Skip to main content

Void Growth in Plastic Solids

  • Chapter
Topics in Fracture and Fatigue

Abstract

An overview is given of the continuum mechanics of void growth pertaining to room temperature ductile fracture processes. Analyses of the growth of isolated voids and of void interaction effects are reviewed. A framework for phenomenological constitutive relations for porous plastic solids is discussed. Calculations of localization and failure in porous plastic solids are reviewed that illustrate the progressive development of ductile failure. Additional considerations, including the effect of the constraint provided by contact between the growing void and the void-nucleating particle, cavitation, and the effect of non-uniform porosity distributions are briefly noted.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Abeyaratne, R. and Hou, H.-S. (1989). Growth of an infinitesimal cavity in rate dependent solid. J. Appl. Mech., 56:40.

    Article  Google Scholar 

  • Andersson, H. (1977). Analysis of a model for void growth and coalescence ahead of a moving crack tip. J. Mech. Phys. Solids, 25:217.

    Article  Google Scholar 

  • Ball, J. M. (1982). Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Phil Trans. R. Soc. London, A306:557.

    Google Scholar 

  • Bishop, R. F. and Hill, R. (1951). A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. Phil. Mag. Ser. 7, 42:414.

    MathSciNet  MATH  Google Scholar 

  • Bishop, R. F., Hill, R. and Mott, N. F. (1945). The theory of indentation and hardness tests. Proc. Phys. Soc., 57:147.

    Article  Google Scholar 

  • Beachem, C. D. (1963). An electron fractographic study of the influence of plastic strain conditions upon ductile rupture processes in metals. Trans. ASM 56:318.

    Google Scholar 

  • Becker, R. (1987). The effect of porosity distribution on failure. J. Mech. Phys. Solids, 35:577.

    Article  Google Scholar 

  • Becker, R. and Needleman, A. (1986). Effect of yield surface curvature on necking and failure in porous plastic solids. J. Appl. Mech., 53:491.

    Article  Google Scholar 

  • Becker, R., Needleman A., Richmond, O., and Tvergaard, V. (1988). Void growth and failure in notched bars. J. Mech. Phys. Solids, 36:317.

    Article  Google Scholar 

  • Berg, C. A. (1962). The motion of cracks in plane viscous deformation. In Rosenberg, R. M., editor, Proc. Fourth U.S. National Congress of Applied Mechanics, ASME, NY, 2:885.

    Google Scholar 

  • Budiansky, B., Hutchinson, J. W. and Slutsky, S. (1982). Void growth and collapse in viscous solids. In H. G. Hokins and M. J. Sewell, editors, Mechanics of Solids, Pergamon Press, Oxford, 13.

    Google Scholar 

  • Cowie, J. G., Azrin, M. A. and Olson, G. B. (1990). Micro-void formation during shear deformation of ultrahigh strength steels. In Olson, G. B. et al., editors, Innovations in Ultrahigh-Strength Steel Technology, Proceedings of the 34th Sagamore Army Materials Research Conference, U.S. Government Publication, 357.

    Google Scholar 

  • Dubensky, E. M. and Koss, D. A. (1987). Void/pore distributions and ductile fracture. Met. Trans., 18A:1887.

    Google Scholar 

  • Fleck, N. A., Hutchinson, J. W. and Tvergaard, V. (1989). Softening by void nucleation and growth in tension and shear. J. Mech. Phys. Solids, 37:515.

    Article  Google Scholar 

  • Fleck, N. A., Otoyo, H. and Needleman, A. (1991). Indentation of porous solids. Int. J. Solids Struct, in press.

    Google Scholar 

  • Gilormini, P., Licht, C. and Suquet, P. (1988). Growth of voids in a ductile matrix: a review. Arch. Mech. 40:43.

    Google Scholar 

  • Guennouni, T. and Francois, D. (1987). Constitutive equations for rigid plastic or viscoplastic materials containing voids. Fatigue Fract. Engng. Mater. Struct., 10:399.

    Article  Google Scholar 

  • Gurland, J. and Plateau, J. (1963). The mechanism of ductile rupture of metals containing inclusions. Trans. ASM., 56:442.

    Google Scholar 

  • Gurson, A. L. (1975). Plastic Flow and Fracture Behavior of Ductile Materials Incorporating Void Nucleation, Growth and Interaction. Ph.D. Thesis, Brown University.

    Google Scholar 

  • Hadamard, J. (1903). Leçons sur la Propagation des Ondes et les Equations de L’Hydrodynamique, Paris, Chp. 6.

    MATH  Google Scholar 

  • Hancock, J. W. and Brown, D. K., (1983). On the role of strain and stress state in ductile failure. J. Mech. Phys. Solids, 31:1.

    Article  Google Scholar 

  • Hancock, J. W. and MacKenzie, A. C. (1976). On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. J. Mech. Phys. Solids, 24:147.

    Article  Google Scholar 

  • Hill, R. (1950). The Mathematical Theory of Plasticity, Clarendon Press, Oxford.

    MATH  Google Scholar 

  • Hill, R. (1958). A general theory of uniqueness and stability in elastic- plastic solids. J. Mech. Phys. Solids, 6:236.

