Continuum framework for the rate-dependent behavior of anisotropically damaged ductile metals

Acta Mechanica

Volumn 186, Issue 1-4, 2006, Pages 37-53

  Brunig M ^a,b  

^a Universität Dortmund ^*

^b TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; COMPUTER SIMULATION; CONTINUOUS CASTING; ELASTOPLASTICITY; STRAIN RATE; TENSILE TESTING;

CONSTITUTIVE EQUATIONS; DEFORMATION BEHAVIOR; IMPACT LOADINGS; MATERIAL PARAMETERS;

METALS;

EID: 33749321213     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-006-0320-0     Document Type: Article

References (67)

1. Abed, F. H., Voyiadjis, G. Z.: Plastic deformation modeling of AL-6XN stainless steel at low and high strain rates and temperatures using a combination of bcc and fee mechanisms of metals. Int. J. Plasticity 21, 1618-1639 (2005).
2. Addessio, F. L., Johnson, J. N., Maudlin, P. J.: The effect of void growth on Taylor cylinder impact experiments. J. Appl. Phys. 73, 7288-7297 (1993).
3. Anand, L.: Constitutive equations for hot-working of metals. Int. J. Plasticity 1, 213-231 (1985).
4. Argyris, J. H., Doltsinis, J. S.: On the natural formulation and analysis of large deformation coupled thermomechanical problems. Comp. Meth. Appl. Mech. Engng. 25, 195-253 (1981).
5. Asaro, R. J.: Macromechanics of crystals and polycrystals. Adv. Appl. Mech. 23, 2-115 (1983).
6. Belytschko, T., Moran, B., Kulkarni, M.: On the crucial role of imperfections in quasi-static viscoplastic solutions. J. Appl. Mech. 58, 658-665 (1991).
7. Benson, D. J.: An analysis of void distribution effects on the dynamic growth and coalescence of voids in ductile metals. J. Mech. Phys. Solids 41, 1285-1308 (1993).
8. Bever, M. B., Holt, D. L., Titchener, A. L.: The stored energy of cold work. Prog. Mater. Sci. 1-190 (1973).
9. Bodner, S. R., Partom, Y.: Constitutive equations for elastic-viscoplastic strain-hardening materials. J. Appl. Mech. 42, 385-389 (1975).
10. Borvik, T., Hopperstad, O. S., Berstad, T.: On the influence of stress triaxiality and strain rate on the behavior of a structural steel. Part II. Numerical study. Eur. J. Mech. A/Solids 22, 15-32 (2003).
11. Brown, S. T., Kim, K. H., Anand, L.: An internal variable constitutive model for hot working of metals. Int. J. Plasticity 5, 95-130 (1989).
12. Bruhns, O. T., Diehl, H.: An internal variable theory of inelastic behaviour at high rates of strain. Arch. Mech. 41, 427-460 (1989).
13. Brünig, M.: Numerical simulation of the large elastic-plastic deformation behavior of hydrostatic stress-sensitive solids. Int. J. Plasticity 15, 1237-1264 (1999).
14. Brünig, M.: Numerical analysis and large strain elastic-viscoplastic behavior of hydrostatic stress-sensitive metals. Int. J. Solids Struct. 38, 635-656 (2001).
15. Brünig, M.: An anisotropic ductile damage model based on irreversible thermodynamics. Int. J. Plasticity 19, 1679-1713 (2003).
16. Brünig, M.: Numerical analysis of anisotropic ductile continuum damage. Comput. Methods Appl. Mech. Engng. 192, 2949-2976 (2003).
17. Brünig, M.: An anisotropic continuum damage model: Theory and numerical analyses. Lat. Am. J. Solids Struct. (www.lajss.org) 1, 185-218 (2004).
18. Brünig, M.: Phenomenological modelling of the rate-dependent thermo-elastic-plastic behavior of ductile metals. Technical Report 02.05, Dortmund, 2005.
19. Canadija, M., Brnic, J.: Associative coupled thermoplasticity at finite strain with temperature-dependent material parameters. Int. J. Plasticity 20, 1851-1874 (2004).
20. Carroll, M. M., Holt, A. C.: Static and dynamic pore-collaps relations for ductile porous materials. J. Appl. Phys. 43, 1626-1636 (1972).
