Probabilistic modeling of microstructure evolution using finite element representation of statistical correlation functions

International Journal of Plasticity

Volumn 30-31, Issue , 2012, Pages 62-80

  Sundararaghavan, V ^a   Kumar, A ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

A. Microstructures; B. Crystal plasticity; C. Numerical algorithms; C. Probability and Statistics; Microstructural descriptors

Indexed keywords

B. CRYSTAL PLASTICITY; C. PROBABILITY AND STATISTICS; DEFORMATION ANALYSIS; FINITE ELEMENT MESHES; FINITE-ELEMENT REPRESENTATION; MICROSTRUCTURAL DESCRIPTORS; MICROSTRUCTURE EVOLUTIONS; NUMERICAL ALGORITHMS; ORIENTATION CORRELATION FUNCTIONS; POLYCRYSTALLINE MICROSTRUCTURE; PROBABILISTIC FINITE ELEMENTS; PROBABILISTIC MODELING; PROBABILITY DENSITIES; STATISTICAL CORRELATION FUNCTION; STRAIN FIELDS; TOTAL LAGRANGIAN;

ALGORITHMS; CRYSTAL ORIENTATION; DEFORMATION; LAGRANGE MULTIPLIERS; MICROSTRUCTURE; PROBABILITY; STRAIN;

PROBABILITY DENSITY FUNCTION;

EID: 84857044088     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2011.09.001     Document Type: Article

References (34)

