Skip to main content

Void Growth to Coalescence: Unit Cell and Analytical Modelling

  • Chapter
  • First Online:
  • 2265 Accesses

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 195))

Abstract

The voids in a ductile material subjected to plastic deformation change shape according to the local plastic flow of the material since the voids are not internally pressurized. As a result, the void growth rate and shape evolution are intrinsically linked because the void shape (and orientation) induce anisotropy, altering the stress state and the growth rate in a non-linear fashion. The standard Gurson-Tvergaard model maintains its isotropic formulation by enforcing the void to remain spherical. The influence of the void shape on the stress response of the material is shown in Fig. 4.1 as well as the variation in the growth rate in Fig. 4.2 for a practical stress triaxiality of 2/3 (equal-biaxial stretching).

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Barsoum, I., & Faleskog, J. (2007a). Rupture mechanisms in combined tension and shear – Experiments. International Journal of Solids and Structures, 44, 1768–1786.

    Article  MATH  Google Scholar 

  • Barsoum, I., & Faleskog, J. (2007b). Rupture mechanism in combined tension and shear – Micromechanics. International Journal of Fracture, 44, 5481–5498.

    MATH  Google Scholar 

  • Benzerga, A. A. (2002). Micromechanics of coalescence in ductile fracture. Journal of Mechanics and Physics of Solids, 50, 1331–1362.

    Article  MATH  Google Scholar 

  • Brocks, W., Sun, D. Z., & Honig, A. (1996). Verification of micromechanical models for ductile fracture by cell model calculations. Computational Materials Science, 7, 235–241.

    Article  Google Scholar 

  • Butcher, C. (2011). A multi-scale damage percolation model of ductile fracture. Ph.D. thesis, University of New Brunswick, Fredericton, NB, Canada.

    Google Scholar 

  • Chen, Z. T. (2004). The role of heterogeneous particle distribution in the prediction of ductile fracture. Ph.D. thesis, University of Waterloo, Canada.

    Google Scholar 

  • Finn, M. J. (1999). Private communications.

    Google Scholar 

  • Gologanu, M., Leblond, J. B., Perrin, P., & Devaux, J. (1997). Recent extensions of Gurson’s model for porous ductile metals. In P. Suquet (Ed.), Continuum micromechanics (pp. 61–130). New York: Springer.

    Google Scholar 

  • Gurson, A. L. (1975). Plastic flow and fracture behaviour of ductile materials incorporating void nucleation, growth and interaction. Ph.D. thesis, Brown University, Providence, R.I.

    Google Scholar 

  • Gurson, A. L. (1977). Continuum theory of ductile rupture by void nucleation and growth – Part I. Yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology, 99, 2–15.

    Article  Google Scholar 

  • Huang, Y. (1991). Accurate dilatation rates for spherical voids in triaxial stress fields. Journal of Applied Mechanics, 58, 1084–1086.

    Article  Google Scholar 

  • Keralavarma, S. M., & Benzerga, A. A. (2010). A constitutive model for plastically anisotropic solids with non-spherical voids. Journal of Mechanics and Physics of Solids, 58, 874–890.

    Article  MathSciNet  MATH  Google Scholar 

  • Koplik, J., & Needleman, A. (1988). Void growth and coalescence in porous plastic solids. International Journal of Solids and Structures, 24, 835–853. 227.

    Article  Google Scholar 

  • Kuna, M., & Sun, D. Z. (1996). Three-dimensional cell model analyses of void growth in ductile materials. International Journal of Fracture, 81, 235–258.

    Article  Google Scholar 

  • Lee, B. J., & Mear, M. E. (1992a). Axisymmetric deformation of power-law solids containing a dilute concentration of spheroidal voids. Journal of Mechanics and Physics of Solids, 40, 1805–1836.

    Article  Google Scholar 

  • Lee, B. J., & Mear, M. E. (1992b). Effect properties of power-law solids containing elliptical inhomogeneities – Part II: Voids. Mechanics of Materials, 13, 337.

    Article  Google Scholar 

  • McClintock, F. (1968). A criterion for ductile fracture by the growth of holes. Journal of Applied Mechanics, 35, 363–371.

    Article  Google Scholar 

  • Orlov, O. (2006). A three-dimensional damage percolation model. Ph.D. thesis, University of Waterloo, Waterloo, Ontario, Canada.

    Google Scholar 

  • Pardoen, T., & Hutchinson, J. (2000). An extended model for void growth and coalescence. Journal of the Mechanics and Physics of Solids, 48, 2467–2512.

    Article  MATH  Google Scholar 

  • Pilkey, A. K. (2001). Private Communications.

    Google Scholar 

  • Ragab, A. R. (2004a). A model for ductile fracture based on internal necking of spheroidal voids. Acta Materialia, 52, 3997–4005.

    Article  Google Scholar 

  • Ragab, A. R. (2004b). Application of an extended void growth model with strain hardening and void shape evolution to ductile fracture under axisymmetric tension. Engineering Fracture Mechanics, 71, 1515–1534.

    Article  Google Scholar 

  • Rice, J. R., & Tracey, D. M. (1969). On the ductile enlargement of voids in triaxial stress fields. Journal of the Mechanics and Physics of Solids, 17, 201–217.

    Article  Google Scholar 

  • Riks, E. (1979). An incremental approach to the solution of snapping and buckling problems. International Journal of Solids and Structures, 15, 529–551.

    Article  MathSciNet  MATH  Google Scholar 

  • Scheyvaerts, F., Pardoen, T., & Onck, P. R. (2010). A new model for void coalescence by internal necking. International Journal of Damage Mechanics, 19, 95–126.

    Article  Google Scholar 

  • Siad, L., Ouali, M. O., & Benabbes, A. (2008). Comparison of explicit and implicit finite element simulations of void growth and coalescence in porous ductile materials. Materials and Design, 29, 319–329.

    Article  Google Scholar 

  • Sovik, O., & Thaulow, C. (1997). Growth of spheroidal voids in elastic–plastic solids. Fatigue and Fracture in Engineering Materials and Structures, 20, 1731–1744.

    Article  Google Scholar 

  • Thomason, P. F. (1990). Ductile fracture of metals. Oxford: Pergamon Press.

    Google Scholar 

  • Winkler, S. L. (2003). Private Communications.

    Google Scholar 

  • Yee, K. C., & Mear, M. E. (1996). Effect of void shape on the macroscopic response of non-linear porous solids. International Journal of Plasticity, 12, 45–68.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Chen, Z., Butcher, C. (2013). Void Growth to Coalescence: Unit Cell and Analytical Modelling. In: Micromechanics Modelling of Ductile Fracture. Solid Mechanics and Its Applications, vol 195. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6098-1_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-6098-1_4

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-6097-4

  • Online ISBN: 978-94-007-6098-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics