ACCESSING THE TEXTURE HULL AND PROPERTIES CLOSURE BY ROTATION AND LAMINATION: RESULTS IN THE PRIMITIVE BASIS OF DILATION FUNCTIONS

摘要

Recent work of Adams and coworkers1 described the theory of Rotations and Laminations as an approach to altering the texture and properties of crystalline materials. The original work used Fourier representations of the Orientation Distribution Function based in the classical generalized spherical harmonic functions. Lamination by ultrasonic consolidation of thin sheet components was demonstrated for two FCC materials. The results were presented in terms of the Texture Hull and the Properties Closure, with uniaxial yield strength versus Young's modulus selected as the particular example.In the present paper the theory of rotations and laminations is extended to a non-classical Fourier basis, consisting of selected dilation functions on the fundamental zone of orientations. The particular approach taken is shown to be an example of a representation of the group of rotations. Special properties of this representation are highlighted. In particular, an exponential form of the representation is explored, including its potential applications to texture design.