21. Cortes, R.: The growth of microvoids under intense dynamic loading. Int. J. Solids Struct. 29, 1339-1350 (1992).
22. Fotiu, P. A., Nemat-Nasser, S.: A universial integration algorithm for rate-dependent elastoplasticity. Comput. Struct. 59, 1173-1184 (1996).
23. Green, A. E., Naghdi, P. M.: Some remarks on elastic-plastic deformation at finite strains, Int. J. Engng. Sci. 9, 1219-1229 (1971).
24. Ourson, A. L.: Continuum theory of ductile rupture by void nucleation and growth: Part I - yield criteria and flow rules for porous ductile media. J. Engng. Mat. Tech. 99, 2-15 (1977).
25. Hopperstad, O. S., Borvik, T., Langseth, M., Labibes, K., Albertini, C.: On the influence of stress triaxiality and strain rate on the behaviour of structural steel. Part I. Experiments. Eur. J. Mech. A/Solids 22, 1-13 (2003).
26. Johnson, J. N.: Dynamic fracture and spallation in ductile solids. J. Appl. Phys. 52, 2812-2825 (1981).
27. Johnson, G. R., Cook, W. H.: A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proc. 7th Int. Symp. Ballistics, The Hague: Netherlands, pp. 541-547, 1983,
28. Johnson, G. R., Cook, W. H.: Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Engng. Fract. Mech. 21, 31-48 (1985).
29. Johnson, G. R., Hoegfeldt, J. M., Lindholm, U. S., Nagy, A.: Response of various metals to large torsional strains over a large range of strain rates - I: Ductile metals. J. Engng. Mater. Technol. 105, 42-47 (1983).
30. Kapoor, R., Nemat-Nasser, S.: Determination of temperature rise during high-strain rate deformation. Mech. Mater. 27, 1-12 (1998).
31. Klöcker, H., Montheillet, F.: Modeling the ductile growth of voids at high strain rates. J. Phys. 49, C3-313-C3-318 (1988).
32. Klopp, R. W., Clifton, R. J., Shawki, T. G.: Pressure-shear impact and the dynamic viscoplastic response of metals. Mech. Mater. 4, 375-385 (1985).
33. Lemonds, J., Needleman, A.: Finite element analysis of shear localization in rate and temperature dependent solids. Mech. Mater. 5, 339-361 (1986).
34. Lestriez, P., Saanouni, K., Mariage, J. F., Cherouat, A.: Numerical prediction of ductile damage in metal forming processes including thermal effects. Int. J. Damage Mech. 13, 59-80 (2004).
35. McClintock, F. A.: A criterion for ductile fracture by growth of holes. J. Appl. Mech. 35, 363-371 (1968).
36. Mićunović, M., Albertini, C., Montagnani, M.: High strain rate thermo-inelasticity of damaged AISI 316H. Int. J. Damage Mech. 12, 267-303 (2003).
37. Miehe, C.: A theory of large-strain isotropic thermoplasticity based on metric transformation tensors. Arch. Appl. Mech. 66, 45-64 (1995).
38. Miller, A. K.: An inelastic constitutive model for monotonic, cyclic and creep deformation. Part I. Equations development and analytical procedures. Trans. ASME J. Engng. Mater. Technol. 98, 106-113 (1976).
39. Molinari, A., Mercier, S.: Micromechanical modelling of porous materials under dynamic loading. J. Mech. Phys. Solids 49, 1497-1516 (2001).
40. Nemat-Nasser, S., Guo, W. G., Kihl, D. P.: Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures. J. Mech. Phys. Solids 49, 1823-1846 (2001).
41. Nishiguchi, I., Sham, T.-L., Krempl, E.: A finite deformation theory of viscoplasticity based on overstress: Part I - Constitutive equations. J. Appl. Mech. 57, 553-561 (1990).
42. Ortiz, M., Molinari, A.: Effect of strain hardening and rate sensitivity on the dynamic growth of a void in a plastic material, J. Appl. Mech. 114, 48-53 (1992).
43. Pan, J., Rice, J. R.: Rate sensitivity of plastic flow and implications for yield-surface vertices. Int. J. Solids Struct. 19, 973-987 (1983).
