An anisotropic ductile damage model based on irreversible thermodynamics

International Journal of Plasticity

Volumn 19, Issue 10, 2003, Pages 1679-1713

  Brünig, Michael ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

A. Microcracking; A. Voids and inclusions; B. Elastic plastic material; B. Finite strain; C. Finite elements

Indexed keywords

ANISOTROPY; COMPUTER SIMULATION; CONTINUUM MECHANICS; DECOMPOSITION; DEGRADATION; DUCTILITY; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; STRAIN; TENSORS;

FINITE STRAIN;

ELASTOPLASTICITY;

EID: 0038685855     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0749-6419(02)00114-6     Document Type: Article

References (70)

1. Alves M., Yu J., Jones N. On the elastic modulus degradation in continuum damage mechanics. Comp. Struct. 76:2000;703-712.
2. Alves M. Measurement of ductile material damage. Mech. Struct. Mach. 29:2001;451-476.
3. Asaro R. Micromechanics of crystals and polycrystals. Adv. Appl. Mech. 23:1983;1-115.
4. Baste S., Audoin B. On internal variables in anisotropic damage. Eur. J. Mech., A/Solids. 10:1991;587-606.
5. Becker R. The effect of porosity distribution on ductile failure. J. Mech. Phys. Solids. 35:1987;577-599.
6. Becker R., Needleman A., Richmond O., Tvergaard V. Void growth and failure in notched bars. J. Mech. Phys. Solids. 36:1988;317-351.
7. Betten J. Net-stress analysis in creep mechanics. Ingenieur-Archiv. 52:1982;405-419.
8. Betten J. Damage tensors in continuum mechanics. J. Méc. Théor. Appl. 2:1983;13-32.
9. Bluhm, J.I., Morrissey, R.J., 1965. Fracture in a tensile specimen. In: Proc. 1st Int. Conf. Fracture, Vol. 3, Sendai, 1739.
10. Brown, L.M., Embury, J.D., 1973. The initiation and growth of voids at second phase particles. In: Proc. 3rd Int. Conf. on Strength of Metals and Alloys, Inst. of Metals, London, pp. 164-169.
11. Brünig M. Numerical simulation of the large elastic-plastic deformation behavior of hydrostatic stress-sensitive solids. Int. J. Plasticity. 15:1999;1237-1264.
12. Brünig M. A framework for large strain elastic-plastic damage mechanics based on metric transformations. Int. J. Eng. Science. 39:2001;1033-1056.
13. Brünig, M., 2003. Numerical analysis of anisotropic ductile continuum damage. Comp. Meth. Appl. Mech. Engng. (submitted for publication).
14. Bruhns O.T., Schiesse P. A continuum model of elastic-plastic materials with anisotropic damage by oriented microvoids. Eur. J. Mech., A/Solids. 15:1996;367-396.
15. Chaboche J.L. Anisotropic creep damage in the framework of continuum damage mechanics. Nuclear Engng. Design. 79:1984;309-319.
16. Chaboche J.L. Continuum damage mechanics. Part I - general concepts J. Appl. Mech. 55:1988;59-64.
17. Chaboche J.L. Continuum damage mechanics. Part II - damage growth, crack initiation, and crack growth J. Appl. Mech. 55:1988;65-72.
18. Chow C.L., Wang J. An anisotropic theory of continuum damage mechanics for ductile fracture. Eng. Frac. Mech. 27:1987;547-558.
19. Cialone H., Asaro R.J. Hydrogen assisted fracture of spherodized plain carbon steels. Met. Trans. 12A:1980;1373-1387.
20. Cordebois, J.P., 1983. Critères d'Instabilité Plastique et Endommagement Ductile en Grandes Deformation. Thèse de Doctorat, Univ. Paris VI, France.
21. Dhar S., Sethuraman R., Dixit P.M. A continuum damage mechanics model for void growth and micro crack initiation. Eng. Fract. Mech. 53:1996;917-928.
22. Dubensky E.M., Koss D.A. Void/pore distributions and ductile fracture. Metal. Trans. A. 18A:1987;1887-1895.
23. Grabacki J. On some desciption of damage processes. Eur. J. Mech., A/Solids. 10:1991;309-325.
24. Hayakawa K., Murakami S., Liu Y. An irreversible thermodynamics theory for elastic-plastic-damage materials. Eur. J. Mech., A/Solids. 17:1998;13-32.
25. Jain M., Allin J., Lloyd D.J. Fracture limit prediction using ductile fracture criteria for forming of an automotive aluminum sheet. Int. J. Mech. Sci. 41:1999;1273-1288.
26. Ju J.W. Isotropic and anisotropic damage variables in continuum damage mechanics. J. Eng. Mech. 116:1990;2764-2770.
27. Kachanov L.M. On rupture time under condition of creep. Izvestia Akademi Nauk USSR, Otd. Techn. Nauk, Moskwa. 8:1958;26-31.
28. Kachanov M. Continuum model of medium with cracks. J. Eng. Mech. Div. 106:1980;1039-1051.
29. Khraishi T.A., Khaleel M.A., Zbib H.M. A parametric-experimental study of void growth in superplastic deformation. Int. J. Plasticity. 17:2001;297-315.
30. Koplik J., Needleman A. Void growth and coalescence in porous plastic solids. Int. J. Solids Structures. 24:1988;835-853.
31. Krajcinovic D. Constitutive equations for damaging materials. J. Appl. Mech. 50:1983;355-360.
32. Krajcinovic D. Damage mechanics. Mech. Mater. 8:1989;117-197.
33. Krajcinovic D., Fonseka G.U. The continuous damage theory of brittle materials. Part 1: general theory. J. Appl. Mech. 48:1981;809-815.
