An analytic method for the prediction of ODFS with application to the shear of FCC polycrystals

Abstract

An analytic method is presented for calculation of the orientation distribution function (ODF). It is very rapid, since the amount of computation does not depend on the value of the applied shear. The existence of a hypothetical reference texture is also demonstrated, which plays a central role in the present approach. With the aid of this `texture' and the initial texture, the current ODF is uniquely defined as a function of strain. Shear textures in face-centred cubic (FCC) polycrystals are predicted analytically in this way on the basis of the uniform strain (Taylor) hypothesis and the theory of rate dependent slip. Two special fibres are examined closely, and it is shown that they undergo periodic variations. The period is fixed for the cube-on-face fibre, but depends on rate sensitivity in the cube-on-edge case. The results obtained for the two fibres compare very well with previous completely numerical predictions, and are also consistent with the only available set of experimental results. The present predictions, which can be obtained very easily and rapidly, are useful for testing large deformation computer codes for texture simulation.