The mesostructure - Properties linkage in polycrystals

Progress in Materials Science

Volumn 43, Issue 1, 1998, Pages 1-87

  Adams, B L ^a   Olson, T ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL ATOMIC STRUCTURE; CRYSTAL LATTICES; CRYSTAL MICROSTRUCTURE; CRYSTAL ORIENTATION; CRYSTAL SYMMETRY; DISLOCATIONS (CRYSTALS); ELECTRON DIFFRACTION; GRAIN BOUNDARIES; MATHEMATICAL OPERATORS; PERTURBATION TECHNIQUES; TENSORS; VARIATIONAL TECHNIQUES;

CORRELATION FUNCTIONS; DEBOTTOM-PONTE CASTANEDA BOUND; DISTRIBUTION FUNCTIONS; FRANK-BILBY RELATION; ORIENTATION IMAGING MICROSCOPY; WALPOLE'S BOUND; WILLIS' BOUND;

POLYCRYSTALLINE MATERIALS;

EID: 0032292721     PISSN: 00796425     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0079-6425(98)00002-4     Document Type: Article

References (117)

1. Smekal A. Strukturemfindliche eigenschaften von kristallen. In: Handbuch der Physik. 2. Berlin: Springer, 1933.
2. Seeger A. Kristallplastizitat. In: Handbuch der Physik. 7/11. Berlin: Springer, 1958.
3. Bishop RL, Goldberg SI. Tensor analysis on manifolds. New York: Dover, 1980.
4. Gurtin ME. An introduction to continuum mechanics. San Diego: Academic Press, 1981.
5. Altmann SL. Rotations, quaternions, and double groups. Oxford: Clarendon Press, 1986.
6. Spencer AJM. Continuum mechanics. New York: Wiley, 1980.
7. Sutton AP, Balluffi RW. Interfaces in crystalline materials. Oxford: Clarendon Press, 1995.
8. Bunge HJ. Texture analysis in materials science. Boston: Butterworths, 1982.
9. Nye JF. Physical properties of crystals. Oxford: Clarendon Press, 1957.
10. Hamermesh M. Group theory and its application to physical problems. Reading: Addison Wesley, 1962.
11. Morawiec A, Field DP. Phil Mag 1996;73:1113.
12. Hansen J, Pospiech J, Lücke K. Tables for texture analysis of cubic crystals. Berlin: Springer, 1978.
13. Zhao J, Adams BL. Acta Crystallographica 1988;A44:326-36.
14. Adams BL, Zhao J, Grimmer H. Acta Crystallographica 1990;A46:620-2.
15. Randle V. Microtexture determination and its applications. London: The Institute of Materials, 1992.
16. DeGraef MG. Private communication.
17. Nye JF. Physical properties of crystals. Oxford: Clarendon Press, 1964.
18. Kröner E. Statistical continuum mechanics. In: Vol. 92 of CISM courses and lectures. Udine: Springer, 1972.
19. Gel'fand IM, Minlos RA, Shapiro ZYa. Representations of the rotation and Lorentz groups and their applications. Oxford: Pergamon Press, 1963.
20. Etingof P, Adams BL. Textures and Microstruct 1993;21:17-37.
21. Kröner E. Statistical modelling. In: Gittus J, Zarka J, editors. Modelling small deformations of polycrystals, chap. 8. New York: Elsevier, 1986. p. 229-91.
22. Adams BL. Metall Trans 1986;17A:2199-207.
23. Weibel ER. Stereological methods, vol. 2, theoretical foundations. London: Academic Press, 1980.
24. Bröcker T, tom Dieck T. Representations of compact lie groups. New York: Springer, 1985.
25. Courant R, Hilbert D. Methods of mathematical physics. New York: Interscience, 1989.
26. Adams BL, Boehler JP, Guidi M, Onat ET. J Mech Phys Solids 1992;40:723.
27. Etingof, Sam DD, Adams BL. Phil Mag A 1995;72:199-208.
28. Kronberg ML, Wilson F. Trans Am Inst Min (Metall) Engrs 1949;185:50.
29. Ranganathan S. Acta Crystallogr 1966;21:197.
30. Brandon DG. Acta Metall 1966;14:479.
31. Kröner E. Continuum theory of dislocation and self stresses. Berlin: Springer, 1958.
32. Nye JF. Acta Metall 1953;1:153.
33. Ashby MF. Phil Mag 1970;21:399.
34. Bilby BA. Report of the conference on defects in crystalline solids. London: The Physical Society, 1955.
35. Bullough R, Bilby BA. Proc Phys Soc 1956;B69:1276-86.
36. McCoy JJ. Macroscopic response of continua with random microstructures. In: Nemat-Nasser S, editors. Mechanics today. Oxford: Pergamon Press, 1981. 6. p. 1-40.
37. Hashin Z. Analysis of composite materials - a survey. J Appl Mech 1983;50:481-503.
38. Willis JR. Variational and related methods for the overall properties of composite materials. In: Yih CS, editors. Advances in applied mechanics. New York: Academic Press, 1981. p. 2-77.
