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A generalization of the O.D.F. representation has been proposed in such a way that its calculation is possible in any axes system of a material provided that is known in one particular system. Using an appropriate rotation matrix T(a,b,c) it is possible to compute crystallographic orientations(   hk  ℓ   )    [uvw] in any macroscopic plane of the material. This calculation method leads also to a direction distribution function    F   π    [    u  1    v  1    w  1    ](   ψ  ,  α   )    which gives the angular distribution of the crystallographic direction[    u  1    v  1    w  1    ]in a macroscopic plane of the material.  This analysis has been applied to the representation of texture and of slip directions in planes at 45 degrees from the directions RD, ND and TD of a mild steel deformed in equi-biaxial expansion.

Generalization of the Orientation Distribution Function: Determination of Crystalline Orientations in any Section of the Specimen