Generalization of the relaxed constraints models for the prediction of deformation textures

The «relaxed constraints » (R.C.) models for the prediction of deformation textures are discussed with emphasis on their shortcomings. A generalized R.C. model is then proposed which takes the increase of plastic work into account associated to the strain misfits caused by the relaxation of the geometrical constraints imposed by the classical Taylor theory. The calculation of the increase of plastic work is based on an upper-bound solution of the problem of finding the plastic flow around an inclusion embedded in a matrix. The new « generalized R.C. model » has been implemented in a self-consistent scheme and can be used for the prediction of deformation textures. The upper-bound solution mentioned above has also been used in a study of the nucleation texture in the case of continuous annealing of an aluminium alloy with hard second phase particles, which were treated as « inclusions ». Another result of this work is a classification of the « relaxations » (difference between local and macroscopic velocity gradient tensors) into an « orthogonal » and a « parallel » class. Finally, the application of the generalized R.C. method for the prediction of the rolling textures of a steel sheet and an aluminium alloy sheet has been described. The results turned out to be slightly better than those of a conventional Taylor model.