Dislocation density tensor characterization of deformation using 3D X-ray microscopy

Journal of Engineering Materials and Technology

Volumn 130, Issue 2, 2008, Pages 0210241-02102410

  Larson, B C ^a   Tischler, J Z ^a   El Azab, Anter ^b,d   Liu, Wenjun ^c  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

^b FAMU FSU COLLEGE OF ENGINEERING   (United States)

^c ARGONNE NATIONAL LABORATORY   (United States)

^d FLORIDA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; GEOMETRY; SILICON; TENSORS; UNCERTAINTY ANALYSIS; X RAY MICROSCOPES;

BRITTLE TO DUCTILE TRANSITION TEMPERATURE; DEFORMATION MICROSTRUCTURE; DISLOCATION DENSITY TENSORS; GEOMETRICALLY NECESSARY DISLOCATIONS; MESOSCOPIC LENGTH SCALE; MULTI-SCALE MODELING; SUB-MICRON RESOLUTIONS; THREEDIMENSIONAL (3-D);

X RAYS;

EID: 47149086773     PISSN: 00944289     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2884336     Document Type: Conference Paper

References (46)

1. Hirth, J. P., and Lothe, J., 1982, Theory of Dislocations, Wiley, New York.
2. Nabarro, F. R. N., 1987, Theory of Crystal Dislocations, Dover, New York.
3. Jourdan, C., and Gastaldi, J., 1977, "X-Ray Topographic Investigation of Dislocations in Ti Single Crystals Grown by Recrystallization," Phys. Status Solidi A, 43, pp. 425-435.
4. Larson, B. C., Yang, W., Ice, G. E., Budai, J. D., and Tischler, J. Z., 2002, "Three-Dimensional X-Ray Structural Microscopy With Sub-micrometre Resolution," Nature (London), 415, pp. 887-890.
5. Larson, B. C., El-Azab, A., Yang, W., Tischler, J. Z., Liu, W., and Ice, G. E., 2007, "Experimental Characterization of the Mesoscale Dislocation Density Tensor," Philos. Mag., 87, pp. 1327-1347.
6. Yang, W., Larson, B. C., Tischler, J. Z., Ice, G. E., Budai, J. D., and Liu, W., 2004, "Differential-Aperture X-Ray Structural Microscopy: A Submicron-Resolution Three-Dimensional Probe of Local Microstructure and Strain," Micron, 35, pp. 431-439.
7. Yang, W., Larson, B. C., Pharr, G. M., Ice, G. E., Budai, J. D., Tischler, J. Z., and Liu, W. J., 2004, "Deformation Microstructure Under Microindents in Single-Crystal Cu Using Three-Dimensional X-Ray Structural Microscopy," J. Mater. Res., 19, pp. 66-72.
8. Levine, L. E., Larson, B. C., Yang, W., Kassner, M. E., Tischler, J. Z., DelosReyes, M. A., Fields, R. J., and Liu, W., 2006, "X-Ray Microbeam Measurements of Individual Dislocation Cell Elastic Strains in Deformed Single-Crystal Copper," Nat. Mater, 5, pp. 619-622.
9. Larson, B. C., and Lengeler, B., 2004, "High Resolution Three-Dimensional X-Ray Microscopy," MRS Bull., 29, pp. 152-156.
10. Ice, G. E., and Larson, B. C., 2004, "Three-Dimensional X-Ray Structural Microscopy Using Polychromatic Microbeams," MRS Bull., 29, pp. 170-176.
11. Poulsen, H. F., Jensen, D. J., and Vaughan, G. B. M., 2004, "Three- Dimensional X-Ray Diffraction Microscopy Using High-Energy X-Rays," MRS Bull., 29, pp. 166-169.
12. Poulsen, H. F., 2004, Three-Dimensional X-Ray Diffraction Microscopy: Mapping Polycrystals and Their Dynamics (Springer, Berlin, 2004).
13. Yang, W., Larson, B. C., Ice, G. E., Tischler, J. Z., Budai, J. D., Chung, K.-S., and Lowe, W. P., 2003, "Spatially Resolved Poisson Strain and Anticlastic Curvature Measurements in Si Under Large Deflection Bending," Appl. Phys. Lett., 82, pp. 3856-3858.
14. Poulsen, H. F., Lienert, U., and Pantleon, W., 2005, " Characterisation of Orientation Distributions of Individual Grains Within Deformed Metals," Mat. Sci. Technol., 21, pp. 1397-1400.
15. Margulies, L., Winther, G., and Poulsen, H. F., 2001, "In Situ Measurement of Grain Rotation During Deformation of Polycrystals," Science, 292, pp. 2392-2394.
16. Ice, G. E., Larson, B. C., Yang, W., Budai, J. D., Tischler, J. Z., Pang, J. W. L., Barabash, R. I., and Liu, W., 2005, "Polychromatic X-Ray Microdiffraction Studies of Mesoscale Structure and Dynamics," J. Synchrotron Radiat., 12, pp. 155-162.
17. Nye, J. F., 1953, "Some Geometric Relations in Dislocated Crystals," Acta Metall., 1, pp. 153-162.
18. El-Azab, A., 2000, "The Boundary Problem of Dislocation Dynamics," Modell. Simul. Mater. Sci. Eng., 8, pp. 37-54.
19. El-Azab, A., 2000, "Statistical Mechanics Treatment of the Evolution of Dislocation Distributions in Single Crystals," Phys. Rev. B, 61, pp. 11956-11966.
20. Limkumnerd, S., and Sethna, J. P., 2006, "Mesoscale Theory of Grains and Cells: Crystal Plasticity," Phys. Rev. Lett., 96, p. 095503.
