Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

XFEM for fatigue and fracture analysis of cracked stiffened panels

  • Kumar, M.R. Nanda (Bhabha Atomic Research Centre) ;
  • Murthy, A. Ramachandra (CSIR-Structural Engineering Research Centre) ;
  • Gopinath, Smitha (CSIR-Structural Engineering Research Centre) ;
  • Iyer, Nagesh R. (CSIR-Structural Engineering Research Centre)
  • Received : 2014.11.19
  • Accepted : 2015.12.02
  • Published : 2016.01.10
⟨ Previous Next ⟩

Abstract

This paper presents the development of methodologies using Extended Finite Element Method (XFEM) for cracked unstiffened and concentric stiffened panels subjected to constant amplitude tensile fatigue loading. XFEM formulations such as level set representation of crack, element stiffness matrix formulation and numerical integration are presented and implemented in MATLAB software. Stiffeners of the stiffened panels are modelled using truss elements such that nodes of the panel and nodes of the stiffener coincide. Stress Intensity Factor (SIF) is computed from the solutions of XFEM using domain form of interaction integral. Paris's crack growth law is used to compute the number of fatigue cycles up to failure. Numerical investigations are carried out to model the crack growth, estimate the remaining life and generate damage tolerant curves. From the studies, it is observed that (i) there is a considerable increase in fatigue life of stiffened panels compared to unstiffened panels and (ii) as the external applied stress is decreasing number of fatigue life cycles taken by the component is increasing.

Keywords

References

  1. Belytschko, T. and Black, T. (1999), "Elastic crack growth in finite elements with minimal remeshing", Int. J. Numer. Meth. Eng., 45, 601-620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
  2. Dexter, R.J., Pilarski, P.J. and Mahmoud, H.N. (2003), "Analysis of crack propagation in welded stiffened panels", Int. J. Fatig., 25, 1169-1174. https://doi.org/10.1016/j.ijfatigue.2003.08.006
  3. Dolbow, J., Moes, N. and Belytschko, T. (2000), "Discontinuous enrichment in finite elements with a partition of unity method", Finite Elem. Anal. Des., 36, 235-260. https://doi.org/10.1016/S0168-874X(00)00035-4
  4. Erdogan, F. and Sih, G.C. (1963), "On the crack extension in plates under plane loading and transverse shear", J. Basic Eng., 85, 519-527. https://doi.org/10.1115/1.3656897
  5. Jamal-Omidi, M., Falah, M. and Taherifar, D. (2014), "3-D fracture analysis of cracked aluminum plates repaired with single and double composite patches using XFEM", Struct. Eng. Mech., 50(4), 525-539. https://doi.org/10.12989/sem.2014.50.4.525
  6. Jiang, S.Y., Du, C.B. and Gu, C.S. (2014), "An investigation into the effects of voids, inclusions and minor cracks on major crack propagation by using XFEM", Struct. Eng. Mech., 49(5), 597-618. https://doi.org/10.12989/sem.2014.49.5.597
  7. Kocanda, D. and Jasztal, M. (2012), "Probabilistic predicting the fatigue crack growth under variable amplitude loading", Int. J. Fatig., 39, 68-74. https://doi.org/10.1016/j.ijfatigue.2011.03.011
  8. Mahmoud, H.N. and Dexter, R.J. (2005), "Propagation rate of large cracks in stiffened panels under tension loading", Mar. Struct., 18(3), 265-288. https://doi.org/10.1016/j.marstruc.2005.09.001
  9. Melenk, J.M. and Babuska, I. (1996), "The partition of unity finite element method: basic theory and applications", Comput. Meth. Appl. Mech. Eng., 139, 289-314. https://doi.org/10.1016/S0045-7825(96)01087-0
  10. Meng, Q. and Wang, Z. (2014), "Extenede finite element method for power law creep crack growth", Eng. Fract. Mech., 127, 148-160. https://doi.org/10.1016/j.engfracmech.2014.06.005
  11. Moes, N., Dolbow, J. and Belytschko, T. (1999), "A finite element method for crack growth without remeshing", Int. J. Numer. Meth. Eng., 46, 131-150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
  12. Murakami (1986), "Stress intensity factor handbook", Pergamon press.
  13. Natarajan, S., Kerfriden, P., Roy Mahapatra, D. and Bordas, S.P.A. (2014), "Numerical analysis of the inclusion-crack interaction by the extended finite element method", Int. J. Comput. Meth. Eng. Sci. Mech., 15, 26-32. https://doi.org/10.1080/15502287.2013.833999
  14. Nechval, K.N., Nechval, N.A., Bausova, I., Skiltere, D. and Strelchonok, V.F. (2006), "Prediction of fatigue crack growth process via artificial neural network process", Int. J. Comput., 5(3), 21-32.
  15. Paris, P., Gomez, M. and Anderson, W. (1961), "A rational analytic theory of fatigue", Trend Eng., 13, 9-14.
  16. Pathak, H., Singh, A. and Vir Singh, I. (2013), "Fatigue crack growth simulations of 3-D problems using XFEM", Int. J. Mech. Sci., 76, 112-131. https://doi.org/10.1016/j.ijmecsci.2013.09.001
  17. Rama Chandra Murthy, A., Palani, G.S. and Iyer, N.R. (2007), "Remaining life prediction of cracked stiffened panels under constant and variable amplitude loading", Int. J. Fatig., 29(6), 1125-1139. https://doi.org/10.1016/j.ijfatigue.2006.09.016
  18. Rama Chandra Murthy, A., Palani, G.S. and Iyer, N.R. (2009a), "Damage tolerant evaluation of cracked stiffened panels subjected to fatigue loading", Sadhana, 37(1), 171-186.
  19. Rama Chandra Murthy, A., Palani, G.S. and Iyer, N.R. (2009b), "Residual strength evaluation of unstiffened and stiffened panels under fatigue loading", SDHM, 5(3), 201-226.
  20. Rasuo, B., Grbovic, A. and Petrasinovic, D. (2013), "Investigation of fatigue life of 2024-T3 aluminium spar using extended finite element method (XFEM) ", SAE Int. J. Aerosp., 6(2), 408-416. https://doi.org/10.4271/2013-01-2143
  21. Rooke, D.P. and Cartwright, D.J. (1976), Compendium of Stress Intensity Factors, Her Majesty's Stationary Office, London.
  22. Sabelkin, V., Mall, S. and Avram, A.V. (2006), "Fatigue crack growth analysis of stiffened cracked panel repaired with bonded composite patch", Eng. Fract. Mech., 73, 1553-1567. https://doi.org/10.1016/j.engfracmech.2006.01.029
  23. Sharma, K., Singh, I.V., Mishra, B.K. and Shedbale, A.S. (2014), "The effect of inhomogeneities on an edge crack: A numerical study using XFEM", Int. J. Comput. Meth. Eng. Sci. Mech., 14, 505-523.
  24. Singh, I.V., Mishra, B.K., Bhattacharya, S. and Patil, R.U. (2012), "The numerical simulation of fatigue crack growth using extended finite element method", Int. J. Fatig., 36, 109-119. https://doi.org/10.1016/j.ijfatigue.2011.08.010
  25. Stolarska, M., Chopp, D.L., Moes, N. and Belyschko, T. (2001), "Modelling crack growth by level sets in the extended finite element method", Int. J. Numer. Meth. Eng., 51, 943-960. https://doi.org/10.1002/nme.201
  26. Tanaka, K. (1974), "Fatigue crack propagation from a crack inclined to the cyclic tension axis", Eng. Fract. Mech., 6, 493-507. https://doi.org/10.1016/0013-7944(74)90007-1
  27. Tong, P. and Pian, T.H. (1973), "On the convergence of the finite element method for problems with singularity", Int. J. Solid. Struct., 9, 313-321. https://doi.org/10.1016/0020-7683(73)90082-6
  28. Yau, J., Wang, S. and Corten, H. (1980), "A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity", J. Appl. Mech., 47, 335-341. https://doi.org/10.1115/1.3153665

Cited by

  1. FE simulation of S-N curves for a riveted connection using two-stage fatigue models vol.2, pp.4, 2016, https://doi.org/10.12989/acd.2017.2.4.333
  2. Fracture behavior modeling of a 3D crack emanated from bony inclusion in the cement PMMA of total hip replacement vol.66, pp.1, 2016, https://doi.org/10.12989/sem.2018.66.1.037
  3. Method using XFEM and SVR to predict the fatigue life of plate-like structures vol.73, pp.4, 2016, https://doi.org/10.12989/sem.2020.73.4.455