Computational Micromechanics

  • V. Tvergaard
Part of the International Centre for Mechanical Sciences book series (CISM, volume 331)


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.


Shear Band Yield Surface Void Growth Void Nucleation Void Volume Fraction 


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  1. 1.
    McClintock, F.A.: A criterion for ductile fracture by growth of holes, J. Appl. Mech., 35 (1968), 363–371.ADSCrossRefGoogle Scholar
  2. 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.ADSCrossRefGoogle Scholar
  3. 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. 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.CrossRefGoogle Scholar
  5. 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. 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. 7.
    Tvergaard, V.: Constitutive relations for creep in polycrystals with grain boundary cavitation, Acta Metall., 32 (1984), 1977–1990.CrossRefGoogle Scholar
  8. 8.
    Tvergaard, V.: Effect of grain boundary sliding on creep constrained diffusive cavitation, J. Mech. Phys. Solids, 33 (1985), 447–469.ADSCrossRefMATHGoogle Scholar
  9. 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.CrossRefGoogle Scholar
  10. 10.
    Nutt, S.R. and Needleman, A.: Void nucleation at fiber ends in Al—SiC composites, Scripta Metallurgica, 21 (1987), 705–710.CrossRefGoogle Scholar
  11. 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.CrossRefGoogle Scholar
  12. 12.
    Tvergaard, V.: Effect of fibre debonding in a whisker—reinforced metal, Materials Science and Engineering, Al25 (1990), 203–213.Google Scholar
  13. 13.
    Green, A.E. and Zerna, W.: Theoretical elasticity, Oxford University Press, Oxford (1968).MATHGoogle Scholar
  14. 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. 15.
    Tvergaard, V.: Influence of voids on shear band instabilities under plane strain conditions, Int. J. Fracture, 17 (1981), 389–407.CrossRefGoogle Scholar
  16. 16.
    Tvergaard, V.: On localization in ductile materials containing spherical voids, Int. J. Fracture, 18 (1982), 237–252.Google Scholar
  17. 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. 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.ADSCrossRefGoogle Scholar
  19. 19.
    Tvergaard, V. and Needleman, A.: Analysis of the cup—cone fracture in a round tensile bar, Acta Metallurgica, 32 (1984), 157–169.CrossRefGoogle Scholar
  20. 20.
    Koplik, J. and Needleman, A.: Void growth and coalescence in porous plastic solids, Int. J. Solids Structures, 24 (1988), 835–853.CrossRefGoogle Scholar
  21. 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.ADSCrossRefGoogle Scholar
  22. 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.CrossRefGoogle Scholar
  23. 23.
    Tvergaard, V.: Effect of yield surface curvature and void nucleation on plastic flow localization, J. Mech. Phys. Solids, 35 (1987), 43–60.ADSCrossRefGoogle Scholar
  24. 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. 25.
    Dafalias, Y.F.: Corotational rates for kinematic hardening at large plastic deformations, J. Appl. Mech., 50 (1983), 561–565.ADSCrossRefMATHGoogle Scholar
  26. 26.
    Loret, B.: On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials, Mechanics of Materials, 2 (1983), 287–304.CrossRefGoogle Scholar
  27. 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.ADSCrossRefMATHGoogle Scholar
  28. 28.
    Ziegler, H.: A modification of Prager’s hardening rule, Quart. Appl. Math., 17 (1959), 55–65.MathSciNetMATHGoogle Scholar
  29. 29.
    Hill, R.: Acceleration waves in solids, J. Mech. Phys. Solids, 10 (1962), 1–16.MathSciNetADSCrossRefMATHGoogle Scholar
  30. 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. 31.
    Marciniak, K. and Kuczynski, K.: Limit strains in the process of stretch forming sheet metals, Int. J. Mech. Sci., 9 (1967), 609–620.CrossRefGoogle Scholar
  32. 32.
    Stören, S. and Rice, J.R.: Localized necking in thin sheets, J. Mech. Phys. Solids, 23 (1975), 421–441.ADSCrossRefMATHGoogle Scholar
  33. 33.
    Hutchinson, J.W. and Tvercard, V.: Shear band formation in plane strain, Int. J. Solids Structures, 17 (1981), 451–470.CrossRefMATHGoogle Scholar
  34. 34.
    Christoffersen, J. and Hutchinson, J.W.: A class of phenomenological corner theories of plasticity, J. Mech. Phys. Solids, 72 (1979), 465–487.MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    Yamamoto, H.: Conditions for shear localization in the ductile fracture of void-containing materials, Int. J. Fracture, 14 (1978), 347–365.CrossRefGoogle Scholar
  36. 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.CrossRefGoogle Scholar
  37. 37.
    Tvergaard, V.: Material failure by void coalescence in localized shear bands, Int. J. Solids Structures, 18 (1982), 659–672.CrossRefMATHGoogle Scholar
