Abstract and keywords
Abstract (English):
General analysis of the distribution of crystals orientation and dislocation density in the polycrystalline system is presented. Recovered information in diffraction of X-rays adopting is new to structure states of polycrystal. Shear phase transformations in metals — at the macroscopic and microscopic levels — become a clear process. Visualizing the advances is produced by program included in package delivered. Mathematical models developing, experimental design, optimal statistical estimation, simulation the system under study and evolution process on loading serves as instrumentation. To reduce advanced methods to research and studies problem-oriented software will promote when installed. Automation programs passed a testing in the National University of Science and Technology “MISIS” (The Russian Federation, Moscow). You score an advantage in theoretical and experimental research in the field of physics of metals.

crystallographic texture, distribution of crystals orientation, rhombic texture components identification, anisotropy of plasticity predicting by optimal spherical harmonics of the orientation density, dislocation structure, correlation and long-range order in the system of dislocations, dislocation density determination by harmonics of the diffraction line physical profile, distribution of dislocation density in inhomogeneously deformed polycrystals, dislocation structure of martensitic transformation of steel
Publication text (PDF): Read Download

1. Barabash R. and Klimanek P., Phenomenological and microscopical description of scattering on different dislocation arrangements, Z. Metallkunde 92, 70–75 (2001).

2. Bard Y., Nonlinear Parameter Estimation (Academic Press, New York, 1974; Statistika, Moscow, 1979).

3. Bol'shakov I. A. and Rakoshits V. S., Applied Theory of Random Flows (Sovetskoe radio, Moscow, 1978) [in Russian].

4. Borodkina M. M. and Spektor E. N., X-ray analysis of the texture of metals and alloys (Metallurgiya, Moscow, 1981) [in Russian].

5. Box J. E. P., Robustness in the strategy of scientific model building. Robustness in statistics, pp. 201–236 (Academic Press, New York, 1979; Mashinostroenie, Moscow, 1984).

6. Breitenberger E., Analogues of the normal distribution on the circle and sphere, Biometrika 50, 81–88 (1963).

7. Bunge H.–J., Mathematische Methoden der Texturanalyse (Akademie Verlag, Berlin, 1969); Texture Analysis in Materials Science. Mathematical Methods (Butterworths Publ., London, 1982).

8. Clément A. and Coulomb P., Eulerian simulation of deformation textures, Script. Metallurg. 13, 899–901 (1979).

9. Computers, models, computational experiment, Ed. A. A. Samarskii (Nauka, Moscow, 1988) [in Russian].

10. Cowley J. M., Diffraction Physics (Elsevier, New York, 1975; Mir, Moscow, 1979).

11. Cox D. R., Hinkley D. V., Problems and Solutions in Theoretical statistics (Wiley, New York, 1978; Mir, Moscow, 1981).

12. Davies G. J., Goodwill D. J. and Kallend J. S., Charts for analysing crystallite distribution function plots for cubic materials, J. Appl. Cryst. 4, 67–70 (1971).

13. Draper N. R. and Smith H., Applied Regression Analysis (Wiley, New York, 1981; Finansy i Statistika, Moscow, 1987).

14. Ebeling W., Formation of Structures in Irreversible Processes. Introduction to the Theory of Dissipative Structures (Mir, Moscow, 1979).

15. Efron B., Non-traditional Methods of Multivariate Statistical Analysis, Collection of articles (Finansy i Statistika, Moscow, 1988).

16. Elliott J. P. and Dawber P. G., Symmetry in Physics, Vol. 1 and 2 (Macmillan Press, London, 1979; Mir, Moscow, 1983).

17. Ermakov S. M., The Monte Carlo Method and Related Questions (Nauka, Moscow, 1975) [in Russian].

18. Eshelby J. D., The Continuum Theory of Dislocations, Collection of articles (In. Lit., Moscow, 1963).

19. Fisher R., Dispersion on a Sphere, Proc. Roy. Soc. A217, 295–305 (1953).

20. Fridman Ya. B., Mechanical Properties of Metals, Vol. 1: Deformation and Failure, 3nd ed. (Mashinostroenie, Moscow, 1974) [in Russian].

21. Genin J. M. R. and Flinn P. A., Mössbauer effect study of the clustering of carbon atoms during the room temperature aging of iron carbon martensite, Trans. Metallurg. Soc. AJME 242, 1419–1430 (1968).

22. Glansdorff P. and Prigogine I., Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley, New York, 1971; Mir, Moscow, 1973).

23. Gnesin B. A. and Yashnikov V. P., The role of a deviation of primary beam from the goniometer horizontal plane in three-dimensional texture analysis, Zavod. Lab. 53 (3), 38–41 (1987).

