On kinematic, thermodynamic, and kinetic coupling of a damage theory for polycrystalline material

International Journal of Plasticity

Volumn 26, Issue 6, 2010, Pages 775-793

  Bammann, D J ^a   Solanki, K N ^a  

^a MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

Damage; Elastic plastic; Finite strain; Kinematics; Thermodynamics

Indexed keywords

CURRENT CONFIGURATION; DAMAGE; DAMAGE EVOLUTION; DAMAGE EVOLUTION EQUATION; DAMAGE THEORY; DEFORMATION GRADIENTS; ELASTIC-PLASTIC; EVOLUTION EQUATIONS; FINITE-STRAIN; INTERMEDIATE CONFIGURATION; KINETIC COUPLING; LATTICE DEFORMATION; MACROSCOPIC DEFORMATIONS; MULTIPLICATIVE DECOMPOSITION; POLYCRYSTALLINE; TEMPERATURE EFFECTS; THERMAL DEFORMATION; VOLUME CHANGE; VOLUMETRIC DEFORMATION;

DIFFERENTIAL EQUATIONS; ELASTOPLASTICITY; KINEMATICS; PLASTICITY; PLASTICS; POLYCRYSTALLINE MATERIALS; THERMAL EXPANSION; THERMODYNAMICS;

DEFORMATION;

EID: 77950459240     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2009.10.006     Document Type: Article

References (81)