  38. 38.
    Tvergaard, V.: Numerical study of localization in a void—sheet, Int. J. Solids Structures, 25 (1989), 1143–1156.CrossRefGoogle Scholar
  39. 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.ADSCrossRefGoogle Scholar
  40. 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.ADSCrossRefMATHGoogle Scholar
  41. 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. 42.
    Tvergaard, V.: Ductile fracture by cavity nucleation between larger voids, J. Mech. Phys. Solids, 30 (1982), 265–286.ADSCrossRefMATHGoogle Scholar
  43. 43.
    Tvergaard, V.: Ductile shear fracture at the surface of a bent specimen, Mechanics of Materials, 6 (1987), 53–69.CrossRefGoogle Scholar
  44. 44.
    Needleman, A. and Tvergaard, V.: An analysis of ductile rupture modes at a crack tip, J. Mech. Phys. Solids, 35 (1987), 151–183.ADSCrossRefMATHGoogle Scholar
  45. 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. 46.
    Rice, J.R.: Constraints on the diffusive cavitation of isolated grain boundary facets in creeping polycrystals, Acta Metallurgica, 29 (1981), 675–681.CrossRefGoogle Scholar
  47. 47.
    Hutchinson, J.W.: Constitutive behaviour and crack tip fields for materials undergoing creep—constrained grain boundary cavitation, Acta Metallurgica, 31 (1983), 1079–1088.CrossRefGoogle Scholar
  48. 48.
    Hull, D. and Rimmer, D.E.: The growth of grain—boundary voids under stress, Phil. Mag., 4 (1959), 673–687.ADSCrossRefGoogle Scholar
  49. 49.
    Needleman, A. and Rice, J.R.: Plastic creep flow effects in the diffusive cavitation of grain boundaries, Acta Metallurgica, 28 (1980), 1315–1332.CrossRefGoogle Scholar
  50. 50.
    Dyson, B.F.: Constraints on diffusional cavity growth rates, Metal Science, 10 (1976), 349–353.CrossRefGoogle Scholar
  51. 51.
    Tvergaard, V.: Creep failure by degradation of the microstructure and grain boundary cavitation in a tensile test, Acta Metallurgica, 35 (1987), 923–933.CrossRefGoogle Scholar
  52. 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.ADSCrossRefMATHGoogle Scholar
  53. 53.
    Tvergaard, V.: On the creep constrained diffusive cavitation of grain boundary facets, J. Mech. Phys. Solids, 32 (1984), 373–393.ADSCrossRefGoogle Scholar
  54. 54.
    Dyson, B.F. and McLean, M.: Particle—coarsening, ao and tertiary creep, Acta Metallurgica, 31 (1983), 17–27.CrossRefGoogle Scholar
  55. 55.
    Sham, T.-L. and Needleman, A.: Effects of triaxial stressing on creep cavitation of grain boundaries, Acta Metallurgica, 31 (1983), 919–926.CrossRefGoogle Scholar
  56. 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. 57.
    Tvergaard, V.: Effect of microstructure degradation on creep crack growth, Int. J. Fracture, 42 (1990), 145–155.CrossRefGoogle Scholar
  58. 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.ADSGoogle Scholar
  59. 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. 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. 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.ADSCrossRefGoogle Scholar
  62. 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. 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.ADSCrossRefMATHGoogle Scholar
  64. 64.
    Tvergaard, V.: Analysis of tensile properties for a whisker—reinforced metal—matrix composite, Acta Metall. Mater., 38 (1990), 185–194.CrossRefGoogle Scholar
  65. 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. 66.
    Nieh, T.G.: Creep rupture of a silicon carbide reinforced aluminum composite, Metallurgical Transactions, 15A (1984), 139–146.ADSCrossRefGoogle Scholar
  67. 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.ADSCrossRefGoogle Scholar
  68. 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.MathSciNetMATHGoogle Scholar
  69. 69.
    Needleman, A.: A continuum model for void nucleation by inclusion debonding, J. Appl. Mech., 54 (1987), 525–531.ADSCrossRefMATHGoogle Scholar
  70. 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.CrossRefGoogle Scholar
  71. 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.CrossRefGoogle Scholar
  72. 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.CrossRefGoogle Scholar
  73. 73.
    Tvergaard, V. and Needleman, A.: Effect of crack meandering on dynamic, ductile fracture, J. Mech. Phys. Solids, 40 (1992), 447–471.ADSCrossRefGoogle Scholar
  74. 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. 75.
    Tvergaard, V. and Needleman, A.: An analysis of the brittle—ductile transition in dynamic crack growth, DCAMM Report No. 436 (1992).Google Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • V. Tvergaard
    • 1
  1. 1.The Technical University of DenmarkLyngbyDenmark

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