21. Limkumnerd, S., and Sethna, J. P., 2007, "Stress-Free States of Continuum Dislocation Fields: Rotations, Grain Boundaries, and the Nye Dislocation Density Tensor," Phys. Rev. B, 75, p. 224121.
22. Larson, B. C., Yang, W., Tischler, J. Z., Ice, G. E., Budai, J. D., Liu, W., and Weiland, H., 2004, "Micron-Resolution 3-D Measurement of Local Orientations Near a Grain-Boundary in Plane-Strained Aluminum Using X-Ray Microbeams," Int. J. Plast, 20, pp. 543-560.
23. Chung, J. S., and Ice, G. E., 1999, "Automated Indexing for Texture and Strain Measurement With Broad-Bandpass X-Ray Microbeams," J. Appl. Phys, 86, pp. 5249-5255.
24. Weygand, D., Friedman, L. H., Van der Giessen, E., and Needleman, A., 2002, "Aspects of Boundary-Value Problem Solutions With Three-dimensional Dislocation Dynamics," Modell. Simul. Mater. Sci. Eng., 10, pp. 437-468.
25. Weygand, D., and Gumbsch, P., 2005, "Study of Dislocation Reactions and Rearrangements Under Different Loading Conditions," Mater. Sci. Eng., A, 400-401, pp. 158-161.
26. El-Azab, A., Deng, J., and Tang, M., 2007, "Statistical Characterization of Dislocation Ensembles," Philos. Mag., 87, pp. 1201-1223.
27. El-Azab, A., 2006, "Statistical Mechanics of Dislocation Systems," Scr. Mater., 54, pp. 723-727.
28. Kosevich, A. M., 1979, "Crystal Dislocations and the Theory of Elasticity," Dislocations in Solids, F. R. N. Nabarro, ed., North-Holland, Amsterdam, Vol. 1, pp. 33-141.
29. Mura, T., 1968, "Continuum Theory of Dislocations and Plasticity," Mechanics of Generalized Continua, E. Kröner, ed., Springer-Verlag, New York, pp. 269-278.
30. Kröner, E., 1981, "Continuum Theory of Defects," Physics of Defects, R. Balian, M. Kléman, and J.-P. Poirier, eds., North-Holland, Amsterdam, pp. 217-315.
31. El-Azab, A., Zaiser, M., and Busso, E., 2007, "Density-Based Modelling of Dislocations," Philos. Mag., 87(8-9), pp. 1159-1160.
32. Eshelby, J. D., 1956, "The Continuum Theory of Lattice Defects," Solid State Phys, F. Seitz and D. Turnbull, eds., volume 3, pp. 79-144.
33. Mura, T., 1987, Micromechanics of Defects in Solids, 2nd ed., Martinus Nijhoff, Dordrecht, The Netherlands.
34. Kossecka, E., 1974, "Mathematical Theory of Defects. Part I. Statics," Arch. Mech., 26, pp. 995-1010.
35. Gurtin, M. E., 2002, "A Gradient Theory of Single-Crystal Viscoplasticity That Accounts for Geometrically Necessary Dislocations," J. Mech. Phys. Solids, 50, pp. 5-32.
36. Needlemann, A., and Sevillano, J. G., 2003, "Preface to the Viewpoint Set on: Geometrically Necessary Dislocations and Size Dependent Plasticity," Scr. Mater., 48, pp. 109-111.
37. Ungar, T., Mughrabi, H., Rönnpagel, D., and Wilkens, M., 1984, "X-Ray Line-Broadening Study of the Dislocation Cell Structure in Deformed (001)-Oriented Vopper Single Crystals," Acta Metall., 32, pp. 333-342.
38. Acharya, A., and Roy, A., 2006, "Size Effects and Idealized Dislocation Microstructure at Small Scales: Predictions of a Phenomenological Model of Mesoscopic Field Dislocation Mechanics: Part I," J. Mech. Phys. Solids, 54, pp. 1687-1710.
39. Roy, A., and Acharya, A., 2006, "Size Effects and Idealized Dislocation Microstructure at Small Scales: Predictions of a Phenomenological Model of Mesoscopic Field Dislocation Mechanics: Part- II," J. Mech. Phys. Solids, 54, pp. 1711-1743.
40. Zaiser, M., Nikitas, N., Hochrainer, T., and Aifantis, E. C., 2007, "Modelling Size Effects Using 3D Density-Based Dislocation Dynamics," Philos. Mag, 87, pp. 1283-1306.
41. Cleveringa, H. H. M., Van der Giessen, E., and Needleman, A., 1999, "A Discrete Dislocation Analysis of Bending," Int. J. Plast, 15, pp. 837-868.
42. Ma, A., Roters, F., and Raabe, D., 2006, "A Dislocation Density Based Constitutive Model for Crystal Plasticity FEM Including Geometrically Necessary Dislocations," Acta Mater., 54, pp. 2169-2179.
43. Arsenlis, A., and Parks, D. M., 1999, "Crystallographic Aspects of Geometrically-Necessary and Statistically-Stored Dislocation Density," Acta Mater., 47, pp. 1597-1611.
44. Jakobsen, B., Poulsen, H. F., Lienert, U., and Pantleon, W., 2007, "Direct Determination of Elastic Strains and Dislocation Densities in Individual Subgrains in Deformation Structures," Acta Mater, 55, pp. 3421-3430.
45. Wert, J. A., Huang, X., Winther, G., Pantleon, W., and Poulsen, H. F., 2007, "Revealing Deformation Microstructures," Mater. Today, 10, pp. 24-32.
46. Liu, W., Ice, G. E., Tischler, J. Z., Khounsary, A., Liu, C., Assoufid, L., and Macrander, A. T., 2005, "Short Focal Length Kirkpatrick-Baez Mirrors for a Hard X-Ray Nanoprobe," Rev. Sci. Instrum, 76, pp. 113701-113706.