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Numerical Simulation of Loading Edge Cracks by Edge Impact Using the Extended Finite Element Method

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Abstract

The extended finite element method is used to analyze a plate with two parallel edge cracks impacted by a cylindrical projectile. The influence of the impact speed, crack length, plate thickness and notch tip radius on the crack initiation and propagation is studied. Dynamics equations are solved by an implicit time integration scheme which is unconditionally stable. Very good agreement is achieved between numerical predictions and experimental results. The critical velocity of the crack initiation under different conditions is examined. The influence of the crack length is greater than that of the impact speed, plate thickness and notch tip radius.

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References

  1. Kalthoff, J.F., Modes of dynamic shear failure in solids. International Journal of Fracture, 2002, 101(1–2): 1–31.

    Google Scholar 

  2. Kalthoff, J.F., Shadow optical analysis of dynamic shear fracture. Optical Engineering, 1988, 27(10): 835–840.

    Article  Google Scholar 

  3. Kalthoff, J.F., Transition in the failure behavior of dynamically shear loaded cracks. Applied Mechanics Reviews, 1990, 43(5): S247–S250.

    Article  Google Scholar 

  4. Erdogan, F. and Sih, G.C., On the crack extension in plates under plane loading and transverse shear. Journal of Basic Engineering-Transactions of the ASME, 1996, 85(4): 519–525.

    Article  Google Scholar 

  5. Lee, Y.J. and Freund, L.B., Fracture initiation due to asymmetric impact loading of an edge cracked plate. Journal of Applied Mechanics-Transactions of the ASME, 1990, 57(1): 104–111.

    Article  Google Scholar 

  6. Mason, J.J., Lambros, J. and Rosakis, A.J., The use of a coherent gradient sensor in dynamic mixed-mode fracture mechanics experiments. Journal of the Mechanics and Physics of Solids, 1992, 40(3): 641–661.

    Article  Google Scholar 

  7. Ravi-Chandar, K., On the failure mode transitions in polycarbonate under dynamic mixed-mode loading. International Journal of Solids and Structures, 1995, 32(6): 925–938.

    Article  Google Scholar 

  8. Zhou, M., Rosakis, A.J. and Ravichandar, G., Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signature and propagation speed. Journal of the Mechanics and Physics of Solids, 1996, 44(6): 981–1006.

    Article  Google Scholar 

  9. Needleman, A. and Tvergaard, V., Analysis of a brittle-ductile transition under dynamic shear loading. International Journal of Solids and Structures, 1995, 32(17): 2571–2590.

    Article  Google Scholar 

  10. Belytschko, T. and Tabbara, M., Dynamic fracture using element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1996, 39(6): 923–938.

    Article  Google Scholar 

  11. Camacho, G.T. and Ortiz, M., Computational modeling of impact damage in brittle materials. International Journal of Solids and Structures, 1996, 33(20): 2899–2938.

    Article  Google Scholar 

  12. Batra, R.C. and Nechitailo, N.V., Analysis of failure modes in impulsively loaded pre-notched steel plates. International Journal of Plasticity, 1997, 13(4): 291–308.

    Article  Google Scholar 

  13. Belytschko, T. and Chen, H., Singular enrichment finite element method for elastodynamic crack propagation. International Journal of Computational Methods, 2004, 1(1): 1–15.

    Article  Google Scholar 

  14. Remmers, J.J.C., de Borst, R. and Needleman, A., The simulation of dynamic crack propagation using the cohesive segments method. Journal of the Mechanics and Physics of Solids, 2008, 56(1): 70–92.

    Article  MathSciNet  Google Scholar 

  15. Zhang, Y.Y. and Chen, L., Impact simulation using simplified meshless method. International Journal of Impact Engineering, 2009, 36(5): 651–658.

    Article  Google Scholar 

  16. Armero, F. and Linder, C., Numerical simulation of dynamic fracture using finite elements with embedded discontinuities. International Journal of Fracture, 2009, 160(2): 119–141.

    Article  Google Scholar 

  17. Réthoré, J., Gravouil, A. and Combescure, A., An energy-conserving scheme for dynamic crack growth using the extended finite element method. International Journal for Numerical Methods in Engineering, 2005, 63(5): 631–659.

    Article  MathSciNet  Google Scholar 

  18. Zi, G., Chen, H., Xu, J.X. and Belytschko, T., The extended finite element method for dynamic fractures. Shock and Vibration, 2005, 12(1): 9–23.

    Article  Google Scholar 

  19. Menouillard, T., Réthoré, J., Combescure, A. and Bung, H., Efficient explicit time stepping for the extended finite element method (X-FEM). International Journal for Numerical Methods in Engineering, 2006, 68(9): 911–939.

