Advertisement

Elastic-Plastic Damage

  • Sumio MurakamiEmail author
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 185)

Abstract

The preceding chapters were concerned with the notion and the fundamental theories of continuum damage mechanics (CDM). Hereafter we will discuss the application of CDM to damage and fracture phenomena encountered in wide range of engineering problems. The present chapter starts with the modeling of elastic-plastic damage and its application. In Section 6.1, we summarized the constitutive and the evolution equations of elastic-plastic isotropic damage of materials developed in Chapter 4, and discuss their application to the problems of ductile damage, brittle damage and quasi-brittle damage. Section 6.2, on the other hand, is concerned with the detailed discussion of ductile damage process, i.e., the discussion of physical and mechanical aspects of ductile damage, their mechanical modeling and its analysis.

Keywords

Representative Volume Element Stress Triaxiality Damage Variable Void Volume Fraction Continuum Damage Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Besson J, Cailletaud G, Chaboche J-L, Forest S, Blétry M (2010) Non-linear mechanics of materials. Springer, DordrechtGoogle Scholar
  2. Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98CrossRefGoogle Scholar
  3. Bao Y, Wierzbicki T (2005) On the cut-off value of negative triaxiality for fracture. Eng Fract Mech 72:1049–1069CrossRefGoogle Scholar
  4. Benzerga AA (2002) Micromechanics of coalescence in ductile fracture. J Mech Phys Solids 50:1331–1362zbMATHCrossRefGoogle Scholar
  5. Benzerga AA, Besson J, Pineau A (2004a) Anisotropic ductile fracture, part I: experiments. Acta Mater 52:4623–4638CrossRefGoogle Scholar
  6. Benzerga AA, Besson J, Pineau A (2004b) Anisotropic ductile fracture, part II: theory. Acta Mater 52:4639–4650CrossRefGoogle Scholar
  7. Berg CA (1970) Plastic dilatation and void interaction. In: Kanninen MF et al (eds) Inelastic behavior of solids. McGraw-Hill, New York, pp 171–210Google Scholar
  8. Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech 19:3–52CrossRefGoogle Scholar
  9. Besson J, Steglich D, Brocks W (2003) Modeling of plane strain ductile rupture. Int J Plast 19:1517–1541zbMATHCrossRefGoogle Scholar
  10. Bonora N (1997) A nonlinear CDM model for ductile failure. Eng Fract Mech 58:11–28CrossRefGoogle Scholar
  11. Bonora N, Gentile D, Pirondi A, Newaz G (2005) Ductile damage evolution under triaxial state of stress: theory and experiments. Int J Plast 21:981–1007zbMATHCrossRefGoogle Scholar
  12. Brownrigg A, Spitzig WA, Richmond O, Teirlinck D, Embury JD (1983) The influence of hydrostatic pressure on the flow stress and ductility of spherodized 1045 steel. Acta Metall 31:1141–1150CrossRefGoogle Scholar
  13. Chaboche JL (1986) Time independent constitutive theories for cyclic plasticity. Int J Plast 2:149–188zbMATHCrossRefGoogle Scholar
  14. Chaboche JL, Boudifa M, Saanouni K (2006) A CDM approach of ductile damage with plastic compressibility. Int J Fract 137:51–75zbMATHCrossRefGoogle Scholar
  15. Chandrakanth S, Pandey PC (1993) A new ductile damage evolution model. Int J Fract 60:73–76Google Scholar
  16. Chow CL, Jie M (2004) Forming limits of AL6022 sheets with material damage consideration -theory and experimental validation. Int J Mech Sci 46:99–122CrossRefGoogle Scholar
  17. Chow CL, Yang XJ (2004) A generalized mixed isotropic-kinematic hardening plastic model coupled with anisotropic damage for sheet metal forming. Int J Damage Mech 13:81–101CrossRefGoogle Scholar
  18. Chow CL, Yu LG, Demeri MY (1997) A unified damage approach for predicting forming limit diagrams. J Eng Mater Technol Trans ASME 119:346–353CrossRefGoogle Scholar
