On elastic gaps in strain gradient plasticity: 3D discrete dislocation dynamics investigation

Although presenting attractive features in dealing with small-scale size effects, strain gradient plasticity (SGP) theories can lead to uncommon phenomena for some boundary value problems. Almost all non-incremental (Gurtin-type) SGP theories including thermodynamically-consistent higher-order dissipation predict elastic gaps under certain non-proportional loading conditions. An elastic gap is defined as a finite change in the equivalent yield stress after an infinitesimal change in the strain conditions, at the occurrence of the non-proportional loading source. The existence of such gaps in reality is largely questioned and represents a major source of uncertainty preventing the development of robust SGP theories for real small-scale applications. Using 3D discrete dislocation dynamics (3D-DDD), the present paper aims at investigating size effects within micron-scale single crystal structures under various non-proportional loading conditions, including tension-compression-passivation, bending-passivation and tension-bending. An in-depth investigation of the occurrence of elastic gaps under these conditions, which are known to entail such gaps when using classical non-incremental SGP theories, is conducted. The obtained 3D-DDD results reproduce well known experimentally confirmed size effects like Hall-Petch effect, Asaro’s type III kinematic hardening and reversible plasticity. However, no evidence of the phenomenon of elastic gaps is found, which constitutes a first indication that this phenomenon may not exist in reality. The simulations are performed on face-centered cubic (FCC) Nickel single grains with cuboid shapes ranging from 2 microns to 15 microns and different orientations.