An Abaqus plug-in to simulate fatigue crack growth

Abstract

Fatigue crack propagation is an important consideration in evaluating the design life of engineering components, especially in the energy and transport industries. Despite its importance, fatigue analyses are not usually supported by commercial Finite Element (FE) codes; in fact, most FE codes require the addition of costly plug-ins to perform fatigue crack growth simulations. Therefore, this paper introduces a new, freely distributed plug-in to simulate fatigue crack growth with the commercial FE code Abaqus. The plug-in includes five different fatigue crack growth models and relies on the extended FE method to simulate crack propagation. The plug-in is limited to 2D analyses, but covers all necessary steps for fatigue crack growth simulations, from creating the geometry to job submission and post-processing. The implementation of the plug-in is validated by comparing its predictions to analytical and experimental results. Finally, we hope that the simplicity of the plug-in and the fact that it is distributed freely will make it a useful simulation tool for industrial, research and educational purposes.

This is a preview of subscription content, access via your institution.

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

Abbreviations

\(a\) :

Crack length (mm)

\(\Delta a\) :

Crack growth incremental length (mm)

\(A\) :

Material constant

\({A}_{k}\), \({B}_{k}\) :

Fitting constants

\(C, m\) :

Paris law empirical coefficients

\({C}_{n}, n, p, q\) :

NASGRO empirical coefficients

\({C}_{f}\), \({m}_{f}\) :

Forman law empirical coefficients

\({C}_{w}\),\({m}_{w}\) :

Walker law empirical coefficients

\(da/dN\) :

Crack growth rate in length/cycle

\(E\) :

Young’s modulus (\(\mathrm{GPa}\))

Г:

Contour integral

G:

Energy release rate

I:

Interaction energy integral

J:

J-integral

\({K}_{I}\), \({K}_{II}\) :

Mode-I and mode-II stress intensity factors (\(\mathrm{MPa}\sqrt{\mathrm{m}}\))

\({K}_{C}\) :

Fracture toughness (\(\mathrm{MPa}\sqrt{\mathrm{m}}\))

\({K}_{IC}\) :

Mode-I fracture toughness (\(\mathrm{MPa}\sqrt{\mathrm{m}}\))

\({K}_{\mathrm{crit}}\) :

Critical value of SIF (\(\mathrm{MPa}\sqrt{\mathrm{m}}\))

\({K}_{\mathrm{max}}, {K}_{\mathrm{min}}\) :

SIF for the maximum and minimum loads in the cycle (\(\mathrm{MPa}\sqrt{\mathrm{m}}\))

\(\Delta K\) :

SIF range (\(\mathrm{MPa}\sqrt{\mathrm{m}}\))

\({\Delta K}_{\mathrm{eq}}\) :

Equivalent \(\Delta K\) for mixed-mode loading condition (\(\mathrm{MPa}\sqrt{\mathrm{m}}\))

\({\Delta K}_{\mathrm{th}}\) :

Threshold \(\Delta K\) (\(\mathrm{MPa}\sqrt{\mathrm{m}}\))

\({\Delta K}_{w}\) :

Walker \(\Delta K\) (\(\mathrm{MPa}\sqrt{\mathrm{m}}\))

\(\gamma \) :

Material constant

\(N\) :

Number of cycles

\({N}_{i}\) :

Number of cycles at each iteration

\(P\) :

Applied load (\(\mathrm{N}\))

P max :

Maximum applied load (\(\mathrm{N}\))

\({p}_{e}\), \({q}_{e}\) :

Material constants

\(R\) :

Stress ratio

r :

Point distance from crack-tip point

\({S}_{max}\),\({S}_{\mathrm{min}}\) :

Maximum and minimum stresses (\(\mathrm{MPa}\))

\({\sigma }_{yld}\) :

Yield strength (\(\mathrm{MPa}\))

\({\upsigma }_{\mathrm{ij}}\), \({\upepsilon }_{\mathrm{ij}}\) :

Stress and strain tensors

\(t\) :

Thickness (mm)

\({t}_{0}\) :

Reference thickness related to the state of plane strain

\({\theta }_{c}\) :

Crack front kinking angle (\(\mathrm{deg}\))

\(W\) :

Width of the specimen (mm)

\({\mathrm{W}}_{\mathrm{enrg}}\) :

Strain energy density

CT:

Compact tension

CCT:

Center-cracked specimen in tension

DCT:

Disk-shaped CT specimen

FCG:

Fatigue crack growth

FE:

Finite element

FEM:

FE method

LEFM:

Linear elastic fracture mechanics

SIF:

Stress intensity factor

SEB:

Single-edge bending specimen

SEN:

Single-edge notched specimen

SENT:

Single-edge notched under tension

XFEM:

Extended FEM

References

  1. 1.

    Lesiuk G, Smolnicki M, Rozumek D, Krechkovska H, Student O, Correia J, Mech R, de Jesus A (2020) Study of the fatigue crack growth in long-term operated mild steel under mixed-mode (I + II, I + III) loading conditions. Materials 13(1):160. https://doi.org/10.3390/ma13010160

    Article  Google Scholar 

  2. 2.

    Silva ALL, Correia JAFO, de Jesus AMP, Lesiuk G, Fernandes AA, Calçad R, Berto F (2019) Influence of fillet end geometry on fatigue behaviour of welded joints. Int J Fatigue 123:196–212. https://doi.org/10.1016/j.ijfatigue.2019.02.025

    Article  Google Scholar 

  3. 3.

    Rozumek D, Marciniak Z, Lesiuk G, Correia JA, de Jesus AMP (2018) Experimental and numerical investigation of mixed mode I+II and I+III fatigue crack growth in S355J0 steel. Int J Fatigue 113:160–170. https://doi.org/10.1016/j.ijfatigue.2018.04.005

    Article  Google Scholar 

  4. 4.

    Paris P, Erdogan F (1963) A critical analysis of crack propagation laws. Trans ASME 85(4):528–533. https://doi.org/10.1115/1.3656900

    Article  Google Scholar 

  5. 5.

    Forman RG, Kearney VE, Engle RM (1967) Numerical analysis of crack propagation in cyclic-loaded structures. J Basic Eng 89(3):459–463. https://doi.org/10.1115/1.3609637

    Article  Google Scholar 

  6. 6.

    Schütz W (1996) A history of fatigue. Eng Fract Mech 54(2):263–300. https://doi.org/10.1016/0013-7944(95)00178-6

    Article  Google Scholar 

  7. 7.

    Correia JAFO, Blasón S, Arcari A, Calvente M, Apetre N, Moreira PMGP, de Jesus AMP, Canteli AF (2016) Modified CCS fatigue crack growth model for the AA2019-T851 based on plasticity-induced crack-closure. Theo Appl Fract Mech 85:26–36. https://doi.org/10.1016/j.tafmec.2016.08.024

    Article  Google Scholar 

  8. 8.

    Correia JAFO, de Jesus AMP, Moreira PMGP, Tavares PJS (2016) Crack closure effects on fatigue crack propagation rates: application of a proposed theoretical model. Adv Mater Sci Eng 3026745. doi: https://doi.org/10.1155/2016/3026745

  9. 9.

    Duan QY, Li JQ, Li YY, Yin YJ, Xie HM, He W (2020) A novel parameter to evaluate fatigue crack closure: Crack opening ratio. Int J Fatigue 141:105859. https://doi.org/10.1016/j.ijfatigue.2020.105859

    Article  Google Scholar 

  10. 10.

    Silva ALL, de Jesus AMP, Xavier J, Correia JAFO, Fernandes AA (2017) Combined analytical-numerical methodologies for the evaluation of mixed-mode (I + II) fatigue crack growth rates in structural steels. Eng Fract Mech 185:124–138

    Article  Google Scholar 

  11. 11.

    Malekan M, Carvalho H (2018) Analysis of a main fatigue crack interaction with multiple micro-cracks/voids in a compact tension specimen repaired by stop-hole technique. J Strain Anal Eng 53(8):648–662. https://doi.org/10.1177/0123456789123456

    Article  Google Scholar 

  12. 12.

    Nesládek M, Španiel M (2017) An Abaqus plugin for fatigue predictions. Adv Eng Softw 103:1–11. https://doi.org/10.1016/j.advengsoft.2016.10.008

    Article  Google Scholar 

  13. 13.

    ZENCRACK manual, Version 7.9.

  14. 14.

    http://gem-innovation.com/project/xfa3d/

  15. 15.

    Lani F, Wyart E, Laurent D (2013) A XFEM-based probabilistic damage tolerant approach with Morfeo/Crack for Abaqus.Simulia Benelux Users' Meeting (Conferentiecentrum Bovendonk—Hoeven, Netherlands, du 13/11/2013 au 14/11/2013)

  16. 16.

    He W, Liu J, Xie D (2014) Numerical study on fatigue crack growth at a web-stiffener of ship structural details by an objected-oriented approach in conjunction with ABAQUS. Marine Struct 35:45–69. https://doi.org/10.1016/j.marstruc.2013.12.001

    Article  Google Scholar 

  17. 17.

    Pedersen MM (2016) Multiaxial fatigue assessment of welded joints using the notch stress approach. Int J Fatigue 83(2):269–279. https://doi.org/10.1016/j.ijfatigue.2015.10.021

    Article  Google Scholar 

  18. 18.

    Malekan M, Khosravi A, St-Pierre L (2019) An Abaqus plug-in to simulate fatigue crack growth—Supporting materials. figshare. Software.

  19. 19.

    Noor AK (1986) Global-local methodologies and their application to nonlinear analysis. Finite Elem Anal Des 2:333–346. https://doi.org/10.1016/0168-874X(86)90020-X

    Article  Google Scholar 

  20. 20.

