Skip to main content

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 331))

Abstract

The development of material models based on micromechanical behaviour is described, with main focus on the application of numerical methods to analyse characteristic unit cells. The models described account for ductile failure by the nucleation and growth of voids, creep rupture by grain boundary cavitation, and the behaviour of metal matrix composites. Some applications of the material models are discussed, including studies of plastic flow localization in shear bands, creep crack growth at elevated temperatures, and dynamic crack growth by a ductile mechanism or in the regime of brittle-ductile transition.

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 89.00
Price excludes VAT (USA)
  • Available as 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

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

  1. McClintock, F.A.: A criterion for ductile fracture by growth of holes, J. Appl. Mech., 35 (1968), 363–371.

    Article  ADS  Google Scholar 

  2. Rice, J.R. and Tracey, D.M.: On the ductile enlargement of voids in triaxial stress fields, J. Mech. Phys. Solids, 17 (1969), 201–217.

    Article  ADS  Google Scholar 

  3. Budiansky, B., Hutchinson, J.W. and Slutsky, S.: Void growth and collapse in viscous solids, Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, (eds. H.G. Hopkins and M.J. Sewell ), Pergamon Press (1982), 13–45.

    Google Scholar 

  4. Gurson, A.L.: Continuum theory of ductile rupture by void nucleation and growth — I. Yield criteria and flow rules for porous ductile media, J. Engng. Materials Technol., 99 (1977), 2–15.

    Article  Google Scholar 

  5. Gurson, A.L.: Porous rigid—plastic materials containing rigid inclusions — yield function, plastic potential, and void nucleation, Proc. Int. Conf. Fracture, (ed. D.M.R. Taplin), 2A (1977), 357–364.

    Google Scholar 

  6. Tvergaard, V.: Material failure by void growth to coalescence, Advances in Applied Mechanics, (eds. J.W. Hutchinson and T.Y. Wu ), Academic Press, Inc., (1990), 83–151.

    Google Scholar 

  7. Tvergaard, V.: Constitutive relations for creep in polycrystals with grain boundary cavitation, Acta Metall., 32 (1984), 1977–1990.

    Article  Google Scholar 

  8. Tvergaard, V.: Effect of grain boundary sliding on creep constrained diffusive cavitation, J. Mech. Phys. Solids, 33 (1985), 447–469.

    Article  ADS  MATH  Google Scholar 

  9. Van der Giessen, E. and Tvergaard, V.: A creep rupture model accounting for cavitation at sliding grain boundaries, Int. J. Fracture, 48 (1991), 153–178.

    Article  Google Scholar 

  10. Nutt, S.R. and Needleman, A.: Void nucleation at fiber ends in Al—SiC composites, Scripta Metallurgica, 21 (1987), 705–710.

    Article  Google Scholar 

  11. Christman, T., Needleman, A., Nutt, S. and Suresh, S.: On microstructural evolution and micromechanical modelling of deformation of a whisker—reinforced metal—matrix composite, Materials Science and Engineering, A107 (1989), 49–61.

    Article  Google Scholar 

  12. Tvergaard, V.: Effect of fibre debonding in a whisker—reinforced metal, Materials Science and Engineering, Al25 (1990), 203–213.

    Google Scholar 

  13. Green, A.E. and Zerna, W.: Theoretical elasticity, Oxford University Press, Oxford (1968).

    MATH  Google Scholar 

  14. Budiansky, B.: Remarks on theories of solid and structural mechanics, in Problems of Hydrodynamics and Continuum Mechanics, (eds. M.A. Lavrent’ev et al.), SIAM, Philadelphia (1969).

    Google Scholar 

  15. Tvergaard, V.: Influence of voids on shear band instabilities under plane strain conditions, Int. J. Fracture, 17 (1981), 389–407.

    Article  Google Scholar 

  16. Tvergaard, V.: On localization in ductile materials containing spherical voids, Int. J. Fracture, 18 (1982), 237–252.

    Google Scholar 

  17. Brown, L.M. and Embury, J.D.: The initiation and growth of voids at second phase particles, Proc. 3rd Int. Conf. on Strength of Metals and Alloys, Inst. of Metals, London, (1973), 164–169.

