Elastic anisotropy and yield surface estimates of polycrystals

International Journal of Solids and Structures

Volumn 46, Issue 16, 2009, Pages 3018-3026

  Brenner, R ^a   Lebensohn, R A ^b   Castelnau, O ^a  

^a UNIVERSITÉ PARIS 13   (France)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Elastic anisotropy; Fast Fourier Transform; Polycrystals; Self consistent model; Yield surface

Indexed keywords

ANISOTROPIC ELASTIC; CONSTITUTIVE BEHAVIOUR; CRITICAL RESOLVED SHEAR STRESS; CRYSTALLINE ORIENTATIONS; CRYSTALLOGRAPHIC TEXTURES; ELASTIC ANISOTROPY; FULL-FIELD; INTRAGRANULAR STRESS; LOCAL FIELDS; NEW CONCEPT; PLASTIC YIELDING; QUANTITATIVE RESULT; SELF-CONSISTENT MODEL; SELF-CONSISTENT SCHEME; SLIP SYSTEM; STANDARD DEVIATION; STATISTICAL DESCRIPTIONS; STRESS FIELD; YIELD CRITERIA; YIELD SURFACE;

ANISOTROPY; CRYSTALLOGRAPHY; FAST FOURIER TRANSFORMS; POLYCRYSTALS; PROBABILITY DENSITY FUNCTION; SHEAR STRESS; SINGLE CRYSTALS; STAINLESS STEEL; STRENGTH OF MATERIALS;

YIELD STRESS;

EID: 65649110900     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2009.04.001     Document Type: Article

References (52)