24. Handbook of Mathematical Functions, Ed. M. Abramowitz and I. A. Stegan (Dover, New York, 1965; Nauka, Moscow, 1979).

25. Handbook on Probability Theory and Mathematical Statistics, Ed. V. S. Korolyuk (Nauka, Moscow, 1985) [in Russian].

26. Head A. K., A continuum model for two-dimensional dislocation distributions, Philosophical Magazine A 55, 617–629 (1987).

27. Hill R., Mathematical Theory of Plasticity (Gostekhizdat, Moscow–Leningrad, 1956).

28. Hill R., Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids 13, 89–101 (1965).

29. Jaakko Kajamaa, Determination of cold rolling and recrystallization texture in copper sheet by neutron diffraction, Trans. Metallurg. Soc. AJME 242, 973–977 (1968).

30. Jenkins G. and Watts D., Spectral Analysis and its Applications (Mir, Moscow, 1972).

31. Johnson N. L. and Leone F. C., Statistics and Experimental Design in Engineering and the Physical Science (Wiley, New York, 1977; Mir, Moscow, 1980).

32. Karmanov V. G., Mathematical Programming (Nauka, Moscow, 1986) [in Russian].

33. Khayutin S. G., Anisotropy of plasticity of textured metal tape, Tsvetnye metally 􀊋 3, 80–83 (1983).

34. Kheyker D. M. and Zevin L. S., X-ray Diffractometry (Fizmatgiz, Moscow, 1963) [in Russian].

35. Kochetov I. I., On a new method for choosing the regularization parameter, Zh. Vychislit. Math. and Math. Fiz. 16, 499–503 (1976).

36. Korin B. P., On the Distribution of a statistic used for testing a covariance matrix, Biometrika 55, 171–178 (1968).

37. Korn G. A. and Korn T. M., Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review (McGraw-Hill, New York, 1968; Nauka, Moscow, 1974).

38. Kozlov D. A., Petrunenkov A. A., Satdarova F. F. and Kekalo A. I., Texture of a thin sheet of low-carbon steel upon recrystallization under rapid heating conditions, Izv. Akad. Nauk SSSR, Met. 􀊋.5, 137–141 (1986).

39. Krivoglaz M. A., Theory of X-ray and Thermal Neutron Scattering by Real Crystals (Nauka, Moscow, 1967; Plenum, New York, 1969).

40. Krivoglaz M. A., Martynenko O. V. and Ryaboshapka K. P., Effect of correlation in arrangement of dislocations on X-ray diffraction by deformed crystals, Fiz. Met. Metalloved. 55, 5–17 (1983).

41. Krivoglaz M. A., Ryaboshapka K. P. and Barabash R. N., Theory of Xray scattering by crystals containing dislocation walls, Fiz. Met. Metalloved. 30, 1134–1145 (1970).

42. Kröner E., Zur plastischen verformung des vielkristalls, Acta Metallurg. 9, 155–161 (1961).

43. Krug G. K., Sosulin Yu. A. and Fatuev V. A., Design of Experiments in Problems of Identification and Extrapolation (Nauka, Moscow, 1977) [in Russian].

44. Landau L. D. and Lifshitz E. M., Course of Theoretical Physics, Vol. 5: Statistical Physics, 3nd ed. (Nauka, Moscow, 1976; Pergamon, Oxford, 1980).

45. Landau L. D. and Lifshitz E. M., Course of Theoretical Physics, Vol. 7: Theory of Elasticity, 3nd ed. (Nauka, Moscow, 1965; Pergamon, Oxford, 1980).

46. Landau L. D. and Lifshitz E. M., Course of Theoretical Physics, Vol. 10: Physical Kinetics (Nauka, Moscow, 1979; Pergamon, Oxford, 1981).

47. Lekhnitsky S. G., Theory of Elasticity of Anisotropic Body (Gostekhizdat, Moscow–Leningrad, 1950) [in Russian].

48. Lifshitz I. M. and Rozentsveig L. N., On theory of elastic properties of polycrystals, Zh. Exp. and Theor. Fiz. 16, 967–980 (1946).

49. Mathematical Theory of Experiment Design, Ed. C. M. Ermakov (Nauka, Moscow, 1983) [in Russian].

50. Miklyaev P. G. and Fridman Ya. B., Anisotropy of the Mechanical Properties of Materials (Metallurgiya, Moscow, 1986) [in Russian].

51. Morris R. R., Elastic constants of polycrystals, Int. J. Eng. Sci. 8, 49–61 (1970).

52. Novikov I. I., Theory of Thermal Treatment of Metals (Metallurgiya, Moscow, 1986) [in Russian].

53. Nye J. F., Physical Properties of Crystals, their Representation by Tensors and Matrices (Mir, Moscow, 1967).

54. Olszak W. and Urbanowski W., The plastic potential and the generalized distortion energy in the theory of non-homogeneous anisotropic elastic-plastic bodies, Archive Mech. Stos. 8, 671–694 (1956).

