Methodology for determining the variance of the taylor factor: Application in Fe-3% Si

Journal of Engineering Materials and Technology

Volumn 129, Issue 1, 2007, Pages 82-93

  Przybyla, Craig P ^a,c   Adams, Brent L ^b   Miles, Michael P ^c  

^a Georgia Institute of Technology   (United States)

^b Brigham Young University   (United States)

^c BRIGHAM YOUNG UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; ERROR DETECTION; NUMERICAL METHODS; PLASTIC DEFORMATION; THREE DIMENSIONAL;

RANDOM SAMPLING METHOD; STATISTICAL VARIANCE RELATIONSHIP; TAYLOR FACTOR;

POLYCRYSTALLINE MATERIALS;

EID: 34248165915     PISSN: 00944289     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2400268     Document Type: Article

References (39)

1. Gao, X., Przybyla, C. P., and Adams, B. L., 2006, "Methodology for Recovering and Analyzing Two-Point Pair Correlation Functions in Polycrystalline Materials," Metall. Mater. Trans. A, 37A, pp. 1279-2387.
2. Ostoja-Starzewski, M., 2004, "Material Spatial Randomness: From Statistical to Representative Volume Element," Probab. Eng. Mech., 21, pp. 112-132.
3. Kanit, T., Forest, S., Galliet, I., Mounoury, V., and Jeulin, D., 2003, "Determination of the Size of the Representative Volume Element for Random Composites: Statistical and Numerical Approach," Int. J. Solids Struct., 40, pp. 3647-3679.
4. Bunge, H. J., 1993, Texture Analysis in Materials Science (English ed.), Cuvillier Verlag, Göttingen.
5. Bunge, H. J., 1982, "Mean Values of Physical Properties," Quantitative Texture Analysis, pp. 383-406.
6. Randle, V., 2003, Microtexture Determination and its Applications, Maney for the Institute of Materials, Minerals and Mining, London.
7. Adams, B. L., Wright, S. I., and Kunze, K., 1993, "Orientation Imaging: The Emergence of a New Microscopy," Metall. Trans. A, 24A, pp. 819-831.
8. Adams, B. L., 1993, "Orientation Imaging Microscopy: Application to the Measurement of Grain Boundary Structure," Mater. Sci. Eng., A, A166, pp. 59-66.
9. Dingley, D. J., and Randle, V., 1992, "Microtexture Determination by Electron Backscatter Diffraction," J. Mater. Sci., 27, pp. 4545-4566.
10. Mason, T. A., and Adams, B. L., 1999, "Use of Microstructural Statistics in Predicting Polycrystalline Material Properties," Metall. Mater. Trans. A, 30, pp. 969-979.
11. Welch, P. I., and Bunge, H. J., 1986, "Influence of Grain Size on Plastic Anisotropy in Low Carbon Steels," Mater. Sci. Technol., 2(4), pp. 354-362.
12. Skrotzki, B., Starke Jr., E. A., and Shiflet, G. J., 1994, "Effect of Texture and Precipitates on Mechanical Property Anisotropy of AI-Cu-Mg-X Alloys," In The 4th International Conference on Aluminum Alloys: Their Physical and Mechanical Properties, 2, pp. 40-47.
13. Lee, P. S., Piehler, H. R., Rollett, A. D., and Adams, B. L., 2002, "Texture Clustering and Long-rang Disorientation Representation Methods: Application to 6022 Aluminum Sheet," Metall. Mater. Trans. A, 33, pp. 3709-3718.
14. Homer, E. R., Basinger, J. A., and Adams, B. L., 2005, "Variance of the Grain Boundary Character Distribution," Mater. Sci. Forum, 495-497, pp. 871-876.
