Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An investigation into the effects of voids, inclusions and minor cracks on major crack propagation by using XFEM

  • Jiang, Shouyan (College of Water Conservancy and Hydropower Engineering, Hohai University) ;
  • Du, Chengbin (College of Mechanics and Materials, Hohai University) ;
  • Gu, Chongshi (College of Water Conservancy and Hydropower Engineering, Hohai University)
  • Received : 2013.02.24
  • Accepted : 2014.01.27
  • Published : 2014.03.10
⟨ Previous Next ⟩

Abstract

For the structures containing multiple discontinuities (voids, inclusions, and cracks), the simulation technologies in the framework of extended finite element method (XFEM) are discussed in details. The level set method is used for representing the location of inner discontinuous interfaces so that the mesh does not need to align with these discontinuities. Several illustrations have been given to verify that the implemented XFEM program is effective. Then, the implemented XFEM program is used to investigate the effects of the voids, inclusions, and minor cracks on the path of major crack propagation. For a plate containing cracks and voids, two possibly crack path can be observed: i) the crack propagates into the void; ii) the crack initially curves towards the void, then, the crack reorients itself and propagates along its original orientation. For a plate with a soft inclusion, the final predicted crack paths tend to close with the inclusion, and an evident difference of crack paths can be observed with different inclusion material properties. However, for a plate with a hard inclusion, the paths tend to away from the inclusion, and a slightly difference of crack paths can only be seen with different inclusion material properties. For a plate with several minor cracks, the trend of crack paths can still be described as that the crack initially curves towards these minor cracks, and then, the crack reorients itself and propagates almost horizontally along its original orientation.

Keywords

References

  1. Belytschko, T. and Black, T. (1999), "Elastic crack growth in finite elements with minimal remeshing", Int. J. Numer. Meth. Eng., 45(5), 601-620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
  2. Dreau, K., Chevaugeon, N., Moes, N. (2010), "Studied X-FEM enrichment to handle material interfaces with higher order finite element", Comput. Method. Appl. Mech. Eng., 199, 1922-1936. https://doi.org/10.1016/j.cma.2010.01.021
  3. Du, C.B, Jiang, S.Y., Qin, W., Xu, H. and Lei, D. (2012), "Reconstruction of internal structures and numerical simulation for concrete composites at mesoscale", Comput. Concrete, 10(2), 135-147. https://doi.org/10.12989/cac.2012.10.2.135
  4. Erdogan, F. and Sih, G.C. (1963), "On the crack extension in plane loading and transverse shear", J. Basic Eng., 85, 519-527. https://doi.org/10.1115/1.3656897
  5. Haboussa, D., Gregoire, D., Elguedj, T., Maigre, H. and Combescure, A. (2011), "X-FEM analysis of the effects of holes or other cracks on dynamic crack propagations", Int. J. Numer. Method. Eng., 86, 618-636. https://doi.org/10.1002/nme.3128
  6. Kim, J., Zi, G., Van, S.N., Jeong, M.C., Kong, J.S. and Kim, M.S. (2011), "Fatigue life prediction of multiple site damage based on probabilistic equivalent initial flaw model", Struct. Eng. Mech., 38(4), 443-457. https://doi.org/10.12989/sem.2011.38.4.443
  7. Liao, J.H. and Zhuang, Z. (2012), "A Lagrange-multiplier-based XFEM to solve pressure Poisson equations in problems with quasi-static interfaces", SCIENCE CHINA Phy., Mech. Astron., 55(4), 693-705. https://doi.org/10.1007/s11433-012-4664-2
  8. Mayer, U.M., Popp, A., Gerstenberger, A. and Wall, W.A. (2010), "3D fluid-structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach", Comput. Mech., 46, 53-67. https://doi.org/10.1007/s00466-010-0486-0
  9. Melenk, J.M. and Babuska, I. (1996), "The partition of unity finite element method: basic theory and applications", Comput. Method. Appl. Mech. Eng., 39, 289-314.
  10. Moes, N., Cloirec, M., Cartraud, P. and Remacle, J.F. (2003), "A computational approach to handle complex microstructure geometries", Comput. Method. Appl. Mech. Eng., 192(28-30), 3163-3177. https://doi.org/10.1016/S0045-7825(03)00346-3
  11. Mohammadi, S. (2008), Extended finite element method, Blackwell Publishing Ltd, Oxford, UK.
  12. Osher, S. and Sethian, J.A. (1988), "Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations", J. Comput. Phys., 79(1), 12-49. https://doi.org/10.1016/0021-9991(88)90002-2
  13. Rice, J.R. (1968), "A path independent integral and the approximate analysis of strain concentrations by notches and cracks", J. Appl. Mech., 35, 379-386. https://doi.org/10.1115/1.3601206
  14. 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. Fatigue, 36, 109-119. https://doi.org/10.1016/j.ijfatigue.2011.08.010
  15. Singh, I.V., Mishra, B.K. and Bhattacharya, S. (2011), "XFEM simulation of cracks, holes and inclusions in functionally graded materials", Int. J. Mech. Mater. Des., 7, 199-218. https://doi.org/10.1007/s10999-011-9159-1
  16. Stolarska, M. and Chopp, D.L. (2003), "Modeling thermal fatigue cracking in integrated circuits by level sets in the extended finite element method", Int. J. Numer. Method. Eng., 41, 2381-2410.
  17. Sukumar, N., Chopp, D.L., Moes, N. and Belytschkoc, T. (2001), "Modeling holes and inclusions by level sets in the extended finite element method", Comput. Method. Appl. Mech. En.g, 190(46-47), 6183-6200. https://doi.org/10.1016/S0045-7825(01)00215-8
  18. Sukumar, N. and Prevost, J.H. (2003), "Modeling quasi-static crack growth with the extended finite element method, Part I: Computer implementation", Int. J. Solid. Struct., 40, 7513-7537. https://doi.org/10.1016/j.ijsolstr.2003.08.002
  19. Sun, H., Waisman, H. and Betti, R. (2013), "Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm", Int. J. Numer. Method. Eng., 95, 871-900. https://doi.org/10.1002/nme.4529
  20. Wu, Z.J. and Wong, L.N.Y. (2013), "Modeling cracking behavior of rock mass containing inclusions using the enriched numerical manifold method", Eng. Geol., 162, 1-13. https://doi.org/10.1016/j.enggeo.2013.05.001
  21. Yan, Y. and Park, S. (2008), "An extended finite element method for modeling near-interfacial crack propagation in a layered structure", Int. J. Solid. Struct., 45, 4756-4765. https://doi.org/10.1016/j.ijsolstr.2008.04.016
  22. Ye, C., Shi, J. and Cheng, G.J. (2012), "An eXtended Finite Element Method (XFEM) study on the effect of reinforcing particles on the crack propagation behavior in a metal-matrix composite", Int. J. Fatigue, 44, 151-156. https://doi.org/10.1016/j.ijfatigue.2012.05.004

