Acta Mechanica Sinica

, Volume 35, Issue 4, pp 828–838 | Cite as

Finite element simulation of elastoplastic field near crack tips and results for a central cracked plate of LE-LHP material under tension

  • X. JiEmail author
  • F. Zhu
Research Paper


The elastoplastic field near crack tips is investigated through finite element simulation. A refined mesh model near the crack tip is proposed. In the mesh refining area, element size continuously varies from the nanometer scale to the micrometer scale and the millimeter scale. Graphics of the plastic zone, the crack tip blunting, and the deformed crack tip elements are given in the paper. Based on the curves of stress and plastic strain, closely near the crack tip, the stress singularity index and the stress intensity factor, as well as the plastic strain singularity index and the plastic strain intensity factor are determined. The stress and plastic strain singular index vary with the load, while the dimensions of the stress and the plastic strain intensity factors depend on the stress and the plastic strain singularity index, respectively. The singular field near the elastoplastic crack tip is characterized by the stress singularity index and the stress intensity factor, or alternatively the plastic strain singularity index and the plastic strain intensity factor. At the end of the paper, following Irwin’s concept of fracture mechanics, \(\sigma_{\delta K}\) criterion and \(\varepsilon_{\delta Q}\) criterion are proposed. Besides, crack tip angle criterion is also presented.


Crack Fracture mechanics Elastoplasticity Finite element method Geometry nonlinearity 



The work was supported by the National Natural Science Foundation of China (Grant 11572226).


  1. 1.
    Irwin, G.R.: Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24, 361–364 (1957)Google Scholar
  2. 2.
    Rice, J.R., Sih, G.C.: Plane problems of cracks in dissimilar media. ASME J. Appl. Mech. 32, 418–423 (1965)CrossRefGoogle Scholar
  3. 3.
    Rice, J.R.: Elastic fracture mechanics concepts for interfacial cracks. ASME J. Appl. Mech. 55, 98–103 (1988)CrossRefGoogle Scholar
  4. 4.
    Rice, J.R.: A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35, 379–386 (1968)CrossRefGoogle Scholar
  5. 5.
    Rice, J.R., Rosengren, G.F.: Plane strain deformation near a crack tip in a power-law hardening material. J. Mech. Phys. Solids 16, 1–12 (1968)CrossRefzbMATHGoogle Scholar
  6. 6.
    Hutchinson, J.W., Suo, Z.G.: Mixed mode cracking in layered materials. Adv. Appl. Mech. 29, 63–191 (1991)CrossRefGoogle Scholar
  7. 7.
    Hutchinson, J.W.: Singular behavior at the end of a tensile crack tip in a hardening material. J. Mech. Phys. Solids 16, 13–31 (1968)CrossRefzbMATHGoogle Scholar
  8. 8.
    Wells, A.A.: Application of fracture mechanics at and beyond general yielding. Br. Weld. J. 10, 563–570 (1963)Google Scholar
  9. 9.
    Anderson, T.L.: Fracture Mechanics—Fundamentals and Applications, 3rd edn. CRC Press, Boca Raton (2005)zbMATHGoogle Scholar
  10. 10.
    Westergaard, H.M.: Bearing pressures and cracks. J. Appl. Mech. 6, 49–53 (1939)Google Scholar
  11. 11.
    Williams, M.L.: On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24, 109–114 (1957)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Ji, X.: SIF-based fracture criterion for interface cracks. Acta Mech. Sin. 32, 491–496 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Zhu, X.K., Joyce, J.A.: Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization. Eng. Fract. Mech. 85, 1–46 (2012)CrossRefGoogle Scholar
  14. 14.
    Bleackley, M.H., Luxmoore, A.R.: Comparison of finite element solutions with analytical and experimental data for elastic-plastic cracked problems. Int. J. Fract. 22, 15–39 (1983)CrossRefGoogle Scholar
  15. 15.
    Larsson, L.H.: A calculational round robin in elastic–plastic fracture mechanics. Int. J. Press. Vess. Pip. 11, 207–228 (1983)CrossRefGoogle Scholar
  16. 16.
    Hibbitt, H.D., Marcal, P.V., Rice, J.R.: A finite element formulation for problems of large strain and large displacement. Int. J. Solids Struct. 6, 1069–1086 (1970)CrossRefzbMATHGoogle Scholar
  17. 17.
    McMeeking, R.M., Rice, J.R.: Finite-element formulations for problems of large elastic–plastic deformation. Int. J. Solids Struct. 11, 601–616 (1975)CrossRefzbMATHGoogle Scholar
  18. 18.
    Levy, N., Marcal, P.V., Ostergren, W.J., et al.: Small scale yielding near a crack in plane strain: a finite element analysis. Int. J. Fract. Mech. 7, 143–156 (1971)CrossRefGoogle Scholar
  19. 19.
    Rice, J.R., Johnson, M.A.: The role of large crack tip geometry changes in plane strain fracture. Inelast. Behav. Solids. pp. 641–672 (1970)Google Scholar
  20. 20.
    Rice, J.R., McMeeking, R.M., Parks, D.M., et al.: Recent finite element studies in plasticity and fracture mechanics. Comput. Methods Appl. Mech. Eng. 17, 411–442 (1979)CrossRefzbMATHGoogle Scholar
  21. 21.
    Rice, J.R.: Elastic–plastic fracture mechanics. Eng. Fract. Mech. 5, 1019–1022 (1973)CrossRefGoogle Scholar
  22. 22.
    Rice, J.R., Tracey, D.M.: Computational fracture mechanics. Numer. Comput. Meth. Struct. Mech. 73, 585–623 (1973)Google Scholar
  23. 23.
    Ma, F., Kuang, Z.B.: Elastic–plastic fracture analysis of finite bodies—I. Description of the stress field. Eng. Fract. Mech. 48, 721–737 (1994)Google Scholar
  24. 24.
    Wei, Y.: Constraint effects on the elastic–plastic fracture behaviour in strain gradient solids. Fatigue Fract. Eng. Mater. Struct. 25, 433–444 (2002)CrossRefGoogle Scholar
  25. 25.
    Kim, Y.J., Son, B., Kim, Y.J.: Elastic–plastic finite element analysis for double-edge cracked tension (DE(T)) plates. Eng. Fract. Mech. 71, 945–966 (2004)CrossRefGoogle Scholar
  26. 26.
    Tarafder, M., Tarafder, S., Dash, B., et al.: Modelling of crack tip blunting using finite element method. Project Completion Report, Report No. NML-GAP0088-03-2006 (2006)Google Scholar
  27. 27.
    Zhang, J., He, X.D., Suo, B., et al.: Elastic–plastic finite element analysis of the effect of compressive loading on crack tip parameters and its impact on fatigue crack propagation rate. Eng. Fract. Mech. 75, 5217–5228 (2008)CrossRefGoogle Scholar
  28. 28.
    Lamain, L.G.: Numerical analysis in EPFM. In: Proceedings of the 4th Advanced Seminar on Fracture Mechanics. Ispra, pp. 227–261 (1983)Google Scholar
  29. 29.
    Ji, X., Zhu, F., He, P.F.: Determination of stress intensity factor with direct stress approach using finite element analysis. Acta Mech. Sin. 33, 1–7 (2017)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Aerospace Engineering and Applied MechanicsTongji UniversityShanghaiChina

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