    Article  MATH  Google Scholar 

  • Hill, R. (1962). Acceleration waves in solids. J. Mech. Phys. Solids, 10:1.

    Article  MathSciNet  MATH  Google Scholar 

  • Horn, C. L. and McMeeking, R. M. (1989) Void growth in elastic-plastic materials. J. Appl. Mech., 56:309.

    Article  Google Scholar 

  • Horgan, C. O. and Abeyaratne, R. (1986). A bifurcation problem for a compressible nonlinearly elastic medium: growth of a microvoid. J. Elast., 16:189.

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, Y. (1989) Accurate dilation rates for spherical voids in triaxial stress fields. Report Mech-155. Division of Applied Sciences. Harvard University.

    Google Scholar 

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

    Article  Google Scholar 

  • Koplik, J., and Needleman, A. (1988). Void growth and coalescence in porous plastic solids. Int. J. Solids Struct., 24:835.

    Article  Google Scholar 

  • Lemaitre, J. (1985). A continuous damage mechanics model for ductile fracture. J. Engng. Mat. Tech., 107:83.

    Article  Google Scholar 

  • Mandel, J. (1966). Conditions de stabilite et postulat de Drucker. In Kravtchenko, J. and Sirieys, P. M., editors, Rheology and Soil Mechanics, Springer-Verlag, 58.

    Google Scholar 

  • Marini, B., Mudry, F. and Pineau, A. (1985). Ductile rupture of A508 steel under nonradial loading. Engng. Fract. Mech22:375.

    Article  Google Scholar 

  • Mear, M. E. (1990). On the plastic yielding of porous metals. Mech. Matl. 9:33.

    Article  Google Scholar 

  • McClintock, F. A. (1968). A criterion for ductile fracture by the growth of holes. J. Appl. Mech., 35:363.

    Google Scholar 

  • McClintock, F. A., Kaplan, S. M. and Berg, C. A. (1966). Int. J. Frac. Mech., 2:614.

    Google Scholar 

  • Nagpal, V., McClintock, F. A., Berg, C. A. and Subudhi, M. (1972). Traction-displacement boundary conditions for plastic fracture by hole growth. In Sawczuk, A., editor, Foundations of Plasticity, Noordhoff, 365.

    Google Scholar 

  • Needleman, A. (1972). Void growth in an elastic-plastic medium. J. Appl. Mech., 39:964.

    Article  Google Scholar 

  • Needleman, A. and Rice J. R., (1978). Limits to ductility set by plastic flow localization. In Koistinen, D. P. and Wang, N. M., editors, Mechanics of Sheet Metal Forming, Plenum Press, New York, 237.

    Google Scholar 

  • Needleman, A. and Triantafyllidis, N. (1978). Void growth and local necking in biaxially stretched sheets. J. Engng. Mat. Tech., 10:164.

    Article  Google Scholar 

  • Puttick, K. E. (1959). Ductile fracture in metals. Phil. Mag., 4:964.

    Article  Google Scholar 

  • Rice, J. R. (1977). The localization of plastic deformation. In Koiter, W. T., editor, Theoretical and Applied Mechanics, North-Holland, 207.

    Google Scholar 

  • Rice, J. R. and Tracey, D. M. (1969). On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids, 17:201.

    Article  Google Scholar 

  • Rogers, H. C. (1960). The tensile fracture of ductile metals. Trans. Metall. Society AIME, 218:498.

    Google Scholar 

  • Shima, S. and Oyane, M. (1976). Plasticity theory for porous metals. Int. J. Mech. Sci., 18:285.

    Article  Google Scholar 

  • Tipper, C. F. (1949). The fracture of metals. Metallurgia, 33:133.

    Google Scholar 

  • Tvergaard, V. (1981). Influence of voids on shear band instabilities under plane strain conditions. Int. J. Fract17:389.

    Article  Google Scholar 

  • Tvergaard, V. (1982). On localization in ductile materials containing spherical voids. Int. J. Fract., 18:237.

    Google Scholar 

  • Tvergaard, V. (1988). 3D-analysis of localization failure in a ductile material containing two size-scales of spherical particles. Engng. Fract. Mech., 31:421.

    Article  Google Scholar 

  • Tvergaard, V. (1990). Material failure by void growth to coalescence. Adv. Appl. Mech., 27:83.

    Article  MATH  Google Scholar 

  • Tvergaard, V. and Needleman, A. (1984). Analysis of cup-cone fracture in a round tensile bar. Acta Metall., 32:157.

    Article  Google Scholar 

  • Worswick, M. J. and Pick, P. J. (1990). Void growth and constitutive softening in a periodically voided solid. J. Mech. Phys. Solids 38:601.

    Article  Google Scholar 

  • Yamamoto, H. (1978). Conditions for shear localization in the ductile fracture of void-containing materials. Int. J. Fract., 14:347.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Needleman, A., Tvergaard, V., Hutchinson, J.W. (1992). Void Growth in Plastic Solids. In: Argon, A.S. (eds) Topics in Fracture and Fatigue. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2934-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2934-6_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7726-2

  • Online ISBN: 978-1-4612-2934-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics