Three Dimensional Surface Representations of Linear Elastic Anisotropy in Cubic Single Crystals

  • Edward J. Tucholski
  • Robert E. GreenJr.
Conference paper


The magnitude of the velocities of the three possible modes of elastic wave propagation are calculated for single crystal chromium, aluminum, and iron at intervals over all possible propagation directions and plotted to form wave velocity surfaces. These materials were chosen because they vary widely in isotropy factor as defined by Kittel [1]. Additionally, the energy flow vectors associated with each mode are found, allowing the angle between the energy flow vector and the propagation direction to be calculated. Energy flux deviation angles are then displayed on three dimensional polar plots to form three dimensional surfaces. The relative elastic anisotropy of these single crystals is compared graphically and quantitatively using isotropy factors.

The maximum longitudinal mode energy flux deviation angles are calculated for a number of cubic crystals. It is shown that near room temperature, maximum longitudinal mode energy flux deviation is linearly related to the isotropy factor. Also the angle with respect to the <100> direction at which this maximum longitudinal mode flux deviation occurs decreases exponentially with the isotropy factor.


Direction Cosine Isotropy Factor Wave Velocity Surface Elastic Representation Surface Nondestructive Characterization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Edward J. Tucholski
    • 1
  • Robert E. GreenJr.
    • 1
  1. 1.Center for Nondestructive Evaluation and Department of Materials Science and EngineeringThe Johns Hopkins UniversityBaltimoreUSA

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