEM:

Extended finite elements

CZM:

Cohesive zone model

References

  1. Barenblatt GI (1959) The formation of equilibrium cracks during brittle fracture. general ideas and hypotheses. axially-symmetric cracks. J Appl Math Mech 23(3): 622–636

    Article  Google Scholar 

  2. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5): 601–620

    Article  Google Scholar 

  3. Belytschko T, Chen H, Xu J, Zi G (2003) Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int J Numer Methods Eng 58(12): 1873–1905

    Article  Google Scholar 

  4. Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33(20-22): 2899–2938

    Article  Google Scholar 

  5. Chandra N, Li H, Shet C et al (2002) Some issues in the application of cohesive zone models for metal-ceramic interfaces. Int J Solids Struct 39(10): 2827–2855

    Article  Google Scholar 

  6. Colavito KW, Kilic B, Celik E, Madenci E, Askari E, Silling S (2007) Effect of nano particles on stiffness and impact strength of composites. In: Proceedings of 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Honolulu, Hawaii number AIAA 2007-2071 American Institute of Aeronautics and Astronautics

  7. Cox BN, Gao H, Gross D, Rittel D (2005) Modern topics and challenges in dynamic fracture. J Mech Phys Solids 53(3): 565–596

    Article  Google Scholar 

  8. Fineberg J, Marder M (1999) Instability in dynamic fracture. Phys Reports-Rev Sect Phys Lett 313(1–2): 2–108

    Google Scholar 

  9. Fineberg J, Gross SP, Marder M et al (1992) Instability in the propagation of fast cracks. Phys Rev B 45(10): 5146–5154

    Article  CAS  Google Scholar 

  10. Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162(1–2): 229–244

    Article  Google Scholar 

  11. Ha YD, Bobaru F (2011) Characteristics of dynamic brittle fracture captured with peridynamics. Eng Fract Mech 78: 1156–1168

    Article  Google Scholar 

  12. Kitey R, Tippur HV (2008) Dynamic crack growth past a stiff inclusion: Optical investigation of inclusion eccentricity and inclusion-matrix adhesion strength. Exp Mech 48(1): 37–53

    Article  Google Scholar 

  13. Kitey R, Phan AV, Tippur HV, Kaplan T (2006) Modeling of crack growth through particulate clusters in brittle matrix by symmetric-galerkin boundary element method. Int J Fract 141(1–2): 11–25

    Article  Google Scholar 

  14. Klein PA, Foulk JW, Chen EP, Wimmer SA, Gao HJ (2001) Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods. Theor Appl Fract Mech 37(1–3): 99–166

    Article  Google Scholar 

  15. Moes N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69(7): 813–833

    Article  Google Scholar 

  16. Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1): 131–150

    Article  Google Scholar 

  17. Ramulu M, Kobayashi AS (1985) Mechanics of crack curving and branching—a dynamic fracture analysis. Int J Fract 27: 187–201

    Article  Google Scholar 

  18. Ravi-Chandar K (1998) Dynamic fracture of nominally brittle materials. Int J Fract 90(1–2): 83–102

    Article  CAS  Google Scholar 

  19. Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture.1. crack initiation and arrest. Int J Fract 25(4): 247–262

    Article  Google Scholar 

  20. Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture.2. microstructural aspects. Int J Fract 26(1): 65–80

    Article  Google Scholar 

  21. Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture.3. on steady-state crack-propagation and crack branching. Int J Fract 26(2): 141–154

    Article  Google Scholar 

  22. Sharon E, Fineberg J (1996) Microbranching instability and the dynamic fracture of brittle materials. Phys Rev B 54(10): 7128–7139

    Article  CAS  Google Scholar 

  23. Sharon E, Fineberg J (1999) Confirming the continuum theory of dynamic brittle fracture for fast cracks. Nature 397(6717): 333–335

    Article  CAS  Google Scholar 

  24. Sharon E, Gross SP, Fineberg J (1995) Local crack branching as a mechanism for instability in dynamic fracture. Phys Rev Lett 74(25): 5096–5099

    Article  CAS  Google Scholar 

  25. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1): 175–209

    Article  Google Scholar 

  26. Silling SA (2003) Dynamic fracture modeling with a meshfree peridynamic code. In: Bathe KJ (eds) Computational fluid and solid mechanics 2003. Elsevier Science Ltd, Oxford, pp 641–644

    Google Scholar 

  27. Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17-18): 1526–1535

    Article  Google Scholar 

  28. Song J, Belytschko T (2009) Cracking node method for dynamic fracture with finite elements. Int J Numer Methods Eng 77(3): 360–385

    Article  Google Scholar 

  29. Song J, Wang H, Belytschko T (2008) A comparative study on finite element methods for dynamic fracture. Comput Mech 42(2): 239–250

    Article  Google Scholar 

  30. Xu X, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42(9): 1397–1434

    Article  Google Scholar 

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Correspondence to Erdogan Madenci.

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Agwai, A., Guven, I. & Madenci, E. Predicting crack propagation with peridynamics: a comparative study. Int J Fract 171, 65 (2011). https://doi.org/10.1007/s10704-011-9628-4

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Keywords

  • Peridynamic theory
  • Dynamic fracture
  • Microbranching
  • Crack branching