39. Milton GW. On characterizing the set of possible effective tensors of composites: the variational method and the translation method. Comm Pure Appl Math 1990;XLIII:63-125.
40. Kröner E. Bounds for effective elastic moduli of disordered materials. J Mech Phys Solids 1977;25:137-55.
41. Beran MJ. Statistical continuum theories. In: Monographs in statistical physics. 9. Providence: Wiley, 1968.
42. Adams BL, Morris PR, Wang TT, Willden KS, Wright SI. Description of orientation coherence in polycrystalline materials. Acta Metall 1987;35(12):2935-46.
43. Wright SI, Adams BL. Automatic analysis of electron backscatter diffraction patterns. Metall Trans A 1992;23A:759-67.
44. Kunze K, Wright SI, Adams BL, Dingley DJ. Advances in automatic EBSP single orientation measurements. Textures and Microstructures 1992; in press.
45. Adams BL, Wright SI, Kunze K. Orientation imaging: the emergence of a new microscopy. Metall Trans 1993;24A:819-31.
46. Hashin Z, Shtrikman S. A variational approach to the theory of the elastic behavior of polycrystals. J Mech Phys Solids 1962;10:343-52.
47. Hashin Z, Shtrikman S. On some variational principles in anisotropic and nonhomogeneous elasticity. J Mech Phys Solids 1962;10:335-42.
48. Hashin Z, Shtrikman S. A variational approach to the theory of the effective magnetic permeability of multiphase materials. J Appl Phys 1962;33:3125-31.
49. Hashin Z, Shtrikman S. A variational approach to the theory of the elastic behavior of multiphase materials. J Mech Phys Solids 1963;11:127-40.
50. Walpole LJ. On bounds for the overall elastic moduli of inhomogeneous systems - i. J Mech Phys Solids 1966;14:151-62.
51. Walpole LJ. On bounds for the overall elastic moduli of inhomogeneous systems - ii. J Mech Phys Solids 1966;14:289-301.
52. Hill R. The elastic behavior of a crystalline aggregate. Proc Phys Soc A 1952;65:349-54.
53. Paul B. Prediction of elastic constants of multiphase materials. Trans Metall Soc AIME 1960;218:36-41.
54. Avellaneda M, Milton GW. Optimal bounds on the effective bulk modulus of polycrystals. SIAM J Appl Math 1989;49(3):824-37.
55. Beran M, Molyneux J. Use of classical variational principles to determine bounds for the effective bulk modulus in heterogeneous media. Q Appl Math 1966;24:107-18.
56. Zeller R, Dederichs PH. Elastic constants of polycrystals. Phys Stat Solidi (B) 1973;55:831-42.
57. Willemse MWM, Caspers WJ. Electrical conductivity of polycrystalline materials. J Math Phys 1979;20(8):1824-31.
58. Miller MN. Bounds for effective bulk modulus of heterogeneous material. J Mat Phys 1969;10(11):2005-13.
59. Avellaneda M, Bruno O. Effective conductivity and average polarizability of random polycrystals. J Math Phys 1990;31(8):2047-56.
60. Landau LD, Lifshitz EM. Electrodynamics of continuous media. New York: Pergamon Press, 1960.
61. Love AEH. A treatise on the mathematical theory of elasticity. New York: Dover, 1944.
62. Brown WF Jr., Magnetostatic principles in ferromagnetism. Amsterdam: North-Holland, 1962.
63. Schulgasser K. Bounds on the conductivity of statistically isotropic polycrystals. J Phys 1977;C(10):407-17.
64. Avellaneda M, Cherkaev AV, Lurie KA, Milton GW. On the effective conductivity of polycrystals and a three-dimensional phase-interchange inequality. J Appl Phys 1988;63(10):4989-5003.
65. Nesi V, Milton GW. Polycrystalline configurations that maximize electrical resistivity. J Mech Phys Solids 1991;39(4):525-42.
66. Schulgasser K. Sphere assemblage model for polycrystals and symmetric materials. J Appl Phys 1983;54(3):1380-2.
67. Willis JR. Bounds and self-consistent estimates for the overall properties of anisotropic composites. J Mech Phys Solids 1977;25:185-202.
68. Beran MJ, Mason TA, Adams BL, Olson T. Bounding elastic constants of an orthotropic polycrystal from measurements of the microstructure. J Mech Phys Solids 1996;44(9):1543-63.
