Skip to main content
Log in

Blunt crack-tip elastoplastic zone of mixed mode fracture

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

This article discusses the characterization of fracture process zone at the tip of a blunt crack in elastoplastic materials under mixed mode loading. The analysis includes the description of elastoplastic zone geometry around the blunt crack tip for predicting crack growth direction. The deformed zone appearing at the crack front is described by presenting a criterion based on the subloading surface concept falling within the framework of unconventional plasticity. The mixed mode crack propagates along the minimum value of the elastoplastic region. The present solutions are reduced to those previously reported in literature, when the elastic perfectly plastic material is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Pook, L.P., The effect of crack angle on fracture toughness. Eng. Fracture Mech., 1971, 3(3): 205–218.

    Article  Google Scholar 

  2. Eftis, J. and Subramonian, N., The inclined crack under biaxial load. Eng. Fracture Mech., 1978, 10(1): 43–67.

    Article  Google Scholar 

  3. Chou, C.T. and Kuo, C.P., An analysis of the mixed-type stress field near a crack-tip region. Eng. Fracture Mech., 1982, 16(1): 35–46.

    Article  Google Scholar 

  4. Papadopoulos, G.A., The stationary value of the third stress invariant as a local fracture parameter (Det.-criterion). Eng. Fracture Mech., 1987, 27(6): 643–652.

    Article  Google Scholar 

  5. Papadopoulos, G.A., Crack initiation under biaxial loading. Eng. Fracture Mech., 1988, 29(5): 585–598.

    Article  Google Scholar 

  6. Papadopoulos, G.A., New concepts on the Det.-criterion. Eng. Fracture Mech., 1989, 33(2): 283–293.

    Article  Google Scholar 

  7. Shlyannikov, V.N. and Braude, N.Z., A model for predicting crack growth rate for mixed mode fracture under biaxial loads. Fatigue Fract. Engng. Mater. Struct., 1992, 15(9): 825–844.

    Article  Google Scholar 

  8. Golos, K. and Wasiluk, B., Role of plastic zone in crack growth direction criterion under mixed mode loading. Int. J. Fracture, 2000, 102(4): 341–353.

    Article  Google Scholar 

  9. Jing, P., Khraishi, T. and Gorbatikh, L., Closed-form solutions for the model II crack tip plastic zone shape. Int. J. Fracture, 2003, 122(3): L137–L142.

    Article  Google Scholar 

  10. Li, H. and Chandra, N., Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models. Int. J. Plasticity, 2003, 19(6): 849–882.

    Article  Google Scholar 

  11. Erdogan, F. and Sih, G.C., On the crack extension in plates under plane loading and transverse shear. J. Basic Eng., 1963, 85(4): 519–527.

    Article  Google Scholar 

  12. Sih, G.C., Some basic problems in fracture mechanics and new concepts. Eng. Fracture Mech., 1973, 5(2): 365–377.

    Article  MathSciNet  Google Scholar 

  13. Sih, G.C., Strain-energy-density factor applied to mixed mode crack problems. Int. J. Fracture, 1974, 10(3): 305–321.

    Article  Google Scholar 

  14. Kong, X.M., Schluter, N. and Dahl, W., Effect of triaxial stress on mixed-mode fracture. Eng. Fracture Mech., 1995, 52(2): 379–388.

    Article  Google Scholar 

  15. Theocaris, P.S. and Andrianopoulos, N.P., The Mises elastic-plastic boundary as the core region in fracture criteria. Eng. Fracture Mech., 1982, 16(3): 425–432.

    Article  Google Scholar 

  16. Theocaris, P.S. and Andrianopoulos, N.P., The T-criterion applied to ductile fracture. Int. J. Fracture, 1982, 20: R125–R130.

    Article  Google Scholar 

  17. Khan, S.M.A. and Khraisheh, M.K., Analysis of mixed mode crack initiation angles under various loading conditions. Eng. Fracture Mech., 2000, 67(5): 397–419.

    Article  Google Scholar 

  18. Theocaris, P.S., Kardomateas, G.A. and Andrianopoulos, N.P., Experimental study of the T-criterion in ductile fracture. Eng. Fracture Mech., 1982, 17(5): 439–447.

    Article  Google Scholar 

  19. Papadopoulos, G.A. and Poniridis, P.I., Crack initiation from blunt notches under biaxial loading. Eng. Fracture Mech., 1988, 31(1): 65–78.

    Article  Google Scholar 

  20. Yan, X., Zhang, Z. and Du, S., Mixed-mode fracture criteria for the materials with different yield strengths in tension and compression. Eng. Fracture Mech., 1992, 42(1): 109–116.

    Article  Google Scholar 

  21. Ukadgaonker, V.G. and Awasare, P.J., A new criterion for fracture initiation. Eng. Fracture Mech., 1995, 51(2): 265–274.