    Article  MathSciNet  Google Scholar 

  20. Elguedj, T., Gravouil, A. and Maigre, H., An explicit dynamics extended finite element method—Part 1: Mass lumping for arbitrary enrichment functions. Computer Methods in Applied Mechanics and Engineering, 2009, 198(30): 2297–2317.

    Article  Google Scholar 

  21. Motamedi, D. and Mohammadi, S., Dynamic crack propagation analysis of orthotropic media by the extended finite element method. International Journal of Fracture, 2010, 161(1): 21–39.

    Article  Google Scholar 

  22. Song, J.H., Wang, H.W. and Belytschko, T., A comparative study on finite element methods for dynamic fracture. Computational Mechanics, 2008, 42(2): 239–250.

    Article  Google Scholar 

  23. Menouillard, T. and Belytschko, T., Dynamic fracture with meshfree enriched XFEM. Acta Mechanica, 2010, 213(1–2): 53–69.

    Article  Google Scholar 

  24. Melenk, J.M. and Babuška, I., The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1): 289–314.

    Article  MathSciNet  Google Scholar 

  25. Moës, N., Dolbow, J. and Belytschko, T., A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131–150.

    Article  Google Scholar 

  26. Fleming, M., Chu, Y.A., Moran, B. and Belytschko, T., Enriched element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering, 1997, 40(8): 1483–1504.

    Article  MathSciNet  Google Scholar 

  27. Sukumar, N. and Prévost, J.H., Modeling quasi-static crack growth with the extended finite element method—Part I: Computer implementation. International Journal of Solids and Structures, 2003, 40(26): 7513–7537.

    Article  Google Scholar 

  28. Meng, Q.H. and Wang, Z.Q., Extended finite element method for power-law creep crack growth. Engineering Fracture Mechanics, 2014, 127: 148–160.

    Article  Google Scholar 

  29. Hilber, H.M., Hughes, T.J.R. and Taylor, R.L., Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering and Structural Dynamics, 1977, 5(3): 283–292.

    Article  Google Scholar 

  30. Newmark, N.M., A method of computation for structural dynamics. Journal of the Engineering Mechanics Division-ASCE, 1959, 85(3): 67–94.

    Google Scholar 

  31. Nuismer, R.J., An energy release rate criterion for mixed mode fracture. International Journal of Fracture, 1975, 11(2): 245–250.

    Article  Google Scholar 

  32. Hussain, M.A., Pu, S.L. and Underwood, J.M., Strain energy release rate for a crack under combined mode I and mode II. In: Fracture Analysis, Proceedings of the 1973 National Symposium on Fracture Mechanics, Part II, ASTM Special Technical Publication 560, 1973, 2–28.

  33. Sih, G.C., Strain-energy-density factor applied to mixed mode crack problems. International Journal of Fracture, 1974, 10(3): 305–321.

    Article  Google Scholar 

  34. Yau, J.F., Wang, S.S. and Corten, H.T., A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. Journal of Applied Mechanics-Transactions of the ASME, 1980, 47(2): 335–341.

    Article  Google Scholar 

  35. Shih, C.F. and Asaro, R.J., Elastic-plastic analysis of cracks on bimaterial interfaces—I: Small scale yielding. Journal of Applied Mechanics-Transactions of the ASME, 1988, 55(2): 299–316.

    Article  Google Scholar 

  36. Li, F.Z., Shih, C.F. and Needleman, A., A comparison of methods for calculating energy release rates. Engineering Fracture Mechanics, 1985, 21(2): 405–421.

    Article  Google Scholar 

  37. Shih, C.F., Moran, B. and Nakamura, T., Energy release rate along a three-dimensional crack front in a thermally stressed body. International Journal of Fracture, 1986, 30(2): 79–102.

    Google Scholar 

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Authors and Affiliations

  1. College of Aerospace and Civil Engineering, Harbin Engineering University, 150001, Harbin, China

    Qinghua Meng & Zhenqing Wang

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  1. Qinghua Meng
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  2. Zhenqing Wang
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Correspondence to Qinghua Meng or Zhenqing Wang.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11272096 and 11472086) and the Research Fund for the Doctoral Program of Higher Education of China (No. 20112304110015).

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Meng, Q., Wang, Z. Numerical Simulation of Loading Edge Cracks by Edge Impact Using the Extended Finite Element Method. Acta Mech. Solida Sin. 28, 156–167 (2015). https://doi.org/10.1016/S0894-9166(15)30004-5

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  • DOI: https://doi.org/10.1016/S0894-9166(15)30004-5

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