Latent hardening size effect in small-scale plasticity

Lorenzo Bardella, Javier Segurado, Andrea Panteghini, Javier Llorca

DICATAM, Faculty of Engineering, University of Brescia, Via Branze, 4325123, Brescia, Italy

Department of Materials Science, Polytechnic University of Madrid, E.T.S. de Ingenieros de Caminos--28040 Madrid, Spain; IMDEA Materials Institute, C/ Erick Kandel 2--28906 Getafe, Madrid, Spain


We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scale. By focussing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 micron, 6 micron] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study, so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is put on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

Author Keywords: Discrete Dislocation Dynamics; Latent hardening; Size effect; Crystal plasticity; Strain gradient plasticity; Finite element implicit integration