1. Abu Al-Rub R.Z., and Voyiadjis G.Z. On the coupling of anisotropic damage and plasticity models for ductile materials. Int. J. Solids Struct. 40 (2003) 2611-2643
2. Anand L., and Kothari M. A computational procedure for rate-independent crystal plasticity. J. Mech. Phys. Solids 44 4 (1996) 525-558
3. Armero F., and Garikipati K. An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. Int. J. Solids Struct. 33 (1996) 2863-2885
4. Asaro R.J. Crystal plasticity. J. Appl. Mech. 50 (1983) 921-934
5. Bammann D.J. A model of crystal plasticity containing a natural length scale. Mater. Sci. Eng. (2001) 406-410
6. Bammann D.J., and Aifantis E.C. A damage model for ductile metals. Nucl. Eng. Des. 116 (1989) 355-362
7. Bammann, D.J., Chiesa, M.L., Horstemeyer, M.F., Weingarten, L.I., 1993. Failure in ductile materials using finite element methods. In: Jones, N., Weirzbicki, T. (Eds.), Structural Crashworthiness and Failure, Applied Science.
8. Bammann D.J., Chiesa M.L., and Johnson G.C. Modeling large deformation and failure in manufacturing processes. In: Tatsumi W., and Kambe (Eds). App. Mech. (1996), Elsevier Science 256-276
9. Betten J. Applications of tensor functions to the formulation of constitutive equations involving damage and initial anisotropy. Eng. Fract. Mech. 25 5-6 (1986) 573-584
10. Bhattacharya B., and Ellingwood B. Continuum damage mechanics analysis of fatigue crack initiation. Int. J. Fatigue 20 9 (1998) 631-639
11. Bilby, B.A., Gardner, L.R.T., Stroh, A.N., 1957. Continuous distributions of dislocations and the theory of plasticity. In: Extrait des Actes du IXe Congres International de Mecanique Appliquee, Brussels, pp. 35-44.
12. Bonora N., Gentile D., Pirondi A., and Newaz G. Ductile damage evolution under triaxial state of stress: theory and experiments. Int. J. Plast. 21 5 (2005) 981-1007
13. Brünig M. Numerical analysis and elastic-plastic deformation behavior of anisotropically damaged solids. Int. J. Plast. 18 (2002) 1237-1270
14. Brünig M. An anisotropic ductile damage model based on irreversible thermodynamics. Int. J. Plast. 19 10 (2003) 1679-1713
15. Brünig M., and Ricci S. Nonlocal continuum theory of anisotropically damaged metals". Int. J. Plast. 21 7 (2005) 1346-1382
16. Brünig M., Chyra O., Albrecht D., Driemeier L., and Alves M. A ductile damage criterion at various stress triaxialities. Int. J. Plast. 24 10 (2008) 1731-1755
17. Budiansky, and O'Connell. Elastic moduli of a cracked solid. Int. J. Solids Struct. 12 (1976) 81-97
18. Canova G.R., Favier S., Lebensohn R., and Baudelet B. Modelling of damage due to particles and grain boundaries. Mater. Sci. Forum 217/222 3 (1996) 1441-1448
19. Carol I., and Bazant Z.P. Damage and plasticity in microplane theory. Int. J. Solids Struct. 34 29 (1997) 3807-3835
20. Carol I., Rizzi E., and Willam K. A unified theory of elastic degradation and damage based on a loading surface. Int. J. Solids Struct. 31 20 (1994) 2835-2865
21. Cauvin A., and Testa R.B. Damage mechanics: basic variables in continuum theories. Int. J. Solids Struct. 36 5 (1999) 747-761
22. Celentano D.J., and Chaboche J.L. Experimental and numerical characterization of damage evolution in steels. Int. J. Plast. 23 10-11 (2007) 1739-1762
23. Chaboche J.L. Development of continuum damage mechanics for elastic solids sustaining anisotropic and unilateral damage. Int. J. Damage Mech. 2 4 (1993) 311-329
24. Chaboche J.L. A review of some plasticity and viscoplasticity constitutive theories. Int. J. Plast. 24 10 (2008) 1642-1693
25. Chow C.L., and Chen X.F. An anisotropic model of damage mechanics based on endochronic theory of plasticity. Int. J. Fract. 55 3 (1992) 115-130
26. Clayton J.D., Bammann D.J., and McDowell D.L. A geometric framework for the kinematics of crystals with defects. Phil. Mag. 85 (2005) 3983
27. Coleman B.D., and Gurtin M.E. Thermodynamics with internal state variables. J. Chem. Phys. 47 (1967) 59
28. Coleman B.D., and Noll W. The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13 (1963) 167-178
29. Cordebois, J.P., Sidoroff, F., 1979. Damage Induced Elastic Anisotropy", Euromech 115, Villard de Lens.
30. Davison L. Kinematics of finite elastoplastic deformation. Mech. Mater. 21 (1995) 73-88
31. Håkansson P., Mathias Wallin M., and Ristinmaa M. Thermomechanical Response of Non-local Porous Material. Int. J. Plast. 22 11 (2006) 2066-2090
32. Halm D., and Dragon A. An anisotropic model of damage and frictional sliding for brittle materials. Eur. J. Mech. A Solids 17 3 (1998) 439-460
33. Hammi Y., and Horstemeyer M.F. A physically motivated anisotropic tensorial representation of damage with separate functions for void nucleation, growth, and coalescence. Int. J. Plast. 23 (2007) 1641-1678
34. Hammi Y., Horstemeyer M.F., and Bammann D.J. An anisotropic damage model for ductile metals. Int. J. Damage Mech. 12 (2003) 245-262
35. Hammi Y., Bammann D.J., and Horstemeyer M.F. Modeling of anisotropic damage for ductile materials in metal forming processes. Int. J. Damage Mech. 13 (2004) 123-146
36. Hayakawa K., Murakami S., and Liu Y. An irreversible thermodynamics theory for elastic-plastic-damage materials. Eur. J. Mech. A - Solids 17 1 (1998) 13-32
37. Horstemeyer M.F., Lathrop J., Gokhale A.M., and Dighe M. Modeling stress state dependent damage evolution in a cast Al-Si-Mg aluminum alloy. Theory Appl. Fract. Mech. 33 (2000) 31-47
38. Kachanov M. Time of the rupture process under creep conditions. Izvestiya Akad. Nauk USSR, Otd. Tech. Nauk 8 (1958) 26-31
39. Kachanov M. Continuum model of medium with cracks. J. Eng. Mech. 106 (1980) 1039-1052
40. Kanatani K. Distribution of directional data and fabric tensors. Int. J. Eng. Sci. 22 2 (1984) 149-164
41. Kattan P.I., and Voyiadjis G.Z. A coupled theory of damage mechanics and finite strain elasto-plasticity - I: damage and elastic deformations. Int. J. Eng. Sci. 28 5 (1990) 421-435
