On the self-consistent modeling of elastic-plastic behavior of polycrystals

Mechanics of Materials

Volumn 26, Issue 1, 1997, Pages 43-62

  Molinari, A ^a   Ahzi, S ^b   Kouddane, R ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

^b AMRL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; DEFORMATION; ELASTOPLASTICITY; INCLUSIONS; MATHEMATICAL MODELS;

ELASTIC COMPRESSIBILITY; SELF CONSISTENT POLYCRYSTAL MODELING; TAYLOR'S UPPER BOUND FORMULATION;

POLYCRYSTALLINE MATERIALS;

EID: 0031187394     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6636(97)00017-3     Document Type: Article

References (47)

1. Agah-Tehrani, A., Ahzi S., Nemat-Nasser, S., 1992. Presented at the SEM meeting, San Diego CA, September, 1992. Ms. in preparation.
2. Ahzi, S., Ph.D. thesis. University of Metz, France, 1987.
3. Ahzi, S., Molinari, A., Canova, G.R., 1990. Effects of the grain shape on the texture evolution in polycrystalline materials. In: Boehler, J.P. (Ed.), Yielding, Damage and Failure of Anisotropic Solids, p. 425.
4. Ahzi, S., Asaro, R.J., Parks, D., 1993. Application of crystal plasticity theory for mechanically processed BSCCO superconductors. Mech. Mater. 15, 201.
5. Asaro, RJ., Needleman, A., 1985. Texture development and strain hardening in rate dependent polycrystals. Acta Metall. 33, 923.
6. Batdrof, S.B., Budianski, B., 1949. A Mathematical Theory of Plasticity Based on the Concept of Slip. NACA, TN-1871.
7. Berveiller, M., Zaoui, A., 1979. An extension of the self-consistent scheme to plastically flowing polycrystals. J. Mech. Phys. Solids 26, 325.
8. Brown, G.M., 1970. A self-consistent polycrystalline model for creep under combined stress state. J. Mech. Phys. Solids 18, 367.
9. Budianski, B., Wu, 1962. Theoretical prediction of plastic strains of polycrystals. Proc. of the 4th U.S. National Congress of Applied Mechanics, ASME, p. 1175.
10. Dederichs, P.H., Zeller, P., 1973. Variational treatment of the elastic constants of disordered materials. Z. Phys. 259, 103.
11. Eshelby, J.D., 1957. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. London A241, 376.
12. Gilormini, 1995. Private communication.
13. Gilormini, P., Germain, Y., 1987. A finite element analysis of the inclusion problem for power law viscous materials. Int. J. Solids Struct. 23, 413.
14. Harren, S.V., 1991. The finite deformation of rate-dependent polycrystals. II: A comparison of the self-consistent and Taylor methods. J. Mech. Phys. Solids 39, 361.
15. Hill, R., 1965. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13, 89.
16. Hutchinson, J.W., 1964a. Plastic stress-strain relations of FCC polycrystalline metals hardening according to Taylor rule. J. Mech. Phys. Solids 12, 11.
17. Hutchinson, I.W., 1964b. Plastic deformation of BCC polycrystals. J. Mech. Phys. Solids 12, 25.
18. Hutchinson, J.W., 1970. Elastic-plastic behavior of polycrystalline metals and composites. Proc. R. Soc. London A319, 247.
19. Hutchinson, J.W., 1976. Bounds and self-consistent estimate for creep of polycrystalline materials. Proc. R. Soc. A348, 101.
20. Iwakuma, T., Nemat-Nasser, S., 1984. Finite elastic-plastic deformation of polycrystalline metals. Proc. R. Soc. London A394, 87.
21. Kalidindi, S.R., Bronkhorst, C.A., Anand, L., 1992. Crystallographic texture evolution in bulk deformation procession of FCC metals. J. Mech. Phys. Solids 40, 537.
22. Kouddane, R., 1994. Approche autocoherente en élastoviscoplastic des matériaux hétérogénes. Ph.D. thesis. University of Metz, France.