44. Rajendran, A. M., Dietenberger, M. A., Grove, D. J.: A void nucleation and growth based failure model for spallation. J. Appl. Phys. 65, 1521-1527 (1988).
45. Rice, J. R.: Inelastic constitutive relations for solids: An internal variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433-455 (1971).
46. Rice, J. R., Tracey, D. M.: On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids 17, 201-217 (1969).
47. Rosakis P., Rosakis, A. J., Ravichandran, G., Hodowany, J.: A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals. J. Mech. Phys. Solids 48, 581-607 (2000).
48. Rule, W. K., Jones, S. E.: A revised form for the Johnson-Cook strength model. Int. J. Impact Engng. 21, 609-624 (1998).
49. Simo, J. C., Miehe, C.: Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation. Comp. Meth. Appl. Mech. Engng. 98, 41-104 (1992).
50. Spitzig, W. A., Richmond, O.: The effect of pressure on the flow stress of metals. Acta Metall. 32, 457-463 (1984).
51. Spitzig, W. A., Smelser, R. E., Richmond, O.: The evolution of damage and fracture in iron compacts with various initial porosities. Acta Metall. 36, 1201-1211 (1988).
52. Spitzig, W. A., Sober, R. J., Richmond, O.: Pressure dependence of yielding and associated volume expansion in tempered martensite. Acta Metall 23, 885-893 (1975).
53. 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. A 7A, 1703-1710 (1976).
54. Taylor, G. I., Quinney, H.: The latent heat remaining in a metal after cold working. Proc. Roy. Soc. Lond. A 163, 157-181 (1937).
55. Tong, W., Ravichandran, G.: Dynamic pore collapse in viscoplastic materials. J. Mech. Phys. Solids 17, 2425-2435 (1993).
56. Tong, W., Ravichandran, G.: Inertial effects on void growth in porous viscoplastic materials. J. Appl. Mech. 62, 633-639 (1995).
57. Tvergaard, V.: Material failure by void growth to coalescence. Adv. Appl. Mech. 27, 83-151 (1990).
58. Van Slycken, J., Verleysen, P., Degrieck, J., Bouquerel, J., De Cooman, B. C.: Dynamic response of Al-TRIP-steel and the constituent phases. In: Impact loading of engineering structures (Alves, M., Jones, N., eds.), pp. 535-548 Southampton, Boston: WIT Press 2005.
59. Voyiadjis, G. Z., Abu Al-Rub, R. K., Palazotto, A. N.: Non-local coupling of viscoplasticity and anisotropic viscodamage for impact problems using the gradient theory. Arch. Mech. 55, 39-89 (2003).
60. Wang, Z. P.: Void-containing nonlinear materials subject to hogh-rate loading. J. Appl. Phys. 81, 7213-7227 (1997).
61. Wang, Z. P., Jiang, Q.: A yield criterion for porous ductile media at high strain rate. J. Appl. Mech. 64, 503-509 (1997).
62. Worswick, M. J., Pick, R. J.: Void growth and coalescence during high velocity impact. Mech. Mater. 19, 293-309 (1995).
63. Wu, X. Y., Ramesh, K. T., Wright, T. W.: The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading. J. Mech. Phys. Solids 51, 1-26 (2003).
64. Wu, X. Y., Ramesh, K. T., Wright, T. W.: The effects of thermal softening and heat conduction on the dynamic growth of voids. Int. J. Solids Struct. 40, 4461-4478 (2003).
65. Wriggers, P., Miehe, C., Kleiber, M., Simo, J. C.: On the coupled thermomechanical treatment of necking problems via finite element methods. Int. J. Numer. Meth. Engng. 33, 869-883 (1992).
66. Zavaliangos, A., Anand, L.: Thermo-elasto-viscoplasticity of isotropic porous metals. J. Mech. Phys. Solids 41, 1087-1118 (1993).
67. Zerilli, F. J., Armstrong, R. W.: Dislocation-mechanics-based constitutive relations for material dynamics calculations. J. Appl. Phys. 61, 1816-1825 (1987).