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Estimation of Ahisotropy of X-Ray Elastic Modulus in Steel Sheets

  • Shin-ichi Nagashima (a1), Masaki Shiratori (a1) and Ryuichi Nakagawa (a1)

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The oscillation from a linear relation in the 20 vs. sin2ψ diagram has been a most important problem in X-ray stress measurement. There are, therefore, a number of papers concerned with the X-ray elastic constant, lattice strains under stresses and evaluation of stresses of textured materials.

The purpose of the present study is to analyze the three-dimensional orientation distribution of steel sheets by means of the Vector method proposed by Ruer and Baro, and to calculate the elastic modulus of textured sheets by means of a finite element method (FEM) using the three-dimensional orientation distribution, and then to calculate the strain/stress ratios vs. the directions defined by the angles between the specimen normal and the normal to the diffracting planes.

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1. Taira, G. and Hayashi, K.,.X-Ray Investigation of polycrystalline Materials (On the Effect of Fiber Texture on the Elastic Constants of a- Iron, Proc. 13th Japan Cong, on Materials Research 20-24 (1970).
2. Shiraiwa, T. and Sakamoto, Y., The X-Ray Stress Measurement of the Deformed Steel Having Preferred Orientation, Proc. 13th Japan Cong. on Materials Research 25-32 (1970).
3. Hauk, V., Herlach, D. und Sesemann, H., Uber nichtlineare Gitterebenenab- Standsverteilungen in Stählen, ihre Entstehung, Berechnung und Berücksichtigung bei der Spannungsermittlung, Z. Metallkde. 66:734- 737 (1975).
4. Hauk, V. und Sesemann, H., Abweichungen von linearen Gitterebenenabstands verteilungen in kubischen Metalien und ihr Berücks ichtigung beider röntgenographischen Spannungsermittlung, Z. Metallkde, 67: 646-650 (1976).
5. Marion, R.H. and Cohen, J.B., The Heed for Experimentally Determined X-Ray Elastic Constants, Advances in X-ray Analysis 20: 355-377 (1977).
6. Dölie, H., The Influence of Multiaxial Stress States, Stress Gradients and Elastic Anisotropy on the Evaluation of (Residual) Stresses by X-Rays, Appl. Cryst, 12: 489-501 (1979).
7. Honda, K., Hosokawa, N. and Sarai, T., Effect of Texture on Stress Measured by X-ray Diffraction Method, J. HPT. Japan 26: 539-545 (1977).
8. Honda, K. and Sarai, T., X-Ray Strain Analysis and Elastic Deformation of Polycrystalline Metals, J. Soc. Mat. Sci. Japan 33: 367-373 (1984)
9. Voigt, W., Lehrbuch der Kristallphysik (Leipzig, Teubner Verlag), 716 (1928).
10. Reuss, A., Angew, Z.. Math. Mech., 9: 49 (1929)
11. Ruer, D. and Baro, R., A new Method for the Determination of the Texture of Materials of Cubic Structure from Incomplete Rëflection Pole Figures, Advances in X-ray Analysis 20: 187-200 (1977).
12. Nagashima, S., A new Method for the Three Dimensional Analysis of Preferred Orientation of Metallic Materials, Korean, J. Inst. Metals 22: 41-52 (1984).
13. Nagashima, S., Shlratori, T. and Fujiu, T., The Estimation of Elastic Constants for the X-Ray Stress Analysis of Textured Metallic Materials, Proc. IC0T0M. : Vol. II. 1148-1157 (1981).
14. Nagashima, S., Shiratori, M. and Matsukawa, K., “The Effect of Grain Distribution on the Elastic Moduli in Metallic Materials Which Give the Same Pole Figure, Trans. ISIJ. 23:B-26 (1983).
15. Hill, R., Proc. Phys. Soc., A65: 349 (1952).

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