23. Kouddane, R., Molinari, A., Canova, G.R., 1991. Self-consistent modeling of heterogeneous viscoelastic and elastic-viscoplastic materials. Presented at Mecamat 91, Fontainebleau, France.
24. Kouddane, R., Molinari, A., Canova, G.R., 1993. Self-consistent modeling of heterogeneous viscoelastic and elastic-viscoplastic materials. In: Teodosiu, T. et al. (Eds.), Large Plastic Deformations, Fundamentals and Applications of Metal Forming, p. 121.
25. Kröner, E., 1961. Zur plastischen Verformung des vielkristalls. Acta Metall. 9, 155.
26. Lebensohn, R.A., Tomé, C.N., 1993. A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys. Acta Metall. Mater. 41, 2611.
27. Lebensohn, R.A., Tomé, C.N., 1994. A self-consistent viscoplastic model: Prediction of rolling textures of anisotropic polycrystals. Mater. Sci. Eng. A175, 71.
28. Lin, T.H., 1957. Analysis of elastic and plastic strains of face-centered cubic crystals. J. Mech. Phys. Solids 5, 143.
29. Lipinski, P., Krier, J., Berveiller, M., 1990. Elastoplasticite des metaux en grandes deformations: Comportement global et evolution de la structure interne. Rev. Phys. Appl. 25, 361.
30. Lipinski, P., Naddari, A., Berveiller, M., 1992. Recent results concerning the modeling of polycrystalline plasticity at large strains. Int. J. Solids Struct. 29, 1873.
31. Molinari, A., Toth, L.S., 1994. Tuning a self-consistent viscoplastic model by finite element results - I: Modeling. Acta Metall. Mater. 42, 2453.
32. Molinari, A., Canova, R.G., Ahzi, S., 1987. A self-consistent approach to the large deformation polycrystal viscoplasticity. Acta Metall. 35, 2983.
33. Nemat-Nasser, S., 1996. Private communication.
34. Nemat-Nasser, S., Obata, M., 1986. Rate-dependent, finite elasto-plastic deformation of polycrystals. Proc. R. Soc. London A407, 343.
35. Ponte-Castneda, P., De Botton, G., 1992. On the homogenized yield strength of two-phase composites. Proc. R. Soc. London A438, 419.
36. Rice, J.R., 1971. Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433.
37. Rougier, Y., Stolz, C., Zaoui, A., 1994. Self-Consistent Modeling of elastic-Viscoplastic Polycrystals. C.R. Acad. Sci. Paris, t. 318, Serie II, p. 145.
38. Sachs, G., 1928. Plasticity problems in metals. Z. Ver. Dent. Ing. 72, 734.
39. Schapery, R.A., 1974. Viscoelastic behavior and analysis of composite materials. In: Sendeckyj, G.P. (Ed.), Mechanics of Composite Materials. Academic Press, p. 85.
40. Taylor, G.I., 1938. Plastic strain in metals. J. Inst. Metals 62, 307-324.
41. Toth, L.S., Molinari, A., 1994. Tuning a self-consistent viscoplastic model by finite element results - II: Application to torsion textures. Acta Metall. Mater. 42, 2459.
42. Turner, P.A., Tomé, C.N., 1993. Self-consistent modeling of viscoelastic polycrystals: Application to irradiation creep and growth. J. Mech. Phys. Solids 41, 1191.
43. Turner, P.A., Tomé, C.N., Woo, C.H., 1994. Self-consistent modeling of nonlinear visco-elastic polycrystals - An approximate scheme. Philos. Mag. 70, 689.
44. Weng, G.J., 1982. A unified self-consistent theory for the plastic-creep deformation of metals. J. Appl. Mech. 49, 728.
45. Weng, G.J., Chiang, C.R., 1984. Self-consistent relation in polycrystalline plasticity with a non-uniform matrix. Int. J. Solids Struct. 20, 689.
46. Zaoui, A., 1970. Thèse de Doctorat Distribution Continue de Dislocations: Théorie Générale et Quelques Applications. Université de Paris.
47. Zaoui, A., Raphanel, 1991. On the nature of the intergranular accommodation in the modeling of elastic-plastic behavior of crystalline materials. In: Teodosiu, T. et al. (Eds.), Large Plastic Deformations, Fundamentals and Applications of Metal Forming. p. 185.