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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Barsoum, I., & Faleskog, J. (2007a). Rupture mechanisms in combined tension and shear – Experiments. International Journal of Solids and Structures, 44, 1768–1786.
Barsoum, I., & Faleskog, J. (2007b). Rupture mechanism in combined tension and shear – Micromechanics. International Journal of Fracture, 44, 5481–5498.
Benzerga, A. A. (2002). Micromechanics of coalescence in ductile fracture. Journal of Mechanics and Physics of Solids, 50, 1331–1362.
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.
Butcher, C. (2011). A multi-scale damage percolation model of ductile fracture. Ph.D. thesis, University of New Brunswick, Fredericton, NB, Canada.
Chen, Z. T. (2004). The role of heterogeneous particle distribution in the prediction of ductile fracture. Ph.D. thesis, University of Waterloo, Canada.
Finn, M. J. (1999). Private communications.
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.
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.
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.
Huang, Y. (1991). Accurate dilatation rates for spherical voids in triaxial stress fields. Journal of Applied Mechanics, 58, 1084–1086.
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.
Koplik, J., & Needleman, A. (1988). Void growth and coalescence in porous plastic solids. International Journal of Solids and Structures, 24, 835–853. 227.
Kuna, M., & Sun, D. Z. (1996). Three-dimensional cell model analyses of void growth in ductile materials. International Journal of Fracture, 81, 235–258.
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.
Lee, B. J., & Mear, M. E. (1992b). Effect properties of power-law solids containing elliptical inhomogeneities – Part II: Voids. Mechanics of Materials, 13, 337.
McClintock, F. (1968). A criterion for ductile fracture by the growth of holes. Journal of Applied Mechanics, 35, 363–371.
Orlov, O. (2006). A three-dimensional damage percolation model. Ph.D. thesis, University of Waterloo, Waterloo, Ontario, Canada.
Pardoen, T., & Hutchinson, J. (2000). An extended model for void growth and coalescence. Journal of the Mechanics and Physics of Solids, 48, 2467–2512.
Pilkey, A. K. (2001). Private Communications.
Ragab, A. R. (2004a). A model for ductile fracture based on internal necking of spheroidal voids. Acta Materialia, 52, 3997–4005.
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.
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.
Riks, E. (1979). An incremental approach to the solution of snapping and buckling problems. International Journal of Solids and Structures, 15, 529–551.
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.
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.
Sovik, O., & Thaulow, C. (1997). Growth of spheroidal voids in elastic–plastic solids. Fatigue and Fracture in Engineering Materials and Structures, 20, 1731–1744.
Thomason, P. F. (1990). Ductile fracture of metals. Oxford: Pergamon Press.
Winkler, S. L. (2003). Private Communications.
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.
Author information
Authors and Affiliations
Rights 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)