Cited by

  1. XFEM for fatigue and fracture analysis of cracked stiffened panels vol.57, pp.1, 2016, https://doi.org/10.12989/sem.2016.57.1.065
  2. Crack propagation and deviation in bi-materials under thermo-mechanical loading vol.50, pp.4, 2014, https://doi.org/10.12989/sem.2014.50.4.441
  3. Damage Tolerant Analysis of Cracked Al 2024-T3 Panels repaired with Single Boron/Epoxy Patch vol.99, pp.2, 2018, https://doi.org/10.1007/s40030-018-0279-6
  4. Effect of normal load on the crack propagation from pre-existing joints using Particle Flow Code (PFC) vol.19, pp.1, 2014, https://doi.org/10.12989/cac.2017.19.1.099
  5. Study on dynamic interaction between crack and inclusion or void by using XFEM vol.63, pp.3, 2017, https://doi.org/10.12989/sem.2017.63.3.329
  6. Fracture behavior modeling of a 3D crack emanated from bony inclusion in the cement PMMA of total hip replacement vol.66, pp.1, 2014, https://doi.org/10.12989/sem.2018.66.1.037
  7. Calculation of dynamic stress intensity factors and T-stress using an improved SBFEM vol.66, pp.5, 2014, https://doi.org/10.12989/sem.2018.66.5.649
  8. Method using XFEM and SVR to predict the fatigue life of plate-like structures vol.73, pp.4, 2014, https://doi.org/10.12989/sem.2020.73.4.455
  9. Numerical study of edge crack interaction with inclusion and void of an isotropic plate under different loadings by extended finite element method vol.814, pp.None, 2020, https://doi.org/10.1088/1757-899x/814/1/012017
  10. Composite coating effect on stress intensity factors of aluminum pressure vessels with inner circumferential crack by X-FEM vol.194, pp.no.pb, 2014, https://doi.org/10.1016/j.ijpvp.2021.104445