Skip to main content
SpringerLink
Log in

Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface cracktip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Williams, M. L. The stresses around a fault or crack in dissimilar media. Bulletin of the Seismological Society of America, 49(2), 199–204 (1959)

    MathSciNet  Google Scholar 

  2. Ricci, V., Shukla, A., and Chalivendra, V. B. Subsonic interfacial fracture using strain gages in isotropic-orthotropic biomaterial. Theoretical and Applied Fracture Mechanics, 39(3), 143–161 (2003)

    Article  Google Scholar 

  3. Xia, L. and Wang, T. C. Asymptotic fields for interface crack in elastic-plastic materials. Acta Mechanica Solida Sinica, 13(3), 191–200 (1992)

    MathSciNet  Google Scholar 

  4. Dai, Y. and Ji, X. Analyses of stress singularity at interface end and interfacial stress distribution. Science China (Series G), 37(4), 535–543 (2007)

    Google Scholar 

  5. Cheng, Z. Q. and Zhong, Z. Fracture analysis of a functionally graded strip sandwiched between two homogeneous materials. Science China (Series G), 36(5), 530–542 (2006)

    Google Scholar 

  6. Li, X. M. and Lei, Z. K. Digital photoelasticity analysis of stress singularity of bimaterial joints. Engineering Mechanics, 28(12), 7–12 (2011)

    Article  MathSciNet  Google Scholar 

  7. Shang, F. L. and Kitamura, T. Molecular dynamics simulations of interfacial crack nucleation and propagation. Chinese Journal of Theoretical and Applied Mechanics, 39(4), 571–576 (2007)

    Google Scholar 

  8. Wang, B. L., Han, J. C., and Du, S. Y. Cracks problem for non-homogeneous composite material subjected to dynamic loading. International Journal of Solids and Structures, 37(9), 1251–1274 (2000)

    Article  MATH  Google Scholar 

  9. Viggo, T. Resistance curves for mixed mode interface crack growth between dissimilar elasticplastic solids. Journal of the Mechanics and Physics of Solids, 49(11), 2689–2703 (2001)

    Article  MATH  Google Scholar 

  10. Lü, N. C., Yang, D. N., Cheng, Y. H., and Cheng, J. Asymmetrical dynamic propagation problems on mode III interface crack. Applied Mathematics and Mechanics (English Edition), 28(4), 501–510 (2007) DOI 10.1007/s10483-007-0411-x

    Article  MATH  Google Scholar 

  11. Yang, W. Y., Zhang, S. Q., Li, J. L., and Ma, Y. L. Interface crack problems for mode II of double dissimilar orthotropic composite materials. Applied Mathematics and Mechanics (English Edition), 30(5), 585–594 (2009) DOI 10.1007/s10483-009-0505-z

    Article  MATH  MathSciNet  Google Scholar 

  12. Sun, S. Y. and Chen, H. R. Quasi-static and dynamic fracture behavior of composite sandwich beams with a viscoelastic interface crack. Composites Science and Technology, 70(6), 1011–1016 (2010)

    Article  Google Scholar 

  13. Liang, W. Y., Wang, Z. Q., and Yang, Z. J. Steady-state growing crack-tip field characteristics of mode III elastic-viscoplastic/rigid interface cracks. Applied Mathematics and Mechanics (English Edition), 31(2), 227–235 (2010) DOI 10.1007/s10483-010-0210-9

    Article  MATH  MathSciNet  Google Scholar 

  14. Wei, P. J., Wu, Y. L., and Zhang, S. Y. The shock response of interface crack between dissimilar viscoelastic bodies. Acta Mechanica Sinica, 33(1), 109–114 (2001)

    Google Scholar 

  15. Liu, Y. W., Xie, C., Deng, M., Fang, Q. H., and Jin, B. Screw dislocations and an interfacial blunt crack with viscoelastic interface. Theoretical and Applied Fracture Mechanics, 52(3), 146–153 (2009)

    Article  Google Scholar 

  16. Li, Y. D., Zhang, N., and Tang, L. Q. Researches on the enhancement of fracture toughness induced by friction between crack faces. Acta Mechanica Sinica, 37(3), 280–286 (2005)

    Google Scholar 

  17. Tang, L. H. and Xu, J. Q. Viscoelastic fields near interface crack tip. Chinese Quarterly of Mechanics, 28(1), 116–123 (2007)

    Google Scholar 

  18. Liang, W. Y., Wang, Z. Q., and Zhou, B. The elastic-viscoplastic field at the mixed-mode steadily propagating crack-tip under compression and shear. Chinese Journal of Theoretical and Applied Mechanics, 38(5), 618–625 (2009)

    Google Scholar 

  19. Viggo, T. and Brian, N. L. Effect of anisotropic plasticity on mixed mode interface crack growth. Engineering Fracture Mechanics, 74(16), 2603–2614 (2007)

    Article  Google Scholar 

  20. Shih, C. F. Small-scale yielding analysis of mixed mode plane-strain crack problems. ASTM STP, 560, 187–210 (1974)

    Google Scholar 

  21. Ye, Z. M. Plastic zone characteristics of crack tip in anisotropic solids. International Journal of Fracture, 74(1), R3–R10 (1995)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Smart Structures and Advanced Composites Laboratory, College of Aerospace and Civil Engineering of Harbin Engineering University, Harbin, 150001, P. R. China

    Wen-yan Liang  (梁文彦), Zhen-qing Wang  (王振清), Fang Liu  (刘 方) & Xiao-duo Liu  (刘晓铎)

Authors
  1. Wen-yan Liang  (梁文彦)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhen-qing Wang  (王振清)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fang Liu  (刘 方)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiao-duo Liu  (刘晓铎)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen-yan Liang  (梁文彦).

Additional information

Project supported by the National Natural Science Foundation of China (No. 11302054) and the Fundamental Research Funds for the Central Universities (No.HEUCF130216)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liang, Wy., Wang, Zq., Liu, F. et al. Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear. Appl. Math. Mech.-Engl. Ed. 35, 887–896 (2014). https://doi.org/10.1007/s10483-014-1838-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-014-1838-9

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation