Skip to main content
SpringerLink
Log in

Growth of a spherical micro-void in an infinite elastoplastic body under thermal load

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The growth of preexisting spherical micro-void in an infinite elastoplastic body under thermal load is analyzed. Based on the geometrical nonlinearity with large deformation and the yield criterion of perfect plasticity, a mathematical model of the problem is presented. The Lagrangian and Euler coordinate systems are introduced to describe the thermal expansion deformation. By the elastoplastic analysis, the distributions of the stresses near the cavity are obtained. When the initial radius of a preexisting micro-void tends to be infinitely small, the critical temperature of cavitation can be calculated. The instability of the micro-void inside the infinite body is discussed. The results of numeric computation indicate that the radius of the cavity and the radius of the plastic zone would rapidly grow when the remote temperature increases and approaches the critical temperature.

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. Hill R.: The Mathematical Theory of Plasticity. Oxford University Press, London (1950)

    MATH  Google Scholar 

  2. Gent A.N., Lindley P.B.: Internal rupture of bounded rubber cylinders in tension. Proc. R. Soc. Lond. 249, 195–205 (1958)

    Article  Google Scholar 

  3. Ball J.M.: Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Philos. Trans. R. Soc. Lond. Ser. A 306, 557–611 (1982)

    Article  MATH  Google Scholar 

  4. Horgan C.O., Abeyaratne R.: A bifurcation problem for a compressible nonlinearly elastic medium: growth of micro-void. J. Elast. 16, 189–200 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  5. Robert J.A., Vlado A.L.: Mechanics of Solids and Materials. Cambridge University Press, New York (2006)

    Google Scholar 

  6. Shang X.C., Cheng C.J.: Exact solution for cavitated bifurcation for compressible hyperelastic materials. Int. J. Eng. Sci. 39, 1101–1117 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang Y., Huang Z.P.: Void growth and cavitation in nonlinear viscoelastic solids. Acta Mech. Sinica 19, 380–384 (2003)

    Article  Google Scholar 

  8. Shang, X.C., Cheng, C.J.: Cavitated Bifurcation in Hookean Elastic and Elastic-Plastic Materials. The Fourth International Conference on Nonlinear Mechanics. pp. 315–319 (2002)

  9. Huo B., Zheng Q.S., Huang Y.: A note on the effect of surface energy and void size to void growth. Eur. J. Mech. A/Solids. 18, 987–994 (1999)

    Article  MATH  Google Scholar 

  10. Asaro R.J., Lubarda V.A.: Mechanics of Solids and Materials. Cambridge University Press, New York (2006)

    Book  Google Scholar 

  11. Huang Y., Hutchinson J.W., Tvergaard V.: Cavitation instabilities in elastic-plastic solids. J. Mech. Phys. Solids 39, 223–241 (1991)

    Article  Google Scholar 

  12. Tvergaard V.: Material failure by void growth to coalescence. In: Hutchison, J.W., Theodore, Y.W. (eds.) Advances in Ductile Materials, pp. 83–151. Academic Press Inc, San Diego (1990)

    Google Scholar 

  13. Huang Z.P., Yang L.M., Pan K.L.: Dynamic void growth models in ductile materials. In: Zheng, Z.M., Tna, Q.M. Proceedings of IUTAM Symposium on Impact Dynamics, pp. 310–322. Peking University Press, Beijing (1994)

  14. Hata T.: Thermal Shock in a hollow sphere caused by rapid uniform heating. J. Appl. Mech. 58, 64–69 (1991)

    Article  MATH  Google Scholar 

  15. Ghosh M.K., Kanoria M.: Analysis of thermoelastic response in a functionally graded spherically isotropic hollow sphere based on Green-Lindsay theory. Acta Mech. 207, 51–67 (2009)

    Article  MATH  Google Scholar 

  16. Guo L.C., Naotake N.: An analytical method for thermal stresses of a functionally graded material cylindrical shell under a thermal shock. Acta Mech. 214, 71–78 (2010)

    Article  MATH  Google Scholar 

  17. Ahmadi S.R., Sheikhlou M., Mahmood Gharebagh V.: Thermo-elastic/plastic semi-analytical solution of incompressible functionally graded spherical pressure vessel under thermo-mechanical loading. Acta Mech. 222, 161–173 (2011)

    Article  MATH  Google Scholar 

  18. Monig R., Keller R.R., Volkert C.A.: Thermal fatigue testing of thin metal films. Rev. Sci. Instrum. 75, 4997–5004 (2004)

    Article  Google Scholar 

  19. Persson A., Hogmark S., Bergstorm J.: Thermal fatigue cracking of surface engineered hot work tool steels. Surf. Coat. Technol. 19, 216–227 (2005)

    Article  Google Scholar 

  20. Loiseau A., Lasalmonie A.: Influence of the thermal stability of TiAl on its creep behavior at high temperatures. Mater. Sci. Eng. 67, 163–168 (1984)

    Article  Google Scholar 

  21. Singh T., Gupta V.: Steady-state creep analysis of a functionally graded thick cylinder subjected to internal pressure and thermal gradient. Int. J. Mater. Res. 103, 1042–1051 (2012)

    Article  Google Scholar 

  22. Shang X.C., Zhang Z.B.: Characterization of microscopic damage in aluminum alloy materials under intense thermal shock. J. Mater. Eng. 02, 1–4 (2011)

    Google Scholar 

  23. Shang X.C., Zhang R., Ren H.L.: Analysis of cavitation problem of heated elastic composite ball. Appl. Math. Mech. (English Edition) 32, 587–594 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kammer C.: Aluminum Handbook. Aluminium-Zentrale e. V. Bonneshof, Germany (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, 30 Xueyuan Road, Haidian District, Beijing, 100083, People’s Republic of China

    Xingye Shi & Xinchun Shang

Authors
  1. Xingye Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinchun Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinchun Shang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shi, X., Shang, X. Growth of a spherical micro-void in an infinite elastoplastic body under thermal load. Acta Mech 225, 3237–3245 (2014). https://doi.org/10.1007/s00707-013-1030-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-013-1030-z

Keywords

Search

Navigation