55. Physical Metallurgy, Ed. R. W. Cahn, Ch. XIII–XX (North-Holland Publishing Company, Amsterdam, 1965; Mir, Moscow, 1968).

56. Roe R.–J., Description of crystallite orientation in polycrystalline materials. III. General solution to pole figure inversion, J. Appl. Phys. 36, 2024–2031 (1965).

57. Roe R.–J., Inversion of pole figures for materials having cubic crystal symmetry, J. Appl. Phys. 37, 2069–2072 (1966).

58. Röpke G., Statistische Mechanik für das Nichtgleichgewicht (VEB Verlag, Berlin, 1987; Mir, Moscow, 1990).

59. Rozanov Yu. A., Random Processes (Nauka, Moscow, 1979) [in Russian].

60. Ruhl R. C. and Cohen M, Splat quenching of iron carbon alloys, Trans. Metall. Soc. AJME 245, 241–253 (1969).

61. Ryaboshapka K. P., Possibilities of X-ray analysis of dislocation structures of deformed crystals, Zavod. Lab. 47 (5), 26–33 (1981).

62. Sachs L. Statistische Schätzung (Statistika, Moscow, 1976).

63. Satdarova F. F., X-ray scattering by deformed crystals, Fiz. Met. Metalloved. 49, 467–480 (1980).

64. Satdarova F. F. and Kozlov D. A., Texture analysis by measurements of diffraction intensity in reciprocal space of polycrystal, Fiz. Met. Metalloved. 60, 948–954 (1985).

65. Satdarova F. F., Kozlov D. A. and Blekhman B. N., Generalized parameters for dispersion of orientations of crystals in plane-deformed metals, Fiz. Met. Metalloved. 61, 149–152 (1986).

66. Satdarova F. F., Analysis of the texture function, Fiz. Met. Metalloved. 69, 204–207 (1990).

67. Satdarova F. F., Textural transformation upon recrystallization of sheet low-carbon steel, Phys. Met. Metallography 95, 47–50 (2003).

68. Satdarova F. F., Dislocation structure of martensitic transformation in carbon steel, Phys. Met. Metallography 117, 355–363 (2016).

69. Satdarova F. F. and Kiselev I. K., Analysis of diffraction spectra. I. On optimality and stability in the estimation of structure parameters, Kristallografiya 35, 28–32 (1990).

70. Satdarova F. F. and Kiselev I. K., Analysis of diffraction spectra. II. On X-ray structural study of martensite of steel, Kristallografiya 35, 33–37 (1990).

71. Satdarova F. F., Determination of the components of rhombic texture in metals, Kristallografiya 36, 304–309 (1991).

72. Satdarova F. F., Analysis of a random system of dislocations in a deformed crystal, Crystal. Rep. 50, 427–434 (2005).

73. Satdarova F. F., Identifiability of dislocation structures of strongly distorted crystals, Crystal. Rep. 51, 72–80 (2006).

74. Satdarova F. F. and Kozlov D. A., Determination of the inhomogeneous dislocation density in a crystallographic texture, Crystal. Rep. 52, 284–291 (2007).

75. Satdarova F. F., Distribution of dislocation density in deformed polycrystals, Crystal. Rep. 54, 283–287 (2009).

76. Satdarova F. F., Plastic flow state and evolution of texture of metal sheet, Izv. Ross. Akad. Nauk: Mekh. Tverd. Tela 􀊋 6, 85–96 (2005).

77. Satdarova F. F., Plastic flow state and evolution of texture of metal sheet. II. Numerical analysis of deformation processes in a polycrystalline system, Izv. Ross. Akad. Nauk: Mekh. Tverd. Tela 􀊋 3, 135–143 (2006).

78. Satdarova F. F. and Kozlov D. A., Optimal design of experiment for measuring the texture function, Zavod. Lab. 48 (3), 44–48 (1982).

79. Satdarova F. F. and Kozlov D. A., Optimum estimation of harmonics of the physical profile of the diffraction line, Zavod. Lab. 48 (10), 53–56 (1982).

80. Satdarova F. F., Kozlov D. A. and Blekhman B. N., On the technique of quantitative measurements of texture, Zavod. Lab. 49 (3), 68–72 (1983).

81. Satdarova F. F., Kozlov D. A. and Kekalo A. I., Estimation of the effective elasticity coefficients of plane-deformed metals with a cubic crystal lattice from the measured harmonics of the texture function, Zavod. Lab. 51 (11), 53–56 (1985).

82. Satdarova F. F., Chernyshev A. V. and Yagubov S. A., Dialog system for texture analysis with optimal design of experiment, Zavod. Lab. 55 (1), 98–99 (1989).

83. Satdarova F. F., Critical analysis of texture estimation using simulation experiments, Zavod. Lab. 60 (3), 16–23 (1994).

84. Satdarova F. F., Modern texture analysis on the example of cold-rolled sheet of low-carbon steel, Zavod. Lab. Diagn. Mater. 68 (2), 21–25 (2002).

85. Satdarova F. F., On the application of quantitative texture analysis in technological studies in the making of metal sheet, Zavod. Lab. Diagn. Mater. 69 (7), 24–28 (2003).

86. Satdarova F. F. and Kozlov D. A., Automated system for analysis of the dislocation structure in polycrystals, Zavod. Lab. Diagn. Mater. 74 (9), 26–31 (2008).

87. Satdarova F. F., Analysis of diffraction measurements with adapting to background level, Zavod. Lab. Diagn. Mater. 75 (8), 35–38 (2009).

88. Satdarova F. F., Determination of the physical profile of the diffraction line by the pseudo-maximum likelihood method, Zavod. Lab. Diagn. Mater. 78 (5), 73–77 (2012).

89. Savyolova T. I. and Ivanova T. M., Methods for reconstructing the distribution function of orientations by pole figures, Zavod. Lab. Diagn. Mater. 74 (7), 25–33 (2008).

90. Shermergor T. D., Theory of Elasticity of Microinhomogeneous Media (Nauka, Moscow, 1977) [in Russian].

91. Spector E. N., Gorelik S. S. and Rakhshtadt A. G., Izv. VUZ: Tsvetnaya metallurgiya 􀊋.4, 132–134 (1971).

92. Tables of Integral Transforms (Bateman Manuscript Project) Director A. Erdélyi, Vol. 2 (McGraw-Hill, New York, 1954; Nauka, Moscow, 1970).

93. Tarantsev A. A., On the relation between interval analysis and probability theory, Zavod. Lab. Diagn. Mater. 70 (3), 61–65 (2004).

94. Teodosiu C., Elastic Models of Crystal Defects (Springer-Verlag, Berlin, Heidelberg, New York, 1982; Mir, Moscow, 1985).

95. Tikhonov A. N. and Arsenin V. Ya., Methods for Solving Ill-Posed Problems (Nauka, Moscow, 1979).

96. Trushkovski V., Vezhbinski S. and Kloch Ya., Quantitative analysis of the plastic anisotropy of polycrystalline copper, Fiz. Met. Metalloved. 66, 178–183 (1988).

97. Ungar T. and Borbely A., The effect of dislocation contrast on X-ray line broadening; a new approach to line profile analysis, Appl. Phys. Letters 69, 3173–3175 (1996).

98. Utevsky L. M., Diffraction Electron Microscopy in Metallurgy (Metallurgiya, Moscow, 1973) [in Russian].

99. Viglin A. S., A quantitative measure of texture of a polycrystalline material. Texture function, Fiz. Tverd. Tela 2, 2463–2476 (1960).

100. Vilenkin N. Ya., Special Functions and Theory of Groups Representations (Nauka, Moscow, 1965) [in Russian].

101. Vlasov A. A., Statistical Distribution Functions (Nauka, Moscow, 1966) [in Russian].

102. Warren B., X-ray analysis of deformed metals, Prog. Metal. Phys. 8, 147 (1959).

103. Watson G. S., The Statistics of Orientation Data, J. Geology 74 Pt. 2, 786–797 (1966).

104. Weiss M. and Montagnat M., Long-range spatial correlations and scalingin dislocation and slip patterns, Philosophical Magazine 87, 1161–1177 (2007).

105. Yanossy L., Theory and Practice of the Evaluation of Measurements (Oxford Univ., 1965; Mir, Moscow, 1968).

106. Young R. A., Gerdes R. J. and Wilson A. J. C., Propagation of some systematic errors in X-ray line profile analysis, Acta Cryst. 22, 155–162 (1967).

107. Zasimchuk E. A. and Isaichev V. I., Mechanical instability of a fragmented structure in terms of nonlinear thermodynamics, Doc. Akad. Nauk SSSR 302, 1101–1104 (1988).

108. Zolotarevsky I. Yu. and Rybin V. V., Deformation of fragmenting polycrystals and texture formation, Fiz. Met. Metalloved. 59, 440–449 (1985).

109. Zolotarevsky I. Yu., Rybin V. V. and Zhukovsky I. M., Theory of deformation textures of fragmenting metals, Fiz. Met. Metalloved. 67, 221–232 (1989).

110. Zubarev D. N., Nonequilibrium Statistical Thermodynamics (Nauka, Moscow, 1971) [in Russian].

Login or Create
* Forgot password?