Recherche des systèmes de glissement actifs dans un processus de déformation plastique du polycristal. I. Cas du glissement cristallographique dans les cristaux cubiques

Abstract

The selection of active slip systems in a crystal subjected to a given strain has been solved by use of an analytical algebraic method based upon the interdependence of the slip systems. In the case of glide on the {110} 〈111〉 or the {111} 〈110〉 slip systems, the application of the maximum‐work principle is reduced to a comparison between only four of the twenty‐eight processes connected with the corresponding stress states found by Bishop & Hill [Philos. Mag. (1951). 42, 414–427, 1298–1307]. The proposed method can easily be applied to the case of glide on several sets of slip systems and finally to the case of pencil glide.

Variational Micro‐Macro Model and Deformation Textures Predicted for Steels

“…In the new algorithm, the constraint D* D is utilized (and thus accounted for) to eliminate the strain-rate of the last constituent (k n): (19) so that the list of the optimization variables is Y (D*k)k= _. The function to minimize is written as: Physically relevant aspects of the computation procedure As for the work by Arminjon and Donadille (1990) and Imbault (1993, 1994), which was based on a different polycrystal model in the actual computations, the plastic deformation of bcc crystals was assumed to occur by "pencil-glide" in <111> directions, using the method proposed by Royer et al (1979). Apart from the determination of the strain-rate distribution, which is characteristic from the polycrystal model and has just been described for the present model, the same computation procedure was used for texture prediction as the procedure used in those previous works [except for that part in Imbault (1993, 1994) which concerns the continuity equation for the ODF, not used here].…”