Coupled effects of grain size distributions and crystallographic textures on the plastic behaviour of if steels

International Journal of Plasticity

Volumn 27, Issue 2, 2011, Pages 232-249

  Nicaise, Nicolas ^a   Berbenni, Stéphane ^a   Wagner, Francis ^a   Berveiller, Marcel ^a   Lemoine, Xavier ^a,b  

^a UNIVERSITÉ PAUL VERLAINE METZ   (France)

^b ARCELORMITTAL   (France)

Author keywords

A. Microstructures; A. Strengthening mechanisms; B. Elastic viscoplastic material; B. Metallic material; C. Self consistent scheme

Indexed keywords

A. MICROSTRUCTURES; ELASTIC-VISCOPLASTIC MATERIAL; METALLIC MATERIAL; SELF-CONSISTENT SCHEME; STRENGTHENING MECHANISMS;

ANISOTROPY; CRYSTALLOGRAPHY; ELASTICITY; PLASTICS; SINGLE CRYSTALS; SIZE DETERMINATION; SIZE DISTRIBUTION; STEEL METALLURGY; STRENGTHENING (METAL); STRESS ANALYSIS; STRUCTURAL DESIGN; TENSILE TESTING; TEXTURES; VISCOPLASTICITY;

GRAIN SIZE AND SHAPE;

EID: 78449284370     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2010.05.001     Document Type: Article

References (73)

