The complete ODF of titanium, cold rolled up to 80% deformation, was calculated using the series expansion method, including the zero range method. The rolling texture obtained after 80% deformation is mainly characterized by the well-known orientation {0001}〈101¯0〉 ± 40°TD but with distinct spread ranges about it. At about 40% deformation several other texture components are found of which the component {0001}〈112¯0〉 must be mentioned. Further features of the obtained textures are a minor component as well as characteristic zero ranges. Texture development as function of the rolling degree can be divided into three ranges
judged by increase or decrease of various texture components. In the early stages twinning in two different types of twinning systems is assumed whereas at higher deformation degrees the formation of the rolling texture is ascribed to glide deformation only.
Because of the superposition of pole figures corresponding to symmetrically
equivalent crystal directions, only the reduced orientation distribution function f∼(g)
can be obtained directly by pole figure inversion. The additional information
contained in the positivity condition of the ODF allows, however, the determination
of an approximation to the “indeterminable” part and hence of the complete ODF
f(g), if the texture has sufficiently large zero-ranges. The application of the method
and the accuracy of the results was tested using two theoretical and one experimental
textures. The accuracy of the complete ODF depends on the size of the zero-range,
the errors in its determination, and on the errors, experimental and truncational, of
the reduced ODF. The “physical zero” used in order to determine the zero-range is
defined according to the statistical error of the pole figure measurement.
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