34. Krajcinovic D., Fonseka G.U. The continuous damage theory of brittle materials. Part 2: uniaxial and plane response modes. J. Appl. Mech. 48:1981;816-824.
35. Leblond J.-B., Perrin G. A self-consistent approach to coalescence of cavities in inhomogeneously voided ductile solids. J. Mech. Phys. Solids. 47:1999;1823-1841.
36. Lehmann Th. Some thermodynamical considerations on inelastic deformations including damage processes. Acta Mech. 79:1989;1-24.
37. Lehmann Th. Thermodynamical foundations of large inelastic deformations of solid bodies including damage. Int. J. Plasticity. 7:1991;79-98.
38. Lemaitre J. A continuous damage mechanics model for ductile fracture. J. Eng. Mater. Tech. 107:1985;83-89.
39. Lemaitre J. Coupled elasto-plasticity and damage constitutive equations. Comp. Meth. Appl. Mech. Eng. 51:1985;31-49.
40. Lemaitre J. Local approach of fracture. Eng. Frac. Mech. 25:1986;523-537.
41. Lemaitre J. A Course on Damage Mechanics. second ed:1996;Springer, Berlin.
42. Lemaitre J., Dufailly J. Damage measurements. Eng. Fract. Mech. 28:1987;643-661.
43. Le Roy G., Embury J.D., Edward G., Ashby M.F. A model of ductile fracture based on the nucleation and growth of voids. Acta Metall. 29:1981;1509-1522.
44. Li, Z., Wang, C., Chen, C., 2003. The evolution of voids in the plasticity strain hardening gradient materials. Int. J. Plasticity 19, 213-234.
45. Lu T.J., Chow C.L. On constitutive equations of inelastic solids with anisotropic damage. Theor. Appl. Fract. Mech. 14:1990;187-218.
46. Lubarda V.A., Krajcinovic D. Damage tensors and crack density distribution. Int. J. Solids Struct. 30:1993;2859.
47. Lubarda V.A., Krajcinovic D. Some fundamental issues in rate theory of damage-elastoplasticity. Int. J. Plasticity. 11:1995;763-797.
48. Mackenzie A.C., Hancock J.W., Brown D.K. On the influence of state of stress on ductile failure initiation in high strength steels. Eng. Fract. Mech. 9:1977;167-188.
49. Magnusen P.E., Dubensky E.M., Koss D.A. The effect of void arrays on void linking during ductile fracture. Acta Metall. 36:1988;1503-1509.
50. McClintock F.A. A criterion for ductile fracture by growth of holes. J. Appl. Mech. 35:1968;363-371.
51. Melander A., Stahlberg U. The effect of void size and distribution on ductile fracture. Int. J. Fracture. 16:1980;431-440.
52. Moussy, F., 1985. Les differentes echelles du developpement de l'endommagement dans del aciers. Influence sur la localization de la deformation a l'echelle microscopique. In: Salencon, J. (Ed.), Proc. Int. Symp. on Plastic Instability - Considere Memorial, Presses Ponts et Chaussees, pp. 263-272.
53. Murakami S. Mechanical modeling of material damage. J. Appl. Mech. 55:1988;280-286.
54. Murakami S., Ohno N. A continuum theory of creep and creep damage. Ponter A.R.S., Hayhurst D.R. Creep in Structures. 1981;422-443 Springer Verlag, Berlin.
55. Needleman A., Kushner A.S. An analysis of void distribution effects on plastic flow in porous solids. Eur. J. Mech., A/Solids. 9:1990;193-206.
56. Orsini V.C., Zikry M.A. Void growth and interaction in crystalline materials. Int. J. Plasticity. 17:2001;1393-1417.
57. Rabotnov, I.N., 1963. On the equations of state for creep. In: Progress in Appl. Mech. - The Prager Anniversary Volume. MacMillan, New York, pp. 307-315.
58. Rice J.R., Tracey D.M. On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids. 17:1969;201-217.
59. Simo J.C., Ju J.W. Strain- and stress-based continuum damage models - I. Formulation. Int. J. Solids Structures. 23:1987;821-840.
60. Spitzig W.A., Richmond O. The effect of pressure on the flow stress of metals. Acta Metall. 32:1984;457-463.
61. Spitzig W.A., Smelser R.E., Richmond O. The evolution of damage and fracture in iron compacts with various initial porosities. Acta Metall. 36:1988;1201-1211.
62. Spitzig W.A., Sober R.J., Richmond O. Pressure dependence of yielding and associated volume expansion in tempered martensite. Acta Metall. 23:1975;885-893.
63. Spitzig W.A., Sober R.J., Richmond O. The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory. Metall. Trans. 7A:1976;1703-1710.
64. Steinmann P., Carol I. A framework for geometrically nonlinear continuum damage mechanics. Int. J. Eng. Sci. 36:1998;1793-1814.
65. Taylor M.B., Zbib H.M., Khaleel M.A. Damage and size effects during superplastic deformation. Int. J. Plasticity. 18:2002;415-442.
66. Tvergaard V. Material failure by void growth to coalescence. Adv. Appl. Mech. 27:1990;83-151.
67. Tvergaard V., Needleman A. Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 32:1984;157-169.
68. Voyiadjis G.Z., Kattan P.I. A plasticity-damage theory for large deformation of solids - I. Theoretical formulation. Int. J. Eng. Sci. 30:1992;1089-1108.
69. Voyiadjis G.Z., Kattan P.I. Advances in Damage Mechanics: Metals and Metal Matrix Composites. 1999;Elsevier, Amsterdam.
70. Voyiadjis G.Z., Park T. The kinematics of damage for finite-strain elasto-plastic solids. Int. J. Eng. Sci. 37:1999;803-830.