Homogenization estimates for the average behavior and field fluctuations in cubic and hexagonal viscoplastic polycrystals

Journal of the Mechanics and Physics of Solids

Volumn 52, Issue 5, 2004, Pages 1175-1211

  Liu, Yi ^a   Ponte Castañeda, Pedro ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

A. creep; B. polycrystalline material; C. homogenization; Microstructures; Viscoplastic material

Indexed keywords

CREEP; CRYSTAL ORIENTATION; MATHEMATICAL MODELS; MICROSTRUCTURE; SINGLE CRYSTALS; TENSORS; VISCOPLASTICITY;

ISOTROPIC TEXTURES; VISCOPLASTIC MATERIALS;

POLYCRYSTALS;

EID: 1642312079     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2003.08.006     Document Type: Article

References (51)

1. Adams B.L., Olson T. The mesostructure-properties linkage in polycrystals. Prog. Mater. Sci. 43:1998;1-88.
2. Balasubramanian, S., 1998. Polycrystalline plasticity: application to deformation processing of lightweight materials. Ph.D. Dissertation, Massachusetts Institute of Technology, USA.
3. Bhattacharya, K., Suquet, P., 2003. Transformation domains for a class of model polycrystals, in preparation.
4. Bobeth M., Diener G. Static elastic and thermoelastic field fluctuations in multiphase composites. J. Mech. Phys. Solids. 35:1987;37-149.
5. Bornert M., Masson R., Ponte Castañeda P., Zaoui A. Second-order estimates for the effective behavior of viscoplastic polycrystalline materials. J. Mech. Phys. Solids. 49:2001;2737-2764.
6. Carter N.L., Heard H.C. Temperature and rate dependent deformation of halite. Am. J. Sci. 269:1970;193-249.
7. Castelnau O., Canova G.R., Lebensohn R.A., Duval P. Modelling viscoplastic behavior of anisotropic polycrystalline ice with a self-consistent approach. Acta Mater. 45:1997;4823-4834.
8. deBotton G., Ponte Castañeda P. Variational estimates for the creep behavior of polycrystals. Proc. R. Soc. London A. 448:1995;121-142.
9. Dendievel R., Bonnet G., Willis J.R. Bounds for the creep behavior of polycrystalline materials. Dvorak G. Inelastic Deformation of Composite Materials. 1991;175-192 Springer, New York.
10. Duval P., Ashby M.F., Anderman I. Rate-controlling processes in creep of polycrystalline ice. J. Phys. Chem. 87:1983;4066-4074.
11. Gilman J.J. Plastic anisotropy of LiF and other rocksalt-type crystals. Acta Metall. 7:1959;608-613.
12. Groves G.W., Kelly A. Independent slip systems in crystals. Philos. Mag. 8:1963;877-887.
13. Hashin Z., Shtrikman S. A variational approach to the theory of the elastic behavior of polycrystals. J. Mech. Phys. Solids. 10:1962;343-352.
14. Hershey A.V. The elasticity of an isotropic aggregate of anisotropic cubic crystals. ASME J. Appl. Mech. 21:1954;236-240.
15. Hill R. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids. 13:1965;89-101.
16. Hutchinson J.W. Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. London A. 348:1976;101-127.
17. Hutchinson J.W. Creep and plasticity of hexagonal polycrystals as related to single crystal slip. Metall. Trans. 8A:1977;1465-1469.
18. Kocks U.F., Tomé C.N., Wenk H.-R. Texture and Anisotropy. 1998;Cambridge University Press, Cambridge.
19. Kreher W. Residual stresses and stored elastic energy of composites and polycrystals. J. Mech. Phys. Solids. 38:1990;115-128.
20. Kröner E. Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls. Z. Phys. 151:1958;504-518.
21. Laws N. On the thermostatics of composite materials. J. Mech. Phys. Solids. 21:1973;9-17.
22. Lebensohn R.A. N-site modelling of a 3D viscoplastic polycrystal using the Fast Fourier Transform. Acta. Mater. 49:2001;2723-2737.
23. Lebensohn R.A., Tomé C.N. A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals. application to zirconium alloys Acta. Metall. Mater. 41:1993;2611-2624.
24. Lebensohn R.A., Dawson P.R., Kern H.M., Wenk H.R. Heterogeneous deformation and texture development in halite polycrystals. comparison of different modelling approaches with experimental data Techtonophysics. 370:2003;287-311.
