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

Abstract

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 2μm to 15μm and different orientations.