Critical thickness phenomenon in single-crystalline wires under torsion

Analysis of single crystalline microwires under torsion using a dislocation-based continuum formulation

“…Here, the total dislocation density -consisting mainly of GNDs (about 74 % screw GNDs and 26 % edge GNDs) -pile up in the middle of the wire forming a plateau-like distribution with ≈ 3 µm −2 . The results of the screw GND density can be compared to the density predicted by the Critical Thickness Theory (CTT) according to [18]. The computed density in the center of the wire shows similar results as the theoretically predicted CTT density, that takes into account only screw GNDs and considers a surface shear γ R Fig.…”

“…Gradient plasticity formulations were used to analyze the relation between surface energy and boundary conditions [10], the plastic spin contribution [2], as well as the influence of texture on the size effect for oligocrystalls [3]. Basic theoretical considerations have been carried out to investigate the size effect at the onset of yielding and the distribution of stresses and geometric necessary dislocations (GNDs) [18], as well as the role of the accumulation and pile-ups of GNDs for the size effect [15]. To investigate the size effect of yielding and plastic flow due to a critical thickness effect and the role of GNDs, [17] performed experiments with polycrystalline microwires.…”

Thermodynamic dislocation theory: Size effect in torsion

“…It is therefore impossible to derive the theory from the first principle calculation. The alternative continuum dislocation theory (CDT) accounting for excess dislocations, proposed for instance in [22]- [25], is more predictive as kinematic hardening and size effect are captured by the first principle calculation of energy of dislocated crystals. However, since redundant dislocations and the disorder temperature are completely ignored, the above CDT cannot describe the isotropic hardening and the sensitivity of the torque-twist curves to temperature and strain rates.…”

A bottom‐up continuum approach of crystal plasticity for the analysis of fcc microwires under torsion

“…With the critical thickness theory (CTT) there are analytical studies on this topic [5]. When the strain reaches a critical state, the area under the elastic strain curve remains constant in the following.…”