25. Lebensohn, R.A., Liu, Y., Ponte Castañeda, P., 2003b. Macroscopic properties and field fluctuations in model power-law polycrystals: full-field solutions versus self-consistent estimates. Proc. R. Soc. London A, in press.
26. Lequeu Ph., Gilormini P., Montheillet F., Bacroix B., Jonas J.J. Yield surfaces for textured polycrystal - I. Crystallographic approach. Acta Metall. 35:1987;439-451.
27. Leroy Y., Ponte Castañeda P. Bounds on the self-consistent approximation for nonlinear media and implications for the second-order method. C.R. Acad. Sci. Paris IIb. 329:2001;571-577.
28. Liu, Y., 2003. Macroscopic behavior, field fluctuations and texture evolution in viscoplastic polycrystals. Ph.D. Dissertation, University of Pennsylvania, USA.
29. Liu, Y., Ponte Castañeda, P., 2003. Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals. J. Mech. Phys. Solids, in press.
30. Masson R., Bornert M., Suquet P., Zaoui A. An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals. J. Mech. Phys. Solids. 48:2000;1203-1227.
31. Michel J., Moulinec H., Suquet P. A computational method based on augmented Lagrangians and Fast Fourier Transforms for composites with high contrast. Comput. Modelling Eng. Sci. 1:2000;79-88.
32. Molinari A., Canova G.R., Ahzi S. A self-consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall. Mater. 35:1987;2983-2994.
33. Moulinec H., Suquet P. A fast numerical method for computing the linear and nonlinear properties of composites. C. R. Acad. Sci. Paris II. 318:1994;1417-1423.
34. Nebozhyn, M.V., 2000. Variational self-consistent estimates for the effective behavior of viscoplastic polycrystals. Ph.D. Dissertation, University of Pennsylvania, USA.
35. Nebozhyn M.V., Gilormini P., Ponte Castañeda P. Variational self-consistent estimates for viscoplastic polycrystals with highly anisotropic grains. C.R. Acad. Sci. Paris IIb. 328:2000;11-17.
36. Nebozhyn M.V., Gilormini P., Ponte Castañeda P. Variational self-consistent estimates for cubic viscoplastic polycrystals. the effect of grain anisotropy and shape J. Mech. Phys. Solids. 49:2001;313-340.
37. Parton V.Z., Buryachenko V.A. Stress fluctuations in elastic composites. Sov. Phys. Dokl. 35(2):1990;191-193.
38. Ponte Castañeda P. The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids. 39:1991;45-71.
39. Ponte Castañeda P. Exact second-order estimates for the effective mechanical properties of nonlinear composite materials. J. Mech. Phys. Solids. 44:1996;827-862.
40. Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I - Theory. J. Mech. Phys. Solids. 50:2002;737-757.
41. Ponte Castañeda P., Nebozhyn M. Variational estimates of the self-consistent type for some model nonlinear polycrystals. Proc. R. Soc. London A. 453:1997;2715-2724.
42. Ponte Castañeda P., Suquet P. Nonlinear composites. Adv. Appl. Mech. 34:1998;171-302.
43. Reuss A. Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. Z. Angew. Math. Mech. 9:1929;49-58.
44. Santhanam A.T., Reed-Hill R.E. The influence of strain rate dependent work hardening on the necking strain in. α -titanium at elevated temperatures Metall. Trans. 2A:1971;2619-2622.
45. Suquet P. Overall properties of nonlinear composites. a modified secant moduli theory and its link with Ponte Castañeda's nonlinear variational procedure C.R. Acad. Sci. Paris II. 320:1995;563-571.
46. Suquet P., Ponte Castañeda P. Small-contrast perturbation expansions for the effective properties of nonlinear composites. C.R. Acad. Sci. Paris II. 317:1993;1515-1522.
47. Taylor G.I. Plastic strains in metals. J. Inst. Metals. 62:1938;307-324.
48. Van Houtte P., Aernoudt E. Consideration on the crystal and the strain symmetry in the calculation of deformation textures with the Taylor theory. Mater. Sci. Eng. 23:1976;11-22.
49. Willis J.R. Bounds and self-consistent estimates for the overall moduli of anisotropic composites. J. Mech. Phys. Solids. 25:1977;185-202.
50. Willis J.R. Variational and related methods for the overall properties of composites. Adv. Appl. Mech. 21:1981;1-78.
51. Willis J.R. Upper and lower bounds for nonlinear composite behavior. Mater. Sci. Eng. A. 175:1994;7-14.