The relation between macroscopic and microscopic strain hardening in F.C.C. polycrystals

Inapplicability of the Hencky Formalism to the Description of Large Deformations in Shear

“…Here the expression "significant" refers to systems that carry at least 10% of the shear of the most active system. 4) It can be seen that, at shear strains beyond about 1.5, more slip systems are active in tension than in compression and that the smallest number of active systems is associated with the shear mode. Because work hardening takes place as a result of dislocation interaction on intersecting slip planes, it is clear that the rate of work hardening during deformation will be highest when the number of intersecting slip systems is the highest.…”

“…Finally, it should be added that the relationships between these quantities (and their average values) and S and dE are described in more detail than can be done here in Ref. 4).…”

“…2. These quantities were calculated using appropriate crystal plasticity models in which both full constraint (FC) and relaxed constraint (RC) boundary 4) as required. Here it can be seen that, at shear strains beyond about 1.5, the average Taylor factor is highest in tension, intermediate in compression, and lowest in torsion.…”

“…1, in which the experimental results of Ref. 4) for tests carried out in tension, compression and torsion are reproduced. For illustration purposes, a schematic flow curve representing plane strain compression has been added to this diagram; it is the remaining basic strain path and its flow curve again differs from the others.…”

Standard and strain gradient crystal plasticity models: application to Titanium

“…The geometry of the strip can be observed in Fig. A (Tomé et al, 1984;Kocks et al, 2000) h .6) where h The materials parameters are listed in the Table A.1. In order to trigger the localisation of the geometrically perfect specimen we assume a material imperfection in the center of the specimen which is established by a reduction of 10% in the hardening properties.…”