42. Krajcinovic D. Damage Mechanics (1996), Elsevier, Amsterdam
43. Krajcinovic D., and Mastilovic S. Some fundamental issues of damage mechanics. Mech. Mater. 21 3 (1995) 217-230
44. Kratochvil J., and Dillon Jr. O.W. Thermodynamics of elastic-plastic materials as a theory with internal state variables. J. Appl. Phys. 40 (1969) 3207
45. Kröner E. Allgemeine Kontinuums Theorie der Versetzungen und Eigenspannungen. Arch. Rat. Mech. Anal. 4 (1960) 273-334
46. Lee E.H. Elastic-plastic deformation at finite strains. J. Appl. Mech. 36 (1969) 1-6
47. Lemaitre J. Continuous damage mechanics model for ductile fracture. Trans. ASME J. Eng. Mater. 107 (1985) 83-89
48. Lubarda V.A., and Krajcinovic D. Damage tensors and the crack density distribution. Int. J. Solids Struct. 30 20 (1993) 2859-2877
49. Mandel J. Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques. Int. J. Solids Struct. 9 6 (1973) 725-740
50. Marin, E.B., 2007. On the formulation of a classical crystal plasticity model. In: Proceeding of the 13th International Symposium on Plasticity and its Current Applications, Girwood, Alaska, June 2-6.
51. Marin E.B., and McDowell D.L. Associative versus non-associative porous viscoplasticity based on internal state variable concepts. Int. J. Plast. 12 (1996) 629-669
52. Menzel A., Ekh M., Runesson K., and Steinmann P. A framework for multiplicative elastoplasticity with kinematic hardening coupled to anisotropic damage. Int. J. Plast. 21 3 (2005) 397-434
53. Murakami S. Mechanical modeling of material damage. J. Appl. Mech. 55 (1988) 280-286
54. Murakami, S., 1990. A continuum mechanics theory of anisotropic damage. In: Boehler, J.P. (Ed.), Yielding, Damage, and Failure of Anisotropic Solids, London, pp. 465-482.
55. Nemat-Nasser S. Decomposition of strain measures and their rates in finite deformation elastoplasticity. Int. J. Solids Struct. 15 (1979) 155-166
56. Onat E.T., and Leckie F.A. Representation of mechanical behavior in the presence of changing internal structure. J. Appl. Mech. 55 1 (1988) 1-10
57. Ortiz M. A constitutive theory for the inelastic behavior of concrete. Mech. Mater. 4 1 (1985) 67-93
58. Park T., and Voyiadjis G.Z. Kinematic description of damage. J. Appl. Mech. 65 (1998) 93-98
59. Peirce D., Asaro R.J., and Needleman A. Material rate dependence and localization in crystalline solids. Acta. Metall. 31 (1983) 1951-1976
60. Potirniche G.P., and Daniewicz S.R. Analysis of crack tip plasticity for microstructurally small cracks using crystal plasticity theory. Eng. Fract. Mech. 70 13 (2003) 1623-1643
61. Rabotnov, YU.N., 1968. Creep rupture. In: Proceedings of the XII International Congress on Applied Mechanics, Stanford-Springer, pp. 342-349.
62. Rashid M.M., and Nemat-Nasser S. A constitutive algorithm for rate dependent crystal plasticity. Comp. Meth. Appl. Mech. Eng. 94 (1992) 201-228
63. Regueiro R.A., Bammann D.J., Marin E.B., and Garikipati V. A nonlocal phenomenological anisotropic finite deformation plasticity model accounting for dislocation defects. J. Eng. Mater. Technol. - Trans. ASME 124 (2002) 380-387
64. Rice J.R. Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19 6 (1971) 433-455
65. Rice J.R. The localization of plastic deformation. In: Koiter W.T. (Ed). Proc. 14th Int. Cong. Theo. Appl. Mech. (1976), North-Holland, Amsterdam 207-220
66. Saczuk J., Hackl K., and Stumpf H. Rate theory of nonlocal gradient damage-gradient viscoinelasticity. Int. J. Plast. 19 5 (2003) 675-706
67. Solanki, K.N., 2008. Physically Motivated Internal State Variable form of A Higher Order Damage Model for Engineering Materials with Uncertainty. In Mississippi State University (Eds.), Ph.D. Dissertation.
68. Steinmann P., and Carol I. A framework for geometrically nonlinear continuum mechanics. Int. J. Eng. Sci. 36 (1998) 1793-1814
69. Stumpf H., and Saczuk J. On a general concept for the analysis of crack growth and material damage. Int. J. Plast. 17 7 (2001) 991-1028
70. Tikhomirov D., Niekamp R., and Stein E. On three-dimensional microcrack density distribution. ZAMM.Z. Angew. Math. Mech. 81 1 (2001) 3-16
71. Tvergaard V., and Niordson C. Nonlocal plasticity effects on interaction of different size voids. Int. J. Plast. 20 1 (2004) 107-120
72. Voyiadjis G.Z. Model of inelastic behavior coupled to damage. Handbook Mater. Behavior Models (2001) 814-820
73. Voyiadjis G.Z., and Dorgan R.J. Framework using functional forms of hardening internal state variables in modeling elasto-plastic-damage behavior. Int. J. Plast. 23 10-11 (2007) 1826-1859
74. Voyiadjis G.Z., and Kattan P.I. A coupled theory of damage mechanics and finite strain elasto-plasticity - II: damage and finite strain plasticity. Int. J. Eng. Sci. 28 6 (1990) 505-524
75. Voyiadjis G.Z., and Park T. Kinematics of large elastoplastic damage deformation. Stud. Appl. Mech. 46 (1998) 45-64
76. Voyiadjis G.Z., and Park T. The kinematics of damage for finite strain elasto-plastic solids. Int. J. Eng. Sci. 37 (1999) 803-830
77. Voyiadjis G.Z., Abu Al-Rub R.K., and Palazotto A.N. Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory. Int. J. Plast. 20 6 (2004) 981-1038
78. Voyiadjis G.Z., Taqieddin Z.N., and Kattan P.I. Anisotropic damage - plasticity model for concrete. Int. J. Plast. 24 10 (2008) 1946-1965
79. Yazdani S., and Schreyer H.L. An anisotropic damage model with dilatation for concrete. Mech. Mater. 7 3 (1988) 231-244
80. Zbib H. On the mechanics of large inelastic deformations: kinematics and constitutive modeling. Acta Mech. 96 (1993) 119-138
81. Zhou, M., Zhai, J., 1999. Modelling of micromechanical fracture using a cohesive finite element method. In: Furnish, M.D., Chhabildas, L.C., Hixson, R.S. (Eds.), Shock Compression of Condensed Matter - 1999, Proc. of the Conf. of the American Physical Society Topical Group on Shock Compression of Condensed Matter, June 27-July 2, 1999. Snowbird, Utah, pp. 623-628.