15. Lu, B. L., and Torquato, S., 1990, "Local Volume Fraction Fluctuations in Heterogeneous Media," J. Chem. Phys., 93, pp. 3453-3459.
16. Quintanilla, J., and Torquato, S., 1998, "Local Volume Fraction Fluctuations in Random Media," J. Chem. Phys., 110, pp. 3215-3219.
17. Wright, S. I., and Field, D. P., 1998, "Recent Studies of Local Texture and Its Influence on Failure," Mater. Sci. Eng., A, 257(1), pp. 165-170.
18. Duncan, J. L., Goni, E., and Johnson, W., 1967, "Measurement of Normal Plastic Anisotropy in Sheet Metal," J. Aust. Inst. Met., 12, pp. 127-138.
19. Liu, Y. C., 1983, "On the R-value Measurements," Metall. Trans. A, 14, pp. 1199-1205.
20. Przybyla, C. P., Adams, B. L., and Miles, M. P., 2004, "A Method for Determining Properly Variance in Polycrystalline Materials," NUMIFORM 2004: 8th International Conference on Numerical Methods in Industrial Forming Processes, S. Ghosh et al., eds., Columbus, OH, pp. 1760-1764.
21. Morawiec, A., 2004, Orientations and Rotations: Computations in Crystallographic Textures, Springer, New York.
22. Paul, B., 1960, "Prediction of Elastic Constants of Multiphase Materials," Trans. AIME, 218, pp. 36-41.
23. Hill, R., 1952, "The Elastic Behavior of a Crystalline Aggregate," Proc. R. Soc. London, Ser. A, 65, pp. 349-354.
24. Reuss, A., 1929, "Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle," Z. Angew. Math. Mech., 9, pp. 49-58.
25. Voigt, W., 1928, Lehrbuch der Kristallphysik, Teubner, Leipzig.
26. Kocks, U. F., 1970, "The Relation Between Polycrystal Deformation and Single-Crystal Deformation," Metall. Trans., 1, pp. 1121-1143.
27. Bishop, J. F. W., and Hill, R., 1951, Philos. Mag., 42, pp. 414-427.
28. Bishop, J. F. W., and Hill, R., 1951. Philos. Mag., 42, pp. 1298-1307.
29. McCoy, J. J., 1981, "Macroscopic Response of Continua with Random Microstructures," Mechanics Today, S. Nemat-Nasser, ed., 6, Pergamon, New York, pp. 1-40.
30. Kroner, E., 1972, Statistical Continuum Mechanics, Springer, Berlin.
31. Gokhale, A. M., Tewari, A., and Garmestani, H., 2005, "Constraints on Microstructural Two-point Correlation Functions," Scr. Mater., 53, pp. 989-993.
32. Torquato, S., 2002, Random Heterogeneous Materials, Springer-Verlag. Berlin.
33. Chin, G. Y., and Mammel, W. L., 1969, "Generalization and Equivalence of the Minimum Work (Taylor) and Maximum Work (Bishop-Hill) Principles for Crystal Plasticity," Trans. Metall. Soc. AIME, 245, pp. 1211-1214.
34. Chin, G. Y., and Mammel, W. L., 1967, "Computer Solutions of the Taylor Analysis for Axisymmetric Flow," Trans. Metall. Soc. AIME, 239, pp. 1400-1405.
35. Taylor, G. I., 1938, "Plastic Strain in Metals," J. Inst. Met., 62, pp. 307-324.
36. Hutchinson, J. W., 1976, "Bounds and Self-consistent Estimates for Creep of Polycrystalline Materials," Proc. R. Soc. London, Ser. A, 348(1652), pp. 101-127.
37. Lankford, W. T., Snyder, C. S., and Bauscher, J. A., 1950, "New Criteria for Predicting the Press Performance of Deep Drawing Sheets," Trans. ASME, 42, pp. 1197-1232.
38. Hosford, W. F., 2005, Mechanical Behavior of Materials, Cambridge.
39. Choi, S. H.. and Barlat, F., 1999, "Prediction of Macroscopic Anisotropy in Rolled Aluminum-Lithium Sheet," Scr. Mater., 41(9), pp. 981-987.