  19. Chow CL, Yu IG, Tai WH, Demeri MY (2001) Prediction of forming limit diagrams for AL6111-T4 under non-proportional loading. Int J Mech Sci 43:471–486zbMATHCrossRefGoogle Scholar
  20. Chow CL, Jie M, Wu X (2007) Localized necking criterion for strain- softening materials with anisotropic damage. Int J Damage Mech 16:265–281CrossRefGoogle Scholar
  21. Chu CC, Needleman A (1980) Void nucleation effects in biaxially stretched sheets. J Eng Mater Technol Trans ASME 102:249–256CrossRefGoogle Scholar
  22. Desmorat R, Kane A, Seyedi M, Sermage JP (2007) Two scale damage model and related numerical issues for thermo-mechanical high cycle fatigue. Eur J Mech A/Solids 26:909–935zbMATHCrossRefGoogle Scholar
  23. Gologanu M, Leblond JB, Devaux J (1993) Approximate models for ductile metals containing non-spherical voids – case of symmetric prolate ellipsoidal cavities. J Mech Phys Solids 41:1723–1754zbMATHCrossRefGoogle Scholar
  24. Gologanu M, Leblond JB, Devaux J (1994) Approximate models for ductile metals containing non-spherical voids – case of axisymmetric oblate ellipsoidal cavities. J Eng Mater Technol Trans ASME 116:290–294CrossRefGoogle Scholar
  25. Graf A, Hosford W (1994) The influence of strain-path changes on forming limit diagrams of A 6111-T4. Int J Mech Sci 36:897–910CrossRefGoogle Scholar
  26. Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I Yield criteria and flow rules for porous ductile media. J Eng Mater Technol Trans ASME 99:2–15CrossRefGoogle Scholar
  27. Hancock JW, Mackenzie AC (1976) On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states. J Mech Phys Solids 24:147–169CrossRefGoogle Scholar
  28. Leblond JB, Perrin G, Devaux J (1995) An improved Gurson-type model for hardenable ductile metals. Eur J Mech A/Solids 14:499–527MathSciNetzbMATHGoogle Scholar
  29. Lemaitre J (1985) A continuous damage mechanics model for ductile fracture. J Eng Mater Technol Trans ASME 107:83–89CrossRefGoogle Scholar
  30. Lemaitre J (1990) Micro-mechanics of crack initiation. Int J Frac 42:87–99CrossRefGoogle Scholar
  31. Lemaitre J (1992) A course on damage mechanics. Springer, Berlin; 2nd Edition (1996)zbMATHGoogle Scholar
  32. Lemaitre J, Desmorat R (2005) Engineering damage mechanics. Springer, BelrinGoogle Scholar
  33. Lemaitre J, Doghri I (1994) Damage 90: a post-processor for crack initiation. Comput Methods Appl Mech Eng 115:197–232CrossRefGoogle Scholar
  34. Lemaitre J, Sermage JP, Desmorat R (1999) A two scale damage concept applied to fatigue. Int J Fract 97:67–81CrossRefGoogle Scholar
  35. Mahnken R (2002) Theoretical, numerical and identification aspects of a new model class for ductile damage. Int J Plast 18:801–831zbMATHCrossRefGoogle Scholar
  36. Mazars J (1986) A description of micro- and macro-scale damage of concrete structures. Eng Fract Mech 25:729–737CrossRefGoogle Scholar
  37. Nahshon K, Hutchinson JW (2008) Modification of the Gurson model for shear failure. Eur J Mech A/Solids 27:1–17zbMATHCrossRefGoogle Scholar
  38. Nahshon K, Xue Z (2009) A modified Gurson model and its application to puch-out experiments. Eng Fract Mech 76:997–1009CrossRefGoogle Scholar
  39. Needleman A, Triantafyllidis N (1978) Void growth and local necking in biaxially stretched sheets. J Eng Mater Technol Trans ASME 100:164–169CrossRefGoogle Scholar
  40. Needleman A, Tvergaard V (1984) An analysis of ductile rupture in notched bars. J Mech Phys Solids 32:461–490CrossRefGoogle Scholar
  41. Ohno N, Wang JD (1994) Kinematic hardening rules for simulation of ratchetting behavior. Eur J Mech A/Solids 13:519–531zbMATHGoogle Scholar
  42. Oñate E, Kleiber M, Saracibar CA (1988) Plastic and viscoplastic flow of void-containing metals; applications to axisymmetric sheet forming problems. Int J Numer Methods Eng 25:227–251zbMATHCrossRefGoogle Scholar
  43. Pardoen T (2006) Numerical simulation of low stress triaxiality ductile fracture. Comput Struct 84:1641–1650CrossRefGoogle Scholar
  44. Pedersen TO (2000) Numerical modelling of cyclic plasticity and fatigue damage in cold-forging tools. Int J Mech Sc 42:799–818zbMATHCrossRefGoogle Scholar
  45. Pirondi A, Bonora N (2003) Modeling ductile damage under fully reversed cycling. Comput Mater Sci 26:129–141CrossRefGoogle Scholar
  46. Rice JR, Tracy DM (1969) On ductile enlargement of voids in triaxial stress fields. J Mech Phys Solids 17:210–217CrossRefGoogle Scholar
  47. Rousselier G (1981) Finite deformation constitutive relations including ductile fracture damage. In: Nemat-Nasser S (ed) Three-dimensional constitutive relations and ductile fracture. North-Holland, Amsterdam, pp 331–355Google Scholar
  48. Rousselier G (1987) Ductile fracture models and their potential in local approach of fracture. Nucl Eng Des 105:97–111CrossRefGoogle Scholar
  49. Saanouni K (ed) (2003) Numerical modelling in damage mechanics. Kogan Page Science, LondonGoogle Scholar
  50. Saanouni K (2006) Virtual metal forming including the ductile damage occurrence: actual state of the art and main perspectives. J Mater Process Technol 177:19–25CrossRefGoogle Scholar
  51. Saanouni K, Chaboche JL (2003) Computational damage mechanics: application to metal forming. In: Milne I, Ritchie RO, Karihaloo B (eds) Comprehensive structural integrity, vol 3. Elsevier, Oxford, pp 321–376CrossRefGoogle Scholar
  52. Saanouni K, Nesnas K, Hammi Y (2000) Damage modeling in metal forming processes. Int J Damage Mech 9:196–240Google Scholar
  53. Saanouni K, Mariage JF, Cherouat A, Lestriez P (2004) Numerical prediction of discontinuous central bursting in axisymmetric forward extrusion by continuum damage mechanics. Comput Struct 82:2309–2332CrossRefGoogle Scholar
  54. Saanouni K, Lestriez P, Labergère C (2011) 2D adaptive FE simulations in finite thermo-elasto-viscoplasticity with ductile damage: application to orthogonal metal cutting by chip formation and breaking. Int J Damage Mech 20:23–61CrossRefGoogle Scholar
  55. Tai WH, Yang BX (1986) A new microvoid-damage model for ductile fracture. Eng Fract Mech 25:377–384CrossRefGoogle Scholar
  56. Tanaka E (1994) A nonproportionality parameter and a cyclic viscoplasic constitutive model taking into account amplitude dependences and memory effects of isotropic hardening. Eur J Mech A/Solids 13:155–173zbMATHGoogle Scholar
  57. Thomason PF (1990) Ductile fracture of metals. Pergamon Press, OxfordGoogle Scholar
  58. Thomson RD, Hancock JW (1984) Ductile failure by void nucleation, growth and coalescence. Int J Fract 26:99–112CrossRefGoogle Scholar
  59. Tvergaard V (1990) Material failure by void growth to coalescence. In: Hutchinson JW, Wu TY (eds) Advances in applied mechanics, vol 27. Academic, New York, pp 83–151Google Scholar
  60. Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32:157–169CrossRefGoogle Scholar
  61. Xia L, Shih C, Hutchinson J (1995) A computational approach to ductile crack growth under large scale yielding conditions. J Mech Phys Solids 43:389–413zbMATHCrossRefGoogle Scholar
  62. Besson J, Guillemer-Neel C (2003) An extension of the Green and Gurson models to kinematic hardening. Mech Mater 35:1–18CrossRefGoogle Scholar
  63. Brünig M, Chyra O, Albrecht D, Driemeier L, Alves M (2008) A ductile damage criterion at various stress triaxialities. Int J Plast 24:1731–1755zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Nagoya UniversityNagoyaJapan

Personalised recommendations