69. Avellaneda M. 1990. Personal communication.
70. Bacon DJ, Barnett DM, Scattergood RO. Anisotropic continuum theory of lattice defects. Prog Mater Sci 1979;23:51-262.
71. Gel'fand IM, Shilov GE. Generalized functions. New York: Academic Press, 1964.
72. Mason T, Adams BL. Metall Trans 1998; in press.
73. Talbot DRS, Willis JR. Variational principles for inhomogeneous non-linear media. IMA J Appl Math 1985;35:39-54.
74. Ponte Castañeda P. The effective mechanical properties of nonlinear isotropic composites. J Mech Phys Solids 1991;39(1):45-71.
75. Olson T. Improvements on Taylor's upper bound for rigid/plastic composites. Mater Sci Engng 1994;A175(1):15-20.
76. Ponte Castañeda P, DeBotton G. On the homogenized yield strength of two-phase composites. Proc Royal Soc London A 1992;438:419-31.
77. Michel JC, Suquet PM. On the strength of the composite materials: variational bounds and computational aspects. In: Bendsoe MP, editors. Topology design of structures. Sesimbra, Portugal, NATO Advanced Research Workshop, Dordrecht: Kluwer, 1992. p. 20-6.
78. DeBotton G, Ponte Castañeda P. Variational estimates for the creep behavior of polycrystals. Proc Royal Society of London 1995;A(448):121-42.
79. Taylor GI. Plastic strain in metals. J Inst Metals 1938;62:307-24.
80. Bishop JFW, Hill R. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. Phil Mag 1951;42:414.
81. Sam DD. Evaluation of bounds to the effective yield surface for face-centered cubic polycrystalline materials. PhD thesis. Yale University, 1994.
82. Lejček P, Hofmann S. CRC Critical Rev Solid St Mater Sci 1995;20:1.
83. Shvindlerman LL, Straumal BB. Acta Metall 1985;33:1735-49.
84. Goodhew PJ. Metal Sci J 1979;13:108-17.
85. Aust KT, Rutter JW. Trans AIME 1959;215:119.
86. Priester L. Revue Phys Appl 1989;21:418-38.
87. Kokawa H, Watanabe T, Karashima S. Phil Mag A 1981;40:1239-54.
88. Don J, Majumdar S. Acta Metall 1986;34:961-7.
89. Field D, Adams BL. Metall Trans 1992;23A:2515-26.
90. Palumbo G. Mater Res Soc Symp Proc 1992;238:311.
91. Watanabe T. J Phys 1988;5:507-19.
92. Palumbo G, Lehockey EM, Lin P. JOM 1998;50(2):40-3.
93. Thaveeprungsriporn V, Mansfield JF, Was GS. J Mater Res 1994;9:1877.
94. King E, Schwartz AJ. Scripta Metall 1998; in press.
95. Palumbo G. Briant CL et al., editors. Interfacial engineering for optimized properties. Pittsburgh: Materials Research Society, 1997. p. 273.
96. Was GS, Thaveeprungsriporn V, Crawford DC. JOM 1998;50(2):44-9.
97. Thaveeprungsriporn V, Was GS. Metall Trans 1997;28A:2101-12.
98. Pan Y, Adams BL, Olson T, Panayotou N. Grain boundary structure effects on intergranular stress corrosion cracking of alloy X750. Acta Metall Mater 1996;44(12):4685-95.
99. Bunge HJ. Z Metallkde 1965;56:872-4.
100. Roe RJ. J Appl Phys 1965;36:2024-31.
101. Matthies S, Vinel GW, Helming K. Standard distributions in texture analysis. Berlin: Akademie, 1987.
102. Schwarzer RA. Micron 1997;28:249-65.
103. Kikuchi S. Jap J Phys 1928;5.
104. Nishikawa Sh, Kikuchi S. Proc Imp Acad Japan 1928;4:475-7.
105. Alam MN, Blackman M, Pashley DW. Proc Royal Society 1954;221:224-42.
106. Venables JA, Harland CJ. Phil Mag 1973;27:1193-200.
107. Dingley DJ. Scanning Electron Microscopy 1984;2:569-75.
108. Wright SI, Zhao J, Adams BL. Textures Microstruct 1991;13:123-31.
109. Juul-Jensen D, Schmidt NH. Textures Microstruct 1991;14-18,97-102.
110. Delesse A. Ann Mines 1848;379 (4th series).
111. Chu BT. 1990. Personal correspondence.
112. Hilliard JE. Trans Met Soc AIME 1962;224:1201-11.
113. Adams BL, Field DP. Metall Trans A 1992;23A:2501-13.
114. Adams BL. Mater Sci Engng 1993;A166:59-66.
115. Arnold VI. Mathematical methods of classical mechanics. 2nd ed. New York: Springer, 1989.
116. Hashin Z, Shtrikman S. Conductivity of polycrystals. Phys Rev 1963;130(1):129.
117. Olson T. Overall properties of granular piezoelectrics: bounds and effective medium approximations. PhD thesis. New York University, UMI Publication no. 92-12368, 1991.