    Google Scholar 

  18. Andersson, H.: Analysis of a model for void growth and coalescence ahead of a mooving crack tip, J. Mech. Phys. Solids, 25 (1977), 217–233.

    Article  ADS  Google Scholar 

  19. Tvergaard, V. and Needleman, A.: Analysis of the cup—cone fracture in a round tensile bar, Acta Metallurgica, 32 (1984), 157–169.

    Article  Google Scholar 

  20. Koplik, J. and Needleman, A.: Void growth and coalescence in porous plastic solids, Int. J. Solids Structures, 24 (1988), 835–853.

    Article  Google Scholar 

  21. Becker, R., Needleman, A., Richmond, O. and Tvergaard, V.: Void growth and failure in notched bars, J. Mech. Phys. Solids, 36 (1988), 317–351.

    Article  ADS  Google Scholar 

  22. Mear, M.E. and Hutchinson, J.W.: Influence of yield surface curvature on flow localization in dilatant plasticity, Mechanics of Materials, 4 (1985), 395–407.

    Article  Google Scholar 

  23. Tvergaard, V.: Effect of yield surface curvature and void nucleation on plastic flow localization, J. Mech. Phys. Solids, 35 (1987), 43–60.

    Article  ADS  Google Scholar 

  24. Needleman, A. and Rice, J.R.: Limits to ductility set by plastic flow localization. in Mechanics of Sheet Metal Forming, (eds. D.P. Koistinen et al.), Plenum Publishing Corporation, (1978), 237–267.

    Google Scholar 

  25. Dafalias, Y.F.: Corotational rates for kinematic hardening at large plastic deformations, J. Appl. Mech., 50 (1983), 561–565.

    Article  ADS  MATH  Google Scholar 

  26. Loret, B.: On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials, Mechanics of Materials, 2 (1983), 287–304.

    Article  Google Scholar 

  27. Tvergaard, V. and Van der Giessen, E.: Effect of plastic spin on localization predictions for a porous ductile material, J. Mech. Phys. Solids, 39 (1991), 763–781.

    Article  ADS  MATH  Google Scholar 

  28. Ziegler, H.: A modification of Prager’s hardening rule, Quart. Appl. Math., 17 (1959), 55–65.

    MathSciNet  MATH  Google Scholar 

  29. Hill, R.: Acceleration waves in solids, J. Mech. Phys. Solids, 10 (1962), 1–16.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Rice, J.R.: The localization of plastic deformation. in Theoretical and Appl. Mech, (ed. W.T. Koiter ), North-Holland, (1977), 207–220.

    Google Scholar 

  31. Marciniak, K. and Kuczynski, K.: Limit strains in the process of stretch forming sheet metals, Int. J. Mech. Sci., 9 (1967), 609–620.

    Article  Google Scholar 

  32. Stören, S. and Rice, J.R.: Localized necking in thin sheets, J. Mech. Phys. Solids, 23 (1975), 421–441.

    Article  ADS  MATH  Google Scholar 

  33. Hutchinson, J.W. and Tvercard, V.: Shear band formation in plane strain, Int. J. Solids Structures, 17 (1981), 451–470.

    Article  MATH  Google Scholar 

  34. Christoffersen, J. and Hutchinson, J.W.: A class of phenomenological corner theories of plasticity, J. Mech. Phys. Solids, 72 (1979), 465–487.

    Article  MathSciNet  ADS  Google Scholar 

  35. Yamamoto, H.: Conditions for shear localization in the ductile fracture of void-containing materials, Int. J. Fracture, 14 (1978), 347–365.

    Article  Google Scholar 

  36. Saje, M., Pan, J. and Needleman, A.: Void nucleation effects on shear localization in porous plastic solids, Int. J. Fracture, 19 (1982), 163–182.

    Article  Google Scholar 

  37. Tvergaard, V.: Material failure by void coalescence in localized shear bands, Int. J. Solids Structures, 18 (1982), 659–672.

    Article  MATH  Google Scholar 

  38. Tvergaard, V.: Numerical study of localization in a void—sheet, Int. J. Solids Structures, 25 (1989), 1143–1156.

    Article  Google Scholar 

  39. Fleck, N.A., Hutchinson, J.W. and Tvergaard, V.: Softening by void nucleation and growth in tension and shear, J. Mech. Phys. Solids, 37 (1989), 515–540.