1. H. Abdolvand, M.R. Daymond, and C. Mareau Incorporation of twinning into a crystal plasticity finite element model: evolution of lattice strains and texture in Zircaloy-2 Int. J. Plasticity. 27 11 2011 1721 1738
2. B.L. Adams, G.R. Canova, and A. Molinari A statistical formulation of viscoplastic behavior in heterogeneous polycrystals Textures Microstruct. 11 1989 57 71
3. B.L. Adams, J.P. Boehler, M. Guidi, and E.T. Onat Group theory and representation of microstructure and mechanical behavior of polycrystals J. Mech. Phys. Solids 40 1992 723 737
4. B.L. Adams, X. Gao, and S.R. Kalidindi Finite approximations to the second-order properties closure in single phase polycrystals Acta Mater. 53 13 2005 3563 3577 (Pubitemid 40833840)
5. J. Allison, D. Backman, and L. Christodoulou Integrated computational materials engineering: a new paradigm for the global materials profession journal of the minerals Metals Mater. Soc. 58 11 2006 25 27 (Pubitemid 44803469)
6. R.J. Asaro, and A. Needleman Texture development and strain hardening in rate dependent polycrystals Acta Metall. 33 1985 923 953 (Pubitemid 15565280)
7. A.J. Beaudoin, H. Mecking, and U.F. Kocks Development of localized orientation gradients in fcc polycrystals Philos. Mag. A 73 1996 1503 1518 (Pubitemid 126086452)
8. R. Becker, and S. Panchanadeeswaran Effects of grain interactions on deformation and local texture in polycrystals Acta Metall. Mater. 43 1995 2701 2719
9. M.J. Beran Statistical Continuum Theories 1968 Interscience Publishers New York
10. M.J. Beran, T.A. Mason, B.L. Adams, and T. Olson Bounding elastic constants of an orthotropic polycrystal from measurements of the microstructure J. Mech. Phys. Solids 44 1996 1543 1563 (Pubitemid 126370890)
11. C.A. Bronkhorst, S.R. Kalidindi, and L. Anand Polycrystalline plasticity and the evolution of crystallographic texture in fcc metals Philos. Trans. R. Soc. Lond. A 341 1992 443 477
12. H.J. Bunge Texture Analysis in Materials Science 1982 Butterworth London
13. A. Clement Prediction of deformation texture using a physical principle of conservation Mater. Sci. Eng. 55 1982 203 210
14. P.B. Corson Correlation functions for predicting properties of heterogeneous materials. II. Empirical construction of spatial correlation functions for two phase solids J. Appl. Phys. 45 1976 3165 3170
15. H. Garmestani, S. Lin, B.L. Adams, and S. Ahzi Statistical continuum theory for large plastic deformation of polycrystalline materials J. Mech. Phys. Solids 49 3 2001 589 607 (Pubitemid 32875516)
16. S.V. Harren, and R.J. Asaro Nonuniform deformations in polycrystals and aspects of the validity of the Taylor model J. Mech. Phys. Solids 37 1989 191 232
17. S.R. Kalidindi, and H.K. Duvvuru Spectral methods for capturing crystallographic texture evolution during large plastic strains in metals Acta Mater. 53 13 2005 3613 3623 (Pubitemid 40822923)
18. U.F. Kocks, C.N. Tomé, and H.R. Wenk Texture and Anisotropy-preferred Orientations in Polycrystals and their Effect on Materials Properties 2000 Cambridge University Press Cambridge
19. E. Kroner Modelling Small Deformation of Polycrystals J. Gittus, J. Zarka, 1987 Elsevier/Applied Science New York 229
20. A. Kumar, and P.R. Dawson The simulation of texture evolution using finite elements over orientation space. I. Development Comput. Methods Appl. Mech. Eng. 130 1996 227 246 (Pubitemid 126382778)
21. A. Kumar, and P.R. Dawson The simulation of texture evolution using finite elements over orientation space. II. Application to planar crystals Comput. Methods Appl. Mech. Eng. 130 1996 247 261 (Pubitemid 126382779)
22. R.A. Lebensohn N-site modeling of a 3d viscoplastic polycrystal using fast fourier transform Acta Mater. 49 2001 2723 2737 (Pubitemid 32672837)
23. S.-B. Lee, R.A. Lebensohn, and A.D. Rollett Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transforms Int. J. Plasticity 27 5 2011 707 727
24. D.L. McDowell A perspective on trends in multiscale plasticity Int. J. Plasticity 26 9 2010 1280 1309
25. A. Mikdam, A. Makradi, S. Ahzi, H. Garmestani, D.S. Li, and Y. Remond A new approximation for the three-point probability function Int. J. Solids Struct. 46 21 2009 3782 3787
26. A. Molinari, G.R. Canova, and S. Ahzi A self consistent approach of the large deformation polycrystal viscoplasticity Acta Metall. 35 1987 2983 2994 (Pubitemid 18547483)
27. M.A.S. Qidwai, A.C. Lewis, and A.B. Geltmacher Using image-based computational modeling to study microstructure-yield correlations in metals Acta Mater. 57 14 2009 4233 4247
28. G.B. Sarma, B. Radhakrishnan, and P.R. Dawson Mesoscale modeling of microstructure and texture evolution during deformation processing of metals Adv. Eng. Mater. 4 2002 509 514
29. V. Sundararaghavan, and N. Zabaras Design of microstructure-sensitive properties in elasto-viscoplastic polycrystals using multi-scale homogenization Int. J. Plasticity 22 2006 1799 1824 (Pubitemid 43831511)
30. V. Sundararaghavan, and N. Zabaras Linear analysis of texture-property relationships using process-based representations of Rodrigues space Acta Mater. 55 5 2007 1573 1587 (Pubitemid 46241928)
31. V. Sundararaghavan, and N. Zabaras A multi-length scale continuum sensitivity analysis for the control of texture-dependent properties in deformation processing Int. J. Plasticity 24 2008 1581 1605
32. G.I. Taylor Plastic strain in metals J. Inst. Metals 62 1938 307 325
33. S. Torquato Random Heterogeneous Materials: Microstructure and Macroscopic Properties 2002 Springer-Verlag New York
34. G.S. Was, V. Thaveeprungsriporn, and D.C. Crawford Grain boundary misorientation effects on creep and cracking in Ni-based alloys J. Metals 50 1998 44 49