    Article  Google Scholar 

  22. Harmain, G.A. and Provan, J.W., Fatigue crack-tip plasticity revisited—the issue of shape addressed. Theor. Appl. Fract. Mech., 1997, 26: 63–79.

    Article  Google Scholar 

  23. Qiang, H.F., Lu, N. and Liu, B.J., Unified solutions of crack tip plastic zone under small scale yielding. J. Mech. Eng., 1999, 35(1): 34–38.

    Google Scholar 

  24. Zhang, Y., Qiang, H.F. and Yang, Y.C., The unified solutions to mixed mode crack tip under small scale yielding. J. Mech. Eng., 2007, 43(2): 50–54.

    Article  Google Scholar 

  25. Yu, M.H., Advances in strength theories for materials under complex stress state in the 20th century. J. Appl. Mech., 2002, 55(3): 169–218.

    Article  Google Scholar 

  26. Wu, X.F. and Dzenis, Y.A., Closed-form solution for the size of plastic zone in an edge-cracked strip. Int. J. Eng. Sci., 2002, 40(15): 1751–1759.

    Article  Google Scholar 

  27. Wasiluk, B. and Golos, K., Prediction of crack growth direction under plane stress for mixed-mode I and II loading. Fatigue Fract. Engng. Mater. Struct., 2000, 23(5): 381–386.

    Article  Google Scholar 

  28. Khan, S.M.A. and Khraisheh, M.K., A new criterion for mixed mode fracture initiation based on the crack tip plastic core region. Int. J. Plasticity, 2004, 20(1): 55–84.

    Article  Google Scholar 

  29. Khan, S.M.A. and Khraisheh, M.K., The anisotropic R-criterion for crack initiation. Eng. Fract. Mech., 2008, 75(14): 4257–4278.

    Article  Google Scholar 

  30. Kaminsky, A.A., Kurchakov, E.E. and Gavrilov, G.V., Study of the plastic zone near a crack in an anisotropic body. Int. Appl. Mech., 2006, 42(7): 749–764.

    Article  MathSciNet  Google Scholar 

  31. Xin, G., Hangong, W., Xingwu, K. and Liangzhou, J., Analytic solutions to crack tip plastic zone under various loading conditions. European Journal of Mechanics-A/Solids, 2010, 29(4): 738–745.

    Article  Google Scholar 

  32. Drucker, D.C., Conventional and unconventional plastic response and representation. Appl. Mech. Rev. (ASME), 1988, 41(4): 151–167.

    Article  Google Scholar 

  33. Hashiguchi, K., Constitutive equations of elastoplastic materials with elastic-plastic transition. J. Appl. Mech. (ASME), 1980, 47(2): 266–272.

    Article  Google Scholar 

  34. Hashiguchi, K., Subloading surface model in unconventional plasticity. Int. J. Solids Struct., 1989, 25(8): 917–945.

    Article  Google Scholar 

  35. Hashiguchi, K., Saitoh, K., Okayasu, T. and Tsutsumi, S., Evaluation of typical conventional and unconventional plasticity models for prediction of softening behavior of soils. Geotechnique, 2002, 52: 561–573.

    Article  Google Scholar 

  36. Hashiguchi, K. and Protasov, A., Localized necking analysis by the subloading surface model with tangential-strain rate and anisotropy. Int. J. Plasticity, 2004, 20(10): 1909–1930.

    Article  Google Scholar 

  37. Khojastehpour, M., Murakami, Y. and Hashiguchi, K., Antisymmetric bifurcation in an elastoplastic cylinder with tangential plasticity. Mechanics of Materials, 2006, 38(11): 1061–1071.

    Article  Google Scholar 

  38. Khojastehpour, M. and Hashiguchi, K., Axisymmetric bifurcation analysis in soils by the tangential-subloading surface model. J. Mech. Phys. Solids, 2004, 52(10): 2235–2262.

    Article  Google Scholar 

  39. Khojastehpour, M. and Hashiguchi, K., Plane strain bifurcation analysis of soils by the tangential-subloading surface model. Int. J. Solids and Struct., 2004, 41(20): 5541–5563.

    Article  Google Scholar 

  40. Creager, M. and Paris, P.C., Elastic field equations for blunt cracks with reference to stress corrosion cracking. Int. J. Fracture, 1967, 3(4): 247–252.

    Google Scholar 

  41. Anderson, T.L., Fracture Mechanics: Fundamentals and Applications. Second ed., CRC Press, USA, 1995.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mehdi Khojastehpour.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khojastehpour, M. Blunt crack-tip elastoplastic zone of mixed mode fracture. Acta Mech. Solida Sin. 27, 531–541 (2014). https://doi.org/10.1016/S0894-9166(14)60061-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S0894-9166(14)60061-6

Key Words

Navigation