Ultrasonic Measurement of the Kearns Texture Parameter in Zircaloy

  • A. J. Anderson
  • R. B. Thompson
  • C. S. Cook


The Kearns basal pole factors (fi) are industrially important measures of texture in hexagonal materials like Zircaloy1,2. They describes the effective number of crystallites with the basal pole aligned along certain sample axes, for example, the rolling, transverse or normal direction in a rolled sheet. In this case, the fi are given by:
$$\begin{array}{*{20}{c}} {{{f}_{3}} = {{f}_{{ND}}} = \tfrac{1}{N}\int\limits_{0}^{{\pi /2}} {\int\limits_{0}^{{2\pi }} {I(\chi ,\eta )\sin (\chi ){{{\cos }}^{2}}(\chi )d\eta d\chi } } } \hfill \\ {{{f}_{2}} = {{f}_{{TD}}} = \tfrac{1}{N}\int\limits_{0}^{{\pi /2}} {\int\limits_{0}^{{2\pi }} {I(\chi ,\eta ){{{\sin }}^{3}}(\chi ){{{\sin }}^{2}}(\eta )d\eta d\chi } } } \hfill \\ {{{f}_{1}} = {{f}_{{RD}}} = \tfrac{1}{N}\int\limits_{0}^{{\pi /2}} {\int\limits_{0}^{{2\pi }} {I(\chi ,\eta ){{{\sin }}^{3}}(\chi ){{{\cos }}^{2}}(\eta )d\eta d\chi } } } \hfill \\ \end{array}$$
where I(χ,η) is the x-ray intensity for a pole figure having χ as the polar angle and η as the azimuthal angle,
$$N = \int\limits_{0}^{{\pi /2}} {\int\limits_{0}^{{2\pi }} {I(\chi ,\eta )\sin (\chi )d\eta d\chi } }$$
and the 1,2 and 3 directions have been associated with the rolling, transverse and normal directions, respectively.


Pole Figure Ultrasonic Velocity Orientation Distribution Function Reference Direction Ultrasonic Measurement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • A. J. Anderson
    • 1
  • R. B. Thompson
    • 1
  • C. S. Cook
    • 2
  1. 1.Ames Laboratory Department of Materials ScienceIowa State UniversityAmesUSA
  2. 2.Westinghouse Science and Technology CenterPittsburghUSA

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