    Article  ADS  Google Scholar 

  40. Tvergaard, V., Needleman, A. and Lo, K.K.: Flow localization in the plane strain tensile test, J. Mech. Phys. Solids, 29 (1981), 115–142.

    Article  ADS  MATH  Google Scholar 

  41. Needleman, A. and Tvergaard, V.: Finite element analysis of localization in plasticity. in Finite Elements, Special Problems in Solid Mechanics, (eds. J.T. Oden and G.F. Carey), Prentice-Hall, Inc., V (1984), 94–157.

    Google Scholar 

  42. Tvergaard, V.: Ductile fracture by cavity nucleation between larger voids, J. Mech. Phys. Solids, 30 (1982), 265–286.

    Article  ADS  MATH  Google Scholar 

  43. Tvergaard, V.: Ductile shear fracture at the surface of a bent specimen, Mechanics of Materials, 6 (1987), 53–69.

    Article  Google Scholar 

  44. Needleman, A. and Tvergaard, V.: An analysis of ductile rupture modes at a crack tip, J. Mech. Phys. Solids, 35 (1987), 151–183.

    Article  ADS  MATH  Google Scholar 

  45. Ashby, M.F. and Dyson, B.F.: Creep damage mechanics and micro—mechanisms, National Physical Laboratory, Report DMA(A), 77 (1984).

    Google Scholar 

  46. Rice, J.R.: Constraints on the diffusive cavitation of isolated grain boundary facets in creeping polycrystals, Acta Metallurgica, 29 (1981), 675–681.

    Article  Google Scholar 

  47. Hutchinson, J.W.: Constitutive behaviour and crack tip fields for materials undergoing creep—constrained grain boundary cavitation, Acta Metallurgica, 31 (1983), 1079–1088.

    Article  Google Scholar 

  48. Hull, D. and Rimmer, D.E.: The growth of grain—boundary voids under stress, Phil. Mag., 4 (1959), 673–687.

    Article  ADS  Google Scholar 

  49. Needleman, A. and Rice, J.R.: Plastic creep flow effects in the diffusive cavitation of grain boundaries, Acta Metallurgica, 28 (1980), 1315–1332.

    Article  Google Scholar 

  50. Dyson, B.F.: Constraints on diffusional cavity growth rates, Metal Science, 10 (1976), 349–353.

    Article  Google Scholar 

  51. Tvergaard, V.: Creep failure by degradation of the microstructure and grain boundary cavitation in a tensile test, Acta Metallurgica, 35 (1987), 923–933.

    Article  Google Scholar 

  52. He, M.Y. and Hutchinson, J.W.: The penny—shaped crack and the plane strain crack in an infinite body of power—law material, J. Appl. Mech., 48 (1981), 830–840.

    Article  ADS  MATH  Google Scholar 

  53. Tvergaard, V.: On the creep constrained diffusive cavitation of grain boundary facets, J. Mech. Phys. Solids, 32 (1984), 373–393.

    Article  ADS  Google Scholar 

  54. Dyson, B.F. and McLean, M.: Particle—coarsening, ao and tertiary creep, Acta Metallurgica, 31 (1983), 17–27.

    Article  Google Scholar 

  55. Sham, T.-L. and Needleman, A.: Effects of triaxial stressing on creep cavitation of grain boundaries, Acta Metallurgica, 31 (1983), 919–926.

    Article  Google Scholar 

  56. Budiansky, B., Hutchinson, J.W. and Slutsky, S.: Void growth and collapse in viscous solids, in Mechanics of Solids. The Rodney Hill 60th Anniversary Volume, (eds. H.G. Hopkins and M.J. Sewell ), Pergamon Press, Oxford (1982), 13–45.

    Google Scholar 

  57. Tvergaard, V.: Effect of microstructure degradation on creep crack growth, Int. J. Fracture, 42 (1990), 145–155.

    Article  Google Scholar 

  58. Hayhurst, D.R., Brown, P.R. and Morrison, C.J.: The role of continuum damage in creep crack growth, Philosophical Transactions, Royal Society London, A311 (1984), 131–158.