1. Bergman D.J. The dielectric constant of a composite material - a problem in classical physics. Phys. Rep. 43 (1978) 377-407
2. Bobeth M., and Diener G. Static and thermoelastic field fluctuations in multiphase composites. J. Mech. Phys. Solids 35 (1987) 137-149
3. Brenner R., Castelnau O., and Badea L. Mechanical field fluctuations in polycrystals estimated by homogenization techniques. Proc. R. Soc. Lond. A460 (2004) 3589-3612
4. Budiansky, B., Hashin, Z., Sanders, J.L., 1960. The stress field of a slipped crystal and the early plastic behavior of polycrystalline materials. In: Plasticity, Proc. 2nd Symp. Naval Struct. Mech. Pergamon, Oxford, p. 239.
5. Castelnau O., Blackman D.K., Lebensohn R.A., and Ponte Castañeda P. Micromechanical modeling of the viscoplastic behavior of olivine. J. Geophys. Res. 113 (2008) B09202
6. Castelnau O., Brenner R., and Lebensohn R.A. The effect of strain heterogeneity on the work hardening of polycrystals predicted by mean-field approaches. Acta Mater. 54 (2006) 2745-2756
7. Castelnau O., Goudeau P., Geandier G., Tamura N., Béchade J., Bornert M., and Caldemaison D. White beam microdiffraction experiments for the determination of the local plastic behaviour of polycrystals. Mater. Sci. Forum (2006) 103-108
8. Clausen B., Lorentzen T., and Leffers T. Self-consistent modelling of the plastic deformation of fcc polycrystals and its implications for diffraction measurements of internal stresses. Acta Mater. 46 (1998) 3087-3098
9. Eshelby J.D. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A241 (1957) 376-396
10. Eyre D.J., and Milton G.W. A fast numerical scheme for computing the response of composites using grid refinement. J. Phy. III 6 (1999) 41-47
11. Frigo M., and Johnson S.G. The design and implementation of FFTW3. Proceedings of the IEEE 93 2 (2005) 216-231 special issue on Program Generation, Optimization, and Platform Adaptation
12. Geandier, G., Gélébart, L., Castelnau, O., Bourhis, E.L., Renault, P.-O., Goudeau, P., Thiaudière, D., 2008. Micromechanical modeling of the elastic behavior of multilayer thin films; comparison with in situ data from X-ray diffraction. In: IUTAM Book Series. Springer.
13. Hashimoto K., and Margolin H. The role of elastic interaction stresses on the onset of slip in polycrystalline alpha brass - I. Experimental determination of operating slip systems and qualitative analysis. Acta Metall. 31 (1983) 773-785
14. Hashimoto K., and Margolin H. The role of elastic interaction stresses on the onset of slip in polycrystalline alpha brass - II. Rationalization of slip behavior. Acta Metall. 31 (1983) 786-800
15. Hershey A.V. The elasticity of an isotropic aggregate of anisotropic cubic crystals. J. Appl. Mech. 21 (1954) 236-240
16. Hill R. The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. A65 (1952) 349-354
17. Hill R. Elastic properties of reinforced solids : some theoretical principles. J. Mech. Phys. Solids 11 (1963) 357-372
18. Hill R. The essential structure of constitutive laws for metal composites and polycrystals. J. Mech. Phys. Solids 15 (1967) 79-95
19. Hook R.E., and Hirth J. The deformation behavior of isoaxial bicrystals of fe-3%Si. Acta Metall. 15 (1967) 535-551
20. Houdaigui, F.E., Forest, S., Gourgues, A.-F., Jeulin, D., 2007. On the size of the representative volume element for isotropic elastic polycrystalline copper. In: Bai, Y. (Ed.), IUTAM Symposium on Mechanical Behavior and Micro-mechanics of Nanostructured Materials. pp. 171-180.
21. Hutchinson J.W. Elastic-plastic behaviour of polycrystalline metals and composites. Proc. R. Soc. Lond. A319 (1970) 247-272
22. Kreher W. Residual stresses and stored elastic energy of composites and polycrystals. J. Mech. Phys. Solids 38 (1990) 115-128
23. Kröner E. Berechnung der elastischen konstanten des vielkristalls aus den konstanten des einkristalls. Z. Physik 151 (1958) 504-518
24. Kröner E. Zur plastischen verformung des vielkristalls. Acta Metall. Mater. 9 (1961) 155-191
25. Kröner E. Bounds for effective elastic moduli of disordered materials. J. Mech. Phys. Solids 25 (1977) 137-156
26. Kröner E. Self-consistent scheme and graded disorder in polycrystal elasticity. J. Phys. F: Metal Phys. 8 (1978) 2261-2267
27. Kumar S., and Kurtz S.K. Simulation of material microstructure using a 3d voronoi tesselation: calculation of effective thermal expansion coefficient of polycrystalline materials. Acta Metall. Mater. 42 (1994) 3917-3927
28. Kumar S., Kurtz S.K., and Agarwala V.K. Micro-stress distribution within polycrystalline aggregate. Acta Mech. 114 (1996) 203-216
29. Lebensohn R.A. N-site modeling of a 3D viscoplastic polycrystal using fast fourier transform. Acta Mater. 49 (2001) 2723-2737
30. Lebensohn R.A., Liu Y., and Ponte Castañeda P. On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations. Acta Mater. 52 (2004) 5347-5361
31. Margolin H., Wang Z., and Chen T.-K. A model for yielding in anisotropic metals. Metall. Trans. A 17A (1986) 107-114
32. Mehrabadi M.M., and Cowin S.C. Eigentensors of linear anisotropic elastic materials. Quart. J. Mech. Appl. Math. 43 (1990) 15-41
33. Mendelson K.S. Bulk modulus of a polycrystal. J. Phys. D: Appl. Phys. 14 (1981) 1307-1309
34. Meyers M.A., and Ashworth E. A model for the effect of grain size on the yield stress of metals. Philosophical Magazine A 46 (1982) 737-759
35. Michel J.C., Moulinec H., and Suquet P. A computational scheme for linear and non-linear composites with arbitrary phase contrast. Int. J. Numer. Meth. Engng. 52 (2001) 139-160
36. Moulinec H., and Suquet P. A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Methods Appl. Mech. Engrg. 157 (1998) 69-94
37. Moulinec H., and Suquet P. Intraphase strain heterogeneity in nonlinear composites: a computational approach. Eur. J. Mech. A/Solids 22 (2003) 751-770
38. Nygards M. Number of grains necessary to homogenize elastic materials with cubic symmetry. Mech. Mater. 35 (2003) 1049-1057
39. Nygards M., and Gudmundson P. Three-dimensional periodic voronoi grain models and micromechanical fe-simulations of a two-phase steel. Comput. Mater. Sci. 24 (2002) 513-519
40. Pang J., Holden T., Turner P., and Mason T. Intergranular stresses in zircaloy-2 with rod texture. Acta Mater. 47 2 (1999) 373-383
41. Ponte Castañeda P., and Suquet P. Nonlinear composites. Adv. Appl. Mech. 34 (1998) 171-302
42. Sab K. On the homogenization and the simulation of random materials. Eur. J. Mech. A/Solids 11 (1992) 585-607
43. Sauzay M. Cubic elasticity and stress distribution at the free surface of polycrystals. Acta Mater. 55 (2007) 1193-1202
44. Tamura N., MacDowell A., Spolenak R., Valek B., Bravman J., Brown W., Celestre R., Padmore H., Batterman B., and Patel J. Scanning X-ray microdiffraction with submicrometer white beam for strain/stress and orientation mapping in thin films. J. Synch. Rad. 10 (2003) 137-143
45. Turner P.A., Christodoulou N., and Tomé C.N. Modeling the mechanical response of rolled zircaloy-2. Int. J. Plasticity 11 (1995) 251-265
46. Ungár T., Castelnau O., Ribárik G., Drakopoulos M., Béchade J., Chauveau T., Snigirev A., Snigireva I., Schroer C., and Bacroix B. Grain to grain slip activity in plastically deformed zr determined by X-ray micro-diffraction line profile analysis. Acta Mater. 55 (2007) 1117-1127
47. Wikström A., and Nygards M. Anisotropy and texture in thin copper films : an elastoplastic analysis. Acta Mater. 50 (2002) 857-870
48. Willis J.R. Bounds and self-consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Solids 25 (1977) 185-202
49. Yaguchi M., and Busso E.P. On the accuracy of self-consistent elasticity formulations for directionally solidified polycrystal aggregates. Int. J. Solids Struct. 42 (2005) 1073-1089
50. Zeghadi A., N'Guyen F., Forest S., Gourgues A.-F., and Bouaziz O. Ensemble averaging stress-strain fields in polycrystalline aggregates with a constrained surface microstructure - part 1: anisotropic elastic behaviour. Phil. Mag. A 87 (2007) 1401-1424
51. Zeller R., and Dederichs P.H. Elastic constants of polycrystals. Phys. Status Solidi (b) 55 (1973) 831-842
52. Zener C. Elasticity and Anelasticity of Metals (1948), University Chicago Press