    Malekan M, Barros FB (2016) Well-conditioning global–local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics. Comput Mech 58(5):819–831. https://doi.org/10.1007/s00466-016-1318-7

    MathSciNet  Article  MATH  Google Scholar 

  21. 21.

    Malekan M, Barros F, Pitangueira RLS (2018) Fracture analysis in plane structures with the two-scale G/XFEM method. Int J Solids Struct 155:65–80. https://doi.org/10.1016/j.ijsolstr.2018.07.009

    Article  Google Scholar 

  22. 22.

    Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45:601–620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5%3c601::AID-NME598%3e3.0.CO;2-S

    Article  MATH  Google Scholar 

  23. 23.

    Strouboulis T, Copps K, Babuska I (2000) The generalized finite element method: an example of its implementation and illustration of its performance. Int J Numer Methods Eng 47:1401–1417. https://doi.org/10.1002/(SICI)1097-0207(20000320)47:8%3c1401::AID-NME835%3e3.0.CO;2-8

    MathSciNet  Article  MATH  Google Scholar 

  24. 24.

    Dassault Systémes Simulia Corp., Abaqus user’s manual, version 6.14–2, Providence, Rhode Island, USA, 2014.

  25. 25.

    Erdogan F, Shi GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85(4):519–525. https://doi.org/10.1115/1.3656897

    Article  Google Scholar 

  26. 26.

    Pais MJ (2011) Variable amplitude fatigue analysis using surrogate models and exact XFEM reanalysis. PhD thesis, University of Florida, USA.

  27. 27.

    Tanaka K (1974) Fatigue crack propagation from a crack inclined to the cyclic tension axis. Engrg Fract Mech 6:493–507. https://doi.org/10.1016/0013-7944(74)90007-1

    Article  Google Scholar 

  28. 28.

    Richard HA, Buchholz FG, Kulmer G, Schollmann M (2003) 2D and 3D mixed mode criteria. Adv Fract Damage Mech 251:251–260. https://doi.org/10.4028/www.scientific.net/KEM.251-252.251

    Article  Google Scholar 

  29. 29.

    Tanaka K, Akiniwa Y, Kato T, Takahashi H (2005) Prediction of fatigue crack propagation path from a pre-crack under combined torsional and axial loading. Jpn Soc Mech Eng 71(703):607–614 [in Japanese]. doi: https://doi.org/10.1299/kikaia.71.607

  30. 30.

    Erdogan F, Ratwani M (1970) Fatigue and fracture of cylindrical shells containing circumferential cracks. Int J Fract Mech 6(4):379–392. https://doi.org/10.1007/BF00182626

    Article  Google Scholar 

  31. 31.

    Paris PC, Gomez M, Anderson W (1961) A rational analytic theory of fatigue. Trend in Eng. 9–14.

  32. 32.

    Paris PC (1963) A critical analysis of crack propagation laws. J Basic Eng 85:528–534

    Article  Google Scholar 

  33. 33.

    Forman RG, Kearney VE, Engle RM (1967) Numerical analysis of crack propagation in cyclic loaded structures. J Basic Eng 89(3):459–463

    Article  Google Scholar 

  34. 34.

    Walker K (1970) The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 Aluminum. In Effects of Environment and Complex Load History for Fatigue Life, Special Technical Publication 462, pp. 1–14. Philadelphia: American Society for Testing and Materials.

  35. 35.

    Anderson TL (2005) Fracture Mechanics: Fundamentals and Applications. Third Edition, CRC press.

  36. 36.

    AFGROW. Fracture mechanics and fatigue crack growth analysis software tool. V. 4.12.15.0, LexTech Inc., USA.

  37. 37.

    ASTM (2015) ASTM International, 2015. ASTM E647—15 Standard test method for measurement of fatigue crack growth rates. In United States: ASTM International, p. 43. Available at: http://www.astm.org/Standards/E647.

  38. 38.

    Simunek D, Leitner M, Maierhofer J, Gänser H-P (2015) Fatigue crack growth under constant and variable amplitude loading at semi-elliptical and V-notched steel specimens. Proc Eng 133:348–361. https://doi.org/10.1016/j.proeng.2015.12.670

    Article  Google Scholar 

  39. 39.

    Rubinstein AA (1991) Mechanics of the crack path formation. Int J Fract 41:29 l-305. doi: https://doi.org/10.1007/BF00012948

  40. 40.

    Malekan M, Barros FB (2018) Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method. Comput Mech 62(4):783–801. https://doi.org/10.1007/s00466-017-1527-8

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Mohammad Malekan.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Malekan, M., Khosravi, A. & St-Pierre, L. An Abaqus plug-in to simulate fatigue crack growth. Engineering with Computers (2021). https://doi.org/10.1007/s00366-021-01321-x

Download citation

Keywords

  • Fatigue crack growth
  • Abaqus plug-in
  • Python scripting
  • Finite element method
  • Life estimation