Skip to main content
SpringerLink
Log in

Numerical investigation of mixed-mode crack growth in ductile material using elastic–plastic XFEM

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

In the present work, the corrected extended finite element method (XFEM) is extended to conduct fatigue analysis of arbitrary crack growth in ductile materials. In corrected XFEM, the crack is modeled by adding enrichment functions into the approximation; optimal convergence rate and independent mesh discretization can be achieved, and the re-meshing and refinement during crack evolving can be avoided. von Mises yield criterion along with isotropic hardening is used to model finite strain plasticity. The nonlinear problem is solved by Newton–Raphson iterative method. Interaction integral method is employed to calculate mixed-mode stress intensity factors. Crack growth angle and rate are determined by the maximum principal stress criterion and the modified Paris law, respectively. Two problems, i.e., ductile crack growth in round compact tension specimen and ductile crack growth in overhanging beam are presented. The numerical results are compared with experimental data as well as FE simulation, to demonstrate the excellent capability of XFEM for simulating arbitrary crack growth in ductile materials.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Weng TL, Sun CT (2000) A study of fracture criteria for ductile materials. Eng Fail Anal 7(2):101–125

    Article  Google Scholar 

  2. Nikishkov G (2013) Accuracy of quarter-point element in modeling crack-tip fields. CMES Comp Model Eng 93(5):335–361

    MathSciNet  Google Scholar 

  3. Miranda ACO, Meggiolaro MA, Castro JTP, Martha LF (2003) Fatigue life prediction of complex 2D components under mixed-mode variable amplitude loading. Int J Fatigue 25(9–11):1157–1167

    Google Scholar 

  4. Meggiolaro MA, Miranda ACO, Castro JTP, Martha LF (2005) Crack retardation equations for the propagation of branched fatigue cracks. Int J Fatigue 27(10–12):1398–1407

    Article  Google Scholar 

  5. Meggiolaro MA, Miranda ACO, Castro JTP, Martha LF (2005) Stress intensity factor equations for branched crack growth. Eng Fract Mech 72(17):2647–2671

    Article  Google Scholar 

  6. Portela AA, Aliabadi M, Rooke D (1991) The dual boundary element method effective implementation for crack problems. Int J Numer Meth Eng 33:269–1287

    MATH  Google Scholar 

  7. Leonel ED, Chateauneuf A, Venturini WS (2012) Probabilistic crack growth analyses using a boundary element model: applications in linear elastic fracture and fatigue problems. Eng Anal Bound Elem 36(6):944–959

    Article  MathSciNet  Google Scholar 

  8. Yan X (2006) A boundary element modeling of fatigue crack growth in a plane elastic plate. Mech Res Commun 33(4):470–481

    Article  MATH  Google Scholar 

  9. Belytschko T, Gu L, Lu YY (1994) Fracture and crack growth by element free Galerkin methods. Model Simul Mater Sci 2:519

    Article  Google Scholar 

  10. Belytschko T, Lu YY, Gu L (1995) Crack propagation by element-free Galerkin methods. Eng Fract Mech 51(2):295–315

    Article  Google Scholar 

  11. Dai KY, Liu GR, Lim KM, Han X, Du SY (2004) A meshfree radial point interpolation method for analysis of functionally graded material (FGM) plates. Comput Mech 34(3):213–223

    Article  MATH  Google Scholar 

  12. Tal Y, Hatzor YH, Feng X (2014) An improved numerical manifold method for simulation of sequential excavation in fractured rocks. Int J Rock Mech Min 65:116–128

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Daux C, Mos N, Dolbow J, Sukumar N, Belytschko T (2000) Arbitrary branched and intersecting cracks with the extended finite element method. Int J Numer Meth Eng 48:1741–1760

    Article  MATH  Google Scholar 

  15. Fries TP (2008) A corrected XFEM approximation without problems in blending elements. Int J Numer Meth Eng 75(5):503–532

    Article  MathSciNet  MATH  Google Scholar 

  16. Unger JF, Eckardt S, Könke C (2007) Modelling of cohesive crack growth in concrete structures with the extended finite element method. Comput Method Appl Mech 196(41–44):4087–4100

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  18. Khoei AR, Nikbakht M (2006) Contact friction modeling with the extended finite element method (X-FEM). J Mater Process Tech 177(1–3):58–62

    Article  Google Scholar 

  19. Khoei AR, Nikbakht M (2007) An enriched finite element algorithm for numerical computation of contact friction problems. Int J Mech Sci 49(2):183–199

    Article  Google Scholar 

  20. Liu ZL, Menouillard T, Belytschko T (2011) An XFEM/Spectral element method for dynamic crack propagation. Int J Fracture 169(2):183–198

    Article  MATH  Google Scholar 

  21. Sukumar N, Mo SN, Moran B, Belytschko T (2000) Extended finite element method for three-dimensional crack modelling. Int J Numer Meth Eng 48(11):1549–1570

    Article  MATH  Google Scholar 

  22. Yu TT, Gong ZW (2013) Numerical simulation of temperature field in heterogeneous material with the XFEM. Arch Civ Mech Eng 13(2):199–208

    Article  MathSciNet  Google Scholar 

  23. Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method, 6th edn, Butterworth-Heinemann, Buston,  USA

  24. Jovicic G, Zivkovic M, Jovicic N, Milovanovic D, Sedmak A (2010) Improvement of algorithm for numerical crack modelling. Arch Civ Mech Eng 10(3):19–35

    Article  Google Scholar 

  25. Elguedj T, Gravouil A, Combescure A (2006) Appropriate extended functions for X-FEM simulation of plastic fracture mechanics. Comput Method Appl Mech 195(7–8):501–515

    Article  MATH  Google Scholar 

  26. Seabra MRR, Šuštarič P, Cesar De Sa JMA, Rodič T (2013) Damage driven crack initiation and propagation in ductile metals using XFEM. Comput Mech 52(1):161–179

    Article  MathSciNet  MATH  Google Scholar 

  27. Shedbale AS, Singh IV, Mishra BK (2013) Nonlinear simulation of an embedded crack in the presence of holes and inclusions by XFEM. Procedia Eng 64:642–651

    Article  Google Scholar 

  28. Kumar S, Singh IV, Mishra BK (2014) XFEM simulation of stable crack growth using J–R curve under finite strain plasticity. Int J Mech Mater Des 10(2):165–177

    Article  Google Scholar 

  29. Miranda ACO, Meggiolaro MA, Martha LF, Castro JTP (2012) Stress intensity factor predictions: comparison and round-off error. Comp Mater Sci 53(1):354–358

    Article  Google Scholar 

  30. Singh IV, Bhardwaj G, Mishra BK (2015) A new criterion for modeling multiple discontinuities passing through an element using XIGA. J Mech Sci Technol 29(3):1131–1143

    Article  Google Scholar 

  31. Huang X, Torgeir M, Cui W (2008) An engineering model of fatigue crack growth under variable amplitude loading. Int J Fatigue 30(1):2–10

    Article  Google Scholar 

  32. Singh IV, Mishra BK, Bhattacharya S, Patil RU (2012) The numerical simulation of fatigue crack growth using extended finite element method. Int J Fatigue 36(1):109–119

    Article  Google Scholar 

  33. Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Meth Eng 46:131–150

    Article  MATH  Google Scholar 

  34. ASTM B 209 (2007) Standard specification for aluminum and aluminum-alloy sheet and plate. ASTM committee

  35. Wang C, Wang X, Ding Z, Xu Y, Gao Z (2015) Experimental investigation and numerical prediction of fatigue crack growth of 2024-T4 aluminum alloy. Int J Fatigue 78:11–21

    Article  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge the supports from the National Natural Science Foundation of China (Nos. 51278297 and 11172174) and the Major Program of the National Natural Science Foundation of China (No. 51490674), Research Program of Shanghai Leader Talent(No. 20)and Doctoral Disciplinary Special Research Project of Chinese Ministry of Education (No. 20130073110096).

Author information

Authors and Affiliations

  1. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, People’s Republic of China

    Guangzhong Liu, Dai Zhou & Jin Ma

  2. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE); State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, People’s Republic of China

    Dai Zhou

  3. Cullen College of Engineering, University of Houston, Houston, USA

    Zhaolong Han

Authors
  1. Guangzhong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dai Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jin Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhaolong Han
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dai Zhou.

Additional information

Technical Editor: Marcelo A. Savi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, G., Zhou, D., Ma, J. et al. Numerical investigation of mixed-mode crack growth in ductile material using elastic–plastic XFEM. J Braz. Soc. Mech. Sci. Eng. 38, 1689–1699 (2016). https://doi.org/10.1007/s40430-016-0557-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-016-0557-z

Keywords

Search

Navigation