1. R.W. Armstrong, I. Codd, Douthwaite, and N.J. Petch The plastic deformation of polycrystalline aggregates Philos. Mag. 7 1962 45 58
2. R.J. Asaro, and A. Needleman Texture development and strain hardening in rate dependent polycrystals Acta Metall. 33 6 1985 923 953
3. D.S. Balint, V.S. Deshpande, A. Needleman, and E.V. der Giessen Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals Int. J. Plast. 24 12 2008 2149 2172
4. S. Berbenni, V. Favier, X. Lemoine, and M. Berveiller Micromechanical modeling of the elastic-viscoplastic behaviour of steels having different microstructures Mater. Sci. Eng. A372 2004 128 136
5. S. Berbenni, V. Favier, and M. Berveiller Impact of the grain size distribution on the behaviour of heterogeneous materials Int. J. Plast. 23 2007 114 142
6. S. Berbenni, V. Favier, and M. Berveiller Micro-macro modelling of the effects of the grain size distribution on the plastic flow stress of heterogeneous materials Comput. Mater. Sci. 39 2007 96 105
7. S. Berbenni, M. Berveiller, and T. Richeton Intra-granular plastic slip heterogeneities: discrete vs. mean field approaches Int. J. Solids Struct. 45 2008 4147 4172
8. M. Berveiller, and A. Zaoui An extension of the self-consistent scheme to plastically-flowing polycrystals J. Mech. Phys. Solids 26 1979 325 344
9. S.B. Biner, and J.R. Morris The effects of grain size and dislocation source density on the strengthening behaviour of polycrystals: a two-dimensional discrete dislocation simulation Philos. Mag. A83 2003 3677 3690
10. S. Bouvier, J. Alves, M. Oliveira, and L. Menezes Modelling of anisotropic work-hardening behaviour of metallic materials subjected to strain-path changes Comput. Mater. Sci. 32 2005 301 315
11. R. Brenner, R. Masson, O. Castelnau, and A. Zaoui A "quasi- elastic" affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites Eur. J. Mech. A/Solids 21 6 2002 943 960
12. H.J. Bunge Texture Analysis in Materials Science 1982 Academic-Verlag
13. H.J. Bunge, F. Wagner, P.I. Welch, and P. Van Houtte A new way to include the grain shape in texture simulations with the Taylor model J. Phys. Lett. 46 1985 L1109 L1113
14. L. Delannay, P.J. Jacques, and S.R. Kalidindi Finite element modeling of crystal plasticity with grains shaped as truncated octahedrons Int. J. Plast. 22 10 2006 1879 1898
15. L. Delannay, M.A. Melchior, J.W. Signorelli, J.-F. Remacle, and T. Kuwabara Influence of grain shape on the planar anisotropy of rolled steel sheets - evaluation of three models Comput. Mater. Sci. 45 2009 739 743
16. J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion and related problems Proc. R. Soc. London A241 1957 376 396
17. J.D. Eshelby, F.C. Frank, and F.R.N. Nabarro The equilibrium of linear arrays of dislocations Philos. Mag. 42 1951 351 364
18. P. Franciosi Glide mechanisms in b.c.c. crystals: an investigation of the case of α-iron through multislip and latent hardening tests Acta Metall. 31 9 1983 1331 1342
19. P. Franciosi The concepts of latent hardening and strain hardening in metallic single crystals Acta Metall. 33 9 1985 1601 1612
20. G. Franz, F. Abed-meraim, J.P. Lorrain, T. Ben Zineb, X. Lemoine, and M. Berveiller Ellipticity loss analysis for tangent moduli deduced from a large strain elastic-plastic self-consistent model Int. J. Plast. 25 2 2009 205 238
21. B.S. Fromm, B.L. Adams, S. Ahmadi, and M. Knezevic Grain size and orientation distributions: application to the yielding of α-titanium Acta Mater. 57 2009 2339 2348
22. B. Haddag, T. Balan, and F. Abed-Meraim Investigation of advanced strain-path dependent material models for sheet metal forming simulations Int. J. Plast. 23 6 2007 951 979
23. E.O. Hall The deformation and ageing of mild steel Proc. Phys. Soc. London B64 1951 747 753
24. S.V. Harren The finite deformation of rate-dependent polycrystals-I: A self-consistent framework-I: A self-consistent framework, II: A comparison of the self-consistent and Taylor methods J. Mech. Phys. Solids 39 3 1991 345 383
25. A.V. Hershey The elasticity of an isotropic aggregate of anisotropic cubic crystals J. Appl. Mech. 21 1954 236 240
26. R. Hill Continuum micromechanics of elastoplastic polycrystals J. Mech. Phys. Solids 13 1965 89 101
27. F.J. Humphreys, and M. Hatherly Grain Growth Following Recrystallization (Chapter 9) 1st ed. Recrystallization and Related Annealing Phenomena 1995 Elsevier Science Oxford, UK pp. 281-325
28. J.W. Hutchinson Bounds and self-consistent estimates for creep of polycrystalline materials Proc. R. Soc. London A348 1976 101 127
29. Jaoul, B., 1965. Etude de la plasticité et application aux métaux, Dunod.
30. W.C. Jeong Strength and formability of ultra-low-carbon Ti-IF steels Metall. Mater. Trans. A 31 4 2000 1305 1307
31. B. Jiang, and G.J. Weng A generalized self-consistent polycrystal model for the yield strength of nanocrystalline materials J. Mech. Phys. Solids 52 2004 1125 1149
32. Kanjarla, A.K., Van Houtte, P., Delannay, L., in press. Assessment of plastic heterogeneity in grain interaction models using crystal plasticity finite element method. Int. J. Plast. doi:10.1016/j.ijplas.2009.05.005.
33. U.F. Kocks, C.N. Tomé, and H.-R. Wenk Texture and Anisotropy: Preferred Orientations in Polycrystals and their Effect on Materials Properties 1998 Cambridge University Press
34. W. Kreher Residual stresses and stored elastic energy of composites and polycrystals J. Mech. Phys. Solids 38 1990 115 128
35. E. Kröner Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einskristalls Z. Phys. 151 1958 504 518
36. E. Kröner Modified Green Functions in the theory of heterogeneous and/or anisotropic linearly elastic media G.J. Weng, M. Taya, M. Abe, Micromechanics and Inhomogeneity 1989 Springer Berlin 197 211
37. I.A. Kunin An algebra of tensor operators and its applications to elasticity Int. J. Eng. Sci. 19 1981 1551 1561
38. I.A. Kunin Elastic Media with Microstructure II: Three Dimensional Models Springer Series in Solid-State Sciences vol. 44 1983 Springer Verlag Berlin, Heidelberg, New-York, Tokyo
39. K.J. Kurzydlowski A model for the flow stress dependence on the distribution of grain size in polycrystals Scripta Metall. Mater. 24 1990 879 884
40. W.F. Lankford, S.C. Snider, and J.A. Bausch New criteria for predicting the press performance of deep drawing steels Trans. Am. Soc. Metals 42 1950 1197 1232
41. R.A. Lebensohn, and C.N. Tomé 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
42. S. Lefebvre, B. Devincre, and T. Hoc Yield stress strengthening in ultrafine-grained metals: a two-dimensional simulation of dislocation dynamics J. Mech. Phys. Solids 55 4 2007 788 802
43. J.C.M. Li, and G.C.T. Liu Circular dislocation pile-ups: I. Strength of ultra-fine polycrystalline aggregates Philos. Mag. 15 1967 1059 1063
44. J. Li, and G.J. Weng A secant-viscosity approach to the time-dependent creep of an elastic-viscoplastic composite J. Mech. Phys. Solids 45 1997 1069 1083
45. B.L. Li, W.Q. Cao, Q. Liu, and W. Liu Flow stress and microstructure of the cold-worked IF steel Mater. Sci. Eng. A356 2003 37 42
46. P. Lipinski, and M. Berveiller Elastoplasticity of micro-inhomogeneous metals at large strains Int. J. Plast. 5 1989 149 172
47. P. Lipinski, M. Berveiller, E. Reubrez, and J. Morreale Transition theories of elastic-plastic deformation of metallic polycrystals Arch. Appl. Mech. 65 1995 291 311
48. R. Masson, and A. Zaoui Self-consistent estimates for the rate-dependent elastoplastic behaviour of polycrystalline materials J. Mech. Phys. Solids 47 1999 1543 1568
49. H. Mecking, and U.F. Kocks Kinetics of flow and strain-hardening Acta Metall. 29 1981 1865 1875
50. S. Mercier, and A. Molinari Homogenization of elastic-viscoplastic heterogeneous materials: self-consistent and mori-tanaka schemes Int. J. Plast. 25 2009 1024 1048
51. A. Molinari Averaging models for heterogeneous viscoplastic and elastic-viscoplastic materials J. Eng. Mater. Technol. 124 2002 62 70
52. A. Molinari, G.R. Canova, and S. Ahzi A self-consistent approach of the large deformation polycrystal viscoplasticity Acta Metall. 35 1987 2983 2994
53. S. Nemat-Nasser, and M. Obata Rate dependent, finite elasto-plastic deformation of polycrystals Proc. R. Soc. London A 407 1986 343 375
54. A. Paquin, S. Berbenni, V. Favier, X. Lemoine, and M. Berveiller Micromechanical modeling of the elastic-viscoplastic behaviour of polycrystalline steels Int. J. Plast. 17 2001 1267 1302
55. B. Peeters, M. Seefeldt, C. Teodosiu, S.R. Kalidindi, P. Van Houtte, and E. Aernoudt Work-hardening/softening behaviour of b.c.c. polycrystals during changing strain paths: I. An integrated model based on substructure and texture evolution, and its prediction of the stress-strain behaviour of an IF steel during two-stage strain paths Acta Mater. 49 9 2001 1607 1619
56. A. Perlade, O. Bouaziz, and Q. Furnémont A physically based model for TRIP-aided carbon steels behaviour Mater. Sci. Eng. A356 2003 145 152
57. N.J. Petch The cleavage strength of polycrystals J. Iron Steel Inst. 174 1953 25 28
58. O. Pierard, and I. Doghri An enhanced affine formulation and the corresponding numerical algorithms for the mean field homogenization of elastoviscoplastic composites Int. J. Plast. 22 2006 131 157
59. M. Rabahallah, T. Balan, S. Bouvier, B. Bacroix, F. Barlat, K. Chung, and C. Teodosiu Parameter identification of advanced plastic strain rate potentials and impact on plastic anisotropy prediction Int. J. Plast. 2 3 2009 491 512
60. B. Raeisinia, and C.W. Sinclair A representative grain size for the mechanical response of polycrystals Mater. Sci. Eng. A 525 2009 78 82
61. B. Raeisinia, C.W. Sinclair, W.J. Poole, and C.N. Tomé On the impact of grain size distribution on the plastic behaviour of polycrystalline metals Modell. Simul. Mater. Sci. Eng. 16 025001 2008 1 15
62. S. Ramtani, H.Q. Bui, and G. Dirras A revisited generalized self-consistent polycrystal model following an incremental small strain formulation and including grain-size distribution effect Int. J. Eng. Sci. 47 4 2009 537 553
63. F.N. Rhines, and B.P. Patterson Effect of the degree of prior cold work on the grain volume distribution and the rate of grain growth of recrystallized aluminium Metall. Trans. 13A 1982 985 993
64. T. Richeton, S. Berbenni, and M. Berveiller Grain-size dependent accommodation due to intragranular distributions of dislocation loops Acta Mater. 57 2009 1347 1356
65. H. Sabar, M. Berveiller, V. Favier, and S. Berbenni A new class of micro-macro models for elastic-viscoplastic heterogeneous materials Int. J. Solids Struct. 39 2002 3257 3276
66. L. Tabourot, M. Fivel, and E. Rauch Generalized constitutive laws for f.c.c. single crystal Mater. Sci. Eng. A 234-236 1997 639 642
67. G.I. Taylor Plastic Strain in metals J. Inst. Metals 61 1938 307 324
68. S. Tiem, M. Berveiller, and G.R. Canova Grain shape effects on the slip system activity and on the lattice rotations Acta Metall. 34 1986 2139 2149
69. P. Van Houtte, S. Li, M. Seefeldt, and L. Delannay Deformation texture prediction: from the Taylor model to the advanced Lamel model Int. J. Plast. 21 2005 589 624
70. Wagner, F., Bunge, H.J., Welch, P.I., Van Houtte, P., 1987. Grain shape effect in Taylor simulations. In: Theoretical Methods of Texture Analysis, DGM, pp. 251-258.
71. J. Wang, V. Levkovitch, F. Reusch, B. Svendsen, J. Huétink, and M. van Riel On the modeling of hardening in metals during non-proportional loading Int. J. Plast. 24 6 2008 1039 1070
72. G.J. Weng Constitutive equations of single crystals and polycrystalline aggregates under cyclic loading Int. J. Eng. Sci. 18 1980 1385 1397
73. G.J. Weng A micromechanical theory of grain size dependence in metal plasticity J. Mech. Phys. Solids 31 1983 193 203