    ADS  Google Scholar 

  59. Van der Giessen, E. and Tvergaard, V.: Interaction of cavitating grain boundary facets in creeping polycrystals, Delft Technical University, Mechanical Engineering, Report No. 970 (1992).

    Google Scholar 

  60. Divecha, A.P., Fishman, S.G. and Karmarkar, S.D.: Silicon carbide reinforced aluminum — A formable composite, J. of Metals, 33 (1981), 12–17.

    Google Scholar 

  61. McDanels, D.L.: Analysis of stress—strain, fracture, and ductility behaviour of aluminum matrix composites containing discontinuous silicon carbide reinforcement, Metallurgical Transactions, 16A (1985), 1105–1115.

    Article  ADS  Google Scholar 

  62. Zok, F., Embury, J.D., Ashby, M.F. and Richmond, O.: The influence of pressure on damage evolution and fracture in metal—matrix composites, in Mechanical and Physical Behaviour of Metallic and Ceramic Composites, (eds. S.I. Andersen et al.), Riso Nat. Lab., Denmark (1988), 517–526.

    Google Scholar 

  63. Teply, J.L. and Dvorak, G.J.: Bounds on overall instantaneous properties of elastic—plastic composites, J. Mech. Phys. Solids, 36 (1988), 29–58.

    Article  ADS  MATH  Google Scholar 

  64. Tvergaard, V.: Analysis of tensile properties for a whisker—reinforced metal—matrix composite, Acta Metall. Mater., 38 (1990), 185–194.

    Article  Google Scholar 

  65. Bao, G., Hutchinson, J.W. and McMeeking, R.M.: Particle reinforcement of ductile matrices against plastic flow and creep, Materials Department, Univ. of California Santa Barbara (1990).

    Google Scholar 

  66. Nieh, T.G.: Creep rupture of a silicon carbide reinforced aluminum composite, Metallurgical Transactions, 15A (1984), 139–146.

    Article  ADS  Google Scholar 

  67. Levy, A. and Papazian, J.M.: Tensile properties of short fiber—reinforced SiC/Al composites: Part II. Finite element analysis, Metallurgical Transactions, 21A (1990), 411–420.

    Article  ADS  Google Scholar 

  68. Bishop, J.F.W. and Hill, R.: A theory of the plastic distortion of a polycrystalline aggregate under combined stresses, Phil. Mag., 42 (1951), 414–427.

    MathSciNet  MATH  Google Scholar 

  69. Needleman, A.: A continuum model for void nucleation by inclusion debonding, J. Appl. Mech., 54 (1987), 525–531.

    Article  ADS  MATH  Google Scholar 

  70. Tvergaard, V.: Micromechanical modelling of fibre debonding in a metal reinforced by short fibres. in Inelastic Deformation of Composite Materials, (ed. G.J. Dvorak ), Springer-Verlag, New York (1991), 99–111.

    Chapter  Google Scholar 

  71. Needleman, A. and Tvergaard, V.: An analysis of dynamic, ductile crack growth in a double edge cracked specimen, Int. J. of Fracture, 49 (1991), 41–67.

    Article  Google Scholar 

  72. Needleman, A. and Tvergaard, V.: A numerical study of void distribution effects on dynamic, ductile crack growth, Engineering Fracture Mechanics, 38 (1991), 157–173.

    Article  Google Scholar 

  73. Tvergaard, V. and Needleman, A.: Effect of crack meandering on dynamic, ductile fracture, J. Mech. Phys. Solids, 40 (1992), 447–471.

    Article  ADS  Google Scholar 

  74. Prakash, V. and Clifton, R.J.: Experimental and analytical investigation of dynamic fracture under conditions of plane strain, Proceedings 22nd National Symposium on Fracture Mechanics, in press.

    Google Scholar 

  75. Tvergaard, V. and Needleman, A.: An analysis of the brittle—ductile transition in dynamic crack growth, DCAMM Report No. 436 (1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Wien

About this chapter

Cite this chapter

Tvergaard, V. (1993). Computational Micromechanics. In: Herrmann, G. (eds) Modeling of Defects and Fracture Mechanics. International Centre for Mechanical Sciences, vol 331. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2716-2_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2716-2_4

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82487-0

  • Online ISBN: 978-3-7091-2716-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics