21:T49f,The Taylor theory and the Bishop–Hill theory for the plastic deformation of polycrystals are expressed in a mathematical way which makes extensive use of vectors. These vectors represent either plastic strain rate tensors or deviatoric stress tensors, both in a unified five‐dimensional stress‐strain space. Such formulation permits a unified formulation of both theories, which can then easily be solved by means of linear programming. The computer implementation of this formalism (in Pascal) conserves this mathematical formalism to a high extent. Relaxed constraints (or “mixed boundary conditions”) can very easily be incorporated in the method. The concept of a “relaxed constraint” is formulated in a much more general way than has ever been done before. It is not only shown why there are often multiple solutions for the slip rates, but also that such difficulties can arise for the stress state as well. A few methods for making an appropriate choice among these equivalent solutions are explained, one based on the Renouard–Wintenberger theory that proposes a secondary energy criterion, and another that takes strain rate sensitivity effects into account.22:T53b,Methods of modern quantitative texture analysis are applied in order to characterize the crystallographic texture of various non-oriented electrical steel grades in view of their relation with the magnetic properties of the steel sheet. A texture parameter is defined which quantifies the density of ‹100› easy magnetic directions in the sheet planes. An extensive correlation study revealed the relation of this parameter with the hysteresis losses, determined at an induction of 1.5 T, and with the induction measured at an applied external field of 25 A/cm. It is shown that the latter magnetic property is the more texture dependent, whereas the former one is more sensitive to the grain size of the steel. Also various strategies for texture control are critically reviewed. It is shown that the conventional manufacturing process only provides poor tools for optimizing the texture of the final product. In order to obtain a quantum-leap improvement of the magnetic quality of the texture, in combination with other important microstructural features, nonstandard processing strategies are required, such as cross-rolling, two-stage cold rolling, or surface annealing.23:T6db,

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